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

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 ______.

`cos  (2π)/7 + cos  (4π)/7 + cos  (6π)/7`

The value of `tan  π/5 + 2 tan  (2π)/5 + 4 cot  (4π)/5` is ______.

If x and y are acute angles, such that cos x + cos y = `3/2` and sin x + sin y = `3/4`, then sin (x + y) equals:

The value of cos 52° + cos 68° + cos 172° is ______.

If sin θ + sin 2θ + sin 3θ = sin α and cos θ + cos 2θ + cos 3θ = cos α, then θ is equal to ______.

tan 20° tan 40° tan 60° tan 80° is equal to ______.

`lim_(x rightarrow ∞) sum_(x = 1)^20 cos^(2n) (x - 10)` is equal to ______.

`lim_(x rightarrow π/2) ([1 - tan (x/2)] (1 - sin x))/([1 + tan (x/2)] (π - 2x)^3` is ______.

The value of `int ((x^2 - 1)dx)/(x^3 sqrt(2x^4 - 2x^2 + 1)` is ______.