List of top Questions asked in JEE Main

If C1: (x-α)² +(y-β)² =r₁², c₂: (x-6)²+ (y - 15/2)² = r₂² touches each other at (6, 6). If line joining centres of c₁ & C₂ is divided by (6, 6) in 2: 1 internally, then (α + β) + 4(r₁² +r₂²) is equal to:

If |a| = 2, |b| = 3 and a = b × 2, then minimum value of $|\hat{c} - a|^2$ is:

$I(x)=\int\frac{6dx}{sin^2x(1+\cot x)^2}$and I(0) then I ($\frac{\pi}{2}$) is equal to

Two lines passing through (2, 3) parallel to coordinate axes. A circle of unit radius touches both the lines and lies on the origin side. Then the shortest distance of point (5,5) from the circle is:

The value of

lim_{x \to 0} \frac{\int_{0}^{x^{2}} \sec^{2} t d t}{x \sin x}

is

Let p, q and r be three mutually perpendicular vectors of the same magnitude. If a vector x satisfies equation p x {(x - q) x p} + q x {(x - r) x r} + r x {(x - p) x r} = 0, then x is given by

Let $y=y(x)$ be the solution of the differential equation $\left(x^2-3 y^2\right) d x+3 x y d y=0, y(1)=1$.Then $6 y^2( e )$ is equal to

The general solution of

\cot θ + \tan θ = 2

Bag X contains five one-rupee coins, four five rupee coins. Bag Y contains 4 one rupee and 5 five rupees. Bag Z contains 3 one-rupee coins and 6 five rupee coins. If 1 rupee coin is selected at random, what is the probability it is drawn from bag Y?

If the orthocentre of triangle formed by (8, 3), (5, 1) and (h, k) is (6, 1), then (h, k) lie on

$\lim\limits_{n\rightarrow \infin}\frac{\sum(n^4-2n^3+n^2)}{\sum ((3n)^4+n^3-n^2)}$ is equal to

If the system of linear equations $ 8 x+y+4 z=-2 $, $ x+y+z=0 $, $ \lambda x-3 y=\mu$ has infinitely many solutions, then the distance of the point $\left(\lambda, \mu,-\frac{1}{2}\right)$ from the plane $8 x + y +4 z +2=0$ is :

Chemical formula of compound present in tooth enamel?

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The diameter of colloidal particles in solution should not be much smaller than wavelength of light to show Tyndall effect.
Reason R : The light scatters in all directions when the size of particles is large enough.
In the light of the above statements, choose the correct answer from the options given below

Identify the correct Lewis dot structure of NO^-₂.

Ba+2 cannot be precipitated as?

X ⇌ Y;K₁ = 1
Y ⇌ Z; K₂ = 2
Z ⇌ W; K₃ = 4
Find K_eq for X ⇌ W

Which of the following has sp² hybridisation?

What happens when methane undergoes combustion in systems A and B respectively?

CoCl₃.xNH₃ on reaction with excess AgNO₃(aq.) gives two moles of AgCl as precipitate.
Summation of oxidation state of Co in CoCl₃.xNH₃ and x is:

The correct increasing order of the magnitude of standard enthalpies of formation for group-1 halides is?

A wave is given by the equation y= Asin{ π(330t-x) },then frequency of the wave is

A person covers the first half of the distance with 6 m/s and the rest half with 9 m/s and 15 m/s in two equal time intervals. Find the average speed of the journey.

A particle oscillates in simple harmonic motion such that its speed and acceleration at distance 2 m from mean position are 4 m/s and 16 m/s² respectively. Find the amplitude of oscillation of the particle.

A solenoid of 10 turns cross section area 36 cm² and of resistance 10 mΩ is placed in a magnetic field which is varying at a constant rate of 0.5 T/sec. Find power of heat dissipation.