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

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 \[ x = 1 + \frac{dy}{dx} + \frac{1}{2!} \left( \frac{d^2y}{dx^2} \right) + \frac{1}{3!} \left( \frac{d^3y}{dx^3} \right) + ... \]

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

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

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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

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

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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

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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:

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