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

If A + B + C = π, then sin 2A + sin 2B + sin 2C is equal to ______.

If A + B = C, then cos² A + cos² B + cos² C – 2 cos A cos B cos C is equal to ______.

If α + β – γ = π, then sin² α + sin² β – sin² γ is equal to ______.

If A + B + C = 180°, then `sum tan  A/2 tan  B/2` is ______.

In a ΔABC, `cos((B + 2C + 3A)/2) + cos((A - B)/2)` is ______.

Let A, B and C are the angles of a triangle and `tan(A/2) = 1/3, tan(B/2) = 2/3`. Then, `tan(C/2)` is equal to ______.

If A + B + C = 270°, then cos 2A + cos 2B + cos 2C is equal to ______.

If A + B + C = π, then sin 2A + sin 2B – sin 2C is equal to ______.

In a ΔABC, if cos A cos B cos C = `(sqrt(3) - 1)/8` and sin A sin B sin C = `(3 + sqrt(3))/8`, then the angles of the triangle are ______.

If A + B + C = π, then cos² A + cos² B + cos² C is equal to ______.

ΔABC is a right angled isosceles triangle with ∠B = 90°. If D is a point on AB, ∠CDB = 15° and AD = 35 cm, then CD is equal to ______.

If sin A + sin B = C, cos A + cos B = D, then the value of sin(A + B) = ______.

The mean of a set of observation is `overlinex`. If each observation is divided by α, α ≠ 0 and then is increased by 10, then the mean of the new set is ______.

A rod AB of length 16 cm. rests between the wall AD and a smooth peg, 1 cm from the wall and makes an angle θ with the horizontal. The value of θ for which the height of G, the midpoint of the rod above the peg is minimum, is ______.

If A + B + C = π and sin C + sin A cos B = 0, then tan A . cot B is equal to ______.

If x + y + z = 180°, then cos 2x + cos 2y – cos 2z is equal to ______.

If A + B + C = π(A, B, C > 0) and the ∠C is obtuse, then ______.

If a ΔABC, the value of sin A + sin B + sin C is ______.

If A + B + C = 270°, then cos 2A + cos 2B + cos 2C + 4 sin A sin B sin C is equal to ______.

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 ______.