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

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 0} \frac{a^x - 1}{x} $ is equal to

$ (1 + 2i)^6 $ is equal to:

A long string with a charge of a per unit length passes through an imaginary cube of edge L.
The maximum possible flux of electric field through the cube will be
The following equations indicate reactions that occur spontaneously.
Fe(s) + NiCl$_2$(aq) $\rightarrow$ FeCl$_2$(aq) + Ni(s)
Zn(s) + FeCl$_2$(aq) $\rightarrow$ ZnCl$_2$(aq) + Fe(s)
Ni(s) + PbCl$_2$(aq) $\rightarrow$ NiCl$_2$(aq) + Pb(s)
Which is the increasing order of the reactivity of the metals?
What is the oxidation state of sulfur in HSO$_4^{-}$?
Gas A decomposed according to the following reaction:
A(g) $\rightarrow$ B(g) + C(g)
A student conducted an experiment and determined that the equilibrium pressure of gas A was 0.20 P, where P was the total pressure of the system. What is the equilibrium constant $K_p$ for this reaction?
What is the molality of a 10% (by weight) C$_6$H$_{12}$O solution (molecular weight = 90)?
The maximum and minimum distances of a comet from the Sun are $8 \times 10^{12} \, \text{m}$ and $1.6 \times 10^{12} \, \text{m}$. If its velocity when nearest to the Sun is $60 \, \text{m/s}$, what will be its velocity in m/s when it is farthest?
A 25 mL sample of hard water is titrated with a 0.001 M solution of EDTA, and the end point of the titration is reached at 50 mL of EDTA added. What is the concentration of Ca$^{2+}$ and Mg$^{2+}$ ions in solution?
2CrO$_4^{2-}$ + 3SnO$_2^{2-}$ + H$_2$O → 2CrO$_2^{-}$ + 3SnO$_3^{2-}$ + 2OH$^{-}$
How many moles of OH$^{-}$ form when 50.0 mL of 0.100 M CrO$_4^{2-}$ is added to a flask containing 50.0 mL of 0.100 M SnO$_2^{2-}$?
Which of the following compounds will give racemic mixture on nucleophilic substitution by OH$^{-}$ ions?
The density of ice is $9.2 \times 10^2 \, \text{kg/m}^3$. If a chunk displaces $10^{-2} \, \text{m}^3$, the buoyant force on the ice is most nearly:
The Young's modulus of brass and steel are $10 \times 10^{10} \, \text{Nm}^{-2}$ and $20 \times 10^{10} \, \text{Nm}^{-2}$, respectively. A brass wire and steel wire of the same length are extended by 1 mm under the same force. If the radii of the brass and steel wires are $R_B$ and $R_S$ respectively, then
\(\lim_{x \to \infty} \frac{\ln x}{x^n}\) is equal to
On the sphere \((x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 25\), compute the distance from the point \(M_0\) to the plane \(3x - 4z + 19 = 0\)
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
Find the component of the vector a = (-1, 2, 0) perpendicular to the plane of the vectors \(\mathbf{e}_1(1, 0, 1)\) and \(\mathbf{e}_2(1, 1, 1)\)
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 \(2\sqrt{3}\)?
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:
\[ \lim_{n \to \infty} \left[ 5 - \frac{1}{5} + \frac{1}{25} - \dots + (-1)^{n-1} \cdot \frac{1}{5^n} \right] \]
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 \(\mathbf{e}_2 = (1, 1, 1)\).