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Find the modulus of (1+i)/(1-i) – (1-i)/(1+i).

Solution: (1+i)/(1-i) - (1-i)/(1+i) = [(1+i)(1+i) - (1-i)(1-i)]/(1+i)(1-i) = (1-1+2i - 1+ 1 + 2i)/(1+1) = 4i/2 = 2i Modulus of z = x+iy is... View Article

The mean of the cubes of the first n natural numbers is

(a) n(n+1)2/2 (b) n(n+1)2/4 (c) n2+n+1 (d) n(n+1)(n+2)/8 Solution: Sum of cubes of n natural numbers = 13 + 23 + 33 + ..n3 = n2(n+1)2/4... View Article

A man bought 3 toffees for a rupee. How many toffees for a rupee should he sell to gain 50%?

(a) 2 (b) 3 (c) 4 (d) 1 Solution: Cost price of 3 toffees = 1 Rs Profit = 50% CP of 1 toffee = 1/3 Rs SP of 1 toffee = (1 + 50/100)⅓ =... View Article

Solve the following 7 + 2 x = 37

Solution: Given 7 + 2x = 37 => 2x = 37 - 7 => 2x = 30 => x = 30/2 => x = 15 Hence the value of x is 15.... View Article

Find the solution of 2x – 3 > 7

Solution: Given 2x - 3 >7 => 2x > 10 => x > 5 Therefore x ∈ (5, ∞).... View Article

Write the smallest equivalence relation on the set {1, 2, 3}.

Solution: A relation is an equivalence relation if and only if it is reflexive, symmetric and transitive: A = {1,2,3} A×A =... View Article

Which of the following equations has no real roots?

(A) x2 - 4x + 3√2 = 0 (B) x2 + 4x - 3√2 = 0 (C) x2 - 4x - 3√2 = 0 (D) 3x2 + 4√3 x + 4 = 0 Solution:... View Article

Which of the following numbers is not a perfect cube?

(A) 512 (B) 2917 (C) 2197 (D) 343 Solution: (A) 2197 is the cube of 13. (B) 512 is the cube of 8. (C) 2916 is not a perfect cube. (D) 343... View Article

Check whether the following are perfect cubes?

(i) 400 (ii) 216 (iii) 729 (iv) 250 (v) 1000 (vi) 900 Solution: The perfect cube is the result of multiplying the same integer three times.... View Article

Write the following sets in descriptive form

(i) A = {a, e, i, o, u} (ii) B = {1, 3, 5, 7, 9, 11} (iii) C = {1, 4, 9, 16, 25} (iv) P = {x : x is a letter in the word ‘set... View Article

Evaluate the following 150 ÷ (-25)

Solution: 150 ÷ (-25) = 150/-25 = -6 Hence -6 is the answer.... View Article

Find the missing number in the series? 4, 18, ?, 100, 180, 294, 448

(A) 48 (B) 50 (C) 58 (D) 60 Solution: Given series 4, 18, ?, 100, 180, 294, 448 23 - 22 = 4 33 - 32 = 18 43 - 42 = 48 53 - 52 = 100 63... View Article

What is the square root of 32 over 4 expressed in simplest radical form?

Solution: √32/4 = √(16×2)/4 = 4√2/4 = √2 We get the simplest radical form of √32/4 as √2.... View Article

Triangle having two sides of equal length is

(A) Equilateral (B) Scalene (C) Isosceles (D) Acute angled Solution: Triangle having all sides equal is an equilateral triangle. Triangle... View Article

If HCF (336, 54) = 6, find LCM (336, 54).

Solution: We know LCM × HCF = product of two numbers Given HCF = 6 and numbers are 336 and 54. LCM = Product of numbers/HCF =... View Article

The sum of prime numbers, out of the numbers 17, 8, 21,13, 41, 2, 27, 31, 51 is:

(A) 125 (B) 102 (C) 104 (D) 155 Solution: Given numbers are 17, 8, 21,13, 41, 2, 27, 31, 51. Prime numbers are 2, 17, 13, 41, 31. Sum of... View Article

Find the mode of given data.

Marks 0-10 10-20 20-30 30-40 40-50 Frequency 20 24 40 36 20 Solution:... View Article

A square whose diagonal is 10 cm long has an area equal to

Solution: Diagonal of square = √2a = 10 => a = 10/√2 Area of square = a2 = (10/√2)2 = 50 cm2 Hence the area of a... View Article

Find the principal solution or solution of sin x = 1/√2.

Solution: Given sin x = 1/√2 => x = π/4 sin (π - x) = sin x => sin π/4 = sin (π - π/4) = sin 3π/4 sin π/4... View Article

Find 2 times 6.

Solution: 2 times 6 = 2× 6 = 12 Hence 2 times 6 equals 12.... View Article