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

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

The expression \[ \left| (a + 1)^2 \, (b + 1)^2 \, (c + 1)^2 \right| \] is equal to

Find the points of intersection of the given surface $\frac{x^2}{81} + \frac{y^2}{36} + \frac{z^2}{4} = 1$ and the straight line  $\frac{x - 3}{3} = \frac{y - 4}{-6} = \frac{z + 2}{4}$

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

Evaluate $ \int_0^1 x^5 \sqrt{1 - x^3} \, dx $

\(\lim_{x \to \infty} \frac{\ln x}{x^n}\) is equal to

What is the equation of the curve traced by point \(M\), if the sum of distances to \(A(-1, -1)\) and \(B(1, 1)\) is constant and equals \(2\sqrt{3}\)?

On the sphere \((x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 25\), compute the distance from the point \(M_0\) to the plane \(3x - 4z + 19 = 0\)

Find the component of the vector a = (-1, 2, 0) perpendicular to the plane of the vectors \(\mathbf{e}_1(1, 0, 1)\) and \(\mathbf{e}_2(1, 1, 1)\)

If \(y = \sec(\tan^{-1} x)\), then \(y\) at \(x = 1\) is equal to term is the sum of two preceding terms. Then, the common ratio of the G.P. is:

Every term of G.P. is positive and also every term is the sum of two preceding terms. Then, the common ratio of the G.P. is

What is the shape of the figure given by the following equations?

\[ \lim_{n \to \infty} \left[ 5 - \frac{1}{5} + \frac{1}{25} - \dots + (-1)^{n-1} \cdot \frac{1}{5^n} \right] \]

Find the angle between unit vectors \(\mathbf{e_1}\) and \(\mathbf{e_2}\) if vectors \[ \mathbf{a} = \mathbf{e_1} + 2\mathbf{e_2},\quad \mathbf{b} = 5\mathbf{e_1} - 4\mathbf{e_2} \] are mutually perpendicular.

Find the component of the vector \((-1, 2, 0)\) perpendicular to the plane of the vectors \(\mathbf{e}_1 = (1, 0, 1)\) and \(\mathbf{e}_2 = (1, 1, 1)\).

If \(i = \sqrt{-1}\), then \[ \lim_{n \to \infty} \frac{(n + 2i)(3 + 7in)}{(2 - i)(6n^2 + 1)} \] is equal to:

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

Which of the following complex numbers is conjugate to its square?

\[ \lim_{x \to \pi/4} \frac{(1 - \cos x)^2}{\tan^2 x - \sin^2 x} \text{ is equal to:} \]

\[ \frac{1}{2 \sin 10^\circ} - 2 \sin 70^\circ \text{ is equal to} \]

Given \(\varepsilon = \cos\left(\frac{2\pi k}{n}\right) + i \sin\left(\frac{2\pi k}{n}\right)\), find the value of \[ \prod_{k=0}^{n-1} \left( \varepsilon^2k - 2\varepsilon k \cos \theta + 1 \right) \]

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