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

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 ______.

The value of cos 20° cos 40° cos 60° cos 80° is ______.

The value of `cos  π/15  cos  (2π)/15  cos  (4π)/15  cos  (8π)/15` is ______.

If A = 35°, B = 15° and C = 40°, then tan A tan B + tan B tan C + tan C tan A is equal to ______.

If sin θ = 3 sin (θ + 2α), then the value of tan (θ + α) + 2 tan α is ______.

If α, β, γ ∈ [0, π] and α, β, γ are in AP, then `(sin α - sin γ)/(cos γ - cos α)` is equal to ______.