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

`int_(π/3)^(π/2) x sin(π[x] - x)dx` is equal to ______.

The maximum value of z = 5x + 2y, subject to the constraints x + y ≤ 7, x + 2y ≤ 10, x, y ≥ 0 is ______.

The equation of the plane through the line x + y + z + 3 = 0 = 2x – y + 3z + 1 and parallel to the line `x/1 = y/2 = z/3`, is ______.

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)` = ______.

The line 5x + y – 1 = 0 coincides with one of the lines given by 5x² + xy – kx – 2y + 2 = 0 then the value of k is ______.

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

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

The maximum value of 2x + y subject to 3x + 5y ≤ 26 and 5x + 3y ≤ 30, x ≥ 0, y ≥ 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` = ______.

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 ______.