List of top Mathematics Questions asked in IPU CET

The value of the integral $ \int_{-3}^{5} |x - 3| \, dx $ is

Let $ f(x) = x^2 + 6x + 1 $ and let $ R $ denote the set of points $ (x, y) $ in the coordinate plane such that $ f(x) + f(y) $ so and $ f(x) - f(y) \leq 0 $. Which of the following is closest to the area of $ R $?

The series $ 1 + 1 + \frac{3}{2^2} + \frac{4}{2^3} + \frac{5}{2^4} + \cdots $ is equal to

In a class, there are 10 boys and 8 girls. When 3 students are selected at random, the probability that 2 girls and 1 boy are selected, is

If A and B are independent events such that $ P(B) = \frac{2}{7} $, $ P(A \cup B) = 0.8 $, then $ P(A) = $?

The integral $ \int 34x^4 dx $ is equal to

The line $ y = mx + C $ will be tangent to the ellipse $ \frac{x^2}{9} + \frac{y^2}{4} = 1 $ if $ C $ is equal to

The eccentricity of the hyperbola $ \frac{\sqrt{1999}}{3} \left( x^2 - y^2 \right) = 1 $ is

The value of $ \int_0^{\frac{\pi}{2}} e^x \cos x \, dx $ is equal to:

Choose the most appropriate options. If $a, b, c$ are positive real numbers, then \[ \frac{1}{\log_{abc}} + \frac{1}{\log_{abc}} + \frac{1}{\log_{abc}} = \]

The determinant of the matrix \[ \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \] is equal to

The integral $ \int e^{\sec x} \tan x \sec x \, dx $ is equal to

It is known that $ AB = 2a - 6b $ and $ AC = 3a + b $, where $ a $ and $ b $ are mutually perpendicular unit vectors. Determine the angles of the AABC.

If $ \alpha $ and $ \beta $ are non-real numbers satisfying $ x^3 - 1 = 0 $, then the value of \[ \left| \begin{matrix} \lambda+1 & \alpha & \beta \\ \beta & \lambda + \beta & 1 \\ 1 & \lambda + \alpha & \lambda + \alpha \end{matrix} \right| \] is:

The value of $ \int \frac{\sin^2 x \cos^2 x}{(\sin^3 x + \cos^3 x)^2} \, dx $ is

A line segment with the end points $ A(3,-2) $ and $ B(6,4) $ is divided into three equal parts. Find the coordinates of the division points.

Find $ \frac{dy}{dx} $ where $ a^y = \left( \frac{x}{y} \right)^a $

Find the limit \[ \lim_{x \to 0} \left( 1 + \tan^2 \sqrt{x} \right)^{3/x} \]

The exradii of a triangle $ r_1, r_2, r_3 $ are in harmonic progression, then the sides $ a, b $ and $ c $ are in

The value of \[ \lim_{x \to 0} \int_0^x \sec^2 t \, dt \] is:

For all $ n \in \mathbb{N}, 72n - 48n - 1 $ is divisible by

The solution of the differential equation \[ \frac{d^2y}{dx^2} + 3y = -2x \] is

Choose the most appropriate options.
If $ A(2,3) $ and $ B(-2,1) $ are two vertices of a triangle and the third vertex moves on the line $ 2x + 3y = 9 $, then the locus of the centroid of the new set of observations will be the triangle is

The inverse of matrix \[ \begin{pmatrix} 0 & 1 & -1 \\ 4 & -3 & 4 \\3 & -3 & 4 \end{pmatrix} \] is

Let $x_1$ and $x_2$ be the roots of the equation $ax^2 + bx + c = 0$ ($ac \neq 0$). Find the value of $\frac{1}{x_1} + \frac{1}{x_2}$.