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

If f(x) = `x/(x^2 + 1)` is increasing function then the value of x lies in ______.

If a line makes angles 120° and 60° with the positive directions of X and Z axes respectively then the angle made by the line with positive Y-axis is ______.

If `int 1/sqrt(9 - 16x^2)dx` = α sin^–1 (βx) + c, then `α + 1/β` = ______.

Which of the following statement pattern is a tautology?

`int 1/sqrt(8 + 2x - x^2) dx` is equal to ______.

Derivative of log (sec θ + tan θ) with respect to sec θ at θ = `π/4` is ______.

If `log_10 ((x^2 - y^2)/(x^2 + y^2))` = 2, then `dy/dx` is equal to ______.

The acute angle between the line `vecr = (hati + 2hatj + hatk) + λ(hati + hatj + hatk)` and the plane `vecr xx (2hati - hatj + hatk)` is ______.

The value of sin 50° – sin 70° + sin 10° is ______.

The value of `cos^2x + cos^2(x + π/3) + cos^2(π - (2π)/3)` is ______.

If A, B and C are the angles of a triangle, such that sec (A – B), sec A and sec (A + B) are in arithmetic progression, then ______.

If `cosx/(cos(x - 2y))` = λ, then tan (x – y) tan y is eqµal to ______.

sin 47° + sin 61° – sin 11° – sin 25° is equal to ______.

If sin (x + 3 α) = 3 sin (α – x), then ______.

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

sin 12° sin 48° sin 54° is equal to ______.

The value of sin 36° sin 72° sin 108° sin 144° is ______.

If p = cos 55°, q = cos 65° and r = cos 175°, then the value of `1/p + 1/q + r/(pq)` is ______.

If α + β + γ = 2 θ, then cos θ + cos (θ – α) + cos (θ – β) + cos (θ – γ) is equal to ______.

If cos x = 3 cos y, then `2 tan  (y - x)/2` is equal to ______.