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

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 ______.

It is given that the events A and B are such that P(A) = `1/4, P(A/B) = 1/2` and `P(B/A) = 2/3`, then P(B) is equal to ______. 

The value of (cos α + cos β)² + (sin α + sin β)² is ______.

cos² x + cos² y – 2 cos x cos y cos (x + y) is equal to ______.

The value of tan 3A – tan 2A – tan A is ______.

The circles x² + y² + 6x + 6y = 0 and x² + y² – 12x –12y = 0

The differential equation of all parabolas having vertex at the origin and axis along positive Y-axis is ______.

`int_-1^1 (17x^5 - x^4 + 29x^3 - 31x + 1)/(x^2 + 1) dx` is equal to ______.

What will be the equation of plane passing through a point (1, 4, – 2) and parallel to the given plane – 2x + y – 3z = 9?

Find k, if the slope of one of the lines given by kx² + 8xy + y² = 0 exceeds the slope of the other by 6.

Let g(x) be the inverse of the function f(x) and f'(x) = `2/(x^2 + 3)`, then 2g'(x) is equal to 

The maximum value of P = 7x + 6y subject to constraints x + 2y ≤ 24, 2x + y ≤ 30 and x ≥ 0, y ≥ 0 is ______.

If m₁ and m₂ are slopes of lines represented by 6x² - 5xy + y² = 0, then (m₁)³ + (m₂)³ = ?

The angle between the tangents to the circle x² + y² = 25 from the point (7, -1) is ______.