List of top Questions asked in JEE Main

Two points (5, 2) and (2, a). Line passes through these points makes an angle of π/4 at origin. The product of all values of a is equal to

A triangle is drawn inside a bounded region of y² = 2x and x = 24. Then maximum area of triangle is

If |x + 1||x + 3| – 4|x + 2| + 5 = 0, then sum of squares of solutions is

If solution of differential equation xdy - ydx = xy(xdy - ydx) and y(1) = 1 is α|y| = |x|e^{(xy - β)} then (α + β) is equal to

If the complex number (1 + 2i cosθ) / (1 - 3i cosθ) is purely imaginary, then find the number of values of θ in the interval [-2π, 2π].

Given \(f(x) =   \begin{cases}     \frac{tan((a+1)x)+tanx\cdot b}{x}       & \quad x\lt 0\\     3  & \quad x=0\\ \frac{\sqrt{ax+b^2x^2}-\sqrt{ax}}{\sqrt{a}bx\sqrt{x}}  & \quad x\gt 0\end{cases}\) It is a continuous function at x=0, then find \(\frac{b}{a}\)

Molecular orbital σ* represents:

Velocity of a particle of mass m as a function of displacement x is given by v = ɑ√x. Work done to move it from x = 0 to x = d is:

Two persons are pulling a rope towards themselves with a force of 200 N each. If the Young's modulus is 2 x 10¹¹ N/m² and area of cross-section is 2 cm² for the rope, the elongation in the rope is ____.
(distance between the persons holding the ropes is 2 m.)

Assertion (A): Object at radius of curvature of biconvex lens made by glass (u = 1.5) form image at same distance an other side of the lens.
Reason (R): Image of a real object formed by concave lens is always virtual and erect.

Find the equivalent resistance between terminal A and B for the given network.

Consider the following electronic configuration:
Cu²⁺ = [Ar] 3d⁴4s⁰
Cu⁺ = [Ar] 3d¹⁰4s⁰
Which option is correct?

Consider the following compound.

Correct order of their basicity is:

Which of the following is colorless?

Which among the following have a single unpaired electron?
N₂, 0₂, CN^-, O₂^-, C₂^2- , N^2-

S-I: Sulphur exists as S8 while oxygen exists as O2.
S-II: In oxygen, pπ-pπ bonding occurs while it is not effective in sulphur.

Consider the reaction between PbS and HNO₃.
PbS + HNO₃ →
Which of the following is not formed.

A ray of light passing through (1, 2) after reflecting on x-axis at point Q passes through R(3, 4). If S(h, k) is such that PQRS is a parallelogram, then find the value of hk².

A, B and C are given as
A = αî + 4j + 5k
B = 2î + 5j + 6k
C=A+B
|C| = | A - B |
Find the value of α and |C|² is:

If set A = { z: |z - 1| ≤ 1} and set B = { z: |z - 5i| ≤ |z - 5| }, if z = a + ib, where a, b ∈ I, then find the sum of modulus squares of A ∩ B.

What will be the remainder when (428)²⁰²⁴ is divided by 21?

If A is 3 x 3 matrix, det(3adj (2 adj A)) = 2^-13. 3^-10 and det(3adj (2A)) = 2^-m. 3^-n, then find 2m + 2n.d by 21?

If f(x) = 3ax³ + bx² + cx + 1 and f(1) = 41, f'(1) = 2 and f''(2)= 4, then find (a² + b² + c²).

If the domain of \(f(x)=\sin^{-1}(\frac{x-1}{2x+3})\) is R – (α, β] then find the value of 12αβ.

A = {2,4,6,8}, B = {3,7,6,9}. R: A × B → A × B such that (a₁, b₁) R (a₂, b₂) ⇔ a₁ + a₂ = b₁ + b₂ where (a₁, b₁) ∈ A, (a₂, b₂) ∈ B. Find the number of elements in the relation.2)= 4, then find (a² + b² + c²).