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If cos (α + β) = 0, then sin (α – β) can be reduced to

(A) cos β (B) cos 2β (C) cos 2α (D) sin 2α Solution: Given cos (α + β) = 0... View Article

A machinery worth Rs.10,500 depreciated by 5% . Find its value after one year.

Solution: Price of machinery = 10500 5% of 10500 = 10500×5/100 = 525 Depreciated amount = 525 So value after... View Article

Select the most appropriate antonym: safe

(A) unsafe (B) safeless (C) insafe (D) none of these Answer: The opposite of safe is unsafe. Hence option A... View Article

Find the zeros of the polynomial f(x) = x² – 2 and verify the relationship between its zeros and coefficients.

Solution: f(x) = x2 – 2 = x2 – (√2)2 This is of the form a2 – b2. We know... View Article

The point where two rays meet to form an angle is called the

(A) vertex (B) terminal point (C) side (D) arm Solution: Rays are used to represent angles. When two rays meet... View Article

Factorise x²– 12x + 36.

Solution: x2– 12x + 36 = x2 – 6x – 6x + 36 = x(x – 6) – 6(x –... View Article

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)) =... 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... 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... 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,... 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... 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... 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) =... 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... 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... View Article

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