List of top Questions asked in JEE Main

The distance of the point P(1,2,3) P(1, 2, 3) from the plane 3x−4y+12z−7=0 3x - 4y + 12z - 7 = 0 is:

Match the following List-I with List-II and choose the correct option: List-I (Compounds) | List-II (Shape and Hybridisation) (A) PF3_{3} (I) Tetrahedral and sp3^3 (B) SF6_{6} (III) Octahedral and sp3^3d2^2 (C) Ni(CO)4_{4} (I) Tetrahedral and sp3^3 (D) [PtCl4_{4}]2−^{2-} (II) Square planar and dsp2^2

Let A be a 3 × 3 matrix such that det(A)=5\text{det}(A) = 5. If det(3 adj(2A))=2α⋅3β⋅5γ\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}, then (α+β+γ) (\alpha + \beta + \gamma) is equal to:

The sum of all rational numbers in (2+3)8 (2 + \sqrt{3})^8 is:
If the sum, ∑r=19r+32r⋅(9r) \sum_{r=1}^9 \frac{r+3}{2r} \cdot \binom{9}{r} is equal to α⋅(32)9−β \alpha \cdot \left( \frac{3}{2} \right)^9 - \beta , then the value of (α+β)2 (\alpha + \beta)^2 is equal to:
An ideal gas with an adiabatic exponent 1.5, initially at 27°C is compressed adiabatically from 800 cc to 200 cc. The final temperature of the gas is:
Order of limiting molar conductivities of these cations at 298 K is:
Which of the following has the highest atomic number?
Which of the following ions shows spin only magnetic moment of 4.9 B.M.?
The electrostatic potential on the surface of a uniformly charged spherical shell of radius R=10 cm R = 10 \, \text{cm} is 120 V. The potential at the centre of the shell, at a distance 5 cm from the centre, and at a distance 15 cm from the centre of the shell are:
A particle is released from height ss above the surface of the earth. At a certain height its K.E is 3 times of P.E. The height from the surface of the earth and the speed of the particle at the instant are respectively:

If dydx+2ysec⁡2x=2sec⁡2x+3tan⁡x⋅sec⁡2x \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x and

and f(0)=54 f(0) = \frac{5}{4} , then the value of 12(y(π4)−1e2) 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) equals to:

If α+iβ \alpha + i\beta and γ+iδ \gamma + i\delta are the roots of the equation x2−(3−2i)x−(2i−2)=0 x^2 - (3-2i)x - (2i-2) = 0 , i=−1 i = \sqrt{-1} , then αγ+βδ \alpha\gamma + \beta\delta is equal to:
What are the units of viscosity, intensity of wave, and pressure gradient?
If the system of equations (λ−1)x+(λ−4)y+λz=5 (\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 λx+(λ−1)y+(λ−4)z=7 \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 (λ+1)x+(λ+2)y−(λ+2)z=9 (\lambda + 1)x + (\lambda + 2)y - (\lambda + 2)z = 9 has infinitely many solutions, then λ2+λ \lambda^2 + \lambda is equal to:
Let the parabola y=x2+px−3y = x^2 + px - 3 meet the coordinate axes at the points P, Q and R. If the circle C with centre at (-1, -1) passes through the points P, Q and R, then the area of △PQR\triangle PQR is:
If y=y(x) y = y(x) is the solution of the differential equation, 4−x2dydx=((sin⁡−1(x2))2−y)sin⁡−1(x2), \sqrt{4 - x^2} \frac{dy}{dx} = \left( \left( \sin^{-1} \left( \frac{x}{2} \right) \right)^2 - y \right) \sin^{-1} \left( \frac{x}{2} \right), where −2≤x≤2 -2 \leq x \leq 2 , and y(2)=π2−84 y(2) = \frac{\pi^2 - 8}{4} , then y2(0) y^2(0) is equal to:

If the domain of the function f(x)=13x+10−x2+1x+∣x∣ f(x) = \frac{1}{\sqrt{3x + 10 - x^2}} + \frac{1}{\sqrt{x + |x|}} is (a,b) (a, b) , then (1+a)2+b2 (1 + a)^2 + b^2 is equal to:

Statement-I: Melting point of neopentane is greater than that of n-pentane.
Statement-II: Neopentane gives only one mono-substituted product.
The domain of the function f(x)=110+3x−x2+1x+∣x∣ f(x) = \frac{1}{\sqrt{10 + 3x - x^2}} + \frac{1}{\sqrt{x + |x|}} is (a,b) (a, b) . Then (1+a2)+b2 (1 + a^2) + b^2 is:
Two water drops each of radius r r coalesce to form a bigger drop. If T T is the surface tension, the surface energy released in this process is:
If θ∈[−7π6,4π3] \theta \in \left[ -\frac{7\pi}{6}, \frac{4\pi}{3} \right] , then the number of solutions of the equation 3csc⁡2θ−2(3−1)csc⁡θ−4=0 \sqrt{3} \csc^2 \theta - 2 (\sqrt{3} - 1) \csc \theta - 4 = 0 is:
If lim⁡x→0cos⁡(2x)+acos⁡(4x)−bx4 \lim_{x \to 0} \frac{\cos(2x) + a \cos(4x) - b}{x^4} is finite, then a+b= a + b = __.
A particle moves on a circular path of radius 1 m. Find its displacement when it moves from A→B→A A \rightarrow B \rightarrow A . Also, its distance are it moves from A→B→A A \rightarrow B \rightarrow A .
The moment of inertia of a ring of mass M M and radius R R about an axis passing through a tangential point in the plane of ring is: