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

If slopes of lines represented by kx² + 5xy + y² = 0 differ by 1, then k = ______.

The area of the region bounded by the lines y = 2x + 1, y = 3x + 1 and x = 4 is ______.

The value of `cos^-1(cos(π/2)) + cos^-1(sin((2π)/2))` is ______.

The particular solution of the differential equation x dy + 2y dx = 0, when x = 2,y = 1 is ______.

Derivative of `tan^-1(x/sqrt(1 - x^2))` with respect sin^–1(3x – 4x³) is ______.

If 2 tan^–1 (cosx) = tan^–1 (2 cosec x), then sin x + cos x is equal to ______.

`(tan^-1 (sqrt(3)) - sec^-1(-2))/("cosec"^-1(-sqrt(2)) + cos^-1(-1/2))` is equal to ______.

The area of the region bounded by the curve y = 2x – x² and X-axis is ______.

If a = `veca = hati + hatj - 2hatk, vecb = 2hati - hatj + hatk` and `vecc = 3hati - hatk` and `vecc = mveca + nvecb`, then m + n is equal to ______.

The particular solution of the differential equation `y(1 + log x) dx/dy - x log x = 0`, when x = e, y = e² is ______.

If `veca = hati - hatj + hatk, vecb = 2hati + λhatj + hatk, vecc = hati - hatj + 4hatk` and `veca.(vecb xx vecc)` = 10, then λ is equal to ______.

Let A, B, C be finite sets. Suppose that n (A) = 10, n (B) = 15, n (C) = 20, n (A ∩ B) = 8 and n (B ∩ C) = 9. Then the possible value of n (A ∪ B ∪ C) is ______.

Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Then ______.

Let AB be a chord of the circle x² + y² = r² subtending a right angle at the centre, then the locus of the centroid of the ΔPAB as P moves on the circle is ______.

Let a = `hati + 2hatj + hatk`, b = `hati - hatj + hatk`, c = `hati + hatj - hatk`. A vector coplanar to a and b has a projection along with c of magnitude `1/sqrt(3)`, then the vector is ______.

If `dy/dx + 2y tan x = sin x, 0 < x < π/2` and `y(π/6)` = 0, then the maximum value of y(x) is ______.

The complex number z = x + iy which satisfy the equation `|(z - 5i)/(z + 5i)|` = 1, lie on ______.

The area bounded by y = `sinx/x`, X-axis and the ordinates x = 0, x = π / 4 is ______.

If a, b and c are three non-zero vectors which are pairwise non-collinear. If a + 3b is collinear with c and b + 2c is collinear with a, then a + 3b + 6c is ______.

sin [cot^–1 (cos (tan^–1 x))] = ______.