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

The micro-organisms double themselves in 3 h. Assuming that the quantity increases at a rate proportional to itself, then the number of times it multiplies themselves in 18 yr is ______.

If the fines given by `(x - 1)/(2lambda) = (y - 1)/(- 5) = (z - 1)/2` and `(x + 2)/lambda = (y + 3)/lambda = (z + 5)/1` are parallel, then the value of λ is ______.

The symbolic form of the following circuit is (where p, q represents switches S₁ and S₂ closed respectively)

The angle between two adjacent sides `overlinea` and `overlineb` of parallelogram is `pi/6`. if `overlinea` = (2, -2, 1) and `|overlineb| = 2|overlinea|`, then area of this parallelogram is ______ 

Solution of the differential equation `x(dy/dx)^2 + 2sqrt(xy) dy/dx + y = 0` is ______

If q: There are clouds in the sky then p: it is raining. The symbolic form is ______

The solution of the equation (3y - 2) dx - (3x + 7) dy = 0 is ______

The differential equation of all circles which passes through the origin and whose centre lies on the X-axis is ______

Which of the following function is not continuous at x = 0?

Solution of differential equation `xdy/dx - y = x^3` is ______ 

The value of cot `(tan^-1 2x + cot^-1 2x)` is ______ 

If 2x - 4y = 9 and 6x - 12y + 7 = 0 are the tangents of same circle, then its radius will be ______ 

The area of the region bounded by the curve y = 2x - x² and the line y = x is ______ square units.

The general solution of x `"dy"/"dx" = "y" - x tan ("y"/x)`is ________.

The angle between the pair of straight lines 2x² - 6xy + y² = 0 is tan^-1 (p), where p = ______

The angle between lines `(x - 2)/2 = (y - 3)/(- 2) = (z - 5)/1` and `(x - 2)/1 = (y - 3)/2 = (z - 5)/2` is ______.

The area enclosed between the curves y = x^2, and y = `sqrtx` is, (in square units) ______ 

The solution of the differential equation `dy/dx = (x - 2y + 1)/(2(x - 2y))` is ______ 

The solution of the differential equation `(y^2 + xy^2)dx/dy + x^2 - yx^2 = 0` is ______ 

`sin^-1x + sin^-1  1/x + cos^-1x + cos^-1  1/x` = ______