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

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 line 3x - 2y = 0 coincides with one of the lines given by ax² + 2hxy + by² = 0, then ______

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 = ______.

In Δ ABC; with usual notations, if cos A = `(sin "B")/(sin "C")`, then the triangle is _______.

Which of the following equation does not represent a pair of lines?

If the c.d.f (cumulative distribution function) is given by F(x) = `(x - 25)/10`, then P(27 ≤ x ≤ 33) = ______.

If A = {x ∈ R : x² - 5 |x| + 6 = 0}, then n(A) = _____.

`int_0^log5 (e^xsqrt(e^x - 1))/(e^x + 3)` dx = ______ 

The differential equation `x((d^2y)/dx^2)^3 + ((d^3y)/dx^3)^2y = x^2` is of ______ 

The number of ways in which a garland can be formed by using 10 identical pink flowers and 9 identical white flowers is ______

If f(x) = `{:{(tan^-1|x|; "when"  x ≠ 0), (pi/4;  "when"  x = 0):}`, then ______