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

Let A, B be two events such that the probability of A is `3/10` and conditional probability of A given B is `1/2`. The probability that exactly one of the events A or B happen equals.

If `vecp, vecq` and `vecr` are nonzero, noncoplanar vectors then `[(vecp + vecq - vecr, vecp - vecq, vecq - vecr)]` = ______.

If `int_0^K dx/(2 + 18x^2) = π/24`, then the value of K is ______.

If y = (tan^–1 x)² then `(x^2 + 1)^2 (d^2y)/(dx^2) + 2x(x^2 + 1) (dy)/(dx)` = ______.

`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.

If `2sin(θ + π/3) = cos(θ - π/6)`, then tan θ, = ______.

The point of intersection of line represented by x² – y² + 3y – 2 = 0 is ______.

`int_0^(π/4) x. sec^2 x  dx` = ______.

`int_0^1 x tan^-1 x  dx` = ______.

If `int_0^(π/2) log cos x  dx = π/2 log(1/2)`, then `int_0^(π/2) log sec dx` = ______.

Which of the following statement pattern is a tautology?

The differential equation of all parabolas whose axis is Y-axis, is ______.

Let X ~ B(n, p) if E(X) = 5, Var(X) = 2.5, then p(X < 1) is equal to ______.

The differential equation of the family of circles touching Y-axis at the origin is ______.

The approximate value of f(x) = x³ + 5x² – 7x + 9 at x = 1.1 is ______.

`int((4e^x - 25)/(2e^x - 5))dx = Ax + B log(2e^x - 5) + c`, then ______.

`int_((-π)/2)^(π/2) log((2 - sinx)/(2 + sinx))` is equal to ______.

If `int (f(x))/(log(sin x))dx` = log[log sin x] + c, then f(x) is equal to ______.

If A and B are foot of perpendicular drawn from point Q(a, b, c) to the planes yz and zx, then equation of plane through the points A, B and O is ______.

`int_0^(π/2)((root(n)(secx))/(root(n)(secx + root(n)("cosec"  x))))dx` is equal to ______.