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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... 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... 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... 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... 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! =... 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... 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,... 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 +... 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)... 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... 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... 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) ×... 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... View Article

Who was Otto Von Bismarck? a) Chief minister of Prussia b) Architect of national unification movement c) Leader of landowners d) both a and b

Answer: The correct answer is option (a) – Chief Minister of Prussia. Otto Von Bismarck was the Chief Minister of... View Article

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