Karnataka 2020-21 NTSE Stage 1 Answer Key & Question Paper With Solutions

Paper: MAT

Directions (Q. No. 1-10): Find the odd word out.

Question 1. Eleven students a, b, c, d, e, f, g, h, i, j and k are sitting in a row of class facing the teacher:

i. ‘d’ who is to the immediate left of ‘f’, is second to the right of ‘c’.

ii. ‘h’ who is to the immediate left of ‘d’, is third to the right of ‘i’.

iii. ‘a’ is second to the right of ‘e’ and ‘e’ is at the end.

iv. ‘j’ is the immediate neighbour of ‘a’ and ‘b’ and third to the left of ‘g’.

The groups of friends who are sitting to the right of ‘g’ is

a. i, b, j, a
b. i, c, d, f
c. c, h, d, f
d. c, h, d, e

Answer: (c)

Question 2. p, q, r, s and t are seated around a circular table facing the centre:

i. ‘t’ sits second to the right of ‘s’.

ii. ‘r’ sits second to the right of ‘t’.

iii. ‘p’ is not an immediate neighbour of ‘s’

Who sits between ‘s’ and ‘t’:

a. q
b. r
c. p
d. t

Answer: (a)

Question 3. The following questions are based on the figures given below. Each circle represents one item. Match the figure with items in the question on the basis of their relationship.

Writers, Teachers, Researchers

a. f
b. d
c. c
d. a

Answer: (d)

Question 4. When the given figure is folded as a cube, the cube formed is:

Answer: (b)

If we fold an open die alternate numbers are on opposite faces will be

1 ⇔ 6

2 ⇔ 4

3 ⇔ 5

Question 5. Three different positions of the same dice are shown below. The letter on the face opposite the face showing ‘c’ is:

a. d
b. e
c. b
d. a

Answer: (d)

e, b, d and f are on adjacent faces of c so ‘a’ is the only possibility to be on the opposite face.

Question 6. A sheet of paper as shown in the figure is folded, so as to form a cube. Select the correct answer from the four alternatives in which the pairs of faces are opposite:

a. 1,3 2,4 5,6
b. 2,6 3,4 1,5
c. 1,5 2,3 4,6
d. 1,4 3,6 5,2

Answer: (a)

If we fold an open die alternate numbers are on opposite faces.

5 ⇔ 6

2 ⇔ 4

1 ⇔ 3

Directions (Questions Numbers 7 – 9): The following questions are based on the numbers and letters arranged in the pyramid pattern. Study the pattern and complete the given analogy.

Question 7. m k t 16 : i g x 20 : : l j u 17 : ?

a. e g t 18
b. h j q 15
c. c v e 20
d. h f y 21

Answer: (d)

Therefore, the answer is “h f y 21”.

Question 8. F j a 1 : H t z 22 : : A e o 13 : ?

a. J v p 14
b. H t p 14
c. J v z 22
d. I u q 15

Answer: (a)

Therefore, the answer is “J v p 14”.

Question 9. p 27 v : z 23 t : : ? : a 22 g :

a. A 28 g
b. p 27 v
c. o 14 i
d. t 23 z

Answer: (c)

Therefore, the answer is “o 14 i”.

Question 10. The date of birth of a person ‘Y’ is 4^th April 2001. Then ‘Y’ was born on :

a. Sunday
b. Monday
c. Tuesday
d. Wednesday

Answer: (d)

In a Leap-century the number of odd days are zero as it is divisible by 400. So till 2000, the number of odd days are zero.

Now in year 2001:

Total number of odd days = 10/7 = 1 week and 3 odd days.

So, Wednesday is the answer.

Question 11. The total age of ‘a’, ‘b’ and ‘c’ is 93 years. Ten years ago the ratio of their ages was 2 : 3 : 4. Then the present age of ‘c’ is

a. 18 years
b. 28 years
c. 38 years
d. 48 years

Answer: (c)

a + b + c = 93

(a – 10) : (b – 10) : (c – 10) = 2 : 3 : 4 years

Total ages 10 year ago = 93 – 10 = 63

2x + 3x + 4x = 63

x = 7

So ages are 14,21 and 28 years

Present age of c = 28 + 10 = 38 yrs.

Question 12. Ratio of Ravi’s age to Raju’s age is equal to 4 : 3. Ravi will be 26 years old after 6 years. The present age of Raju is:

a. 15 years
b. 14 years
c. 13 years
d. 12 years

Answer: (a)

Ravi age = x

Raju’s age = y

x/y = 4/3

x + 6 = 26

x = 20

20/y = 4/3

This implies, y = 15 years

Question 13. The ages of two persons differ by 18 years. 12 years ago the elder one was 4 times as old as the younger one. The present age of the elder one is :

a. 24 years
b. 36 years
c. 48 years
d. 60 years

Answer: (b)

Let the age of younger person = x

Age of elder person = x + 18

12 years ago:-

Age of younger person (x–12)

Age of elder person (18 + x –12) = (6 + x)

Given

4(x – 12) = (x + 6)

4x – 48 = x + 6

3x = 54

x = 18

Present age of elder person = 18 + 18

= 36 years

Question 15. If the total area under wheat is 5.4 million acres, then the area under rice in million acres:

a. 21.6
b. 10.8
c. 32.4
d. 7.6

Answer: (a)

5x/100 = 5.4 m.a.

x = 108 m.a.

Rice = 20x/100=(20×108)/106 = 21.6

Question 16. If the production of rice is 2 times that of wheat, then the ratio of yield/acre of rice and wheat is :

a. 2 : 3
b. 3 : 1
c. 1 : 2
d. 1 : 3

Answer: (c)

rice : 2 wheat

2x/(20% of y):x/(5% of y)

10 : 20 = 1 : 2

Direction (Question Numbers 17 to 18): The problem figure in the following questions is hidden in the given four alternatives in every question. Find the alternative in which the problem figure is hidden

Question 17. Find the alternative

Answer: (a)

Question 18. Find the alternative

Answer: (d)

Directions (Questions Number: 19 – 20): Two matrices containing letters are given below. The rows and columns are numbered 0 to 4 in matrix 1 and 5 to 9 in matrix II. Each letter from these matrices are represented by its row number and the next by its column number.

Question 19. The Set of numbers which represents the word PALM is

a. 12, 73, 21, 43
b. 21, 33, 58, 03
c. 34, 42, 86, 24
d. 12, 20, 87, 32

Answer: (c)

First Number → Row Number

Second Number → Column Number

Option c is the only possibility where all alphabet can be matched with their number, all other option has one or more letter not matching with their number

Question 20. The set of numbers that represents the word WARD is

a. 01, 42, 43, 59
b. 30, 33, 41, 88
c. 44, 20, 31, 98
d. 13, 04, 40, 75

Answer: (d)

First Number → Row Number

Second Number → Column Number

Option d is the only possibility where all alphabet can be matched with their number, all other option has one or more letter not matching with their number

Direction: (Question Numbers 21 to 24) Complete the given number analogy by choosing the correct answer from the four alternatives given below.

Question 21. 31 : 69 : : 351 : ?

a. 496
b. 511
c. 521
d. 707

Answer: (c)

3³ + 4 : 4³ + 5 : : 7³ + 8 : 8³ + 9 = 521

Question 22. 7124 : 48 : : 3218 : ?

a. 27
b. 45
c. 57
d. 75

Answer: (b)

(7 + 1) × (2 + 4) : : (3 + 2) × (1+ 8) = 45

Question 23. 24 : 21 : : 336 : ?

a. 555
b. 170
c. 290
d. 105

Answer: (d)

3³ – 3 : 3(3 × 2 + 1) : : 7³ – 7 : 7 (7 × 2 + 1) = 105

Question 24. 10 : 115 : 22 : : ? : 204 : ?

a. 12, 26
b. 14, 30
c. 15, 27
d. 18, 19

Answer: (a)

10:[(10/2)³-10]:2(10)+2::12:[(12/2)³-12]:2(12)+2

Directions (Questions Number: 25-27): The words are given under column – I. Their codes are given under column – II. The order of coding for the letters of the words in the column – I do not follow the same order in column – II. Find the codes from the letters of words in the column – I and find the codes for the given words in questions.

Question 25. TRIANGLE :

a. kmbsandp
b. mkbsandp
c. kmpsndap
d. mkbsanpd

Answer: (Bonus)

In the question we can see the word HEN and TILE have only one common word ‘E’ whereas their code ‘pab’ and ‘bpdm’ have two common ‘p’ and ‘b’, hence there is no clarity between code for H, I , B.

Question 26. LEATHER:

a. dpsmbpk
b. pdsmbpk
c. spdmbpk
d. dpmsbkp

Answer: (Bonus)

In the question we can see the word HEN and TILE have only one common word ‘E’ whereas their code ‘pab’ and ‘bpdm’ have two common ‘p’ and ‘b’, hence there is no clarity between code for H, I , B.

Question 27. PATIENT:

a. tsbmpam
b. asmbpmt
c. smtbpam
d. tsmbpam

Answer: (Bonus)

In the question we can see the word HEN and TILE have only one common word ‘E’ whereas their code ‘pab’ and ‘bpdm’ have two common ‘p’ and ‘b’, hence there is no clarity between code for H, I , B.

Direction (Question Number 28 – 29): Ramu’s bag cannot carry more than twelve books. He has to carry at least one book each of mathematics, social, map and graph. For each mathematics book he has to carry two or more graph books, and for each social book, he has to carry two or more map books. He earns 4,3,2 and 1 point for carrying each mathematics, social, map and graph book respectively in his bag. He has to earn maximum points. This he can do by carrying a proper combination of books.

Question 28. The number of social books he would carry is :

a. 1
b. 2
c. 3
d. 4

Answer: (c)

He has to earn maximum points

One combination :- [M + G + G] = 6

Second combination:- [S + M + M] = 7

For maximum points considering Twelve books in mind:-

I → 3 × 6 + 7 = 25

II → 3 × 7 + 6 = 27

No. of social book = 3

Question 29. The maximum points that he can earn by selecting the combination of books is:

a. 26
b. 27
c. 28
d. 29

Answer: (b)

For maximum points considering Twelve books in mind:-

I → 3 × 6 + 7 = 25

II →3 × 7 + 6 = 27

Maximum no. of point will be 27

Direction (Question Number 30 – 32): In the questions given below the numbers in the figures are related. Identify their relationships and find the missing numbers in the given figures.

Question 30. Find the missing numbers in the given figures.

a. 2502
b. 2702
c. 2603
d. 2707

Answer: (b)

(4 +12 + 6 + 4)² – 2 = 674

(4 + 14 +6 + 18)² – 2 = 1762

(12 + 10 + 14 + 16)² – 2 = 2702

Question 31. Find the missing numbers in the given figures.

a. 9/4
b. 3
c. 7/2
d. 7

Answer: (a)

(4×8×5)/(2×5×8) = 2

(7×6×3)/(7×4×3) = 3/2

Similarly, (9×6×4)/(4×4×6) = 9/4

Question 32. Find the missing numbers in the given figures.

a. 3
b. 2
c. 1
d. 4

Answer: (c)

5² + 6² + 4² – 4² = 61

7² + 8² + 5² – 4² = 122

11² + 5² + 4² – x² =161

x = 1

Directions (Questions: 33 – 35): Complete the given figure analogy by choosing the correct answers from the given alternative.

Question 33. Choose the correct answers from the given alternative.

Answer: (b)

Question 34. Choose the correct answers from the given alternative.

Answer: (d)

Question 35. Choose the correct answers from the given alternative.

Answer: (c)

Turn the triangle by 45^o and move the arrow 45^o closer

Corner left side rectangle is half from the right side only in diagram c.

Directions (Questions Number: 36 – 37): Study the given Pie-chart and Bar diagram and answer the following questions: Number of boys in each school out of 6000 students.

Question 36. The sum of the number of girls in school C, the number of girls in school E and the number of boys in school D together is :

a. 1700
b. 1900
c. 1600
d. 1800

Answer: (d)

No. of girls in school C

= 26% of 6000 – No. of Boys in C

= 26 × 60 – 900

= 1560 – 900

= 660

No. of girls in school E

= 29% of 6000 – No. of Boys in E

= 29 × 60 – 1200

= 1740 – 1200

= 540

No. of Boys in school D = 600

So, 660 + 540 + 600 = 1800

Question 37. The ratio of the number of boys in school C, the number of girls in school B and the total number of students in school E is :

a. 45 : 7 : 97
b. 43 : 9 : 97
c. 45 : 7 : 87
d. 43 : 9 : 87

Answer: (c)

No. of boys in school C ⎯→ 900

No. of girls in school ⎯→ 9% of 6000 – No. of Boys in 8 = 140

Total No. of Students in school E = 29% of 6000 = 1740

So ratio will be 900 : 140 : 1740

= 45 : 7 : 87

Question 39. If POND is coded as NKHV, then the word HEAR can be coded as :

a. GHIJ
b. HGIZ
c. FAUJ
d. FACL

Answer: (c)

Question 40. If the word FATHER is written as HCVJGT, then MOTHER can be coded as:

a. OQVJGT
b. KOTHER
c. OQJGTV
d. KMOQSU

Answer: (a)

Direction (Question Numbers 41 to 43): Study the following Pie-chart and the table. Answer the questions based on them. Total books in a library.

Question 41. If the total number of books in the library is 10,000, then the total number of Hindi books that are in bad condition is:

a. 82
b. 84
c. 90
d. 80

Answer: (b)

Hindi books = 14% of 10000 = 1400

6% are Bad = 6% of 1400 = 84

Question 42. If the number of Kannada books in bad condition is 92, then total number of English books in the library will be :

a. 1200
b. 1600
c. 4800
d. 4000

Answer: (d)

Total no. of books = x

23% of x = (23x)/100 (no. of kannada books)

Bad condition 2% of (23x)/100 = 92

2(23x)/10⁴ = 92

x = (92×10⁴)/(23×2) = 40000/2 = 20,000

No. of English books = (20/100) × 20,000 = 4000

Question 43. If the total number of books in bad condition is 860, then total number of books in the library will be:

a. 20,000
b. 8600
c. 4300
d. 43,000

Answer: (a)

Let the total no. of books be x.

Then

Question 44. If 1st January 2019 is Tuesday, then 31st December 2021 will be :

a. Sunday
b. Friday
c. Saturday
d. Tuesday

Answer: (b)

Question 45. The date which cannot represent second Saturday of any month is :

a. 7
b. 8
c. 9
d. 10

Answer: (a)

So 7^th cannot be the 2^nd Saturday.

Question 46. The number of years in which February 29 appears between 1901 and 2001 years is :

a. 75
b. 50
c. 26
d. 25

Answer: (d)

Total no. of year → 100

So, No. of leap years → 100/4 = 25

1904,1908,1912,………..1996 (Total 25 times)

So, 25 times 29^th of February will appear.

Direction (Question Numbers 47 to 49): In each of the following questions, numbers / letters have been given, out of which three are alike in some manner and the fourth one is different. Choose out the odd one.

Question 47. Choose out the odd one.

a. DW
b. GT
c. KP
d. HR

Answer: (d)

HR is odd one out

Since all others have sum of 27

DW → 4 + 23 = 27

GT → 7 + 20 = 27

KP → 11 + 16 = 27

HR → 8 + 18 = 26

Question 48. Choose out the odd one.

a. 243
b. 6561
c. 32
d. 1024

Answer: (b)

(a) 243 = 3⁵

(b) 6561 = 3⁸ = 9⁴

(c) 32 = 2⁵

(d) 1024 = 2¹⁰ = 4⁵

All the other can be written with their power 5 or multiple of 5 except 6561

Question 49. Choose out the odd one.

a. E J O T
b. Y E J O
c. T Y E S
d. O J E Y

Answer: (c)

EJOT [2 Vowels]

YEJO [2 Vowels]

TYES [1 Vowel]

OJEY [2 Vowels]

Directions (Questions: 50 – 52): Study the following information carefully and answer the following questions.

1) ‘b’ and ‘e’ are experts in Kannada and Hindi

2) ‘a’ and ‘b’ are experts in Hindi and Tamil

3) ‘a’, ‘d’ and ‘c’ are experts in Tamil and Bangali

4) ‘c’ and ‘a’ are experts in Tamil and Sanskrit

5) ‘d’ and ‘e’ are experts in Kannada and Bangali

Question 50. Expert in Kannada, Tamil and Bangali is:

a. a
b. b
c. c
d. d

Answer: (d)

With the given condition we can have the following table

Question 51. Expert in Hindi, Bangali and Kannada is:

a. b
b. e
c. a
d. c

Answer: (b)

From the table, we can see ‘e’ is common in Hindi, Bangali and Kannada.

Question 52. Expert in Kannada, Hindi and Tamil is:

a. b
b. c
c. a
d. d

Answer: (a)

From the table, we can see ‘b’ is common in Kannada, Hindi and Tamil.

Question 53. ‘a’ and ‘b’ together can complete a piece of work in 9 days. ‘a’ alone can complete the work in 36 days. The number of days ‘b’ alone take to complete the work :

a. 18
b. 30
c. 12
d. 14

Answer: (c)

1 day work if a and b work together.

1/a + 1/b = 1/9

1/a = 1/36 and 1/b = 1/9 – 1/36

(4-1)/36 = 3/36 = 1/12

So, b can complete in 12 days.

Question 54. If the sum of one-third of a number and half of the same number exceeds two-third of the number by 5, then two-fifth of the number is equal to :

a. 12
b. 15
c. 18
d. 30

Answer: (a)

Let the number be x

x/3 + x/2 = 2x/3 + 5

5x/6 = (2x+15)/3

5x = 4x + 30

x = 30

So, 2/5 of x = 2/5×30 = 12

Question 55. A fruit seller bought 72 oranges at Rs. 600. He sold 50 of them at Rs. 11 each and the remaining at Rs. 236. His profit in this business is :

a. Rs. 786
b. Rs. 600
c. Rs. 442
d. Rs. 186

Answer: (d)

Cost Price of 72 oranges = Rs. 600

Selling price of 72 oranges = 11 × 50 = Rs. 550

The selling price of remaining oranges = Rs. 236

Total Selling price of oranges = 236 + 550 = Rs. 786

So profit = Selling price – Cost price

= Rs. 786 – Rs. 600

= Rs. 186

Directions (Questions : 56 – 58): Study the given information carefully and answer the following questions :

A number / letter / word re-arrangement machine, when given an input, re-arranges them following a particular rule in each step. The following is an illustration of input and output steps of re-arrangement.

Question 56. If the input is Kit, My, Leo, Ji, Sum, then the step 3 output will be :

a. Kit Ji Sum My Leo
b. Ji Sum My Kit Leo
c. Ji My Sum Kit Leo
d. Ji My Kit Leo Sum

Answer: (c)

Question 57. If the step 3 output is 40, 33, 12, 21, 68, then the input is :

a. 21 68 33 12 40
b. 21 33 68 40 12
c. 40 33 21 12 68
d. 21 40 12 68 33

Answer: (b)

STEP 3

Question 58. If the step 2 output is Sot, Yin, Mens, Tog, Guv then the step 1 output will be:

a. Sot Mes Yin Guv Tog
b. Sot Mes Tog Yin Guv
c. Guv Mes Tog Sot Yin
d. Guv Tog Mes Yin Sot

Answer: (d)

Question 60. Choose the correct figure.

Answer: (b)

Directions (Questions Number 61 – 63): The order of the letters that need to come in the boxes to complete a certain pattern is :

Question 61. BY DW GT ?

a. JP
b. JQ
c. KQ
d. KP

Answer: (d)

Question 62. L ▭ MN ▭ K ▭ N ▭ LM
a. MLML
b. KLML
c. NMLL
d. KMML

Answer: (b)

The term LKMN keep on repeating

Question 63. YEB WFD UHG SKI ?

a. QOL
b. QGL
c. TOL
d. QNL

Answer: (a)

Third letter is alternate +2 and +3

B + 2 = D

D + 3 = G

G + 2 = I

I + 2 = L

Question 64. The number of ways in which the letters of the work ‘VOWEL’ be arranged so that the vowel letters are always together:

a. 52
b. 48
c. 24
d. 20

Answer: (b)

(OE) VWL

It can be arranged in 4! Ways and OE can be in 2! ways.

So, the total is 4 × 3 × 2 × 2 = 48 ways.

Question 65. A beaker half filled with water weighs 600 g. When it is empty it weighs 150 g. The weight of the beaker when 2/5 of it is filled with water is:

a. 240 g
b. 450 g
c. 360 g
d. 510 g

Answer: (d)

Mass of water inside beaker = 600 – 150 = 450 gm

As 50% is 450 gm so full beaker water will weigh = 900 grams

2/5 of 900 will be 360 gm

Total weight 360 gm + 150 = 510.

Question 66. If the length of a rectangle is increased by 30% and breadth is decreased by 20%, then the variation in the area of new rectangle is:

a. Decreases by 4%
b. Increases by 4%
c. Decreases by 25%
d. Increases by 25%

Answer: (b)

Let the length and breadth be L and B respectively.

New L’ = 1.3L

New B’ = 0.8B

New Area = L’B’ = (1.3L)(0.8B) = 1.04 LB

% Increase in area = ((1.04 LB)/LB)×100 = 4%

Question 68. Identify their relationship and find the missing number.

a. 8
b. 3
c. 4
d. 5

Answer: (a)

18 – (12 ÷ 6) × 8 = 2

15 – (30 ÷ 6) × 2 = 5

Similarly,

20 – (10 ÷ 5) × 6 = 8

Question 69. Identify their relationship and find the missing number.

a. 74
b. 95
c. 84
d. 120

Answer: (c)

(5 + 3) × (16 – 6) = 80

(6 + 8) × (10 – 5) = 70

Similarly

(5 + 9) × (13 – 7) = 84

Question 70. Raju walked 20 m towards the south, then turning to his right and he walks 25 m, then turning to his left and he walks 30 m. Again he turns to his left and walks 25 m. How far is he from his initial position (Assuming that all turns are at right angles) :

a. 20 m
b. 30 m
c. 100 m
d. 50 m

Answer: (d)

Question 71. A person starting from ‘A’ drives 10 km eastwards to reach point ‘B’, then turns to the north and goes 3 km to reach ‘C’. Then turns west and drives 14 km to reach ‘D’. Then the distance between ‘A’ and ‘D’ is

a. 4 km
b. 5 km
c. 7 km
d. 10 km

Answer: (b)

From the Pythagoras theorem, we have 3,4,5 as a Pythagorean triplet

Hence AD = 5 km

Question 72. A girl starts from ‘A’ and walks towards South-East to reach ‘B’. She turns towards the west and walks to reach ‘C’. Then she turns North-West and walks to reach ‘D’. Finally she turns east and walks to reach ‘E’. The figure which exactly shows the path the girl has traced is :

Answer: (a)

Question 74. Find the missing number in the given matrices.

a. 15
b. 14
c. 10
d. 7

Answer: (b)

Question 75. Find the missing number in the given matrices.

a. 36
b. 46
c. 26
d. 62

Answer: (c)

Question 77. Find the missing part of the given figure.

Answer: (d)

Question 79. Find the correct mirror image

Answer: (c)

Question 80. Find the correct water image for the following problem figure choosing from the four options: UPAT58476

Answer: (a)

Question 81. If then the code for GAME is:

a. 2 1 4 3
b. 3 7 1 6
c. 3 5 2 6
d. 4 5 7 3

Answer: (c)

By Last Column

2M + A = 9

Solving this and other columns we get these possibility

Option (ii) and (iii) ruled out as G is not integer

So, GAME can be either 3526 OR 2148

Question 82. If the product of (1 P 6) and (2 Q) is 4 2 1 2, then the values of P and Q are respectively

a. 4 and 2
b. 5 and 7
c. 4 and 7
d. 5 and 2

Answer: (b)

Q can be either 2 or 7

Satisfying with these two value we will get P = 5

Question 83. When [D U C K] is multiplied by K, the product 5 5 U D U. If the value of U is 1, the values of C and D respectively are:

a. 7 and 2
b. 4 and 6
c. 2 and 3
d. 2 and 6

Answer: (d)

9 × C + 8 = D

K x K = 1

So K = 1 or 9

It can’t be 1 as answer will be DUCK only

Hence, K = 9

D = 9C + 8

1 = 9 + carry 2

clearly if carry is 2,

9C + 8 > 20

Hence, C = 2

Solving further with different cases we get

D = 6

Direction (Question Number 84-86): Assume the given statements as true and decide which of the following conclusions follow logically from these statements.

Question 84. Choose the conclusion that follows logically from these statements.

Statements:

a. All books are tables.

b. All tables are boxes.

Conclusions:

I. All boxes are books.

II. Some boxes are tables.

a. Only conclusion I follows
b. Only conclusions II follows
c. Neither conclusion I nor II follows
d. Both conclusions I and II follow

Answer: (b)

Here we can see that some boxes are tables.

Question 85. Choose the conclusion that follows logically from these statements.

Statements:

a. All ants are elephants.

b. No elephants

t is an animal.

c. All elephants are tigers.

Conclusions:

I. No ant is an animal.

II. Some tigers are elephants.

a. Only conclusions I follows
b. Only conclusion II follows
c. Both conclusions I and II follow
d. Neither conclusion I nor II follows

Answer: (c)

Here we can see, No ant is an animal, as well as some tigers, are elephants.

Question 86. Choose the conclusion that follows logically from these statements.

Statements:

a. All roses are jasmine.

b. No jasmine is a flower.

Conclusions:

I. Some roses are flowers.

II. Some flowers are jasmine.

a. Only conclusion I follows
b. Only conclusion II follows
c. Conclusions I and II both follow
d. Neither conclusion I nor II follows

Answer: (d)

Here we can see that none of the roses are flowers, and none of the flowers are jasmine.

Question 87. In a code 2357 stands for the word WORK and the code 14649 stands for the word STATE, then the code 14359 stands for:

a. S C O R E
b. S T O R E
c. S T E O R
d. S T O E R

Answer: (b)

So, mapping the value we get,

14359 = S T O R E

Question 88. If a word BALL is coded as 288, then the word JACK is coded as:

a. 330
b. 240
c. 220
d. 140

Answer: (a)

Using the numerical order value of the alphabet, we get

B A L L

2 × 1 × 12 × 12 = 288

Question 89. If a word PAT is coded as 22318, then the word COW is coded as:

a. 25175
b. 23153
c. 31725
d. 31523

Answer: (a)

Using the numerical order value of the alphabet, we get

Question 90. Number of pairs of letters, which are there in the word PARADISE, that have as many letters between them in the word as in the alphabet are:

a. 4
b. 3
c. 2
d. 5

Answer: (b)

(I)AD (II) PR (III) AE

Total 3 such pairs are there.

Question 91. Number of letters skipped between adjacent letters in the series is in the order 2, 5, 7, 8. This given rule is observed by series:

a. P S X C L
b. K N T B J
c. V X B G P
d. D G M U D

Answer: (d)

Question 92. In the word JOURNEY, the 1^st and 5^th letters, 2nd and 6th letters, 3^rd and 7^th letter are interchanged. The 5^th letter from your right after re-arrangement is:

a. N
b. E
c. Y
d. J

Answer: (c)

Direction: (Question 93 – 95): In the following figure circle represents those who play cricket, the triangle represents those who play cricket, the triangle represents those who play football, square represents those who play hockey and rectangle represents those who play tennis. Based on the figure answer the following questions.

Question 93. The number that represents those who play cricket, football and hockey is:

a. 2
b. 4
c. 5
d. 8

Answer: (d)

As it can be seen, the common figure between the other three in the Venn diagram i.e. number 8.

Question 94. The number that represents those who play cricket but not hockey is

a. 18
b. 20
c. 26
d. 28

Answer: (a)

Add circle number excluding hockey i.e. 9 + 5 + 4 = 18

Question 95. The number that represents those who play neither tennis nor football is

a. 9
b. 16
c. 18
d. 26

Answer: (c)

Add number excluding tennis and football i.e. 9 + 2 + 7 = 18

Question 96. The measure of the angle between the hands of the clock at 3:40 is

a. 120^o
b. 130 ^o
c. 140 ^o
d. 150 ^o

Answer: (b)

θ = |30h – (11/2) m|

= |30 × 3 – (11/2) x 40|

= |90 – 220|

= 130^o

Question 97. The calendar of which year among the following is identical to the calendar of the year 1996:

a. 2002
b. 2007
c. 2016
d. 2024

Answer: (d)

Calendars for leap years repeat themselves every 28 years.

1996 + 28 = 2024

Question 98. A bank sanctions loan to a person on 3rd Friday of June 2004. The date on which loan was sanctioned is:

a. 14
b. 15
c. 17
d. 18

Answer: (d)

1^st June 2004

2000 + 3yr. + Jan to May + 1

0 + 3 × 1 + 3 + 1 + 3 + 2 + 3 + 1

3 +6 = 9 ⇒ 2 odd. Days (Tuesday)

∴ 1^st June is Tuesday

So 4^th June is 1^st Friday.

∴ 18^th June is 3^rd Friday.

Question 99. Direction: Answer the following question based on the sequence numbers given.

354867358312358462437145978:

If half the sum of any two consecutive numbers is the very next number, how many times such numbers occur in the given sequence:

a. 8
b. 9
c. 10
d. 11

Answer: (d)

Question 100. In the letter series from A to Z if 5^th, 10^th, 15^th, 20^th and 25^th letters are replaced by their previous second letter and last 13 letters are written in the reverse order, then the number of consonants between K and X are:

a. 4
b. 7
c. 11
d. 13

Answer: (a)

E, J, O, T, Y are the 5^th, 10^th, 15^th, 20^th and 25^th term respectively.

Replacing them by their previous second letter

Last 13 letters in Reverse order and Rearranging:-

The number of consonants between K and X is 4.

Karnataka NTSE 2021 Stage 1 SAT Paper

PAPER – SAT

Question 1. Luggage porters place a round piece of cloth on their head when they have to carry heavy loads. By doing this, the area of contact between the load and head:

a. Decreases and reduces the pressure
b. Increases and reduces the pressure
c. Decreases and increases the pressure
d. Increases as well as increases the pressure

Answer: (b)

Pressure (P) = Force(F)/Area(A)

By the use of a round piece of cloth

Area (A) ↑

Hence, pressure (P) ↓

Question 2. A boy covers a distance of 260 m in 20 s and another distance of 300 m in 20 s. The average speed of the boy is:

a. 14 ms^–1
b. 28 ms^–1
c. 42 ms^–1
d. 56 ms^–1

Answer: (a)

Averages speed = (Total distance)/(total time)= (260+300)/(20+20)= 14 m/sec.

Question 3. In the following, the phenomena which were successfully explained by the law of gravitation are:

(a) Motion of moon around the earth

(b) Formation of tides

(c) Motion of an aeroplane

(d) Force that binds us to the earth

(e) Rotation of blades in a ceiling fan

a. b, c, d
b. d, e, a
c. c, d, e
d. a, b, d

Answer: (d)

Law of gravitation is used to explain the:-

(i) Motion of moon around the earth

(ii) Formation of tides in the ocean due to gravitation between earth and moon.

(iii) Any object that has mass binds with earth because of gravitation.

Question 4. The image formation in a convex lens is shown in the following figure

AB is the object and A′B′ is the image. The focal length of the lens is

a. 40 cm
b. 10 cm
c. 20 cm
d. 05 cm

Answer: (b)

In convex lens, size and distance of image are same as of objects; when the object is at 2F

i.e. u = 2F = 2f

20 = 2f

f = 10cm Ans.

Question 5. The image formation in the human eye is shown in the given diagram.

The lens used to correct this type of eye defect is

a. Plano concave lens
b. Concave lens
c. Cylindrical lens
d. Convex lens

Answer: (d)

In the given human eye, an image is formed behind the retina that means the person is suffering from Hypermetropia i.e. the power of the lens of the human eye has decreased. Hence, to increase the power, convex lenses are used as they converse maximum rays of light at the retina.

Question 6. The lenses of power +3.5D, + 2.5D and + 1D are placed in contact with each other in an optical device. The effective power of the combination of these lenses is

a. 5 D
b. 6 D
c. 7 D
d. 8D

Answer: (c)

Given,

P₁ = + 3.5 D

P₂ = + 2.5 D

P₃ = + 1d

Effective power P_net = P₁ + P₂ + P₃ + …… + P_n

∴ P_net = 3.5 + 2.5 + 1 = 7D Ans.

Question 7. A force acting on a 20 kg mass changes its velocity from 6 m/s to 3 m/s. The work done by the force is

a. + 510 J
b. – 510 J
c. – 270 J
d. + 270 J

Answer: (c)

Given:

M = 20 kg

V₁ = 6m/sec.

V₂ = 3m/sec.

Now, according to the work-energy theorem.

W = ΔE_k = (1/2)MV₂² – (1/2)MV₁²

= 1/2 m(V₂²-V₁²)

= 1/2×20×(3²-6²)

= –270 Joule

Question 8. Consider the following statements and choose the correct alternative.

Statement -I: Heating capacity of biogas is more than that of biomass.

Statement – II: Biogas produces lesser pollution as compared to biomass

a. I is false, II is true
b. I is true, II is false
c. Both I and II are false
d. Both I and II are true

Answer: (d)

The heating capacity of biogas is more than that of biomass because biogas has high calorific values. Biogas produces lesser pollution as compared to biomass because the carbon in biogas comes from plant matter that fixed this carbon from atmospheric CO₂. Thus, biogas production is carbon-neutral and does not add to greenhouse gas emissions.

Question 9. The temperature of the water at the bottom of a waterfall is higher than that of the water at the top because

a. Falling water absorbs heat from the sun
b. Kinetic energy of falling water is converted into heat
c. Water at the bottom has greater potential energy
d. The rocks on the river bed give out heat

Answer: (b)

According to the law of conservation of energy, the kinetic energy of falling water is converted into the heat energy that is used to increase the temperature of water at the bottom. That is why the temperature of water at the bottom is higher than the temperature at the top.

Question 10. Consider the following assertion (a) and the reason (r). Select the correct alternative

Assertion (a): When high voltage power is supplied through domestic wiring immediately the running television (ON condition) will burn out.

Reason (r): DP switch is fitted in domestic wiring to cut off the power supply automatically when high voltage is supplied.

a. ‘a’ is true and ‘r’ is the correct explanation to ‘a’
b. ‘a’ is true and ‘r’ is the wrong explanation to ‘a’
c. ‘a’ is false and ‘r’ is true
d. Both ‘a’ and ‘r’ are false

Answer: (d)

When the safety or protecting appliances are used, then the running television will not burn immediately when the high voltage power is supplied through the domestic wire. Instead, the fuse or MCB will trip. Hence, the fuse or MCB are used as a safety device.

Question 11. A science teacher asked a student to measure the potential difference across the ends of a dry cell. The device that needs to be used by the student is

a. AC Voltmeter
b. AC Ammeter
c. DC Ammeter
d. DC Voltmeter

Answer: (d)

As a dry cell is a DC source, therefore, the potential difference across its ends can only be measured by a DC voltmeter.

Question 12. Among the following, the body possessing the highest momentum is

a. Mass of 8 kg moving with velocity 6 ms^–1
b. Mass of 4 kg moving with velocity 11 ms^–1
c. Mass of 10 kg moving with velocity 4 ms^–1
d. Mass of 45 kg moving with velocity 1 ms^–1

Answer: (a)

Momentum (P) = Mass × Velocity

P = mv

(i) P₁ = 8 × 6 = 48 kg m/sec

(ii) p₂ = 4 × 1= 44 kg m/sec.

(iii) P₃ = 10 × 4 = 40 kg m/sec.

(iv) P₄ = 45 × 1 = 45 kg m/sec.

Question 13. The pole star appears to be stationary when observed from the earth. This is because pole star is

a. Not moving
b. Situated in the direction of the earth’s axis
c. Moves very slowly which is not recognised by our eyes
d. Relative velocity of earth and pole star is zero

Answer: (b)

As the pole star is situated in the direction of the earth’s axis, it appears to be stationary when observed from the earth.

Question 14. Read the following and select the correct option.

Statement (a): When we pour little petrol on our palm, it causes the palm to feel cool.

Reason (b): Particles of petrol evaporate using the energy from our palm which causes the palm to feel cool.

a. ‘a’ is correct and ‘b’ is not the correct reason.
b. ‘a’ is correct and ‘b’ is the correct reason.
c. Both ‘a’ and ‘b’ are correct but ‘b’ is not the reason for ‘a’.
d. ‘a’ is not correct so, ‘b’ is not the correct reason.

Answer: (b)

Acetone, petrol, perfume etc., being volatile, evaporate very fast when exposed to larger surfaces. When we put petrol on our palm, it evaporates. During evaporation, particles of the liquid absorb energy from the surface of the palm to compensate for the loss of energy, making the surroundings cool. Petrol takes this latent heat of vaporisation from our palm. The palm loses heat and feels cold.

Question 15. A solution is prepared by dissolving 60 g of sugar in 480 g of water. Concentration in terms of mass by mass percentage of the solution is:

a. 12.5 %
b. 14.2 %
c. 16.6 %
d. 17.6 %

Answer: BONUS

Mass of sugar (solute) = 60 g

Mass of water (solvent) = 480 g

Mass of the solution = 60 + 480 = 540 g

Concentration by mass percentage = (Mass of solute )/(Mass of solution  )×100

= 60/540×100

= 100/9

= 11.1 %

Question 16. Schematic atomic structure of four elements are given below. Observe and choose the right statement

a. Atomic number of ‘c’ is 8. So, it is an inert gas.
b. ‘a’ is the schematic atomic structure of oxygen.
c. ‘b’ has 8 electrons and it represents octet configuration.
d. ‘d’ is the schematic atomic structure of sodium.

Answer: (b)

Oxygen electronic configuration is 2,6.

Question 17. The bulb is not glowing in this experimental setup because

a. The circuit is open.
b. The battery is not connected properly.
c. The electrodes are too short.
d. Alcohol does not conduct electricity.

Answer: (d)

In the beaker, the solution filled is alcohol and alcohol is an organic compound that does not produce ions in water. Therefore, it is a poor source of electricity.

Question 18. The set of products formed when electricity is passed through brine is :

a. Cl₂, Na₂CO₃ and CO₂
b. Cl₂, NaCl and H₂
c. Cl₂, NaOH and H₂
d. Cl₂, HCl and NaOH

Answer: (c)

When an electric current is passed through the brine, hydrogen gas evolves at the anode, chlorine gas evolves at the cathode and sodium hydroxide is formed in the electrolysing solution.

2NaCl(aq) + 2H₂O(l) → 2NaOH(aq) + Cl₂(g) + H₂(g)

Question 19. The equation of the reaction when aluminium is heated in air is given below.

xAl + yO₂→ zAl₂O₃

The value of ‘z’ when the reaction is balanced is:

a. 2
b. 1
c. 4
d. 3

Answer: (a)

The reaction is as follows:

4Al + 3O₂ → 2Al₂O₃

Question 20. The reactivity series of Aluminium, Copper, Calcium and Lead metals when taken in decreasing order is:

a. Al > Pb > Cu > Ca
b. Cu > Ca > Al > Pb
c. Ca > Al > Pb > Cu
d. Pb > Ca > Cu > Al

Answer: (c)

The decreasing order of chemical reactivity: Ca > Al > Pb > Cu.

Question 21. Dilute HCl is taken in a test tube and pieces of copper turnings are added. The changes you may observe are

a. Formation of bubbles and temperature rises.
b. Neither formation of bubbles nor rising of temperature.
c. No formation of bubbles but temperature rises.
d. Formation of bubbles, but the temperature remains the same.

Answer: (b)

Reaction does not take place when copper turnings are added to the test tube containing dil. hydrochloric acid. Hydrogen is above copper in a metal reactivity series, so the copper cannot replace the hydrogen in HCl.

Question 22. Observe the following chemical equation of carbon compound.

Name of the chemical reaction and the product ‘x’ respectively

a. Oxidation reaction and CH₂Cl
b. Combustion reaction and CH₂Cl₂
c. Substitution reaction and CH₂Cl₂
d. Addition reaction and CH₂Cl

Answer: (c)

A substitution reaction is a chemical reaction during which one functional group in a chemical compound is replaced by another functional group.

Question 23. Number of covalent bonds present in benzene is

a. 12
b. 9
c. 18
d. 15

Answer: (d)

There are 6 C-H bonds, 6 C-C bonds and 3 C=C bonds. Therefore, 12 sigma bonds and 3 pi bonds are present. Benzene is therefore made up of 15 covalent bonds.

Question 24. To convert the structural formula of ethane into ethanol, changes to be done with ethane are

a. Remove one hydrogen and add “OH” group
b. Remove two hydrogen and add “OH” group
c. Remove one hydrogen and add “CHO” group
d. Remove two hydrogen and add “COOH” group

Answer: (a)

Ethene is converted into ethanol by passing its vapours through water.

Question 25. An element ‘P’ which belongs to the 13^th group of the periodic table and another element ‘Q’ belongs to the 16^th group. The formula of the compound formed if they react with each other is:

a. P₃Q₂
b. PQ₃
c. P₂Q
d. P₂Q₃

Answer: (d)

An element P belonging to the 13th group has a valency +3 and element Q belonging to the 16th group has valency +2.

Question 26. Elements with atomic numbers 7, 15, 33 and 51 belong to the same group in the periodic table. Because they have the same number of:

a. Protons
b. Valence Electrons
c. Electrons
d. Neutrons

Answer: (b)

Elements that belong to the same group in the periodic table have the same number of valence electrons, i.e. outermost shell electrons.

Question 27. A few dried raisins are put in water for some time and then placed inside the concentrated salt solution. What we observe is, raisins:

a. Shrink in water and swell in salt solution due to diffusion.
b. Shrink in water and swell in salt solution due to endocytosis.
c. Swell in water and shrink in salt solution due to osmosis.
d. Shrink in water and swell in salt due to plasmolysis.

Answer: (c)

Raisins when placed in salt solution would undergo exosmosis and hence, would shrink whereas when placed in water would undergo endosmosis and hence, would swell due to absorption of water.

Question 28. Observe the given diagram and read the following statements.

(i) These are cells of collenchyma tissue.

(ii) At maturity these cells lose their nucleus and cytoplasm.

(iii) The cells are living and thick at their corners.

(iv) This tissue gives flexibility to plant parts.

Correct statements are:

a. (i), (iii) and (iv)
b. (i), (ii) and (iv)
c. (i) and (iii) only
d. (i) and (iv) only

Answer: (a)

In the given diagram, cells of collenchyma tissue are shown. It is the living mechanical tissue as it provides flexibility and elasticity to the plant. The plant bends without breakage due to the presence of collenchyma. The cells are elongated and have differential thickening at the corners of the cell wall due to the deposition of pectin.

Question: 29. The correct sequence of number of chambers of heart in crocodile, frog, man and fish is:

a. 3, 3, 4 and 2
b. 4, 3, 4 and 2
c. 4, 2, 4 and 2
d. 3, 2, 4 and 2

Answer: (b)

Man has a four-chambered heart. Amphibians like frogs have three-chambered heart except crocodiles which have four-chambered heart. Fish has a two-chambered heart.

Question 30. The function of finger like projections called “villi” in small intestine is to:

a. Supply the digested food to each and every cell of the body.
b. Separate the water from undigested food.
c. Convert the glucose into carbohydrates.
d. Increase the surface area for absorption of digested food.

Answer: (d)

The tiny projections on the inner surface of the small intestine which help in absorbing the digested food are called villi. These help to increase the surface area of intestinal walls.

Question 31. Because of lack of oxygen in muscle cells, 3 carbon molecule pyruvate is converted into:

a. Lactic acid
b. Ethanoic acid
c. Hydrochloric acid
d. Acetic acid

Answer: (a)

During excessive and rigorous exercise the muscle cells shift from aerobic respiration to lactic acid fermentation due to limited supply of oxygen. In the absence of oxygen, pyruvate is converted into a substance called lactic acid.

Question 32. The correct statement which explains the structure of veins is:

a. Thick walled and valves are absent.
b. Thin walled and valves are absent.
c. Thin walled and valves are present.
d. Thick walled and valves are present.

Answer: (c)

Veins bring back blood to heart from different parts of our body. Veins have thin walls and possess valves to ensure blood flow in one direction.

Question 33. The correct pathway of conduction of impulses through a neuron is

a. Nerve ending → dendrites → axon → synapse.
b. Dendrites → cell body → axon → nerve ending.
c. Axon → cell body → dendrites → synapse.
d. Synapse → axon → dendrites → cell body.

Answer: (b)

The nerve impulse is conducted in the following pathway in a neuron:

Dendrites → cell body → axon → nerve ending

Question 34. Identify the relationship between the first two words and suggest the suitable word for the fourth place related to the third word.

Adrenal gland: Adrenalin :: Pancreas: –––––––––

a. Oestrogen
b. Thyroxin
c. Insulin
d. Testosterone

Answer: (c)

The adrenal gland produces the hormone adrenaline and similarly, the pancreas produces the hormone insulin.

Question 35. Pair of an organism and its asexual method of reproduction is given below. Choose the correct pair:

a. Amoeba – Regeneration
b. Bryophyllum – Vegetative reproduction
c. Yeast – Fragmentation
d. Leishmania – Budding

Answer: (b)

Bryophyllum reproduces through vegetative propagation. Buds produced in the notches along the leaf margin of Bryophyllum fall on the soil and develop into new plants. Amoeba and Leishmania reproduce through binary fission and yeast reproduce through budding.

Question 36. Observe the diagrammatic representation of the longitudinal section of the flower. Select the correct statement:

a. Unisexual flower which has only pistil and performs cross pollination.
b. Bisexual flower which has only stamen and performs self pollination.
c. Unisexual flower which has only stamen and performs cross pollination.
d. Bisexual flower which has only pistil and performs self pollination.

Answer: (a)

This is a diagrammatic representation of a unisexual flower. It has only a pistil. It does not have a stamen. Hence, it performs cross-pollination only.

Question 37. The advantage of secretions of the prostate gland and seminal vesicles to sperms is:

a. Maintain a fixed temperature to their survival.
b. Help them to produce certain hormones and enzymes.
c. Provide nutrition and made transport easier.
d. Assist them to remove wastes and provide protection.

Answer: (c)

The male accessory glands include paired seminal vesicles, a prostate and paired bulbourethral glands. Secretions of these glands constitute the seminal plasma which is rich in fructose, calcium and certain enzymes and thus, provide nutrition to the sperms. The secretions of bulbourethral glands also helps in the lubrication of the penis so that sperms can move easily.

Question 38. Read the following statements about the use of coal and petroleum as energy sources.

(i) These are energy sources formed from biomass.

(ii) Inexhaustible energy sources when used continuously.

(iii) On combustion release oxides of sulphur and nitrogen.

(iv) Clean and eco-friendly sources of energy.

Correct statements are:

a. (i) and (iii)
b. (ii) and (iv)
c. (ii) and (iii)
d. (i) and (iv)

Answer: (a)

Natural resources such as coal and petroleum (crude oil) take thousands of years to form naturally and cannot be replaced as fast as they are being consumed continuously. These are formed from the biomass and on combustion release oxides of sulphur and nitrogen. Hence, these fuels are not clean and eco friendly.

Question 39. If a round, green seeded pea plant (RRyy) is crossed with wrinkled, yellow seeded pea plant (rrYY) the seeds produced in F₁ generation are:

a. Rounded green
b. Wrinkled green
c. Wrinkled yellow
d. Rounded yellow

Answer: (d)

If a round, green seeded pea plant (RRyy) is crossed with a wrinkled, yellow seeded pea plant (rrYY), the seeds produced will be round yellow (RrYy).

Question 40. Flow chart of sex determination in humans is given below. Information to be filed in the blanks a, b and c respectively are:

a. a = 22 + y, b = 22 + x, c = Boy baby
b. a = 22 + x, b = 22 + x, c= Girl baby
c. a = 22 + y, b = 22 + x, c = Girl baby
d. a = 22+x, b = 22 + y, c = Boy baby

Answer: (a)

Sperms and eggs are both haploid. Hence, they both will show a haploid number of chromosomes i.e., 22 + Y and 22 + X respectively. These both fertilize to form a diploid zygote whose chromosome pairs are 22 + XY. Thus, it will be a baby boy.

Question 41. Choose the correct statements related to the Ryotwari system

(a) The charge of collecting the revenue and paying it to the company was given to the village headman.

(b) Alexander Reed introduced it in the Baramahal Region.

(c) Farmers had to pay 50% of the produce as revenue to the Government.

a. a only
b. b and c only
c. a and b only
d. a, b and c only

Answer: (b)

Sir Thomas Munro introduced the Ryotwari system in south India in 1820. Sir Alexander Reed introduced it in the Baramahal Region. There was direct contact between the farmers and the government in this system, eliminating the need for intermediaries. Farmers had to pay 50% of the produce in case of drylands and 60% in case of wetlands to the government. Ryots or peasants had no ownership rights but only enjoyed occupancy rights.

Question 42. In List – A Mahajanapadas and in List – B their Capitals are given. Write the correct option by matching them :

a. a – ii b- i c – iv d – iii
b. a – iii b- iv c – i d – ii
c. a-v b-i c – ii d – iv
d. a – ii b- iii c – iv d – v

Answer: (b)

Mahajanapadas were highly developed regions which emerged at the beginning of 6th century BCE in India. Angutara Nikaya is a Buddhist scripture that mentions 16 Mahajanapadas. Some of the important ones are Anga, Kashi, Kosala, Malla. Their capitals were Champa, Varanasi, Saketha and Kushinagara respectively.

Question 43. Select the correct chronological order of wars :

a. The first Anglo-Sikh war, The second Anglo-Marata war, The second Anglo-Mysore war, The third Carnatic war.
b. The first Anglo-Sikh war, The second Anglo-Mysore war, The third Carnatic war, The second Anglo-Marata war.
c. The second Anglo-Marata war, The third Carnatic war, The first Anglo-Sikh war, The second Anglo – Mysore war.
d. The third Carnatic war, The second Anglo-Mysore war, The second Anglo-Marata war, The first Anglo Sikh war.

Answer: (d)

The Third Carnatic War, also known as Battle of Wandiwash, took place from 1757-1763.

The Second Anglo-Mysore War took place from 1780-1784.

The Second Anglo-Marata War took place from 1803-1805.

The First Anglo-Sikh War took place from 1845-1846.

Question 44. Observe the location on the map of India and choose the correct incident related to it.

a. The declaration of complete independence.

b. The Chauri-Chaura incident.

c. Champaran movement began.

d. The first session of Indian National Congress.

Answer: (b)

On 4th February 1922, a group of protestors participating in the Non-Cooperation Movement clashed with the police who opened fire. The angry protestors in turn set the police station on fire, killing all its occupants. This took place in Chauri Chaura, in Gorakhpur district of erstwhile United Provinces. On seeing the movement turn violent, Mahatma Gandhi put a halt to the Non-Cooperation Movement in the subcontinent.

Question 45. Read the following statements, choose the wrong options :

i. The facility of giant granaries was made throughout the kingdom -Aztec Civilization.

ii. The rich were electing an administrator named ‘Archon’ -Greek Civilization.

iii. Used their wealth and power to make their life luxurious in the capital – Inca

Civilization.

iv. Fought for the control of a fertile area, Sicily for 118 years – Roman Civilization.

a. i and ii only
b. ii and iv only
c. i and iii only
d. iii and iv only

Answer: (c)

The facility of giant granaries was made throughout the kingdom in the Inca Civilization.

In the ancient Greek civilization, the rich elected an administrator named ‘Archon’.

The Aztecs used their wealth and power to make their life luxurious in the capital.
The ancient Romans fought for the control of Sicily, a fertile area for 118 years. These wars came to be known as the Punic Wars.

Question 46. Identify the statement that is NOT related to Bahamani Kingdom :

a. Asar Mahal was one of the important monuments.
b. Mir Syed Ali and Abdul Samad were the artists.
c. Kitab-E- Navras, a literary work was written.
d. Shihabuddin Ahmed shifted his capital.

Answer: (b)

Shihabuddin Ahmed shifted the capital of the Bahamani kingdom from Gulbarga to Bidar.

Ibrahim Adil Shah II wrote the ‘Kitab-E-Navras’. The Indo-Saracenic style of architecture was developed by the Bahamani sultans. Asar Mahal was one such monument constructed during this time.

Mir Syed Ali and Abdul Samad were Iranian painters in the court of Mughal emperor Humayun.

Question 47. Read the statements and find out to who do they belong to :

i. He took Deeksha from Govindabhatta.

ii. His Tatva Pandas include Kalaga pada, Alavi pada and Sawal Jawab Pada.

a. Chaithanya
b. Kanakadasa
c. Shishunala Sharifa
d. Guru Nanak

Answer: (c)

Shishunala Sharifa was a Sufi saint from modern-day Karnataka. He was influenced by Islam, Veerashaiva and Vedic philosophy from a young age. He took Deeksha from Govindabhatta. His Tatva Padas include Kalaga pada, Alavi pada and Sawal Jawab Pada.

Question 48. List – A contains the names of poets and List – B with their works. Select the correct answer from the code given below.

Codes: a b c d

a. i iii v iv
b. ii v iv iii
c. iv i ii v
d. iii i v ii

Answer: (d)

Gajashatra was written by Sree Purusha.

Gadya Chintamani was written by Vadiba Simha.

Shabdavathara was written by Durvinita.

Raghava Pandaviya was written by Hemasena.

Question 49. Select the order of events related to the world starting from West to East as shown in the world map.

a. A Newspaper by the name ‘Risorgimento’ was published.

b. People revolted against Czar in 1905.

c. ‘Blood’ and ‘Iron’ policy was adopted.

d. Thirteen colonies were declared independent.

Answer: (a)

The newspaper ‘Risorgimento’ was published by Camillo Benso in 1847 in Turin, Italy. In the year 1905, people in Russia revolted against Nicholas II, the then Czar. This was also known as the Russian Revolution of 1905 or the First Russian Revolution. The ‘Blood’ and ‘Iron’ policy was adopted by Otto von Bismarck in Germany. In 1776, thirteen colonies in the United States of America declared independence from the British rule.

Question 50. Arrange the following rivers in the correct sequence as given in the map.

a. a – Chambal; b – Yamuna; c – Ghagra; d – Sone
b. a – Yamuna; b – Chambal; c – Sone; d – Ghagra
c. a – Ghagra; b – Betwa; c – Gomati; d – Kosi
d. a – Betwa; b – Ganga; c – Rihand; d – Sharda

Answer: (b)

Yamuna(a) is one of the main right bank tributaries of the river Ganga. On the other hand, The Chambal, represented as (b) is the chief tributary of the Yamuna River and rises in the Vindhya Ranges. Sone (c), another southern tributary of the Ganga River, rises in Madhya Pradesh and joins the Ganga above Patna in Bihar. Ghaghra is a major left-bank tributary of the Ganges River. It flows southeast through Uttar Pradesh and Bihar states to enter the Ganges near Chapra in Bihar.

Question 51. Match Column-A with Column-B and choose the correct answer.

Column – A(Ports) Column – B(States)

a. a – ii, b – iv, c – i, d – iii
b. a – v, b – ii, c – iii, d – i
c. a – iii, b – v, c – iv, d – ii
d. a – i, b – iii, c – ii, d – v

Answer:(b)

Question 52. Read the statements and choose the correct option:

Assertion-(a) : During winter season, India gets oblique rays of the sun.

Reason – (r) : The rays of the sun fall vertically over the Southern hemisphere during this season.

a. Both ‘a’ and ‘r’ is correct ‘r’ is the correct explanation of ‘a’.
b. Both ‘a’ and ‘r’ are correct ‘r’ doesn’t explain ‘a’.
c. ‘a’ is true and ‘r’ is false.
d. ‘a’ is false and ‘r’ is true.

Answer: (a)

In the winter season, the northern hemisphere receives less sunlight due to the apparent movement of the Sun. Thus, India too gets oblique rays of the sun. On the other hand, the rays of the sun fall vertically over the Southern hemisphere during this season.

Question 53. Read the following statements and select the correct answer:

(i) It forms from the weathering of Granite and gneiss rocks.

(ii) It has more sandy and less clayey composition.

(iii) It does not retain moisture.

(iv) Total area covered in India about 5.2 lakh sq. kms.

a. Red soil
b. Black soil
c. Laterite soil
d. Alluvial soil

Answer: (a)

Red soil is formed from the weathering of granite, gneiss and other crystalline rocks. This soil is sandy and less clayey. Thus, it does not retain moisture. Red soil covers about 5.2 lakh sq.kms of India’s landmass.

Question 54. Identify the correct group related to the local names of ‘Primitive Subsistence Farming’ in India:

a. Milpa, Andhis, Masole, Ray.
b. Jhumming, Andhis, Kalabaisaki, Kuruva.
c. Andhis, Kalabaisaki, Coffee Blossom, Mango showers.
d. Bewar, Podu, Koman, Khil

Answer: (d)

Primitive subsistence agriculture is practised on small land patches with primitive tools like hoe, dao, digging sticks, and limited labour. ‘Slash and burn’, a type of primitive agriculture, is in practice in many areas of India and is known by different names. In Madhya Pradesh, it is called ‘Bewar’ or ‘Dahiya’, ‘Podu’ or ‘Penda’ in Andhra Pradesh, ‘Pama Dabi’ or ‘Koman’ or Bringa’ in Odisha. In the Himalayan belt, it is known as ‘Khil’.

Question 55. Match List-I with List-II. Select the correct answer from the code given below:

a. a – i, b – ii, c – iii, d – iv
b. a – iii, b – i, c – iv, d – ii
c. a – ii, b – iv, c – i, d – iii
d. a – iv, b – iii, c – ii, d – i

Answer: (c)

Question 56. Read the description and choose the correct answer:

i. It is a joint venture of Punjab, Haryana and Rajasthan.

ii. It is built across the River Sutlej.

iii. It is 226 mts. high and is the highest straight gravity dam in India.

iv. It has four power projects (houses).

a. Hirakud project
b. Bhakra Nangal project
c. Rihand Valley project
d. Damodar Valley project

Answer: (b)

All the given statements describe the Bhakra Nangal Project, one of the earliest river valley development projects undertaken after independence. The dam was completed in 1963.

Question 57. Identify the correct sequence of nuclear power plants on the map of India.

a. i-Tarapur, ii-Rawath Bhata, iii-Kalpakkam, iv-Kakrapara
b. i-Kakrapara, ii-Tarapur, iii-Rawath Bhata, iv-Kalpakkam
c. i-Rawath Bhata, ii-Kakrapara, iii-Tarapur, iv-Kalpakkam
d. i-Kakrapara, ii-Rawath Bhata, iii-Kalpakkam, iv-Tarapur

Answer: (c)

Question 58. Read the following statements:

(i) Delhi, Kolkata, Chennai and Mumbai cities are linked by six lane highways.

(ii) Srinagar to Kanyakumari linking North to South.

(iii)Silchar and Porabander connects East to West.

(iv) The major objective is to reduce the time and distance between the mega cities.

The above statements refer to :

a. National Highways
b. Border Roads
c. State Highways
d. Golden Quadrilateral super highways

Answer: (d)

The statements given in the question refers to the Golden Quadrilateral super highways. It is the largest highway project undertaken in India. It was launched in 2001 as part of the National Highways Development Project (NHDP).

Question 59. Select the correct group of iron ore producing areas:

a. Koraput, Kalahandi, Shivamogga, Palamao
b. Singhbhum, Balaghat, Chitradurga, Saraguja
c. Sunderkand, Bastar, Singhbhum, Cuttack
d. Bastar, Gaya, Salem, Bhavanagar

Answer: (c)

Sunderkand, Bastar, Singhbhum, Cuttack are iron ore mining areas. Sundergad and Cuttack are mining areas located in Odisha. Bastar, part of Bailadila and Dalli-Rajhara areas, is located in the southern part of Chattisgarh. In Jharkhand, Noamandi mines in Singhbhum are the richest in iron ore.

Question 60. The List -A contains the laws and the List-B with their year of implementation. Choose the correct option that matches exactly.

a. a – i, b – ii, c – v, d – iii
b. a – ii, b – iii, c – i, d – iv
c. a – v, b – i, c – iv, d – ii
d. a – iv, b – v, c – ii, d – i

Answer: (c)

Question 61. The correct group of statements related to fundamental duties is:

a. Fundamental duties are delineated in article 51 ‘A’.

b. 11 fundamental duties have been delineated in the 3rd chapter of our constitution.

c. 10 fundamental duties were included as per 42nd amendment in the year 1976.

d. Through the 86th amendment to the constitution in 2002, 11th fundamental duty was included

a. Only a, b and d
b. Only a, c and d
c. Only a, b and c
d. Only c and d

Answer: (b)

Article 51 A under Part-IV A of the Indian Constitution mentions 11 fundamental duties. The 42nd Amendment Act of 1976 added 10 Fundamental Duties to the Indian Constitution. In 2002, 11th fundamental duty was included in the constitution through the 86th amendment.

Question 62. Read the following statements and write the correct option with which all those links.

1. It came into existence on 1^st April 1974.

2. It functions under the High court.

3. It takes up crimes like murder, robbery, dacoity etc.

4. It is also known as District Magistrate court.

a. Civil Court
b. Commissioner’s Court
c. Tahsildar Court
d. Criminal Court

Answer: (d)

A criminal court takes up cases related to crimes like murder, robbery, dacoity etc. It is also known as District Magistrate court, which functions under the High court. It came into existence on 1st April 1974.

Question 63. Choose the correct sequence to indicate the following statements as True (T) or False (F).

1. Food and Agriculture organisation was born in 1945.

2. World Health Organization’s head office is in Geneva.

3. UNICEF received the Nobel Prize in the year 1965.

4. The head office of International Labour Organization in Geneva.

a. TTTT
b. FTFT
c. TTFF
d. TFTF

Answer: (a)

All the above statements are true. Food and Agriculture Organization (FAO), the oldest permanent specialized agency of the United Nations, established in October 1945 to eliminate hunger and improve nutrition.

The World Health Organization is also a specialized agency of the United Nations responsible for international public health, headquartered in Geneva, Switzerland. UNICEF was awarded the Nobel Peace Prize On 26th October, 1965. The International Labour Organization is another United Nations agency with a mandate to advance social and economic justice through setting international labour standards. It has its headquarters in Geneva, Switzerland.

Question 64. Identify the correct chronological sequence in which the following became the Secretary General of the UNO:

i. U.Thant ii. Kurt Waldheim iii. Boutros Boutros Ghali iv. Javier Perez de Cuellar

a. a – i, b – ii, c – iii, d – iv
b. a – ii, b – iii, c – i, d – iv
c. a – i, b – ii, c – iv, d – iii
d. a – ii, b – i, c – iii, d – iv

Answer: (c)

Question 65. Identify the correct statements related to the current account:

(i) It is opened by businessmen who have a large number of regular transactions.

(ii) It includes deposits, withdrawals and contra transactions.

(iii) In current account, amount can be deposited only one time in a day.

(iv) Generally banks do not give any interest on these deposits.

a. Only, i, ii and iii are correct
b. Only ii, iii and iv are correct
c. Only i, ii and iv are correct
d. Only i and ii are correct

Answer: (c)

A current account is opened and run by businessmen, entrepreneurs and traders. These are useful for businessmen who have a large number of regular transactions. It includes deposits, withdrawals and contra transactions. Due to the volume of transactions, and usually high amounts of transactions, banks do not give any interest on these deposits.

Question 66. Read the given statements and identify the correct option related to them.

i. It came into existence on 1st January 1995.

ii. At present 164 countries of the world are its members.

iii. The members meet once in two years to take decisions.

iv. It is the only global international organization dealing with the rules of trade between nations.

a. International Bank for Reconstruction and Development
b. United Nations Conference on Trade and Development
c. International Monetary Fund
d. World Trade Organization

Answer: (d)

The World Trade Organization is the only global international organization dealing with the rules of trade between nations. It came into existence on 1st January 1995, replacing the General Agreement on Trade and Tariffs (GATT). At present, 164 countries of the world are its members, accounting for over 96% of global trade and GDP. The members meet once in two years to make decisions.

Question 67. Read the given statements and select the correct answer :

Assertion (a): Journal is called the book of original entry

Reason (r): The full particulars of the transactions are recorded first in the Journal

a. Both ‘a’ and ‘r are true and ‘r’ is the correct explanation of ‘a’
b. Both ‘a’ and ‘r’ are true and ‘r’ is not the correct explanation of ‘a’
c. ‘a’ is true and ‘r’ is false
d. ‘a’ is false and ‘r’ is true

Answer: (a)

Journal is called the book of original entry. The full particulars of a transaction such as the date of the transaction, accounts affected, amounts are recorded first in the Journal, usually in a double-entry system.

Question 68. In List – ‘A’ the areas of managerial functions and in List – ‘B’ their meanings are given. Choose the correct answer by matching them :

a. a-i, b – iii, c-ii , d-iv
b. a-ii, b-v, c-i, d-iii
c. a-iii, b-ii, c-v, d-i
d. a-iv, b-i, c-iii, d-ii

Answer: (b)

Managerial functions can be divided into several areas. Some of the common ones are Planning, Coordination, Organising, Staffing, Directing and Controlling.

Planning involves the future course of operation for a given period.

Coordination is the harmonious blending of the activities of different departments for the achievements of the desired goals.

Organising involves the process of bringing together manpower and material resources.

Staffing is the function concerned with the recruitment, selection and placement of the workforce. Directing involves leading, instructing, guiding and supervising the workforce of an organization towards the achievement of desired goals.

Controlling covers all managerial activities to achieve the overall efficiency of the organization.

Question 69. Read the given statements and identify the correct option which is related to all of them :

i. It is related to financial institutions which deal with short term funds in the economy.

ii. This type of market arranges funds for working capital.

iii. Here the rate of interest is high.

iv. The funds can be borrowed from this market for a short period varying from a day, a week, a month or 3 to 6 months.

a. Capital Market
b. Stock Market
c. Money Market
d. Open Market

Answer: (c)

Money Market is related to a financial institution which deals with short term funds in the economy. They form one of the pillars of the global financial system. In such a market, working capital funds are arranged but at higher interest rates are high. These are highly liquid near-term investments for a short period varying from a day, a week, a month or 3 to 6 months.

Question 70. The advantages of sole trading concerns are listed. Choose the wrong statement:

i. Legal formalities are required to commence the business.

ii. It can be started by own capital.

iii. No difficulties arise in day to day running of the business.

iv. They are in a position to take quick decisions and maintain business secrets.

a. Only i
b. ii and iii
c. iii and i
d. iv and i

Answer: (c)

A sole trading concern is started, invested and managed by a single person. They can be started by their own capital, which facilitates quick decision making and helps in the maintenance of business secrets easily. The possibilities of difficulties arising in the day to day running of the business are less but not absent. They are the oldest and simplest forms of commercial enterprise. Most businesses of this sort function on a small scale.

Question 71. One of the statements related to Labourers is wrong. Identify it:

a. Organised labourers come under gratuity Act of 1971.
b. Unorganised sector labourers are responsible for child labour.
c. A large section of farmers are unorganised labourers.
d. Migration is the major challenge faced by organised sector labourers.

Answer: (d)

Agriculture in India is one the greatest employers of unorganised labourers. Unorganised sector is mainly responsible for child labour. Children are hired as cheap and fast workers. Moreover, employers do not have to provide any social security, as these children are generally unskilled. This sector also faces the challenges of migration. Organised labour in India is covered under the Gratuity Act of 1971.

Question 72. Read the given statements and identify the correct sociologist related to all of them :

i. He/she worked as the UGC national fellow and as Head of Department of Sociology of Bombay University.

ii. As he/she was following the Marxist ideology in his/her sociological studies, he/she was identified as Marxist Sociologist.

iii. His/her ‘The Sociological Background of Indian Nationalism’ is the best work.

iv. Indian Rural sociology, slums and Urbanisation are his/her major works.

a. Iravati Karve
b. C. Parvathamma
c. M.N. Srinivas
d. A.R. Desai

Answer: (d)

Akshay Ramanlal Desai was a renowned Indian sociologist. Influenced by Leon Trotsky, he was a devout Trotskite Marxist and a social activist. He worked as the UGC national fellow and as the Head of the Department of Sociology in Bombay University. “The Sociological Background of Indian Nationalism” is among one his best works. His other major works include Indian Rural Sociology, Slums and Urbanisation.

Question 73. The Supreme Court declared as a fundamental right to provide free and compulsory education to all children between the age of 6 to 14 years under article 21A in :

a. Golaknath v/s Punjab Government
b. Kesavananda Bharathi v/s Kerala Government
c. Unnikrishnan v/s Andhra Pradesh Government
d. Minerva Mills v/s Union of India

Answer: (c)

Unnikrishnan v/s Andhra Pradesh Government,1993 was a watershed judgement in the history of education in India. In this case, the Supreme Court declared the right to education as a fundamental right. It also mentioned that it was the duty of the state to provide free and compulsory education to all children between the age of 6 to 14 years under Article 21A of the Indian Constitution.

Question 74. In Column – A the authors and in Column – B their works are given. Choose the correct matching :

Answer (1)

Answer: (1)

Question 75. Read the given statements and identify the correct option related to Caucasians Tribe.

i. The people of this tribe are white in skin colour.

ii. They are tall, have long straight sharp nose, bent head, straight cheek, elongated face, small lips as their physical characteristics.

iii. The people of these tribe are found in Europe, North and South America, Palestine, Asia, Iran, and North India

iv. The subtribes of this tribe are Nordic, Alpine, Mediterranean and Hindu.

a. i, ii, iii and iv are correct
b. Only i, ii and iii are correct
c. Only ii, iii and iv are correct
d. Only i, iii and iv are correct

Answer: (a)

The people of the Caucasian tribe can trace their history back to the various ethnic groups living around the Caucasus region. People belonging to this tribe have white skin shade. They are tall, have a long straight sharp nose, bent head, straight cheek, elongated face, small lips as their physical characteristics. They live in Europe, North and South America, Palestine, Asia, Iran, and North India. The subtribes of this tribe are Nordic, Alpine, Mediterranean and Hindu.

Question 76. Choose the correct group of Direct tax:

a. Corporate tax, Wealth tax, Central Excise tax, Service Tax.
b. Income Tax, Stamp Duty, Service Tax, Export Tax.
c. Value Added Tax, Service Tax, Corporate Tax, Export Tax.
d. Income Tax, Corporate Tax, Wealth Tax, Stamp Duty.

Answer: (d)

A direct tax is a tax that is paid directly to an imposing entity, usually the government, by an individual or an organisation. This type of tax cannot be transferred to another individual or entity. Income Tax, Corporate Tax, Wealth Tax, Stamp Duty are direct taxes. The collection and levying of direct taxes is regulated by the Central Board of Direct Taxes.

Question 77. List – A contains economic terms and List – B with their correct meanings. Choose the options that match correctly.

a. a – iii b – i c – iv d – ii
b. a – iii b – iv c – ii d – i
c. a – ii b – iii c – iv d – i
d. a – i b – iii c – ii d – iv

Answer: (b)

Fiscal Deficit – Revenue receipts and non-debt capital receipts minus total expenditure.

Revenue Deficit – Revenue receipt minus Revenue expenditure.

Budget Deficit – Total revenue minus total expenditure.

Primary Deficit – Fiscal deficit minus interest payment.

Question 78. Identify the correct statements related to Antyodaya Anna Yojana.

(i) It was launched in July 2001.

(ii) Under this scheme one crore of the poorest among the BPL families covered under the targeted public distribution system were identified.

(iii) Poor families were identified by the respective state rural development departments through a BPL survey.

(iv) Fifty kilograms of foodgrains were made available to each eligible family.

a. Only i and ii are correct
b. Only ii and iii are correct
c. Only iii and iv are correct
d. Only i and iv are correct

Answer: (b)

Antyodaya Anna Yojana was launched in 2000 to provide foodgrains, namely, rice and wheat to extremely poor families in rural India. Under this scheme, one crore BPL (Below Poverty Line) families covered under the targeted public distribution system were identified. Poor families were identified by the respective state rural development departments through a BPL survey.

It was first implemented in Rajasthan. Each of the identified families was issued 25 kg foodgrains (rice and wheat) initially, but this was later increased to 35 kg per family with effect from 1st April, 2002.

Question 79. Consider the following aspects of deficit financing:

(i) Fiscal deficit = (Revenue Receipts + Non debt capital Receipts) – Total expenditure

(ii) Revenue Deficit = Total Revenue – Total Expenditure

With reference to the above :

a. Both i and ii are correct.
b. Both i and ii are not correct.
c. i is correct, ii is not correct.
d. ii is correct, i is not correct.

Answer: (c)

Fiscal Deficit = (Revenue Receipts + Non debt capital Receipts) – Total Expenditure.

Revenue Deficit = Total Revenue Expenditure – Total Revenue Receipts.

Question 80. Choose the correct sequence to indicate the given statements related to Mahatma Gandhi National Rural Employment Guarantee act as TRUE (T) or FALSE (F)

(1) It was implemented on 2-2-2006.

(2) It provides a legal guarantee for one hundred days of employment in every financial year to adult members of any rural household willing to do public work related to unskilled manual work.

(3) If the government fails to do so, then the person is given unemployment allowance.

(4) It was enacted on August 25, 2005.

a. FFTT
b. TTFT
c. TFTF
d. TTTT

Answer: (d)

Mahatma Gandhi National Rural Employment Guarantee Act was enacted on August 25, 2005. It provides a legal guarantee for 100 days of employment to adult members of all rural households willing to do public work related to unskilled manual work, every fiscal year. In case, a government fails to do so, then the person automatically qualifies for an unemployment allowance. The act was implemented on February 2, 2006. It is the largest work guarantee program in the world and solidifies the role of decentralisation by empowering Panchayati Raj Institutions.

Question 81. Two numbers are in the ratio 4 : 5. If 24 is subtracted from each of them, then the resulting numbers will be in the ratio 2 : 3. The original numbers are:

a. 48 and 60
b. 52 and 65
c. 60 and 75
d. 76 and 95

Answer: (a)

Let two number 4x, 5x

Now, (4x–24)/(5x–24)=2/3 (given)

⇒ 12x – 72 = 10x – 48

⇒ x = 12

⇒ 4x = 48 and 5x = 60

So, numbers are 48 and 60

Question 82. ABC is a right angled triangle such that angle ABC = 90^o, AB = 16cm and BC = 32 cm. If BD perpendicular to AC then AD : AC is

a. 1 : 2
b. 1 : 3
c. 1 : 4
d. 1 : 5

Answer: (d)

Given, that AB = 16cm, BC = 32 cm, BD perpendicular to AC

So, AC = √(16²+32² ) (By Pythagoras)

AC = 16√5

BD × AC = 16 × 32 (Both are twice the area)

BD = (32√5)/5

AD = √(16²–BD² )

AD = √(16²–(32/√5) ²)

AD = ((16√5)/5)

AD : AC = 1 : 5

Question 83. If sinA + sin² A = 1 (A is acute angle) then the value of cos² A + cos⁴ A is :

a. 0
b. 1
c. 2
d. 3

Answer: (b)

sin A = 1 – sin²A (given)

sinA = cos² A …….(1)

cos² A + cos⁴ A = cos² A + sin² A = 1 (using (1))

Questio 84. X and Y walk 24 km each. X walks faster than Y. Sum of their speeds is 7 km/h and the sum of the time taken by them to complete the walk is 14 hours. Speed of X is :

a. 4 km/h
b. 5 km/h
c. 6 km/h
d. 7 km/h

Answer: (a)

Let the speed of X and Y be x and y respectively.

Given

24/y + 24/x = 14  ;   y+x=7

1/(7–x) + 1/x = 7/12

Solving thus we get

x² – 7x + 12 = 0

x = 3,4 and y = 4,3

Since speed of x is higher,

x = 4

Question 85. The cumulative frequency curve for a distribution is represented in the graph. The median for the data is :

a. 10
b. 30
c. 40
d. 60

Answer: (c)

Median = l + ((n/2–Cf)/f)× h

l = lower limit of median

n = number of observations

Cf = cumulative frequency

f = frequency of median class

h = class size.

(Median, N/2) = (40, 30)

Median = 40

Question 86. Four circular plates of same size having diameter ‘a’ units each are placed on the square mat such that each plate touches externally the other two as shown in the figure. The area of the shaded region is:

a. (a²/4)(4+π)Square units
b. (a²/4) (4–π)Square units
c. (4a²) (4+π)Square units
d. (4a²) (4–π)Square units

Answer: (b)

Required shaded area

= area of square – 4 × (shaded area)

= a² – ( 4×1/4× π a²/4)

a² (a–π/4)=a²/4(4–π)

Question 87. The empirical relationship between the three measures of central tendency of data is:

a. 3 median = mode + 2 mean
b. 3 mean = mode + 2 median
c. 3 mode = mean + 2 median
d. 3 mean = median + 2 mode

Answer: (a)

3 median = mode + 2 mean

Question 88. ABC is a triangle whose vertices are A(8, 2), B(5, –3) and C(0,0).BD perpendicular to AC . The length of the altitude BD is

a. 17 units
b. √(17/2)
c. 2√17 units
d. √17

Answer: (d)

AC = √[(8-0)^2+(2-0)^2] = 2√17———–(i)

Area of ABC = 1/2×BD × AC = 1/2|8(–3) + 5(–2)+0|

BD × AC = 34

BD × 2√17= 34 from (i)

BD = √17

Question 89. The value of ‘p’ for which the pair of linear equations px + 3y – (p – 3) = 0 and 12x + py – p = 0 has infinitely many solutions is :

a. 0
b. –6
c. 1/6
d. 6

Answer: (d)

Since the pair of equations have infinitely many solutions.

Then, a₁/a₂ =b₁/b₂ =c₁/c₂

So, p/12=3/p=(-(p-3))/(-p)

⇒ p = 6

Question 90. The distance from the origin to the centroid of the triangle whose vertices are (7,1), (1, 5) and (1, 6) is :

a. 5 units
b. 6 units
c. 9 units
d. 10 units

Answer: (a)

G = centroid = ((x₁+x₂+x₃)/3,(y₁+y₂+y₃)/3)

G = Centroid = ((7+1+1)/3,(1+5+6)/3) = (3, 4)

And distance between (x₁, x₂) & (x₂, y₂) = √[(x₂–x₁)²+(y₂–y₁)²]

OG = √(3²+4²)

OG = 5

Question 91. In ΔABC, angle BAC = 90 degrees BD and CE are the medians. BD = 6cm and CE = 8cm. The length of the hypotenuse BC is :

a. 2√5 cm
b. 3√5 cm
c. 4√5 cm
d. 6√5 cm

Answer: (c)

a² + 4b² = 36 ……(1)

b² + 4a² = 64 …… (2)

Add eq.(1) & (2) we get

⇒ 5 (a²+b²)=100

(a²+b²)=20

Therefore, (2a)² + (2b)² = c² (by Pythagoras theorem)

c² = 4 (a²+b²)=4×20

c = 4 √5

Question 92. In a box there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. The probability that the ball is neither blue nor green is:

a. 13/21
b. 6/21
c. 7/21
d. 8/21

Answer: (d)

Given that: red ball = 8, blue ball = 7 and green ball = 6

So, P(red) = 8/(8+7+6)=8/21

Question 93. 10^th term of an AP is 16 and 16th term of it is 10. The common difference and the 26th term of the AP are respectively:

a. 1 and 0
b. –1 and 0
c. 0 and 1
d. 0 and –1

Answer: (b)

T₁₀ = 16, T₁₆ = 10(given)

a + 9d = 16 …..(1)

a + 15d = 10 ……(2)

Subtract (2) from (1), we get

-6d =6

=> [d = –1]

Put value in equation (1), we get

a = 25

T₂₆ = a + 25d

= 25 + 25 (–1) = 0

Question 94. From an external point T, two tangents TP and TQ are drawn to a circle with centre ‘O’ and radius 6cm as shown in the figure. OT intersects the circle at E. A tangent drawn at E meets TP and TQ at A and B respectively. If OT =10cm then length of AB is :

a. 12 cm
b. 10 cm
c. 8 cm
d. 6 cm

Answer: (d)

Given that: OT = 10cm; OP = 6m (radius)

Let AE = x

In triangle POT

So, TP = √[(10)²–(6) ²]= 8 (By Pythagoras theorem)

In triangle AET

⇒ (8 – x) ² = x² + 4²

⇒ x = 3

⇒ AB = 2x = 6

Question 95. Two tangents TP and TQ are drawn to a circle with centre ‘O’ from an external point T as shown in the figure. If PTQ = 32 degrees then OPQ is :

a. 8°
b. 16°
c. 20°
d. 24°

Answer: (b)

Therefore, θ₁ + θ₃ + θ₄ = 180°

θ₃ = 32° (given)

and θ₁ = θ₂ ( TP & TQ are equal tangents)

2θ₁ = 180 – 32

θ₁ = 74°

Since, tangent is perpendicular to radius angle TPQ = 90°

So, θ₂ = 90° – θ₁ = 16°

Question 96. List – A contains trigonometric expressions and List – B is their values on simplification. Choose the correct option by matching them:

a. (i) – (b) (ii) – (c) (iii) – (a) (iv) – (d)
b. (i) – (c) (ii) – (a) (iii) – (d) (iv) – (b)
c. (i) – (d) (ii) – (a) (iii) – (c) (iv) – (b)
d. (i) – (d) (ii) – (c) (iii) – (b) (iv) – (a)

Answer: (c)

(i) tan1°. tan2°. tan3° …….. tan89^°

= (tan1° . cot1°) (tan2° . cot2°) ……. tan(90 – 1)……(tan 45°) …….(tan89° cot89°)

= 1 (tanθ cotθ = 1)

(ii) cosec31° – sec(90 – 31)

⇒ cosec31° – cosec31° = 0

(iii) sin² 45° + cos² 60°=1/2 + ¼ = 3/4

(iv) (2tan θ)/(1+tan² θ) = sin2θ

Let θ = 30°, So (2tan30°)/(1+tan² 30°) = sin2(30°)

sin60° = √3/2.

Question 97. AB, CD and EF are arcs of three concentric circles with radius 21 cm, 14 cm and 7 cm respectively with centre ‘O’ as shown in the figure. If AOB = 60° then the sum of the areas of two shaded regions are: (consider the approximate value for as 22/7)

a. 154 cm²
b. 1078/3 cm²
c. 770/3 cm²
d. 231 cm²

Answer: (a)

ar(ABDC) = ar(OAB) – ar(COD) + ar(EOF)

(π× 60°)/(360°) (21²–14²+7² )

= (π )/6 (441 -196 +49)

= 154 cm²

So, required area = 154 cm²

Question 98. The condition that one of the roots ax² + bx + c = 0 (a ≠ 0) is twice the other is:

a. 2b² = –4ac
b. 2b² = 9 (c – a)
c. 2b² = 9ac
d. 3b² = 16ac

Answer: (c)

Given that one root is twice the other.

Let roots are α and 2α.

Now, α + 2α = (–b)/a

= α.2α=c/α

So, α = (–b)/3a

2α² = c/a

2(b²/(9a² ))=c/a

2b² = 9ac

Question 99. The angles of depression of two ships as observed from the top of a 80m high light house from the sea-level are 30° and 45°. If two ships are on the same side of the light house and all the three are along a straight line, then distance between the two ships is:

a. 80 m
b. 80(√3–1)m
c. 80(√3+1)m
d. 80√3m

Answer: (b)

Given that : RQ = 80m, ∠RPQ = 30° and ∠RMQ = 45°

tan 45° = RQ/MQ

This implies MQ = 80 ..….(1)

and tan30° = RQ/PQ

⇒ PQ = 80 √3 …..(2)

Distance between ship = PM

PM = PQ – MQ

PM = 80√3–80

⇒ PM = 80(√3–1)

Question 100. A sphere is inscribed in a right cylinder such that the height of the cylinder is equal to the diameter of the sphere. Also the diameter of the base of the right cylinder is equal to the diameter of the sphere as shown in the figure. Read the following statements and choose the correct option:

Statement (a): Ratio of the total surface area of the right cylinder to that of total surface area of the sphere is 3 : 2

Statement (b): Ratio of the volume of the right cylinder to that of the volume of the sphere is 3 : 2

a. Only statement (a) is true.
b. Only statement (b) is true.
c. Both the statements (a) and (b) are true.
d. Both the statements (a) and (b) are false.

Answer: (c)

R_S = R_C ; 2R_S = H_C

⇒ R_C = R_S = R

⇒ H_C = 2R

(Total surface area)_C = 2 πR_CH_C + 2R² = 6πR² ……(1)

(Total surface area)_S = 4πR² ……(2)

From (1) & (2)

⇒ Ratio = 3 : 2

VC = πR² H

= πR² (2R)

= 2πR³ ……(3)

V_s = (4/3) πR_S³ = ( 4/3) πR² ……(4)

From (3) & (4)

⇒ Ratio = 3 : 2

Hence, both the statements are correct.