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List of top Mathematics Questions

The differential equation formed by eliminating arbitrary constants $ A $ and $ B $ from the equation \[ y = A \cos 3x + B \sin 3x \] is:

If a variable straight line passing through the point of intersection of the lines x - 2y + 3 = 0 and 2x - y - 1 = 0 intersects the X and Y axes at A and B respectively, then the equation of the locus of a point which divides the segment AB in the ratio -2 : 3 is:

Evaluate the integral: \[ I = \int \frac{\cos x + x \sin x}{x (x + \cos x)} dx =\]

Find the area of the region (in square units) enclosed by the curves: \[ y^2 = 8(x+2), \quad y^2 = 4(1-x) \] and the Y-axis.

In a triangle ABC, if $ (r_1 + r_2) \csc^2 \frac{C}{2} = $

If the function \[ f(x) = \frac{\sqrt{1+x} - 1}{x} \] is continuous at $ x = 0 $, then $ f(0) $ is:

$\int\frac{2x^{2}\cos(x^{2})-\sin(x^{2})}{x^{2}}dx=$

If 5 letters are to be placed in 5-addressed envelopes, then the probability that at least one letter is placed in the wrongly addressed envelope is:

Evaluate the integral $\int \frac{\pi}{x^n + 1 - x} , dx$:

Let $ a>1 $ and $ 0<b<1 $. -∞$ f : \mathbb{R} \to [0, 1] $ is defined by $ f(x) = \begin{cases} a^x & \text{if } x<0 b^x & \text{if } 0 \leq x \leq 1 \end{cases} $, then $ f(x) $ is:

Evaluate the integral: $ I = \int e^{2x+3} \sin 6x \, dx $.

If Rolle’s theorem is applicable for the function $ f(x) $ defined by $ f(x) = x^3 + Px - 12 $ on $ [0,1] $, then the value of $ C $ of the Rolle's theorem is:

$\int_{0}^{\pi}x \sin^4 x \cos^6 x dx = $

If $y = \tan^{-1} \frac{x}{1+2x^2} + \tan^{-1} \frac{x}{1+6x^2} + \tan^{-1} \frac{x}{1+12x^2}$, then $\left(\frac{dy}{dx}\right)_{x=\frac{1}{2}} =$

If $ f(x) $ is given as: $ f(x) = \begin{cases} 3ax - 2b, & x<1 ax + b + 1, & x<1 \end{cases} $ and $ \lim_{x \to 1} f(x) $ exists, then the relation between $ a $ and $ b $ is:

The general solution of the equation $ \sin^2 \theta + 3 \cos^2 \theta = 5 \sin \theta $ is:

Let $ \overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c} $ be non-coplanar vectors. If $ \alpha \overrightarrow{d} = \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} $, $ \beta \overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c} + \overrightarrow{d} $, then $ | \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} + \overrightarrow{d} | = ? $

The real part of $ \frac{\left( \cos a + i \sin a \right)^6}{\left( \sin b + i \cos b \right)^8} $ is:

The equation of one of the tangents drawn from the point $ (0,1) $ to the hyperbola $ 45x^2 - 4y^2 = 5 $ is:

The equation of a circle which touches the straight lines \[ x + y = 2, \quad x - y = 2 \] and also touches the circle \[ x^2 + y^2 = 1 \] is:

If the $2^{\text{nd}}$, $3^{\text{rd}}$, and $4^{\text{th}}$ terms in the expansion of $ (x + a)^n $ are 96, 216, and 216 respectively, and $ n $ is a positive integer, then $ a + x $ is:

A Circle S passes through the points of intersection of the circles $ x^2 + y^2 - 2x + 2y - 2 = 0 $ and $ x^2 + y^2 + 2x - 2y + 1 = 0 $. If the centre of this circle S lies on the line $ x - y + 6 = 0 $, then the radius of the circle S is:

If $ A = \int_0^{\infty} \frac{1 + x^2}{1 + x^4} dx $ and $ B = \int_0^1 \frac{1 + x^2}{1 + x^4} dx $, then:

If the roots of the equation $x^3 + ax^2 + bx + c = 0$ are in arithmetic progression, then:

If $ f(0) = 0 $, $ f'(0) = 3 $, then the derivative of $ y = f(f(f(f(f(x))))) $ at $ x = 0 $ is: