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In the given question, select the related number from the given alternatives. 3265 : 4376 : : 4673 : ?

(a) 2154 (b) 5487 (c) 3562 (d) 5784 Solution: Given 3265 : 4376 : : 4673 : ? While observing the digits, we can see that every... View Article

Factorise x⁴ – 625.

Solution: Use identity a2 - b2 = (a+b) (a-b) x4 - 625 = (x2)2 - 252 = (x2)2 - (25)2 = (x2 - 25) (x2 + 25) = (x - 5) (x + 5) (x2 + 25) Hence x4 -... View Article

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 => cos (α + β) = cos 90 (since cos 90 = 0) => (α + β) =... 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 one year = 10500 - 525 =... 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 is the answer.... 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 a2- b2 = (a + b) (a - b) So x2 - (√2)2 = (x -√2)... 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 they form... View Article

Factorise x²– 12x + 36.

Solution: x2- 12x + 36 = x2 - 6x - 6x + 36 = x(x - 6) - 6(x - 6) = (x - 6) (x- 6) = (x - 6)2 Hence the factors are (x - 6) and (x - 6).... 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)) = 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