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

The line passing through the points (5, 1, a) and (3, b, 1) crosses the YZ – plane at the point `(0, 17/2, (-13)/2)`, then ______.

If `(tan 3 theta - 1)/(tan 3 theta + 1) = sqrt3`, then the general value of θ is ______.

If `((11 - "n")!)/((10 - "n")!) = 9,`then n = ______.

A line passes through the point of intersection of the lines 3x + y + 1 = 0 and 2x – y + 3 = 0 and makes equal intercepts with axes. The equation of the line is ______.

The general solution of 4sin² x = 1 is ______.

If x² + y² - 2axy = 0, then `dy/dx` equals ______ 

Let f(x) = `(1 - tan x)/(4x - pi), x ne pi/4, x ∈ [0, pi/2]`. If f(x) is continuous in `[0, pi/2]`, then f`(pi/4)` is ______.

Region represented by the inequalities x ≥ 0, y ≤ 0 is ______.

If y = cosec x⁰, then `"dy"/"dx"` = ______.

If `lim_(x->1)(x^5-1)/(x-1)=lim_(x->k)(x^4-k^4)/(x^3-k^3),` then k = ______.

The total number of points on the curve x² - 4y² = 1 at which the tangents to the curve are parallel to the line x = 2y is ______.

The angle of intersection of curves x = y², 3y = 5 - 2x³ at (1, 1) is ______.

The centres of the circles x² + y² = 1, x² + y² + 6x – 2y = 1 and x² + y² – 12x + 4y = 1 are ______.

The volume of a spherical balloon is increasing at the rate of 10 cubic centimetre per minute. The rate of change of the surface of the balloon at the instant when its radius is 4 centimetres, is ______

The general value of θ in the equation `2sqrt(3) cos theta = tan theta` is ______.

`lim_(x -> 0) ((2 + x)^5 - 2)/((2 + x)^3 - 2)` = ______.

The general solution of cosec x = `-sqrt2` is ______ 

The tangent to the curve y = 2e^3x at the point (0, 2) meets the X-axis at ______.

If the tangent to y² = 4ax at the point (at², 2at), where | t | > 1 is a normal to x² – y² = a² at the point (a sec θ' a tan θ), then ______.

The equation 3sin²x + 10 cos x – 6 = 0 is satisfied, if ______.