List of top Mathematics Questions

\(\frac{d}{dx} \left( \cos(\pi x + \sin \pi x) \right) \)
\(\int \tan \left( \tan^{-1} x \right) \, dx = ? \)
\(\int (\sin 3x + 4 \sin^3 x) \, dx \)
\(\int \frac{\cos 2x}{\cos x + \sin x} dx \)
\(\int \log x^2 \, dx \)
\(\int \frac{dx}{e^{-x}} \)
\(\frac{d}{dx} \left[ 2\sqrt{x} \right] \)
\(\frac{d}{dx} \left[ e^{x^2} \right] \)
\(\int \frac{dx}{x^2 + 4} \)
\(\frac{d}{dx} \left[ (1 - \cos 2x) + 2\cos^2 x \right] \)
\(\frac{d}{dx} \left[ 2 \tan^{-1} x \right] \)
\(\frac{d}{dx} \left[ \log x^2 + \log a^2 \right] \)
\(\frac{d}{dx} \left[ (x+2)(x^2 - 2x + 4) \right] \)
\(\frac{d}{dx} \left( \sin^{-1} 2x \right)\)
\(\frac{d}{dx} \left( e^{2x} + 2e^x \right)\)
\(\frac{d}{dx} \left[ \lim_{x \to a} \frac{x^n + a^n}{x + a} \right] \)
\(\frac{d}{dx} \left(\sec^2 x - \tan^2 x\right)\)

If the system of equations \[ x + 2y - 3z = 2, \quad 2x + \lambda y + 5z = 5, \quad 14x + 3y + \mu z = 33 \] has infinitely many solutions, then \( \lambda + \mu \) is equal to:}

Find the mean of the following distribution: 
\[\begin{array}{|c|c|c|c|c|c|c|c|} \hline \textbf{Class-interval} & 11-13 & 13-15 & 15-17 & 17-19 & 19-21 & 21-23 & 23-25 \\ \hline \text{Frequency} & \text{7} & \text{6} & \text{9} & \text{13} & \text{20} & \text{5} & \text{4} \\ \hline \end{array}\] 
 

Prove that \( \frac{\sec\theta - \tan\theta}{\sec\theta + \tan\theta} = 1 + 2\tan^2\theta - 2\sec\theta\tan\theta \)
The slant height of a frustum of a cone is 4 cm and the perimeters (circumferences) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
If 5th and 9th terms of an A.P. are 43 and 79 respectively, find the A.P.
A two digit number is four times of the sum of its digits and twice the product of its digits. Find the number.
Using quadratic formula find the roots of the equation \(2x^2 - 2\sqrt{2}x + 1 = 0\).