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

The point in the interval [0, 2π], where f(x) = e^x sin x has maximum slope, is ______.

A straight line passes through the origin O meet the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then, the point O divides the segment Q in the ratio:

Let x₁, x₂ ,..., x_n be n observations such that `sumx_1^2` = 400 and `sumx_i` = 80. Then, a possible value of n among the following is:

The variance of first n natural numbers is ______.

If x = `sqrt(a^(sin^-1 t)` and y = `sqrt(a^(cos^-1 t)`, then `dy/dx` = ______.

If x = e^2y, then `("d"^2y)/"dx"^2*("d"^2x)/"dy"^2` is equal to

X is a continuous random variable with probability density function

f(x) = `x^3/16,` 0 ≤ x ≤ 1

= 0, otherwise

Then, the value of P(0.2 ≤ X ≤ 0.3) is

If x = a sin t - b cos t, y = a cos t+ b sin t, then `"y"^3 ("d"^2"y")/"dx"^2 + x^2 + y^2` = ?

If f(x) = log (sin x), x ∈ `[π/6, (5π)/6]`, then value of 'c' by applying LMVT is ____________.

The differential equation obtained from the function y = a(x − a)² is ____________.

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 ______