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

The expression cos²(A – B) + cos² B – 2 cos(A – B) cos A cos B is ______.

If tan α, tan β are the roots of the equation x² + px + q = 0 (p ≠ 0), then ______.

If cos(A – B) = `3/5` and tan A tan B = 2, then ______.

tan 100° + tan 125° + tan 100° tan 125° = ______.

If `π/2 < α < π, π < β < (3π)/2`; sin α = `15/17` and tan β = `12/5`, then the value of sin(β – α) is ______.

If tan A – tan B = x and cot B – cot A = y, then cot(A – B) = ______.

sin 4θ can be written as ______.

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is `1/2`. Then the length of the semi-major axis is ______.

If cos 2B = `(cos(A + C))/(cos(A - C))`, then tan A, tan B, tan C are in ______.

cos² 76° + cos² 16° – cos 76° cos 16° is equal to ______.

The value of `sin  π/16 sin  (3π)/16 sin  (5π)/16 sin  (7π)/16` is ______.

The value of cot 70° + 4 cos 70° is ______.

If A, B, C, D are the angles of a cyclic quadrilateral, then cos A + cos B + cos C + cos D is equal to ______.

If ABCD is a cyclic quadrilateral, then the value of cos A – cos B + cos C – cos D is equal to ______.

cos(36° − A) cos(36° + A) + cos(54° + A) cos(54° − A) = ______.

The equation of the plane passes through the point (2, 5, –3) perpendicular to the plane x + 2y + 2z = 1 and x – 2y + 3z = 4 is ______.

The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.

The differential equation of all circles passing through the origin and having their centres on the X-axis is ______.

`1/3(sqrt(3)  cos 23^circ -  sin 23^circ)` is equal to ______.

tan 57° – tan 12° – tan 57° tan 12° is equal to ______.