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

The equation of the circle with centre at (-2, -5) and passing through the centre of the given circle x² + y² + 16y + 29 = 0 is ______ 

Co-ordinates of a point on the curve y = x sin x at which the normal is parallel to the line 4x + 4y = 3 are ______.

The differential equation of the family of curves y = `"ae"^(2(x + "b"))` is ______.

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 ______.

The equation of line passing through the midpoint of the line joining the points (-1, 3, -2) and (-5, 3, -6) and equally inclined to the axes is ______.

The joint equation of pair of lines having slopes `1+sqrt2` and `1-sqrt2` and passing through the origin 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 ______.