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

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 ______.

The shaded part of given figure indicates in feasible region, then the constraints are:

The objective function Z = x₁ + x₂, subject to the constraints are x₁ + x₂ ≤ 10, – 2x₁ + 3x₂ ≤ 15, x₁ ≤ 6, x₁, x₂ ≥ 0, has maximum value ______ of the feasible region.

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 ______.

If α + β = `π/2` and β + γ = α, then the value of tan α is ______.

`(cos 9^circ +  sin 9^circ)/(cos 9^circ -  sin 9^circ)` is equal to ______.

`(tan 80^circ -  tan 10^circ)/(tan 70^circ)` is equal to ______.

If cos(81° + θ) = `sin(k/3 - θ)`, then k is equal to ______.

lf sin θ = cos θ, then the value of 2 tan² θ + sin² θ – 1 is equal to ______.

`(cos 70^circ)/(sin 20^circ) + (cos 59^circ)/(sin 31^circ) - 8 sin^2 30^circ` is equal to ______.

If cos θ = `8/17` and θ lies in the 1st quadrant, then the value of cos(30° + θ) + cos(45° – θ) + cos(120° – θ) is ______.