MAH-MHT CET (PCM/PCB) entrance exam Question Bank Solutions for Mathematics

`"d"^2/("d"x^2) (2 sin 3x cosx)` = ______.

If f'(x) = `2 - 5/x^4` and f(1) = `14/3`, then f(-1) = ______

A random variable X has the following has the following:

Then, the value of P(–1 < X < 3) is ______.

If f(0) = 3, f'(0) = 2, then`"d"/("d"x) { log "f"(sin x + 3x^2)}` at x  0 is ______.

If the p.d.f of a c.r.v. X is
f(x) = `{:("K.e"^(-thetax)";", theta > 0","  0 ≤ x < oo),(0";", "otherwise"):}`
Then, K = ______.

The vector equation of the line passing through the points (3, 2, 1) and (1, 3, 1) is ______.

If y = `x^3 + 1/(x^3 + 1/(x^3 + 1/(x^3 + .....oo)`, ten `("d"y)/("d"x)` = ______.

Given a family of lines a (2x + y + 4) + b(x – 2y – 3) = 0, the number of lines belonging to the family at a distance `sqrt(10)` from P(2, –3) is ______.

Suppose f(x) = e^ax + e^bx, where a ≠ b, and that f"(x) – 2f'(x) – 15f(x) = 0 for all x. Then the product ab is ______.

If x = a(cos t + t sin t) and y = a(sin t – t cos t), then `(d^2y)/(dx^2)` is ______.

If x = f(t) and y = g (t) are differentiable functions of t, then `(d^2y)/(dx^2)` is ______.

If α and β are roots of the equation x² + 5|x| – 6 = 0, then the value of |tan^–1α – tan^–1 β| is ______.

Symbolic form of the given switching circuit is equivalent to:

If M is the arithmetic mean of two distinct real number l and n (I, n > 1) and G₁, G₂ and G₃ are three geometric means between l and n, then `G_1^4 + 2G_2^4 + G_3^4` is equal to ______.

If log₂ x + log₂ y ≥ 6, then the least value of x + y is ______.

If θ lies in the first quadrant and 5 tan θ = 4, then `(5 sin θ - 3 cos θ)/(sin θ + 2 cos θ)` is equal to ______.

The means of two samples of sizes 60 and 120 respectively are 35.4 and 30.9 and the standard deviations are 4 and 5. Obtain the standard deviation of the sample of size 180 obtained by combining the two samples.

For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set is ______ 

If the vectors `"a"hat"i" + "a"hat"j" + "c"hat"k", hat"i" + hat"k", "c"hat"i" + "c"hat"j" + "b"hat"k"` are coplanar, then c is ______.

The sum of n terms of the series 2² + 4² + 6² + ........ is ______.