List of top Questions asked in JEE Main

A solid sphere of mass $5$ kg and radius $10$ cm is kept in contact with another solid sphere of mass $10$ kg and radius $20$ cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is ___________ kg$\cdot$m$^2$.

Consider the following statements for [Ni(dmg)$_2$]: (A) It is a red coloured compound.
(B) It is readily soluble in water at pH = 9.
(C) Central metal ion has two unpaired electrons.
(D) It has four, 5-membered metal containing rings.

1 mole of He and 1 mole A are taken in a 10 L rigid container at 400 K, and equilibrium \( A \rightleftharpoons B \) is established. Calculate the partial pressure of He and B at equilibrium if \( K_c = 4 \).

In a microscope of tube length $10\,\text{cm}$ two convex lenses are arranged with focal lengths $2\,\text{cm}$ and $5\,\text{cm}$. Total magnification obtained with this system for normal adjustment is $(5)^k$. The value of $k$ is ___.

If \[ \lim_{x\to 0} \frac{e^{(a-1)x}+2\cos bx+(c-2)e^{-x}} {x\cos x-\log_e(1+x)} =2, \] then \(a^2+b^2+c^2\) is equal to

Let \( A = \{1, 2, 3, 4, 5\} \) and \( B = \{a, b, c\} \). Then the number of functions which are not onto are:

A solution contains 0.25 moles of non-volatile solute dissolved in one mole of solvent. Then calculate the % vapor pressure of solution relative to the vapor pressure of pure solvent.

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.

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_____.

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 :

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

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.

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 :