List of practice Questions

Consider Bohr's model of a H-atom. If magnetic field at center due to electron in 2$^n$ orbit is $ B_1 $, and magnetic field due to electron in 4$^t$ orbit is $ B_2 $. Find $ \frac{B_1}{B_2} $.

Find potential difference across bulb as shown in the figure.

At 298 K, the mole percentage of N$_2$(g) in air is 80%. Water is in equilibrium with air at a pressure of 10 atm. What is the mole fraction of N$_2$(g) in water at 298 K? ($K_H$ for N$_2$ = $6.5 \times 10^7$ mm Hg)

A particle is moving such that its velocity vector at co-ordinate $(x,y,z)$ is $\vec{v} = -x\hat{i} + 2y\hat{j} - z\hat{k}$. Find magnitude of acceleration at $(1,1,4)$.

If \[ (2\alpha+1,\; \alpha^2-3\alpha,\; \frac{\alpha-1}{2}) \] is the image of the point \[ (\alpha,\; 2\alpha,\; 1) \] in the line \[ \frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}, \] then find the possible values of $\alpha$.

Evaluate \[ (0.2)^{\log_{\sqrt{5}}\alpha} + (0.04)^{\log_{5}\beta} \] if \[ \alpha = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \cdots \] \[ \beta = \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \cdots \]

Match the column-I with column-II:

Choose the correct match.

Soluble in aqueous NaOH

Match the list-I with list-II

Find the voltage $V_{AB}$ and the current $i_{BA}$ in the given circuit.

If moment of inertia of rod about axis AB is equal to moment of inertia of solid sphere about an axis parallel to AB which is at 9m from AB axis as shown in the figure. If $ R = \frac{\alpha}{2} $, then find $ \alpha $.

If power dissipated in a coil having total number of turns 'N', cross-section area 'A' and radius of coil 'R' when kept in a time varying magnetic field is P. Now if another coil having total number of turns '2N', cross-section area '2A' and radius of coil '3R' is placed is same time varying magnetic field power dissipated is $\alpha P$, then value of $\alpha$ is :

Two atoms are bonding along the Z-axis. How will the $ \pi^* $ orbital look like (Z is the internuclear axis)?

Which of the following is most acidic?

If $ L_1 : x - y = 0 $, $ L_2 : y = -3x $, $ L_3 $ is the obtuse angle bisector of $ L_1 $ and $ L_2 $, and $ L_4 : x + 3 = 0 $. Let $ A $ be the point of intersection of $ L_4 $ and $ L_1 $, $ B $ be the point of intersection of $ L_4 $ and $ L_2 $, and $ C $ be the point of intersection of $ L_4 $ and $ L_3 $. Then the value of $ \dfrac{(BC)^2}{(AC)^2} $ is:

(A) Bond angle Cr–O–Cr in $ \text{CrO}_7^{2-} $ is 126° (B) $ \text{Na}_2\text{Cr}_2\text{O}_7 $ is used as primary standard solution in titration. (C) $ \text{K}_2\text{Cr}_2\text{O}_7 $ oxidises $ \text{Fe}^{2+} $ into $ \text{Fe}^{3+} $ in acidic medium. (D) $ \text{CrO}_4^{2-} $ and $ \text{Cr}_2\text{O}_7^{2-} $ are interconvertible by changing pH.

Two cars $A$ and $B$ are moving on a road with speeds $100\,\text{km/h}$ and $80\,\text{km/h}$ respectively. A stone is thrown from car $B$ with speed $V$ km/h relative to it. The stone hits car $A$ with speed $5\,\text{m/s}$ relative to car $A$ (ignore gravity). Find $V$.

List-I presents some physical quantities and List-II presents their dimensions. Match the two lists appropriately.

Consider a ring of radius $R$ which rotates about a horizontal axis as shown (axis is tangent to the ring). Find the time period of small oscillations.

Two strings with lengths $l_1$ and $l_2$, and Young's moduli $Y_1$ and $Y_2$ are elongated under two weights as shown. Find the ratio $\Delta l_1 / \Delta l_2$.
Case (1): String has Young's modulus $Y$, length $l$, cross–sectional area $A$ and a mass $m$ is attached.
Case (2): String has Young's modulus $2Y$, length $0.5l$, cross–sectional area $A$ and a mass $3m$ is attached.

Manganese forms oxide and fluoride with highest oxidation state. The difference in the highest oxidation state of Mn in the oxide and fluoride is:

"X" is an oxoanion of the lightest element of group 7 (in the periodic table). The metal is in +6 oxidation state in "X". The color of the potassium salt of X is

The number of non-negative integer solutions of the equation \[ a + b + 2c = 22 \] is:

If the quadratic expression \[ (\lambda+2)x^2 - 3\lambda x + 4\lambda = 0, \qquad \lambda \ne -2 \] has two positive roots, then the number of possible integral values of $\lambda$ is:

In the expansion of \[ \left(9x-\frac{1}{3\sqrt{x}}\right)^{18}, \] if the coefficient of the term independent of $x$ is $221k$, then the value of $k$ is: