List of top Mathematics Questions

At \( x = \frac{\pi^2}{4} \), \( \frac{d}{dx} \left( \tan^{-1}(\cos\sqrt{x}) + \sec^{-1}(e^x) \right) = \)
The maximum area of a rectangle inscribed in a circle of diameter \( R \) is:
Consider the function \( f(x) = \frac{|x - 1|}{x^2} \). Then \( f(x) \) is:
The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is:
If the angle made by the tangent at the point \((x_0, y_0)\) on the curve \(x = 12(t + \sin t \cos t)\), \(y = 12(1 + \sin t)^2\), with \(0<t<\frac{\pi}{2}\), with the positive x-axis is \(\frac{\pi}{3}\), then \(y_0\) is equal to:
If \( Q(h, k) \) is the inverse point of \( P(1,2) \) with respect to the circle \( x^2 + y^2 - 4x + 1 = 0 \), then \( 2h + k \) is:
The general solution of the differential equation: $$ x \, dy - y \, dx = \sqrt{x^2 + y^2} \, dx. $$ 
The altitude of a cone is 20 cm and its semi-vertical angle is \(30^\circ\). If the semi-vertical angle is increasing at the rate of \(2^\circ\) per second, then the radius of the base is increasing at the rate of:
If \( \theta \) is the angle between the tangents drawn from the point \( (2,3) \) to the circle \( x^2 + y^2 - 6x + 4y + 12 = 0 \), then \( \theta \) is:
If five-digit numbers are formed from the digits 0, 1, 2, 3, 4 using every digit exactly only once, then the probability that a randomly chosen number from those numbers is divisible by 4 is
Quartile coefficient of skewness is
Suppose that there is a chance for a newly constructed house to collapse whether the design is faulty or not. The chance that the design is faulty is 10\%. The chance that the house will collapse if the design is faulty is 95\% and otherwise it is 45\%. It is seen that the house collapsed. What is the probability that the design is faulty?
The probability that a person aged 60 years will live up to 70 is 0.65. What is the probability that out of 10 persons aged 60, at least 7 of them will live up to 70?
The probability that A passes a test is \( \frac{2}{3} \) and the probability that B passes the same test is \( \frac{3}{5} \). The probability that only one passes is
If \( \cot^{-1}(n)>\frac{\pi}{6} \), \( n \in N \), then the maximum value of n is
If \( P(A) = \frac{1}{4} \), \( P(B) = \frac{1}{3} \) and \( P(A \cup B) = \frac{1}{2} \), then \( P(A \cap B) = \)
If \( \cos B = \frac{\sin A}{2 \sin C} \), then the triangle is
The value of \( \frac{1}{\sin 10^\circ} - \frac{\sqrt{3}}{\cos 10^\circ} \) is equal to
The value of \( \sqrt{2 + \sqrt{2 + 2 \cos 4\theta}} \) is
The value of \( \tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) \) is equal to
If \( A = \begin{bmatrix} \cos \theta & \sin \theta & 0 \\ \sin \theta & -\cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix} \), then the value of \( AA' \) is:
What is the annual income derived by investing ₹6800 in 10\% stock at 136?
In the expansion of \( \left( x - \frac{3}{x^2} \right)^9 \), the constant term is:
The distance between the foci of the hyperbola \( \frac{x^2}{16} - \frac{y^2}{9} = 1 \) is:
The angle between \( x^2 = y \) and \( y^2 = x \) at \( (1, 1) \) is: