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

If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______ 

The value of 2 `cot^-1  1/2 - cot^-1  4/3` is ______ 

The centre of the circle x = 3 + 5 cos θ, y = - 4 + 5 sin θ, is ______ 

If the radius of a circle increases from 3 cm to 3.2 cm, then the increase in the area of the circle is ______ 

The argument of the complex number `(4 + 9i)/(13 + 5i)` is ______

The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______

The solution of the differential equation `dy/dx + y/x = 1 - x^3 + 4x` is ______ 

The radius of a circle is increasing uniformly at the rate of 2.5cm/sec. The rate of increase in the area when the radius is 12cm, will be ______ 

The statement, 'If I go to school, then I will get knowledge' is equivalent to ______ 

Particular solution of differential equation `e^{dy/dx} = x:y(1) = 3; x > 0` is ______ 

The area bounded by the curve x = logy, Y-axis and the ordinates y = 1, y = 3 is ______

If `sin^-1x + cos^-1y = (3pi)/10,` then `cos^-1x + sin^-1y =` ______ 

`int1/(4 + 3cos^2x)dx` = ______ 

If `sin^-1  3/5 + cos^-1  12/13 = sin^-1 P`, then P is equal to ______ 

Solution of differential equation `dx/dy = 1/(e^{mx} - ay)` is ______ 

The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______ 

The solution of the differential equation `dy/dx + y = e^x` is ______ 

The principal value of `tan^{-1(sqrt3)}` is ______  

The area bounded by the curves y = log_ex and y = (log_ex)² is ______  

lf y = `ae^{cos^-1x}`, then corresponding to this the differential equation is ______