List of top 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 $\frac{1}{x_1} + \frac{1}{x_2}$.

A wire of arbitrary shape carries a current $ I = 2A $. Consider the portion of wire between $ (0, 0, 0) $ and $ (4, 4, 4) $. A magnetic field given by $ B = \left( 1.2 \times 10^{-4} + 2 \times 10^{-4} \right) \, \hat{k} $ exists in the region. The force acting on the given portion of the wire is:

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 the escape speed of a projectile on Earth's surface is $ 11.2 \, \text{km/s} $ and a body is projected out with thrice this speed, then determine the speed of the body far away from the Earth.

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

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

$2HC = CH_2\text{Cl}_2 \xrightarrow{\text{A}} \text{NH}_4\text{Cl}$ $\xrightarrow{\text{B}}$ $\text{Identify the compounds A and B}$

Consider the following reactions, C(s) + O2(g) → CO2(g), $\Delta$ H = -94$\text{ kcal}$ 2CO(g) + O2 → 2CO2(g), $\Delta$ H = -135.2$\text{ kcal}$ Then, the heat of formation of CO (g) is:

$NH_3$ molecule attract $H^+$ ion towards itself to form ammonium ion ${NH}_4^+$ through:

In the redox reaction \[ \text{MnO}_4^- + \text{C}_2\text{O}_4^{2-} \to \text{Mn}^{2+} + \text{CO}_2 + \text{H}_2\text{O} \] The correct coefficients of $ \text{C}_2\text{O}_4^{2-} $ and $ \text{H}^+ $ are

Consider the following reaction sequence of alkene. \[ \text{CH}_3\text{CH} = \text{CH}_3 \xrightarrow{\text{O}_3} A \xrightarrow{\text{H}_2\text{O}} B \] What is the product B?

Electrons are accelerated through a potential difference $ V_e $, and protons are accelerated through a potential difference of 4 V. The de-Broglie wavelengths are $ \lambda_e $ and $ \lambda_p $ for electrons and protons, respectively. The ratio of $ \frac{\lambda_e}{\lambda_p} $ is given by (given $ m_e $ is mass of electrons and $ m_p $ is mass of protons):

For the reactions $C + O2 \rightarrow CO2$; $\, \Delta H = -393 \, \text{kJ} 2Zn + O2 \rightarrow 2ZnO$, $\, \Delta H = -412 \, \text{kJ}$ $\text{the correct statement is:}$

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

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