List of practice Questions

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 $.

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

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 \[ (2\alpha+1,\; \alpha^2-3\alpha,\; \frac{\alpha-1}{2}) \] 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 $\alpha$.

Find potential difference across bulb as shown in the figure.

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.

Match the list-I with list-II

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:

Diagram shows a circuit consisting of some elements. The input and output of the circuit is shown. Choose the correct option that shows the component in box. (Zener diode has a breakdown potential of 5V)

Options are:

MX is a sparingly soluble salt that follows the given solubility equilibrium at 298 K.
MX(s) $\rightleftharpoons M^{+(aq) }+ X^{-}(aq)$; $K_{sp} = 10^{-10}$
If the standard reduction potential for $M^{+}(aq) + e^{-} \rightarrow M(s)$ is $(E^{\circ}_{M^{+}/M}) = 0.79$ V, then the value of the standard reduction potential for the metal/metal insoluble salt electrode $E^{\circ}_{X^{-}/MX(s)/M}$ is ____________ mV. (nearest integer)
[Given : $\frac{2.303 RT}{F} = 0.059$ V]

Resolving power of a telescope is $5\times10^{-7}\,\text{rad}$. If wavelength of incident light is $500\,\text{nm}$, find the diameter of the aperture of the telescope.

In an AC circuit a resistor $100\Omega$, inductor $0.1\,\text{mH}$ and a capacitor are connected in series across an AC source of $220\,\text{V},\,50\,\text{Hz}$. If the power factor of the circuit is $ \frac{1}{2} $ and $ |X_L - X_C| = \alpha\sqrt{3}\,\Omega $, find $\alpha$.

Find the length of image of rod $AB$. The rod is placed in front of a concave mirror of focal length $f = 10\,\text{cm}$. End $A$ is $20\,\text{cm}$ from the mirror and the length $AB = 10\,\text{cm}$.

Nuclei $A$ and $B$ form a nucleus $C$. Binding energy per nucleon for $A, B$ and $C$ are $3\,\text{MeV}, 7\,\text{MeV}$ and $6\,\text{MeV}$ respectively. Find the energy produced in the reaction: \[ 2A^{3} + B^{4} \rightarrow C^{10} \]