List of top Questions asked in JEE Main

At what distance above and below the surface of the earth a body will have the same weight (take radius of earth as R)?

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A): Enthalpy of neutralisation of strong monobasic acid with strong monoacidic base is always –57 kJ mol^–1
Reason (R): Enthalpy of neutralisation is the amount of heat liberated when one mole of H⁺ ions furnished by acid combine with one mole of ^–OH ions furnished by base to form one mole of water. In the light of the above statements.
Choose the correct answer from the options given below.

If the constant term in the expansion of $(1 + 2x - 3x^3) \left(\frac{3}{2}x^2 - \frac{1}{3x}\right)^9$ is $ p $, then $ 108p $ is equal to _________.

The ratio of heat dissipated per second through the resistance 5 ohm and 10 ohm in the circuit given below is :

If $\vec{a}$ and $\vec{b}$ make an angle $\cos^{-1}\left(\frac{5}{9}\right)$ with each other, then \[ |\vec{a} + \vec{b}| = \sqrt{2} |\vec{a} - \vec{b}| \quad \text{for } |\vec{a}| = n |\vec{b}|. \] The integer value of $n$ is _____.

Functional group present in sulphonic acid is :

Match List-I with the List-II

List-I (Precipitating reagent and conditions)	List-II (Cation)
(A) $NH_4Cl + NH_4OH$	(I) Mn²⁺
(B) $NH_4OH + Na_2CO_3$	(II) Pb²⁺
(C) $NH_4OH + NH_4Cl + H_2S gas$	(III) Al³⁺
(D) dilute HCl	(IV) Sr²⁺

Choose the correct answer from the options given below:

Consider the circle $ C : x^2 + y^2 = 4 $ and the parabola $ P : y^2 = 8x $. If the set of all values of $ \alpha $, for which three chords of the circle $ C $ on three distinct lines passing through the point $ (\alpha, 0) $ are bisected by the parabola $ P $, is the interval $ (p, q) $, then $ (2q - p)^2 $ is equal to ________ .

A train is moving with a speed of 12 m/s on rails which are 1.5 m apart. To negotiate a curve radius of 400 m, the height by which the outer rail should be raised with respect to the inner rail is (Given, $ g = 10 \, \text{m/s}^2 $):

A square loop PQRS having 10 turns, area $3.6 \times 10^{-3} \, \text{m}^2$, and resistance $100 \, \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $B = 0.5 \, \text{T}$ as shown. Work done in pulling the loop out of the field in $1.0 \, \text{s}$ is ______ $ \times 10^{-6} \, \text{J} $.

$\lim\limits_{x→0} \frac {e^{|2sinx|}-2|sinx|-1}{x^2}$ is

Let $ \alpha \in (0, \infty) $ and $ A = \begin{bmatrix} 1 & 2 & \alpha \\ 1 & 0 & 1 \\ 0 & 1 & 2 \end{bmatrix} $. If $ \det(\text{adj}(2A - A^\top) \cdot \text{adj}(A - 2A^\top)) = 2^8 $, then $ (\det(A))^2 $ is equal to:

Let $A = \{1, 2, 3, 4, 5\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $4x \leq 5y$. Let $m$ be the number of elements in $R$ and $n$ be the minimum number of elements from $A \times A$ that are required to be added to $R$ to make it a symmetric relation. Then $m + n$ is equal to:

Let $ z $ be a complex number such that the real part of \[ \frac{z - 2i}{z + 2i} \] is zero. Then, the maximum value of $ |z - (6 + 8i)| $ is equal to:

A liquid drop of radius R is divided into 27 identical drops. If the surface tension of the drops is T, then find work done in this process.

If the domain of the function \[f(x) = \frac{\sqrt{x^2 - 25}}{(4 - x^2)} + \log_{10}(x^2 + 2x - 15)\]is $(-\infty, \alpha) \cup [\beta, \infty)$, then $\alpha^2 + \beta^3$ is equal to:

A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is:

A particle connected with light thread is performing vertical circular motion. Speed at point B (Lowermost point) is sufficient, so that it is able to complete its circular motion. Ignoring air friction, find the ratio of kinetic energy at A to that at B. (A being top-most point)

Let $ \alpha, \beta; \, \alpha > \beta $, be the roots of the equation $$ x^2 - \sqrt{2}x - \sqrt{3} = 0. $$ Let $ P_n = \alpha^n - \beta^n, \, n \in \mathbb{N} $. Then $$ \left( 11\sqrt{3} - 10\sqrt{2} \right) P_{10} + \left( 11\sqrt{2} + 10 \right) P_{11} - 11P_{12} $$ is equal to:

The number of elements in the set S = {(x, y, z) : x, y, z ∈ Z, x + 2y + 3z = 42, x, y, z ≥ 0} equals ____

If n is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then n is equal to:

A vernier callipers has 20 divisions on the vernier scale, which coincides with 19^th division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to ____mm.

If \[ f(x) = \begin{vmatrix} x^3 & 2x^2 + 1 & 1 + 3x \\ 3x^2 + 2 & 2x & x^3 + 6 \\ x^3 - x & 4 & x^2 - 2 \end{vmatrix} \] for all $ x \in \mathbb{R} $, then $ 2f(0) + f'(0) $ is equal to

A parallel plate capacitor of capacitance $ 12.5 \, \text{pF} $ is charged by a battery connected between its plates to a potential difference of $ 12.0 \, \text{V} $. The battery is now disconnected and a dielectric slab ($ \varepsilon_r = 6 $) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ______ $ \times 10^{-12} \, \text{J} $.

List-I (Precipitating reagent and conditions)	List-II (Cation)
(A) \(NH_4Cl + NH_4OH\)	(I) Mn²⁺
(B) \(NH_4OH + Na_2CO_3\)	(II) Pb²⁺
(C) \(NH_4OH + NH_4Cl + H_2S gas\)	(III) Al³⁺
(D) dilute HCl	(IV) Sr²⁺