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

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

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 ______ 

Let f(x) = `inte^x (x - 1)(x - 2)dx,` then f(x) decreases in the interval ______

The ratio in which the area bounded by the curves y² = 8x and x² = 8y is divided by the line x = 2 is ______ 

In a ΔABC, `(sin  "C"/2)/(cos(("A" - "B")/2))` = ______ 

If the probability function of a random variable X is defined by P(X = k) = a`((k + 1)/2^k)` for k - 0, 1, 2, 3, 4, 5, then the probability that X takes a prime value is ______

All the letters of the word PADMAPRIYA are placed at random in a row. The probability that the word PRIY A occurs without getting split is ______

For a random variable X, if Var (X) = 5 and E (X²) = 21, the value of E (X) is ______

The order and degree of the differential equation `(dy/dx)^3 + ((d^3y)/dx^3) + xy = 0` are respectively ______

In a ΔABC, 2ab sin`((A + B - C)/2)` = ______

If one side of a triangle is double the other and the angles opposite to these sides differ by 60°, then the triangle is ______

If A = {x | x ∈ N, x is a prime number less than 12} and B = {x | x ∈ N, x is a factor of 10}, then A ∩ B = ______.

If `int1/(x + x^5)dx = f(x) + c`, then `intx^4/(x + x^5)dx` = ______

If `(- sqrt2, sqrt2)` are cartesian co-ordinates of the point, then its polar co-ordinates are ______.

`intlogx/(1 + logx)^2dx` = ______