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

Choose the most appropriate option. Solve for \(x>0\)
\[ \log_3\left( \frac{3}{x} \right) + \log_3 x = 1 \]
The straight line \( r = (i - j + k) + \lambda (2i + j - k) \) and the plane \( r \cdot (2i + j - k) = 4 \) are
Find the derivative of \[ y = (1 - x)^m (1 + x)^n \text{ at } x = 0, \text{ where } m, n>0 \]
A real solution of the equation \[ \cosh x - 5 \sinh x - 5 = 0 \text{ is} \]
On the ellipse \(9x^2 + 25y^2 = 225\), find the point, the distance from which to the focus \(F_2\) is four times the distance to the focus \(F_1\).
Let \( a = \cos \theta_1 + i \sin \theta_1 \), \( b = \cos \theta_2 + i \sin \theta_2 \), \( c = \cos \theta_3 + i \sin \theta_3 \) and \( a + b + c = 0 \), then \[ \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = ? \]
If the expansion of \(\left(x^2 + \frac{2}{x} \right)^n\) has a term independent of \(x\), then \(n\) is
\[ \int_{-1}^1 \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} dx \text{ is equal to} \]
Find the points of intersection of the given surface \[ \frac{x^2}{81} + \frac{y^2}{36} + \frac{z^2}{4} = 1 \text{ and the straight line } \frac{x - 3}{3} = \frac{y - 4}{-6} = \frac{z + 2}{4} \]
Tangents are drawn from the origin to the curve \(y = \sin x\). Then, the point of contact lie on the curve:
What is the value of \(\tan \left(\frac{\pi}{12}\right)?\)
If \(P(x)\) is a polynomial such that \[ P(x^2 + 1) = \{P(x)\}^2 + 1 \] then \(P'(0)\) is equal to
If \(y^{\frac{1}{m}} + x^{\frac{1}{m}} = 2x\) then
\[ \int_{-\pi/2}^{\pi/2} |\sin x| dx \text{ equals to} \]
\[ \int \frac{x^2}{(x \sin x + \cos x)^2} dx \text{ is equal to} \]
\[ \int_0^1 x e^{2x} dx \text{ is equal to} \]
Choose the most appropriate options.
The period of the function \(f(x) = |\sin x| - |\cos x|\) is
Choose the most appropriate options.
The value of \({}^{40}C_0 + {}^{40}C_1 + {}^{40}C_2 + \ldots + {}^{40}C_{20}\) is
A die is thrown twice and the sum of the numbers appearing is 6. Then, the conditional probability that the number 4 has appeared at least once is
There are 3 true coins and 1 false coin with 'head' on both sides. A coin is chosen at random and tossed 4 times. If 'head' occurs all the 4 times, then the probability that the false coin has been chosen and used is
In how many ways can the four walls of a room be painted with three colours such that no two adjacent walls have the same colour?
\[ \lim_{x \to 0} \frac{\sqrt{1+x} - \sqrt{1 - x}}{x} \]
If \(x = e^y + e^{-y} - x,\, x>0\) then \(\frac{dy}{dx}\) is
Choose the most appropriate options.
\[ \int \frac{x^2 - 2}{x \sqrt{x^2 - 1}}\,dx \text{ equal to} \]