Archives

Which of the following number is divisible by 10?

Find the sum of the series : 1.n + 2.(n-1) + 3.(n-2) +….+ (n-1).2 + n.1.

Solution: 1.n + 2.(n-1) + 3.(n-2) +....+ (n-1).2 + n.1. Let rth term be Tr. Tr = r(n- (r-1)) = rn - r2 + r We have to find the sum of n... View Article

Write two pairs of twin primes between 20 and 50.

(a) 16 and 26, 19 and 29 (b) 29 and 31, 41 and 43 (c) 11 and 21, 61 and 71 (d) 15 and 17, 37 and 39 Solution: Two prime numbers are called... View Article

If 3^x × 27^x = 9^x+4, then what is x equal to?

(a) 4 (b) 5 (c) 6 (d) 7 Solution: 3x × 27x = 9x+4 3x × (33)x = 32(x+4) 34x = 32x+8 => 4x = 2x+8 => 2x = 8 => x = 4 Hence... View Article

The mode and median of the following data 21, 23, 25, 23, 21, 24, 22, 20, 23 respectively, are

(A) 23, 23 (B) 21, 23 (C) 25, 21 (D) 23, 21 Solution: Given data 21, 23, 25, 23, 21, 24, 22, 20, 23 The mode is the value that is... View Article

Find each of the following products: (x² – 3x + 7) (2x + 3)

Solution: Given (x2 - 3x + 7) (2x + 3) We have to multiply each term of one expression with each term of another and simplify. (x2 - 3x... View Article

Write linear equation representing a line which is parallel to y-axis and is at a distance of 2 unit on the left side of y-axis.

Solution: Given that line is parallel to the y-axis and is at a distance of 2 units on the left side of the y-axis. A line that is parallel to... View Article

Prove that : sin 105⁰ + cos 105⁰ = cos 45⁰.

Solution: sin 1050 = sin (60 + 45)0 cos 1050 = cos (60 + 45)0 sin (A + B) = sin A cos B + cos A sin B cos (A + B) = cos A cos B - sin A sin B... View Article

Integrate the function x (log x)².

Solution: ∫x (log x)2dx Take first function as (log x)2 and second function as x and integrate by parts. ∫u v dx = u ∫v dx -... View Article

A metal box with a square base and vertical sides is to contain 1024 cm³. The material for the top and bottom costs Rs 5/cm² and the material for the sides costs Rs 2.50/cm². Find the least cost of the box.

Solution: Given the volume of the box = 1024 cm3 Let length of the side of square base be x cm and height of the box be y cm. Volume of box =... View Article

Solve the following equations : (a) 10p = 100

(a) 10p = 100 (b) 10p + 10 = 100 (c) p/4 = 5 (d) -p/3 = 5 (e) 3p/4 = 6 Solution: (a) 10p = 100 Divide both... View Article

Solve the following simultaneous equation using cramer’s rule. 3x – 4y = 10: 4x + 3y = 5

Solution: Given 3x - 4y = 10 4x + 3y = 5 D = = 9+16 = 25 Dx = = 30 + 20 = 50 Dy = = 15 - 40 = -25... View Article

Find the value of cos (sec^-1 x + cosec^-1x), |x| ≥ 1.

(a) 1 (b) 0 (c) -1 (d) 2 Solution: We know that sec-1 x + cosec-1 x = π/2 cos (sec-1 x + cosec-1 x) = cos π/2 = 0 Hence... View Article

Prove that tan²a – tan²b = [cos² b – cos²a]/cos² a cos² b = (sin²a – sin²b)/(cos²a. cos²b)

Solution: LHS = tan2 a - tan2 b = (sin2 a/cos2 a) - (sin2 b/cos2 b) = (cos2 b sin2 a - cos2 a sin2 b)/cos2 a cos2 b = [cos2b (1 - cos2 a) -... View Article

tan 54⁰ can be expressed as

(a) (cos 90 + sin 90)/(cos 90 - sin 90) (b) (cos 90 - sin 90)/(cos 90 + sin 90) (c) (sin 90 - cos 90)/(cos 90 + sin 90) (d) none of these... View Article

Solve x²+ 7x = 7 and give your answer correct to two decimal places.

Solution: x2 + 7x = 7 x2 + 7x - 7 = 0 Using quadratic formula x = [-b±√(b2- 4ac)]/2a = [-7±√(72 + 28)]/2 =... View Article

Solve: ((1200/x) + 2) (x – 10) – 1200 = 60

Solution: ((1200/x) + 2) (x - 10) - 1200 = 60 ((1200/x) + 2) (x - 10) = 1200 + 60 ((1200/x) + 2) (x - 10) = 1260 (1200 + 2x) (x - 10) = 1260x... View Article

The numeral for ninety million ninety thousand ninety is

(a) 9090095 (b) 90090090 (c) 909090 (d)None of these Solution: We know 1 million = 10,00,000 So 90 million = 900,00,000 90 thousand =... View Article

Which expression is equal to (x^-1+y^-1)^-1?

(A) xy (B) x+y (C) xy/(x+y) (D) (x+y)/xy Solution: We know x-1 = 1/x (x-1+y-1)-1 = (1/x + 1/y)-1 = [(x+y)/xy]-1 = xy/(x+y) Hence option... View Article

Which of the following two sets are equal?

(A) A = {1,2} and B = {1} (B) A = {1,2} and B = {1,2,3} (C) A = {1,2,3} and B = {2,1,3} (D) A = {1,2,4} and B = {1,2,3} Solution: when two... View Article