List of practice Questions

The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level is:

Consider the equilibrium: \[ \text{CO(g)} + \text{3H}_2\text{(g)} \rightleftharpoons \text{CH}_4\text{(g)} + \text{H}_2\text{O(g)} \] If the pressure applied over the system increases by two fold at constant temperature then:

If A and B are two events such that $ P(A \cap B) = 0.1 $, and $ P(A|B) $ and $ P(B|A) $ are the roots of the equation $ 12x^2 - 7x + 1 = 0 $, then the value of $\frac{P(A \cup B)}{P(A \cap B)}$

If $ x = f(y) $ is the solution of the differential equation \[ (1 + y^2) + (x - 2e^{\tan^{-1}y}) \frac{dy}{dx} = 0, \quad y \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right), \] with $ f(0) = 1 $, then $ f\left( \frac{1}{\sqrt{3}} \right) $ is equal to:

An electron projected perpendicular to a uniform magnetic field $ B $ moves in a circle. If Bohr’s quantization is applicable, then the radius of the electronic orbit in the first excited state is:

Match List - I with List - II.

Partial Derivatives Thermodynamic Quantity

Choose the correct answer from the options given below :

Density of 3 M NaCl solution is 1.25 g/mL. The molality of the solution is:

The work function of a metal 3eV. The colour of the visible light that is required to cause emission of photo electrons is:

\[ \cot^{-1}\left(\frac{7}{4}\right) + \cot^{-1}\left(\frac{19}{4}\right) + \cot^{-1}\left(\frac{39}{4}\right) + \dots \, \infty \]

Let $ A = \{0, 1, 2, 3, 4, 5, 6\} $ and $ R_1 = \{(x, y): \max(x, y) \in \{3, 4 \}$. Consider the two statements:
Statement 1: Total number of elements in $ R_1 $ is 18.
Statement 2: $ R $ is symmetric but not reflexive and transitive.

20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The molarity of the sodium iodide solution is _____ M. (Nearest Integer value) (Given : Na = 23, I = 127, Ag = 108, N = 14, O = 16 g mol$^{-1}$)

The axis of a parabola is the line $ y = x $ and its vertex and focus are in the first quadrant at distances $ \sqrt{2} $ and $ 2\sqrt{2} $ units from the origin, respectively. If the point $ (1, k) $ lies on the parabola, then a possible value of $ k $ is:

The amount of calcium oxide produced on heating 150 kg limestone (75% pure) is _______ kg. (Nearest integer)
Given: Molar mass (in g mol$^{-1}$) of Ca-40, O-16, C-12

The percentage increase in magnetic field $ B $ when space within a current-carrying solenoid is filled with magnesium (magnetic susceptibility $ \chi_{mg} = 1.2 \times 10^{-5} $) is:

For a hydrogen atom, the ratio of the largest wavelength of the Lyman series to that of the Balmer series is:

Two wires A and B are made of the same material, having the ratio of lengths $ \frac{L_A}{L_B} = \frac{1}{3} $ and their diameters ratio $ \frac{d_A}{d_B} = 2 $. If both the wires are stretched using the same force, what would be the ratio of their respective elongations?

If $ y(x) = \begin{vmatrix} \sin x & \cos x & \sin x + \cos x + 1 \\27 & 28 & 27 \\1 & 1 & 1 \end{vmatrix} $, $ x \in \mathbb{R} $, then $ \frac{d^2y}{dx^2} + y $ is equal to

A loop ABCD, carrying current $ I = 12 \, \text{A} $, is placed in a plane, consists of two semi-circular segments of radius $ R_1 = 6\pi \, \text{m} $ and $ R_2 = 4\pi \, \text{m} $. The magnitude of the resultant magnetic field at center O is $ k \times 10^{-7} \, \text{T} $. The value of $ k $ is ______ (Given $ \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} $)

Among $ 10^{-10} $ g (each) of the following elements, which one will have the highest number of atoms?
Element : Pb, Po, Pr and Pt

2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is: (Given: Ebullioscopic constant of water = $ 0.52 \, \text{K kg mol}^{-1} $)

During estimation of Nitrogen by Dumas' method of compound X (0.42 g) :

mL of $ N_2 $ gas will be liberated at STP. (nearest integer) $\text{(Given molar mass in g mol}^{-1}\text{ : C : 12, H : 1, N : 14})$

1 + 3 + $5^2$ + 7 + $9^2$ + $\ldots$ upto 40 terms is equal to

Considering the principal values of the inverse trigonometric functions, $\sin^{-1} \left( \frac{\sqrt{3}}{2} x + \frac{1}{2} \sqrt{1-x^2} \right)$, $-\frac{1}{2}<x<\frac{1}{\sqrt{2}}$, is equal to

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let $X$ denote the number of defective pens. Then the variance of $X$ is

Let us consider a reversible reaction at temperature, T . In this reaction, both $\Delta \mathrm{H}$ and $\Delta \mathrm{S}$ were observed to have positive values. If the equilibrium temperature is $\mathrm{T}_{\mathrm{e}}$, then the reaction becomes spontaneous at: