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

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 ______.

The function f(x) = x – |x – x²| is ______.

A ladder is 10 m long rests against a vertical wall with the lower end on the horizontal ground. The lower end of the ladder is pulled along the ground away from the wall at the rate of 3 cm/s. The height of the upper end while it is descending at the rate of 4 cm/s is ______.

The maximum value of Z = 9x + 13y subject to constraints 2x + 3y ≤ 18, 2x + y ≤ 10, x ≥ 0, y ≥ 0 is ______.