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If x₁and x₂ are two distinct roots of the equation a cos x + b sin x = c, then tan (x₁+x₂)/2 is equal to

(a) a/b (b) b/a (c) c/a (d) a/c Solution: Given a cosx + b sinx = c => a [(1-tan2(x/2))/(1+tan2(x/2))] + b [2 tan(x/2)/(1+tan2(x/2))] =... View Article

The radius of a right circular cylinder increases at a constant rate. Its altitude is a linear function of the radius and increases three times as fast as radius.

The radius of a right circular cylinder increases at a constant rate. Its altitude is a linear function of the radius and increases three times... View Article

In what ratio Darjeeling Tea costing Rs. 320 per kg be mixed with Assam Tea costing Rs. 250 per kg so that there is a gain of 20% by selling the mixture at Rs. 324 per kg?

(a) 1:2 (b) 2:3 (c) 3:2 (d) 2:5 Solution: Selling price of the mixture = Rs.324 per kg Gain of the mixture = 20% Cost price =... View Article

The number of points at which the function f(x) = 1/(x-[x]) is not continuous is

(a) 1 (b) 2 (c) 3 (d) none of these Solution: Given f(x) = 1/(x-[x]) The greatest integer function becomes discontinuous at every integer... View Article

A spider climbed 62.5% of the height of the pole in one hour and in the next hour covered 12.5 % of the remaining height. If the height of the pole is 192 m, then the distance climbed in the second hour is

(a) 3m (b) 5m (c) 7m (d) 9m Solution: Height of pole = 192 m Distance covered by the spider in one hour = 62.5% of 192 m = (62.5/100)... View Article

If x = t², y = t³, then d²y/dx² equals

(a) 3/2 (b) 3/4t (c) 3/2t (d) 3t/2 Solution: Given x = t2, y = t3 dx/dt = 2t dy/dt = 3t2 dy/dx = 3t2/2t = 3t/2 d2y/dx2 =... View Article

Evaluate ¹⁴C₃.

(a) 42 (b) 364 (c) 146 (d) 328 Solution: We have nCr = n!/r!(n-r)! 14C3 = 14!/3!(14-3)! = 14!/3!11! = 12×13×14/2×3 =... View Article

Factors of 320

Solution: A factor is a number that divides another number evenly, ie. with no remainder. The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32,... View Article

A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) is

(a) 1/2 (b) 1/6 (c) 2/3 (d) 3/4 Solution: A coin is tossed three times. Sample space = {HHH, HTH, HHT, THH, TTT, TTH, THT, THT} Total... View Article

If ⁿP₃ + ⁿC_n-2 = 14n, then the value of n is

(a) 5 (b) 6 (c) 8 (d) 10 Solution: We have nCr = n!/r!(n-r)! nPr = n!/(n-r)! Given nP3 + nCn-2 = 14n =>[ n!/(n-3)!] + [n!/(n-2)!2!] =... View Article

A point is moving along the curve y³ = 27x. Find the interval of the value of x in which the ordinate changes faster than abscissa is:

(a) x ∈ (-1, 1) (b) x ∈ (-1, -1) - {0} (c) x ∈ [-1, -1] - {0} (d) x ∈ (-1, 0) Solution: Given y3 = 27x ..(i)... View Article

A differential equation associated to the primitive y = a + be^5x + ce^-7x is (where y_n is the nth derivative w.r.t.x)

(a) y3 + 3y2 - y1 = 0 (b) 4y3 + 5y2 - 20y1 = 0 (c) y3 + 2y2 - 35y1 = 0 (d) none of these Solution: Given y = a + be5x + ce-7x ... View Article

Factors of 397

Solution: 397 is a prime number and therefore its factors are 1 and 397 itself. So, it has only one prime factor that is the number... View Article

If f(x) = x + 2, g(x) = x – 4. Find (f g)(x)

Solution: Given f(x) = x + 2 g(x) = x - 4 (f g)(x) = f(x) × g(x) (x+2) × (x-4) = x2 + 2x - 4x - 8 = x2 - 2x - 8 Hence (f g)(x)... View Article

Which one of the following is not written by Kalidasa? a) Kumarasambhava b) Raghuvamsha c) Ritu Samhara d) Mrichchakatikam

Answer: The correct answer is option (D) - Mrichchakatikam. Kumarasambhava is an epic poem written by Kalidasa. It talks about the birth of... View Article