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Write the first four terms of the AP, when the first term a and the common difference d are given as follows: a = 4, d = -3.

Solution: Given a = 4, d = -3 Second term = a+d = 4-3 = 1 Third term = a+2d = 4-6 = -2 Fourth term = a+3d = 4-9 = -5 Hence the first four... View Article

Find a quadratic equation whose roots are α and β such that α + β = 3 and α³ + β³ = 9.

Solution: Given α + β = 3 and α3 + β3 = 9. We know that (α + β)3 = α3 + β3 + 3αβ(α... View Article

We show the smallest whole number on the number line.

(a) true (b) false Answer: The smallest whole number is 0. We can represent 0 on the number line. So the given statement is true. Hence... View Article

Simplify (1/216)^-2/3 divided by (1/27)^-4/3.

Solution: (1/216)-2/3÷ (1/27)-4/3 = (216)2/3÷ (27)4/3 = (63)2/3 ÷ (33)4/3 = 62 ÷ 34 = 36/81 = 4/9 Hence the... View Article

Choose the appropriate word from those given brackets and complete the following sentences.

(1) He is _____ for this post. (eligible/illegible) (2) The atmosphere was calm and _____(quiet/quite) Answer: (1) He is eligible for this... View Article

Fill in the blanks by choosing the most appropriate option. It is unfortunate that he died __ cancer.

(a) of (b) by (c) from (d) with Solution: The most appropriate option is ‘of’. It is unfortunate that he died of cancer. Hence... View Article

Solve the following (5y-4)/8 – (y-3)/5 = (y+6)/4

Solution: [(5y-4)/8] - [(y-3)/5] = [(y+6)/4] LCM of 8, 5, 4 is 40 Hence 5(5y- 4) - 8(y-3) = 10(y+6) 25y - 20 - 8y + 24 = 10y + 60 7y = 56... View Article

If X and Y are two sets such that n(X) = 17, n(Y) = 23 and n(X⋃Y) = 38, find n(X⋂Y).

Solution: Given n(X) = 17 n(Y) = 23 n(X⋃Y) = 38 n(X∪Y) = n(X) + n(Y) - n(X∩Y) 38 = 17 + 23 - n(X∩Y) 38 = 40 - n(X∩Y) =>... View Article

Prove that: x²ⁿ – y²ⁿ is divisible by x+y.

Solution: Let P(n) be divisible by x+y. For n = 1, P(1) = x2 - y2 = (x+y)(x-y) is divisible by (x+y). So P(n) is true for n = 1.... View Article

The areas of two similar triangles are 81 cm and 49 cm respectively. If the altitude of the bigger triangle is 4.5 cm. Find the corresponding altitude of the smaller triangle.

Solution: The ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes. Let x be the altitude... View Article

Get the algebraic expressions in the following cases using variables, constants, and arithmetic operations.

(i) Sum of numbers a and b subtracted from their product. (ii) One-half of the sum of numbers x and y. (iii) The number z multiplied by itself.... View Article

Fill in the blank with the most appropriate word. I was ___ a party last night.

(a) at (b) in (c) on (d) for Solution: Here the most appropriate word is at. I was at a party last night. Hence option a is the answer.... View Article

Write all the twin prime numbers from 51 to 100.

Solution: Two prime numbers whose difference is two are called twin primes. The prime numbers between 51 and 100 are 53, 59, 61, 67, 71, 73, 79,... View Article

What is the seventh term of the sequence 0, 3, 8, 15, 24,…?

(a) 63 (b) 48 (c) 35 (d) 33 Solution: 3 - 0 = 3 8 - 3 = 5 15 - 8 = 7 24 - 15 = 9 We found the difference between two consecutive terms.... View Article

Given 3(log 5- log 3) – (log 5 – 2 log 6) = 2 – log n, Find n.

Solution: Given 3(log 5 - log 3) - (log 5 - 2 log 6) = 2 - log n 3 log 5 - 3 log 3 - log 5 + 2 log (2×3) = 2 - log n 2 log 5 - 3 log 3 +... View Article

The sum of three consecutive multiples of 7 is 777. Find these multiples.

Solution: Let x-7, x , x+7 be the three consecutive multiples of 7. Given that the sum of three consecutive multiples of 7 is 777. So we... View Article

Find x, if 15 + x = 25.

Solution: Given 15 + x = 25 Subtract 15 from both sides of the equation We get 15 + x - 15 = 25 - 15 x = 10 Hence the value of x is 10.... View Article

The mode of the following data is 67. Find the missing frequency x.

Class 40-50 50-60 60-70 70-80 80-90 Frequency 5 x 15 12 7 Solution:... View Article

The number of employees working in a farm is increased by 25% and the wages per head are decreased by 25%. If it results in x% decrease in total wages, then the value of x is

Solution: Let p be the number of employees and q be the wages per head. Total wages = pq Given that the number of employees working in a farm... View Article

Write the units place of 168².

Solution: Given number is 1682. We know 82 = 64 Hence the units place of 1682 will be 4.... View Article