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

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 value of `dy/dx` at x = `π/2`, where y is given by y = `x^sinx + sqrt(x)`, is ______.

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:

The variance of first n natural numbers is ______.

If x = `sqrt(a^(sin^-1 t)` and y = `sqrt(a^(cos^-1 t)`, then `dy/dx` = ______.

If x = e^2y, then `("d"^2y)/"dx"^2*("d"^2x)/"dy"^2` is equal to

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

If x = a sin t - b cos t, y = a cos t+ b sin t, then `"y"^3 ("d"^2"y")/"dx"^2 + x^2 + y^2` = ?

If f(x) = log (sin x), x ∈ `[π/6, (5π)/6]`, then value of 'c' by applying LMVT is ____________.

The differential equation obtained from the function y = a(x − a)² is ____________.