List of top Questions asked in JEE Main

A screw gauge has a pitch of 0.1 mm and 100 divisions on its circular scale. When its both jaws touch, the fifth division of its circular scale coincides with zero. When a sphere is placed between the jaws, the reading of the linear scale is 5 mm and the 50th division of the circular scale coincides with zero of the main scale. Find the diameter of the sphere.

Which of the following pair of species have different Lewis structures? (A) $ \mathrm{SO_3^{2-}, CO_3^{2-}} $
(B) $ \mathrm{O_2^{2-}, F_2} $
(C) $ \mathrm{CN^- , CO} $
(D) $ \mathrm{NH_3, H_3O^+} $
(E) $ \mathrm{MnO_4^- , CrO_4^{2-}} $

The number of distinct real solutions of the equation \[ x|x + 4| + 3|x + 2| + 10 = 0 \] is

The maximum rated power of the LED is $2 \text{ mW}$ and it is used in the circuit with input voltage of $5 \text{ V}$ as shown in the figure below. The current through resistance $R$ is $0.5 \text{ mA}$. The minimum value of the resistance $R_s$, to ensure that the LED is not damaged is ______ $\text{k}\Omega$.

In the provided circuit, the input voltage is $5 \text{ V}$, a series resistor $R_s$ is connected, and the circuit then branches into two parallel paths: one with a resistor $R = 1 \text{ k}\Omega$ in series with a Zener diode, and another with the LED.

Find speed given to particle at lowest point so that tension in string at point A becomes zero.

A light wave described by E = 60[$\sin(3 \times 10^{15})t + \sin(12 \times 10^{15})t$] (in SI units) falls on a metal surface of work function 2.8 eV. The maximum kinetic energy of ejected photoelectron is (approximately)________ eV. (h=$6.6 \times 10^{-34}$ J.s. and e=$1.6 \times 10^{-19}$ C)

The pairs among $A = [SO_3^{2-}, CO_3^{2-}]$, $B = [O_2^-, F_2]$, $C = [CN^-, CO]$, $D = [NH_3, H_3O^+]$ and $E = [MnO_4^-, CrO_4^{2-}]$ that do not have similar Lewis dot structure are

In a microscope, the objective has a focal length $f_o=2$ cm and the eye-piece has a focal length $f_e=4$ cm. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is_____.

Identify the total number of surfaces in the given 3D object.

Given below are two statements:
Statement I: [CoBr₄]²⁻ ion will absorb light of lower energy than [CoCl₄]²⁻ ion.
Statement II: In [CoBr₄]²⁻ ion, the energy separation between the two set of d-orbitals is more than [CoCl₄]²⁻ ion.
In the light of the above statements, choose the correct answer from the options given below :

Find out the statements which are not true.
A. Resonating structures with more covalent bonds and less charge separation are more stable.
B. In electromeric effect, an unsaturated system shows +E effect with nucleophile and –E effect with electrophile.
C. Inductive effect is responsible for high melting point, boiling point and dipole moment of polar compounds.
D. The greater the number of alkyl groups attached to the doubly bonded carbon atoms, higher is the heat of hydrogenation.
E. Stability of carbanion increases with increase in s-character of the carbon carrying negative charge.

The correct order of the rate of the reaction for the following reaction with respect to nucleophiles is :
$ CH_3Br + Nu^\ominus \rightarrow CH_3Nu + Br^\ominus $

Consider the following reaction:

The product $Y$ formed is:

Given below are some of the statements about Mn and $ Mn_2O_7 $. Identify the correct statements.
A. Mn forms the oxide $ Mn_2O_7 $, in which Mn is in its highest oxidation state.
B. Oxygen stabilizes the Mn in higher oxidation states by forming multiple bonds with Mn.
C. $ Mn_2O_7 $ is an ionic oxide.
D. The structure of $ Mn_2O_7 $ consists of one bridged oxygen.
Choose the correct answer from the options given below :

The correct stability order of the following diazonium salts is:

Choose the correct answer from the options given below:

The oxidation state of chromium in the final product formed in the reaction between KI and acidified $K_2Cr_2O_7$ solution is:

A 1 m long metal rod AB completes the circuit as shown in figure. The area of circuit is perpendicular to the magnetic field of 0.10 T. If the resistance of the total circuit is 2 $\Omega$ then the force needed to move the rod towards right with constant speed (v) of 1.5 m/s is _____ N.

Consider an equilateral prism (refractive index $ \sqrt{2} $). A ray of light is incident on its one surface at a certain angle $ i $. If the emergent ray is found to graze along the other surface, then the angle of refraction at the incident surface is close to

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are $2.4 \times 10^8$ m/s and $2.7 \times 10^8$ m/s, respectively, then the value of critical angle is :

For a transparent prism, if the angle of minimum deviation is equal to its refracting angle, the refractive index $n$ of the prism satisfies:

There are three co-centric conducting spherical shells $A$, $B$ and $C$ of radii $a$, $b$ and $c$ respectively $(c>b>a)$ and they are charged with charges $q_1$, $q_2$ and $q_3$ respectively. The potentials of the spheres $A$, $B$ and $C$ respectively are:

A meter bridge with two resistances $ R_1 $ and $ R_2 $ as shown in figure was balanced (null point) at 40 cm from the point $ P $. The null point changed to 50 cm from the point $ P $, when a $ 16\,\Omega $ resistance is connected in parallel to $ R_2 $. The values of resistances $ R_1 $ and $ R_2 $ are

A Wheatstone bridge is initially at room temperature and all arms of the bridge have same value of resistances \[ (R_1=R_2=R_3=R_4). \] When $R_3$ resistance is heated, its resistance value increases by $10%$. The potential difference $(V_a-V_b)$ after $R_3$ is heated is _______ V.

The speed of a longitudinal wave in a metallic bar is $400\,\text{m/s}$. If the density and Young’s modulus of the bar material increase by $0.5%$ and $1%$ respectively, then the speed of the wave is changed approximately to _______ m/s.

An infinitely long straight wire carrying current $I$ is bent in a planar shape as shown in the diagram. The radius of the circular part is $r$. The magnetic field at the centre $O$ of the circular loop is :