List of top Questions asked in Guru Gobind Singh Indraprastha University Common Entrance Test- 2017

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

The number of real roots of

(6 - x)^4 + (8 - x)^4 = 16

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:

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:

Choose the most appropriate option.
The value of $\lim_{x \to a} \frac{\log x - 1}{x - a}$ is equal to