List of top Mathematics Questions asked in Guru Gobind Singh Indraprastha University Common Entrance Test

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

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

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

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

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

Calculate

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

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

If \[ f(x) = \begin{cases} \frac{1 - \sin x}{(n - 2x)^2} & \text{if} \quad x \neq \frac{\pi}{2} \log (\sin x) \cdot \log \left( 1 + \frac{\pi}{4x + x^2} \right) & \text{if} \quad x = \frac{\pi}{2} \end{cases} \] is continuous at $ x = \frac{\pi}{2} $, then $ k $ is equal to

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

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

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

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

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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:

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:

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The value of $\lim_{x \to a} \frac{\log x - 1}{x - a}$ is equal to

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

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

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

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The degree of the differential equation \[ x = 1 + \frac{dy}{dx} + \frac{1}{2!} \left( \frac{d^2y}{dx^2} \right) + \frac{1}{3!} \left( \frac{d^3y}{dx^3} \right) + ... \]