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

`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 ______.

If sin A + cos A = `sqrt(2)`, then the value of cos² A is ______.

The value of cos 15° is ______.

If `0 < β < α < π/4, cos (α + β) = 3/5` and cos (α – β) = `4/5`, then sin 2α is equal to ______.

The value of `tan 40^circ + tan 20^circ + sqrt(3) tan 20^circ tan 40^circ` is ______.

If `α, β ∈ (0, π/2)`, sin α = `4/5` and cos (α + β) = `-12/13`, then sin β is equal to ______.

If cos (α + β) = `4/5` and sin (α – β) = `5/13`, where `0 ≤ α, β ≤ π/4`, then tan 2α is equal to ______.

If A + B = 45°, then (cot A – 1) (cot B – 1) is equal to ______.

If tan α = k cot β, then `(cos(α - β))/(cos(α + β))` is equal to ______.