List of top Questions asked in JEE Main

The temperature of a metal strip having coefficient of linear expansion $\alpha$ is increased from $T_1$ to $T_2$ resulting in increase of its length by $\Delta L_1$. The temperature is further increased from $T_2$ to $T_3$ such that the increase in its length is $\Delta L_2$.
Given $T_3 + T_1 = 2T_2$ and $T_2 - T_1 = \Delta T$, the value of $\Delta L_2$ is ________.

If $x$ and $y$ coordinates of a projectile as a function of time $(t)$ are given as $24t$ and $43.6t - 4.9t^2$, respectively, then the angle (in degrees) made by the projectile with horizontal when $t = 2$ s is _______.

A water spray gun is attached to a hose of cross sectional area $30 \text{ cm}^2$. The gun comprises of 10 perforations each of cross sectional area of $15 \text{ mm}^2$. If the water flows in the hose with the speed of 50 cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because:
A. The size of gold nucleus is very small as compared to the size of gold atom.
B. Alpha particle and gold nucleus have equal charge.
C. The impact parameter is minimum for a few alpha particles.
D. A few alpha particles have very high kinetic energy.
E. Only a few alpha particles undergo head-on collision with the nuclei.
Choose the correct answer from the options given below:

The de Broglie wavelength associated with an electron accelerated through a potential difference V is \( \lambda_e \) and the de Broglie wavelength associated with a proton accelerated through the same potential difference is \( \lambda_p \). If their corresponding masses are \( m_e \) and \( m_p \), respectively, then the ratio of their de Broglie wavelengths \( \frac{\lambda_e}{\lambda_p} \) is:

A uniform disc of radius $R$ and mass $M$ is free to oscillate about the axis A as shown in the figure. For small oscillations the time period is _______.
(g is acceleration due to gravity)

A diode has Zener voltage of 10 V and maximum power dissipation of 0.5 W, then the minimum resistance to be used in series with this diode for safety when it is connected to a 25 V power supply is _______ \(\Omega\).

At $t = 0$, a body of mass 100 g starts moving under the influence of a force $(5\hat{i} + 10\hat{j})$ N. After 2 s its position is $(2x\hat{i} + 5y\hat{j})$ m. The ratio $x : y$ is______.

A circular coil of radius 2 cm and 125 turns carries a current of 1 A. The coil is placed in a uniform magnetic field of magnitude 0.4 T. The axis of the coil makes an angle of \( 30^\circ \) with the direction of the magnetic field. The torque acting on the coil is \( \alpha \times 10^{-4} \text{ N.m} \). The value of \( \alpha \) is _______. (\( \pi = 3.14 \))

From the circuit given below, the capacitance between terminals A and B shown in the circuit is _______ $\mu\text{F}$.
(take $C_1 = C_2 = C_3 = 1 \mu\text{F}$ and $C_4 = 2 \mu\text{F}$.)

A solenoid has a core made of material with relative permeability 400. The magnetic field produced in the interior of solenoid is 1.0 T. The magnetic intensity in SI units is $\alpha \times 10^5$. The value of $\alpha$ is ________.
(Free space permeability $\mu_0 = 4\pi \times 10^{-7}$ SI units.)

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

In the hydrogen atom, the electron makes a transition from the higher orbit ($i$) to a lower orbit ($f$). The ratio of the radius of the orbits in given by $r_i : r_f = 16 : 4$. The wavelength of photon emitted due to this transition is _________ nm. (Given Rydberg constant $= 1.097 \times 10^7 \text{ /m}$)

$L, C$ and $R$ represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula $M L^2 T^{-4} A^{-2}$ corresponds to _________.

A wedge $Y$ with mass of 10 kg and all frictionless surfaces and the inclined surface making $37^\circ$ with horizontal. A block $X$ with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At $t = 0$ wedge ($Y$) is pulled toward right with constant force ($f$) of 24 N. Taking the block $X$ at rest at $t = 0$, the time taken by it to slide down 8.8 m on the slope, while $Y$ is on the move, is ________s.

(take $\tan (37^\circ) = 3/4$ and $g = 10 \text{ m/s}^2$)

Two wires as shown in the figure below, made of steel and have breaking stress of $12 \times 10^8 \text{ N/m}^2$. Area of cross-section of upper wire is $0.008 \text{ cm}^2$ and of lower wire is $0.004 \text{ cm}^2$. The maximum mass that can be added to pan without breaking any wire is _________ kg. (take $g = 10 \text{ m/s}^2$)}

The Young's modulus of steel wire of radius $r$ and length $L$ is $Y$. If the radius $r$ and length $L$ of the wire are doubled then the value of $Y$:

From \(18 \text{ m}\) height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ____ \text{m}. (Take \(g = 10 \text{ m/s}^2\) and neglect air resistance)}

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and $7^{th}$ Vernier division coincides with a main scale reading. If the value of 1 main scale division is 1 mm and there are 10 Vernier scale divisions, then the Vernier caliper has:

An electron of mass $m$ is moving in an electric field $\vec{E} = -2E_0 \hat{i}$ ($E_0 = \text{constant}>0$), with an initial velocity $\vec{v} = v_0 \hat{i}$ ($v_0 = \text{constant}>0$). If $\lambda_0 = \frac{h}{4mv_0}$, its de Broglie wavelength at time $t$ is:

For the given logic circuit, which of the following inputs combination will make both LED-1 and LED-2 to glow?}

Refer to the figure given below, current between terminals $A$ and $B$ is _____}

Three masses $m_1 = 4$ kg, $m_2 = 4$ kg and $m_3 = 6$ kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of $T_1/T_2$ is: (take $g = 10 \text{ m/s}^2$)}

The charged particle moving in a uniform magnetic field of \((3\hat{i} + 2\hat{j}) \text{ T}\) has an acceleration \((4\hat{i} - \frac{x}{2}\hat{j}) \text{ m/s}^2\). The value of \(x\) is ____.

A cube has side length \(5 \text{ cm}\) and modulus of rigidity \(10^5 \text{ N/m}^2\). The displacement produced by a force of \(10 \text{ N}\) in the upper face of the cube is ____ \text{mm}.