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

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))] = ______.

If y = `tan^-1  (sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))`, then `dy/dx` is equal to ______.

The value of `sqrt(2) int (sinx  dx)/(sin(x - π/4))` is ______.

If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.

The solution of the differential equation `(1 + y^2) + (x - e^(tan^-1 y)) dy/dx` = 0 is ______.

If `|(6i, -3i, 1),(4, 3i, -1),(20, 3, i)|` = x + iy, then ______.

Let `(-2 - 1/3i)^2 = (x + iy)/9 (i = sqrt(-1))`, where x and y are real numbers, then x – y equals to ______.

The position vectors of vertices of ΔABC are `4hati - 2hatj; hati + 4hatj - 3hatk` and `-hati + 5hatj + hatk` respectively, then ∠ABC = ______.

`int x/sqrt(1 - 2x^4) dx` = ______.

(where c is a constant of integration)

The particular solution of the differential equation (2x – 2y + 3) dx – (x – y + 1) dy = when x = 0, y = 1 is ______.