List of top Mathematics Questions asked in IPU CET

Gas is being pumped into a spherical balloon. Then, the rate at of $30 \, \text{ft}^3/\text{min}$ which the radius increases when it reaches the value 15 ft, is

The length of the axes of the conic \[ 9x^2 + 4y^2 - 6x + 4y + 1 = 0 \] are

Choose the most appropriate options.
If the SD of a set of observations is 8 and each observation is divided by -2, then the SD of the new set of observation will be:

If $ |a| < 1 $ and $ |b| < 1 $, then the sum of the series $$ a(a + b) + a^2(a^2 + b^2) + a^3(a^3 + b^3) + \cdots $$

The equation of a straight line passing through the point of intersection of $ x - y + 1 = 0 $ and $ 3x + y - 5 = 0 $ and perpendicular to one of them, is:

Choose the most appropriate option.
On the sphere $ (x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 25 $, find the point $ M_0 $ to the plane $ 3x - 4z + 19 $.

The mid-point of the chord $2x + y - 4 = 0$ of the parabola $y^2 = 4x$ is

The sum \[ \sum_{k=0}^5 \left( 5C_k \right)^2 \] is equal to

The number of real roots of $$ (6 - x)^4 + (8 - x)^4 = 16 $$

The solution of the differential equation \[ (x^2 - yx^2) \frac{dy}{dx} + y^2 + xy^2 = 0 \] is

A differentiable function $ f(x) $ has a relative minimum at $ x = 0 $, then the function $ y = f(x) + ax + b $ has a relative minimum at $ x = 0 $ for

Choose the most appropriate option. \[ \lim_{x \to 1} \sin(x - 1) \cdot \tan\left( \frac{\pi}{x} \right) \]

Choose the most appropriate option.

\[ \lim_{x \to 0} \frac{\ln \cos 2x}{\sin 2x} \]

The function $ f:[0,3] \to [1,29] $ defined by \[ f(x) = 2x^3 - 15x^2 + 36x + 1 \] is

Choose the most appropriate options.
Let $ f(x) = ax^3 + 5x^2 - bx + 1 $. If when divided by $ x - 1 $ it leaves a remainder of 5, and $ f(x) $ is divisible by $ 3x - 1 $, then

The number of integral values of $ \lambda $ for which the equation \[ x^2 + y^2 - 2\lambda x + 2\lambda y + 14 = 0 \] represents a circle whose radius cannot exceed 6 is:

The integral \[ \int_0^{\frac{\pi}{2}} \frac{\sqrt{\sin x + \cos x}}{\sin x + \cos x} \, dx \] is equal to

The value of \[ \int_0^{\frac{\pi}{2}} \sin^7 \theta \cos^4 \theta \, d\theta \] is

The area bounded by the curves $ y = \cos x $ and $ y = \sin x $ between the ordinates $ x = 0 $ and $ x = \frac{3\pi}{2} $ is

$\lim_{x \to 0} \frac{\tan^{-1} \left( \frac{-x}{\sqrt{1 - x^2}} \right)}{\ln(1 - x)} =\ ?$

$ (1 + 2i)^6 $ is equal to:

What is the number of ordered pairs of real numbers (a, b) such that \[ (a + bi)^{2002} = a - bi \]

\[ \int_{-\pi/2}^{\pi/2} |\sin x| dx \text{ equals to} \]

\[ \int \frac{x^2}{(x \sin x + \cos x)^2} dx \text{ is equal to} \]

Find the derivative of \[ y = (1 - x)^m (1 + x)^n \text{ at } x = 0, \text{ where } m, n>0 \]