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

Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold is ______.

If a = sin 175°+ cos 175°, then ______.

With usual notations, if the angles A, B, C of a Δ ABC are in AP and b : c = `sqrt3 : sqrt2`.

If Xis a.r.v. with c.d.f F (x) and its probability distribution is given by

then, F(1.5) - F(- 0.5) = ?

The LPP to maximize Z = x + y, subject to x + y ≤ 1, 2x + 2y ≥ 6, x ≥ 0, y ≥ 0 has ________.

The order and degree of the differential equation `[1 + 1/("dy"/"dx")^2]^(5/3) = 5 ("d"^2y)/"dx"^2` are respectively.

In a triangle ABC with usual notations, if `(cos "A")/"a" = (cos "B")/"b" = (cos "C")/"c"`, then area of triangle ABC with a = `sqrt6` is ____________.

The area of the region bounded by the curve y = 4x³ − 6x² + 4x + 1 and the lines x = 1, x = 5 and X-axis is ____________.

If f(x) = `(2"x" + 3)/(3"x" - 2)`, `"x" ≠ 2/3`, then the function fof is ____________.

In a triangle ABC, If `(sin "A" - sin "C")/(cos "C" - cos "A")` = cot B, then A, B, C are in ________.

If in a right-angled triangle ABC, the hypotenuse AB = p, then `overline"AB".overline" AC" + overline"BC".overline" BA" + overline" CA".overline"CB"` is equal to ______ 

The values of θ satisfying sin7θ = sin4θ - sinθ and 0 < θ < `pi/2` are ______

The area bounded by y = `27/x^3`, X-axis and the ordinates x = 1, x = 3 is ______

The area enclosed between the curve y = log_e(x + e) and the coordinate axes is ______.

If f(x) = `{((x^4 - 1/81)/(x^3 - 1/27), x ≠ 1/3), (k, x = 1/3):}` is continuous at x = `1/3`, then the value of k is ______

Let X = time (in minutes) that lapses between the ringing of the bell at the end of a lecture and the actual time when the professor ends the lecture. Suppose X has p.d.f.

f(x) = `{(kx^2","      0 ≤ x ≤ 2), (0","         "othenwise"):}`

Then, the probability that the lecture ends within 1 minute of the bell ringing is ______

The order of the differential equation of all circles whose radius is 4, is ______.

The p.m.f. of a random variable X is

P(x) = `(5 - x)/10`,   x = 1, 2, 3, 4
       = 0,            otherwise

The value of E(X) is ______ 

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour is ______.

If θ = `(17π)/3` then, tan θ – cot θ = ______.