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

If y = cos nx, then `(d^2y)/dx^2 + n^2y` = ______ 

If y =sin (log x), then `x^2 ("d"^2"y")/"dx"^2 + x "dy"/"dx" + "y"` is equal to ______.

The order and degree of the differential equation `("d"^2y)/("d"x^2) = {y + (("d"^3y)/("d"x^3))^3}^(1/5)` are respectively ______.

The differential equation representing the family of curves `y^2 = 2d(x + sqrtd)`, where d is a positive parameter, is of ______ 

If f(x) =log_x (log x), then f'(x) at x = e is ______.

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 y = axⁿ⁺² + bx^-n-1, then `x^2(d^2y)/(dx^2)` is ______.

If y = `sqrt("e"^x + sqrt("e"^x + sqrt("e"^x + .... oo)`, then `("d"y)/("d"x)` is equal to ______.

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

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

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

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

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

Symbolic form of the given switching circuit is equivalent to:

`(x + 1/x)^2 + (x^2 + 1/x^2)^2 + (x^3 + 1/x^3)^2` ....upto n terms is ______.

In a series of observations, S.D. = 5 and mean is 20, then coefficient of variation is ______.