## AP SSC or 10th Class Question Paper Mathematics Paper 2 English Medium 2017 with Solutions – Free Download

Andhra Pradesh SSC (Class 10) Maths 2017 question paper 2 with solutions are available here in a downloadable pdf format and also in the text so that the students can easily obtain them. Along with the solutions, they can also get the Maths question paper 2 2017 Class 10 SSC for reference. All the Andhra Pradesh board previous year Maths question papers are available here. AP 10th Class Mathematics Question Paper 2017 Paper 2 can be downloaded easily and students can understand the concept, solve problems and verify the answers provided by BYJU’S. Solving 2017 Maths question paper 2 for Class 10 will help the students to predict the type of questions that will appear in the exam.

## Download SSC 2017 Question Paper Maths Paper 2

## Download SSC 2017 Question Paper Maths Paper 2 With Solutions

### Andhra Pradesh SSC Class 10th Maths Question Paper 2 With Solution 2017

### QUESTION PAPER CODE 16E(A)

**SECTION – I**

** (4 * 1 = 4)**

**Question 1: Find the coordinates of the point, which divides the line segments joining (2, 0) and (0,2) in the ratio 1:1 **

**Solution:**

_{1}x

_{2}+ m

_{2}x

_{1}] / (m + n), [m

_{1}y

_{2}+ m

_{2}y

_{1}] / (m + n)

= (1 * 0) + (1 * 2) / [1 + 1], (1 * 2) + (1 * 0) / [1 + 1]

= 2 / 2, 2 / 2

= 1, 1

**Question 2: ‘O’ is the centre of a circle. PQ is a tangent to the circle at Q from the external point P. If the radius of the circle is 9 cm and PQ = 12 cm, find the distance of P from O.**

In ∆ PQO,

PO^{2} = PQ^{2} + OQ^{2}

= 9^{2} + 12^{2}

= 81 +144

PO = √225

PO = 15cm

**Question 3: Find the value of x, if 2sinx = √3.**

**Solution:**

2sinx = √3

sinx = √3 / 2

sinx = 60^{o}

x = 60^{o}

**Question 4: You are writing a test of 40 objective type questions. Each question carries 1 mark. What is the probability of marks you may get to be in multiples of 5? **

**Solution:**

Event = {5, 10, 15, 20, 25, 30, 35, 40}

n(A) = 40

P(E) = 8 / 40

= 1 / 5

**SECTION – II**

** (5 * 2 = 10)**

**Question 5: Find the value of k, for which the points (7, 2), (5, 1) and (3, k) are collinear.**

**Solution:**

(1 / 2) (x_{1} [y_{2} – y_{3}] + x_{2} [y_{3} – y_{1}] + x_{3} [y_{1} – y_{2}]) = 0

(1 / 2) ({7 (1 – k) + 5 (k – 2) + 3 (2 – 1)} = 0

7 – 7k + 5k – 10 + 3 = 0

– 2k = 0

k = 0

**Question 6: Find the angle B, if tan (A – B) = 1 / √3 and sin A = √3 / 2. Also find cos B. **

**Solution:**

sinA = √3 / 2

=> sin A = sin 60

=> ∠A = 60°

So, cos A = cos 60° = 1 / 2

tan (A – B) = 1 / √3

=> tan(60 – B) = tan30

=> 60 – B = 30

=> ∠B = 30

So, cos B = cos 30 = √3 / 2

**Question 7: Give two different examples of a pair of**

**(i) Similar figures**

**(ii) Non-similar figures**

**Solution:**

(i) Two triangles

(ii) A square and A triangle

**Question 8: There are 5 cards in a box with numbers 1 to 5 written on them. If 2 cards are picked out from the box, write all the possible outcomes and find the probability of getting both even numbers. **

**Solution:**

Sample space = n(s) = {(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (2, 1) (2, 2) (2, 3) (2, 3) (2, 4) (2, 5) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5)}

Event = {(2, 2) (2, 4) (4, 2) (4, 4)}

P(E) = 4 / 25

**Question 9: A tower is 100√3 m high. Find the angle of elevation of its top when observed from a point 100m away from the food of the tower.**

**Solution:**

tan θ = 100√3 / 100

= √3

θ = 60^{o}

**SECTION – III**

** (4 * 4 = 16)**

**Question 10: **

**(a) A wire of length 18 cm had been tied to an electric pole at an angle of elevation 30 with the ground. As it is covering a long distance, it was cut and tied to the pole at an angle of 60 with the ground. Now, find how much length of the wire was cut?**

** OR**

**(b) Consider the following distribution of daily wages of 50 workers of a factory.**

Daily Wages |
200 – 250 |
250 – 300 |
300 – 350 |
350 – 400 |
400 – 450 |

Number of Workers |
12 |
14 |
8 |
6 |
10 |

**Find the mean daily wages of the workers by choosing an appropriate method.**

**Solution:**

(a) First, sinA = perpendicular / hypotenuse

sin 30 = 1 / 2

H = 18 m

P / H = 1 / 2

P = H / 2

= 9 m

In the second case, the length of the pole P = 9 m will be the same.

sin 60 = √3 / 2 = P / H

To find H.

H = (9 x 2) / √3

= 18 / √3

= (18 x √3) / 3

= 6 x √3

= 6 x 1.72

= 10.32

The new length = 10.32m

The decrease in length = 18 – 10.32 m = 7.68 m

(b)

Daily Wages | 200 – 250 | 250 – 300 | 300 – 350 | 350 – 400 | 400 – 450 |

Number of Workers (x_{i}) |
12 | 14 | 8 | 6 | 10 |

Midpoint (a_{i}) |
225 | 275 | 325 | 375 | 425 |

a_{i }x_{i} |
2700 | 3850 | 2600 | 2250 | 4250 |

Mean = ∑a_{i }x_{i} / ∑x_{i} = 15650 / 50 = 313

**Question 11: **

**[a] Prove that (sin θ – cosec θ) ^{2} + (cos θ – sec θ)^{2} = cot^{2} θ + tan^{2} θ – 1**

** OR**

**[b] Check whether the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angle isosceles triangle or not. Also, find the area of the triangle.**

**Solution:**

^{2}+ (cos θ – sec θ)

^{2}

= (sin θ – 1 / sin θ)^{2 }+ (cos θ – 1 / cos θ)^{2}

= sin^{2 }θ + 1 / sin^{2 }θ – 2 + cos^{2 }θ + 1 / cos^{2 }θ – 2

sin^{2 }θ + cos^{2 }θ = 1

= 1 – 2 – 2 + 1 / sin^{2 }θ + 1 / cos^{2} θ

= cosec^{2 }θ + sec^{2 }θ – 3

cosec^{2}θ = 1 + cot^{2 }θ, sec^{2 }θ = 1 + tan^{2 }θ

= 1 + cot^{2 }θ + 1 + tan^{2 }θ – 3

= cot^{2} θ + tan^{2} θ – 1

= RHS

[b] Let the A(3, 0), B(6, 4) and C(- 1, 3) are three vertices.Using the distance formula for two points A (x_{1}, y_{1}) and B(x_{2}, y_{2})

AB = √(x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{2}

AB = √(6 – 3)^{2} + (4 – 0)^{2}

= √(9) + (16)

= √25

= 5 units

BC = √(-1 – 6)^{2} + (3 – 4)^{2}

= √(49) + (1)

= √50

AC = √(-1 – 3)^{2} + (3 – 0)^{2}

= √(16) + (9)

= √25

= 5 units

AB = AC [they are isosceles]

AB > BC = AC

Therefore, if ABC is a right-angled triangle, AB should be the hypotenuse, BC and AC should be the other two sides. (i.e. perpendicular and base)

**Question 12: **

**(a) A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: **

**(i) Minor segment. **

**(ii) Major segment**

** OR**

**(b) From a deck of 52 playing cards, King, Ace and 10 of clubs were removed and the remaining cards were well shuffled. If a card is drawn at random from the remaining, find the probability of getting a card of **

**(i) Club **

**(ii) Ace **

**(iii) Diamond King **

**(iv) Club 5**

**Solution:**

(a) Radius r = 10cm

Angle = 90^{o}

Area of sector A = 90 / 360𝛑r^{2}

A = 3.14 x 10 x 10 / 4

A = 25 x 3.14

A = 78.5 sq.cm

Let the angle subtended and radius form an arc AOB, then

Area of AOB = r x r sin90 / 2

AOB = 10 x 10 x 1 / 2

Area of AOB = 50 sq.cm

Area of minor segment = 78.5 – 50 = 28.5 q.cm

Area of circle = 𝛑r^{2}

= 3.14 x 10 x 10

= 314 Sq.cm

Area of major segment = area of circle – area of minor segment

= 314 – 28.5

= 285.5 sq.cm

[b] King, Ace and 10 of Club were removed=> Club remained = 13 – 3 = 10

Total cards remaining = 52 – 3 = 49

Ace remaining = 4 – 1 = 3

Probability of club = 10/49

Probability of Ace = 3/49

Probability of Diamond king = 1/49

Probability of Club 5 = 1/49

**Question 13: **

**(a) Draw a circle of radius 3 cm. Take a point ‘P’ at a distance of 5 cm from the centre of the circle. From P, draw 2 tangents to the circle. **

**(or) **

**(b) Draw “greater than Ogive curve” for the following data.**

Classes |
0 – 10 |
10 – 20 |
20 – 30 |
30 – 40 |
40 – 50 |
50 – 60 |
60 – 70 |

Frequency |
4 |
4 |
8 |
10 |
12 |
8 |
4 |

**Solution:**

(a) Steps of construction :

1. Take a point O as the center and with radius 3 cm, draw a circle.

2. Mark a point P outside the circle such that OP = 5 cm. Join O to P.

3. Draw a perpendicular bisector of the OP that cuts OP at M.

4. With M as a centre and radius MO (or MP), draw a circle cutting the first circle at A and B.

5. Join P to A and P to B

Then PA and PB are the required two tangents

The length of the tangent is PA = PB = 4 cm.

(b)

**SECTION – IV**

** (20 * 0.5 = 10)**

**Question 14: If origin is the centroid of a triangle, whose vertices are (3, 2), (-6, y), (3, -2), then y = **

**(A) 0 (B) 3 (C) 2 (D) 6 **

**Answer: A**

**Question 15: Areas of 2 similar triangles are 100 cm ^{2} and 64 cm^{2}. If the median of the bigger triangle is 10 cm, then the median of the smaller triangle is ….. **

**(A) 10 cm (B) 6 cm (C) 4 cm (D) 8 cm **

**Answer: D**

**Question 16: If sin x = 5 / 7 , then cosec x = ……. **

**(A) 5 / 7 (B) 7 / 5 (C) 2 / 5 (D) 2 / 7 **

**Answer: B**

**Question 17: Given ∠A = 75 ^{o}, ∠B = 30^{o}, then tan (A – B) = ….. **

**(A) √3 (B) 1 / √3 (C) 1 (D) 1 / √2 **

**Answer: C**

**Question 18: If P(E) = 0.26, then P(E bar) = …… **

**(A) 0.74 (B) 0 (C) 0.26 (D) 1 **

**Answer: A**

**Question 19: Median of 2, 3, 4, 5, 6, 7 is ……. **

**(A) 2 (B) 5.5 (C) 5 (D) 4.5 **

**Answer: D**

**Question 20: Which of the following cannot be a point on the x-axis? **

**(A) (-2, 0) (B) (0, 2) (C) (2, 0) (D) (4, 0) **

**Answer: B**

**Question 21: Radius of a circle with centre ‘O’ is 5 cm. P is a point at a distance of 3 cm from ‘O’. Then the number of tangents that can be drawn to the circle is …… **

**(A) 1 (B) 2 (C) 0 (D) 3 **

**Answer: C**

**Question 22: If sec θ + tan θ = 1 / 3, then sec θ – tan θ = ____**

**(A) 3 (B) 1 / 3 (C) 1 (D) 0 **

**Answer: A**

**Question 23: Probability of getting 7, when dice are rolled, is …… **

**(a) 1 / 6 (b) 1 / 7 (c) 6 / 7 (d) 0 **

**Answer: D**

**Question 24: To elect the leader of your class from 3 contestants, which of the following measures are to be considered? **

**(A) Mean (B) Mode (C) Median (D) Range **

**Answer: B**

**Question 25: In Heron’s formula, the area of triangle = √s (s – a) (s – b) (s – c), s is …. of the triangle.**

**(A) perimeter (B) height (C) half of perimeter (D) none **

**Answer: C**

**Question 26: Angle made by the minutes-hand in a clock during a period of 20 minutes is …… **

**(A) 120 (B) 20 (C) 360 (D) 90 **

**Answer: A**

**Question 27: Which of the following situations have equally likely events? **

**(1) Getting 1 or 2 or 3 or 4 or 5 or 6 when a dice is rolled. **

**(2) Winning or losing a game. **

**(3) Head or Tail, when a coin is tossed. **

**(A) 1 and 2 (B) 2 and 3 (C) 1 and 3 (D) All **

**Answer: D**

**Question 28: The probability of picking a letter from the set of English alphabets is 5 / 26. That alphabet can be ….. **

**(A) consonant (B) vowel (C) any alphabet (D) none **

**Answer: B**

**Question 29: If △PQR ~ △XYZ and ∠X = 30, ∠Q = 50, then ∠Z = …… **

**(a) 100 (b) ∠R (c) both A and B (d) not Known **

**Answer: B**

**Question 30: From the given figure, x = ……..**

**(A) 3 (B) 2 (C) 5 (D) 1 **

**Answer: A**

**Question 31: Which of the following is the point of intersection of the x-axis and the line y = x + 5? **

**(A) (0, 5) (B) (5, 0) (C) (0, -5) (D) (-5, 0) **

**Answer: D**

**Question 32: Observe the figure. Length of the ladder = …….**

**(A) 5 cm (B) 10 cm (C) 20 cm (D) 2.5 cm **

**Answer: A**

**Question 33: From the given graph of Ogives, the median is …….**

**(A) 15 (B) 10 (C) 40 (D) 20 **

**Answer: A**