List of practice Questions

The major product of the following reaction is $F_3C \rightarrow CH = CH_2 + HBr$
In Bohr's model of the atom, the radius of a hydrogen atom in the ground state is $r_1$ and the radius of a He+ ion in the ground state is $r_2$. Which of the following is correct?
Two wires $A$ and $B$ of the same length are made of the same material. The Load ($F$) vs. elongation ($x$) graph for these two wires is shown in the figure. Then which of the following statement(s) is/are true?
Two wires A and B of the same length are made of same material Load
A hemisphere of radius $R$ is placed in a uniform electric field $E$ so that its axis is parallel to the field. Which of the following statement(s) is/are true?
hemisphere of radius R is placed in a uniform electric field
As shown in the figure, a rectangular loop of length $a$ and width $b$ and made of a conducting material of uniform cross-section is kept in a horizontal plane where a uniform magnetic field of intensity $B$ is acting vertically downward. The resistance per unit length of the loop is $\lambda \, \Omega / m$. If the loop is pulled with uniform velocity $v$ in a horizontal direction, which of the following statement(s) is/are true?
rectangular loop of length 'a' and width 'b' and made of a conducting material of uniform cross-section
A sample of hydrogen atom in its ground state is radiated with photons of $10.2$ eV energies. The radiation from the sample is absorbed by excited ionized He+. Then which of the following statement(s) is/are true?
A particle is moving in the $x$-$y$ plane according to $r = b \cos \omega t \hat{i} + b \sin \omega t \hat{j}$. Where $\omega$ is constant. Which of the following statement(s) is/are true?
How many monobrominated product(s) (including stereoisomers) would form in the free radical bromination of n-butane?
The kinetic energy ($E_k$) of a particle moving along the X-axis varies with its position ($X$) as shown in the figure. The force acting on the particle at $X = 10$ m is
particle moving along the X-axis varies with its position
A particle is moving in an elliptical orbit as shown in the figure. If $p$, $L$, and $r$ denote the linear momentum, angular momentum, and position vector of the particle (from focus $O$) respectively at a point $A$, then the direction of $\alpha = p \times L$ is along
particle is moving in an elliptical orbit
One mole of an ideal monatomic gas expands along the polytrope $P V^3 = \text{constant}$ from $V_1$ to $V_2$ at a constant pressure $P_1$. The temperature during the process is such that molar specific heat $C_v = \frac{3R}{2}$. The total heat absorbed during the process can be expressed as
Three concentric metallic shells $A$, $B$, and $C$ of radii $a$, $b$, and $c$ have surface charge densities $+\sigma$, $-\sigma$, and $\sigma+$ respectively. The potential of shell $B$ is
Three concentric metallic shells
A horizontal semi-circular wire of radius $r$ is connected to a battery through two similar springs $X$ and $Y$ to an electric cell, which sends current $I$ through it. A vertically downward uniform magnetic field $B$ is applied on the wire, as shown in the figure. What is the force acting on each spring?
A horizontal semi-circular wire of radius
Find the equivalent capacitance between $A$ and $B$ of the following arrangement:
equivalent capacitance
A golf ball of mass $50$ gm placed on a tee is struck by a golf club. The speed of the ball as it leaves the tee is $100$ m/s, and the time of contact on the ball is $0.02$ s. If the force decreases to zero linearly with time, then the force at the beginning of the contact is
If the kinetic energies of an electron, an alpha particle, and a proton having the same de-Broglie wavelength are $\varepsilon_1, \varepsilon_2, \varepsilon_3$ respectively, then
In a Young's double slit experiment, the intensity of light at a point on the screen where the path difference between the interfering waves is $\lambda$ (where $\lambda$ is the wavelength of light used) is $1$. The intensity at a point where the path difference is $\frac{\lambda}{4}$ will be (assume two waves have the same amplitude)
A Zener diode having a breakdown voltage $V_z = 6$ V is used in a voltage regulator circuit as shown in the figure. The minimum current required to pass through the Zener to act as a voltage regulator is $10$ mA and the maximum allowed current through the Zener is $40$ mA. The maximum value of $R_\delta$ for Zener to act as a voltage regulator is
A Zener diode having a breakdown voltage
The expression $A(A + B) + (B + AA)(A + B)$ simplifies to
Suppose in a hypothetical world the angular momentum is quantized to be even integral multiples of $\frac{h}{2}$. The largest possible wavelength emitted by hydrogen atoms in the visible range in a world according to Bohr's model will be (consider $h_e = 1224$ MeV-fm)
Given: The percentage error in the measurements of A, B, C, and D are respectively 4%, 2%, 3%, and 1%. The relative error in $Z = \frac{A^4 B^{1/3}}{C D^{3/2}}$ is
The Entropy ($S$) of a black hole can be written as $S = \beta k_B A$, where $k_B$ is the Boltzmann constant and $A$ is the area of the black hole. Then $\beta$ has dimension of
A straight wire is placed in a magnetic field that varies with distance $x$ from origin as $B = B_0 (2 - \frac{x}{n}) \hat{k}$. The ends of the wire are at $(a, 0)$ and $(2n, 0)$ and it carries a current $I$. If the force on the wire is $F = 1 B_0 \left(\frac{k a}{2}\right) \hat{j}$, then the value of $k$ is
In a closed circuit there is only a coil of inductance $L$ and resistance $100\ \Omega$. The coil is situated in a uniform magnetic field. All of a sudden, the magnetic flux linked with the circuit changes by $5$ Weber. What amount of charge will flow in the circuit as a result?
An electron revolves around the nucleus in a circular path with angular momentum $L$. A uniform magnetic field $B$ is applied perpendicular to the plane of its orbit. If the electron experiences a torque $T$, then