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

If `sin A - sqrt(6) cos A = sqrt(7) cos A`, then `cos A + sqrt(6) sin A` is equal to ______.

If sin A + sin B + sin C = 3, then cos A + cos B + cos C is equal to ______.

In a ΔPQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then ∠R is equal to ______.

The value of cos (270° + θ) cos (90° – θ) – sin (270° – θ) cos θ is ______.

The value of the expression sin⁶ θ + cos⁶ θ + 3 sin² θ . cos² θ is ______.

The value of sin 930° is ______.

The value of cos(– 870°) is ______.

The value of sin 135° cosec 225° tan 150° cot 315° is ______.

The value of `(cos(90^circ + θ) sec(-θ)tan(180^circ - θ))/(sec(360^circ - θ)sin(180^circ + θ)cot(90^circ - θ))` is ______.

The value of tan 315° cot(– 405°) + cot 495° tan (– 585°).

The value of sin 150° cos 120° + cos 330° sin 660° is ______.

The value of `2 sin^2  π/6 + "cosec"^2  (7π)/6 cos^2  π/3` is ______.

cos² 5° + cos² 10° + cos² 15° + .... + cos² 85° + cos² 90° is equal to ______.

The greatest value of the term independent of x in the expansion of (x sin p + x^–1 cos p)¹⁰, p ∈ R is ______.

If A = `[(1, 0, 0),(0, 1, 0),("a", "b", -1)]` and I is the unit matrix of order 3, then A² + 2A⁴ + 4A⁶ is equal to ______.

cos 1°. cos 2°. cos 3° ...... cos 179° = ______.

The area (in sq. units) of the region {(x, y) : y² ≥ 2x and x² + y² ≤ 4x, x ≥ 0, y ≥ 0} is ______.

The order and degree of the differential eqµation whose general solution is given by `(d^2y)/(dx^2) + (dy/dx)^50` = In `((d^2y)/dx^2)` respectively, are ______.

Which of the following is not continuous for all x?

The area bounded by the curve | x | + y = 1 and X-axis is ______.