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

If A, B, C are the angles of a triangle, then sin² A + sin² B + sin² C – 2 cos A cos B cos C is equal to ______.

If A + B = C = 180°, then the value of `cot  A/2 + cot  B/2 + cot  C/2` will be ______.

In any ΔABC, if tan A + tan B + tan C = 6 and tan A tan B = 2, then the values of tan A, tan B and tan C are ______.

If A + B + C = 180°, then `(sin 2A + sin 2B + sin 2C)/(cos A + cos B + cos C - 1)` is equal to ______.

If cos A = cos B cos C and A + B + C = π, then the value of cot B cot C is ______.

lf A + B + C = π, then `cosA/(sinBsinC) + cosB/(sinCsinA) + cosC/(sinAsinB)` is equal to ______.

The value of cot A cot B + cot B cot C + cot C cot A is ______.

The value of `tan  A/2 tan  B/2 + tan  B/2 tan  C/2 + tan  C/2 tan  A/2` is ______.

If A, B, C are three points in argand plane representing the complex numbers z₁, z₂ and z₃ such that, z₁ = `(λz_2 + z_3)/(λ + 1)`, where λ ∈ R, then find the distance of point A from the line joining points B and C.

A straight line is drawn through the point P(3, 4) meeting the positive direction of coordinate axes at the points A and B. If O is the origin, then minimum area of ΔOAB is equal to ______.

The point in the interval [0, 2π], where f(x) = e^x sin x has maximum slope, is ______.

A straight line passes through the origin O meet the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at points P and Q respectively. Then, the point O divides the segment Q in the ratio:

Let x₁, x₂ ,..., x_n be n observations such that `sumx_1^2` = 400 and `sumx_i` = 80. Then, a possible value of n among the following is:

If log (x + y) = log (xy) + 3, then `dy/dx` = ______. 

If xy = tan^–1 (xy) + cot^–1 (xy), then `(dy/dx)_((4","  2))` = ______.

where (x, y) ∈ R

The variance of first n natural numbers is ______.

X is a continuous random variable with probability density function

f(x) = `x^3/16,` 0 ≤ x ≤ 1

= 0, otherwise

Then, the value of P(0.2 ≤ X ≤ 0.3) is

The statement pattern p ∧ ( q v ~ p) is equivalent to ______.

If the volume of the parallelepiped whose conterminus edges are along the vectors a, b, c is 12, then the volume of the tetrahedron whose conterminus edges are a + b, b + c and c + a is ______.

If the p.m.f of a. r.v. Xis given by

Givenif x = 0, 1, 2, ........ 5 = 0,

0, otherwise,

then which of the following is not true?