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

If the p.m.f of a. r.v. Xis given by

Givenif x = 0, 1, 2, ........ 5 = 0,

0, otherwise,

then which of the following is not true?

lf f(x) = cos^-1 `[(1 - (log x)^2)/(1 + (log x)^2)]`, then f' (e) = _______.

A stone is dropped into a pond. Waves in the form of circles are generated and radius of outermost ripple increases at the rate of 5 cm/sec. Then area increased after 2 seconds is ______.

A random variable X has following probability distribution

Then P(2 ≤ X < 5) = _____.

The square roots of -18i are ______

If the variance of x₁, x₂, x₃, ... , x_n is 49, then the S.D. of x₁ + 7, x₂ + 7, x₃ + 7, ... , x_n + 7, is ______ 

If the variance of x₁, x₂, x₃, ... , x_n is 49, then the S.D. of x₁ + 7, x₂ + 7, x₃ + 7, ... , x_n + 7, is ______ 

If x = sin θ, y = sin³ θ then `("d"^2"y")/"dx"^2  "at" theta = pi/2` is ______.

If for a function f(x), f'(a) = 0, f"(a) = 0, f"'(a) > 0, then at x = a, f(x) is ______

L and M are two points with position vectors `2veca - vecb` and `veca + 2vecb` respectively. The position vector of the point N which divides the line segment LM in the ratio 2 : 1 externally is ______ 

Let f(x) = tan^-1x. Then f'(x) + f"(x) is equal to 0, when x is equal to ______ 

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 ______.

Let `overlinep` and `overlineq` be the position vectors of P and Q respectively, with respect to O and `|overlinep|` = P, `|overlineq|` = q`. The points R and S divide PQ internally and externally in the ratio 2 : 3 respectively. If OR and OS are perpendicular, then ______

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 ______.

If the p.d.f. of a continuous random variable X is

f(x) = k (x - x²),    0 < x < 1

= 0,             otherwise

then the value of k 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 ______.