List of top Questions asked in IPU CET

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

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

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

A line makes the same angle $\theta$ with each of the X and Z-axes. If the angle $\beta$ which it makes with Y-axis is such that $\sin^2 \beta = 3 \sin^2 \theta$, then $\cos^2 \theta$ equals

Let $ f(x) = (x^3 + 2)^{30} $. If $ f^{(n)}(x) $ is a polynomial of degree $ 20 $, where $ f^{(n)}(x) $ denotes the $ n + h $-order derivative of $ f(x) $, then the value of $ n $ is:

Calculate

\[ \begin{vmatrix} x & y & x + y \\ y & x + y & x \\ x + y & x & y \end{vmatrix} \]

The number of solutions of the equation \[ 3 \sin^2 x - 7 \sin x + 2 = 0 \] in the interval $ [0, 5\pi] $ is

From the bottom of a pole of height h, the angle of elevation of the top of a tower is $ \alpha $. The pole subtends an angle $ \beta $ at the top of the tower. The height of the tower is

If \[ a = \gamma \hat{i} + \delta \hat{j} + 2\zeta \hat{k}, \, b = \alpha \hat{i} + \beta \hat{j} + \gamma \hat{k}, \, r \times a = b \times a \, r \times b = a \times b \] then a unit vector in the direction of $ r $ is

Consider line segments of lengths 1, 2, 3, ..., 10, what is the number of triangles that can be formed from them?

How many paths are there from the point A to the point B in the figure below, if no point in a path is to be traversed more than once?

Given that $ \alpha_1, \alpha_2, \alpha_3 $ are the roots of $ 3x^3 - x^2 - 10x + 8 = 0 $, then the value of $ \alpha_1^2 + \alpha_2^2 + \alpha_3^2 $ is

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If $ A $ is a square matrix such that $ A^2 = A $ and $ B = I $, then $ AB + BA + I - (I - A)^2 $ is equal to:

The set of values of $ x $ satisfying the system of inequalities $ 5x + 2 < 3x + 8 $ and $ \frac{x^2}{x-1} < 4 $ is:

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If $ f(x) = [x \sin n\pi x] $, then which of the following is incorrect?

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The limit \[ \lim_{x \to 0} \frac{1 - \cos 2x}{x \tan 4x} \]

If $n$ is an integer, compute the value of the fraction \[ \frac{(1 + \theta)^n}{(1 - \theta)^{n-2}} \]

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If $ |z^2 - 1| = |z|^2 + 1 $, then $ z $ lies on a

The value of the integral \[ \int_0^0 9 [x - 2\lfloor x \rfloor] \, dx \] where $ [.] $ denotes the greatest integer function, is

If the numbers $a_1, a_2, \ldots, a_n$ are different from zero and form an arithmetic progression, then $$ \frac{1}{a_1} + \frac{1}{a_2} + \frac{1}{a_3} + \dots + \frac{1}{a_n} $$ is equal to

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Find the distance from the point A (2, 3, -1) to the given straight line. \[ x = 3t + 5, \quad y = 2t, \quad z = -2t - 25 \]

The maximum number of points into which 4 circles and 4 straight lines intersect, 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

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

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