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

Number of values of x which lie in [0, 2π] and satisfy the equation

`(cos  x/4 - 2sinx) sinx + (1 + sin  x/4 - 2cosx)cosx` = 0

If α, β, γ and a, b, c are complex numbers such that `α/a +  β/b + γ/c` = 1 + i and `a/α +  b/β + c/γ` = 0, then the value of `α^2/a^2 +  β^2/b^2 + γ^2/c^2` is equal to ______.

Let p, q and r be any three logical statements. Which of the following is true?

If sin^–1a + sin^–1b + sin^–1c = π, then find the value of `asqrt(1 - a^2) + bsqrt(1 - b^2) + csqrt(1 - c^2)`.

If ax + b (sec (tan^–1 x)) = c and ay + b (sec.(tan^–1 y)) = c, then `(x + y)/(1 - xy)` = ______.

The cost of running a bus from A to B, is ₹`(av + b/v)`, where v km/h is the average speed of the bus. When the bus travels at 30 km/h, the cost comes out to be ₹ 75 while at 40 km/h, it is ₹ 65. Then the most economical speed (in km/h) of the bus is ______.

In a binomial distribution `B(n, p = 1/4)`, if the probability of at least one success is greater than or equal to `9/10`, then n is greater than ______.

The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.

`int (x + sinx)/(1 + cosx)dx` is equal to ______.

If x ∈ R – {0}, then `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2)))`

The value of cos (2cos^–1 x + sin^–1 x) at x = `1/5` is ______.

Which of the following is logically equivalent to `∼(∼p \implies q)`?

The area of the region bounded by the curves y = |x – 2|, x = 1, x = 3 and the x-axis is ______.

`int sqrt(x^2 - a^2)/x dx` = ______.

`int 1/(sinx.cos^2x)dx` = ______.

The area of the region bounded by x² = 4y, y = 1, y = 4 and the y-axis lying in the first quadrant is square units.

If tan^–1 (2x) + tan^–1 (3x) = `π/4`, then x = ______.

If X∼B (n, p) with n = 10, p = 0.4 then E(X²) = ______.

The general solution of differential equation `dx/dy` = cos (x + y) is ______.

The solution of the differential equation `dy/dx = tan(y/x) + (y/x)` is ______.