List of top Questions asked in JEE Main

If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar, then the product of all possible values of λ is :

The statement (p∧q) ⇒ (p∧r) is equivalent to :

Given below are two statements.
Statement-I: Stannane is an example of a molecular hydride.
Statement-II: Stannane is a planar molecule
In the light of the above statement, choose the most appropriate answer from the options given below.

In liquation process used for tin (Sn), the metal

Let
$\begin{array}{l} f\left(x\right)=3^{\left(x^2-2\right)^3+4},x\in \mathbb{R}.\end{array}$
Then which of the following statements are true?
P : x = 0 is a point of local minima of f
Q : x = √2 is a point of inflection of f
R : f ′ is increasing for x > √2

Let $\vec{a} = 3\hat{i} + \hat{j}$ and $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$.
Let $\vec{c}$ be a vector satisfying $\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + \lambda \vec{c}$
If $\vec{b}$ and $\vec{c}$ are non-parallel, then the value of $λ$ is

Two identical thin metal plates has charge q₁ and q₂ respectively such that q₁ > q₂. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is

A 1 m long wire is broken into two unequal parts X and Y. The X part of the wire is stretched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.

The angle of elevation of the top of a tower from a point A due north of it is α and from a point B at a distance of 9 units due west of A is $\cos^{-1}\left(\frac{3}{\sqrt{13}}\right)$
If the distance of the point B from the tower is 15 units, then cot α is equal to :

Let$ A(1, 1), B(-4, 3) $and $C(-2, -5)$ be vertices of a triangle ABC, P be a point on side BC, and $Δ1$ and $Δ2$ be the areas of triangles APB and ABC, respectively. If $Δ1 : Δ2 = 4 : 7$, then the area enclosed by the lines AP, AC and the x-axis is

Let a vertical tower AB of height 2h stands on a horizontal ground. Let from a point P on the ground a man can see up to height h of the tower with an angle of elevation 2α.
When from P, he moves a distance d in the direction of $\overrightarrow{AP}$.
he can see the top B of the tower with an angle of elevation α. if $d = \sqrt7$ h, then tan α is equal to

Which of the following 3d-metal ion will give the lowest enthalpy of hydration (Δ_hydH) when dissolved in water?

A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire Y of length 5 m. The wire Y carries a current of 3 A. The distance between two wires is 5 cm and currents flow in the same direction. The force acting on the wire Y is

A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire Y of length 5 m

An unpolarised light beam of intensity 2I₀ is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of 30° relative to that of P. The intensity of the emergent light is

Given below are the quantum numbers for 4 electrons.
A. n=3, l=2, ml=1,m_s=+$\frac{1}{2}$
B. n=4, l=1, ml=0,m_s=+$\frac{1}{2}$
C. n=4, l=2, ml=–2,m_s=–$\frac{1}{2}$
D. n=3, l=1, ml=–1,m_s=+$\frac{1}{2}$
The correct order of increasing energy is

Let $S = \{θ ∈ (0, 2π) : 7 cos^2θ – 3 sin^2θ – 2 cos^22θ = 2\}$.
Then, the sum of roots of all the equations $x^2 – 2 (tan^2θ + cot^2θ) x + 6 sin^2θ = 0, θ ∈ S$, is _______.

C(s)+O₂(g)→CO₂(g)+400 kJ
C(s)+$\frac{1}{2}$ O₂(g)→CO(s)+100 kJ
When coal of purity 60% is allowed to burn in presence of insufficient oxygen, 60% of carbon is converted into ‘CO’ and the remaining is converted into ‘CO₂’. The heat generated when 0.6 kg of coal is burnt is _______.

The number of points, where the function $f: \mathbb{R} \to \mathbb{R}$, $$ f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|, $$ is NOT differentiable, is

Given below are the critical temperatures of some of the gases :

Gas	Critical temperature (K)
He	5.2
CH₄	190.0
CO₂	304.2
NH₃	405.5

The gas showing least adsorption on a definite amount of charcoal is

Let $\hat a$ and $\hat b$ be two unit vectors such that the angle between them is $\frac{\pi}{4}$. If θ is the angle between the vectors ($\hat a$+$\hat b$) and ($\hat a$+2$\hat b$+2($\hat a$×$\hat b$)), then the value of 164 cos²θ is equal to :

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

A thermodynamic system is taken from an original state D to an intermediate state

A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity x√F rad s⁻¹. If F be the force exerted by the liquid at the other end then the value of x will be______.

Let $A = \begin{bmatrix} 0 & -2 \\[0.3em] 2 & 0 \end{bmatrix}$. If $M$ and $N$ are two matrices given by $M = \displaystyle\sum_{k=1}^{10} A^{2k}$ and $N = \displaystyle\sum_{k=1}^{10} A^{2k-1}$
then $MN^2 $ is :

If
$\begin{array}{l}\sum_{K=1}^{10}K^2\left(^{10}C_K\right)^2 = 22000L,\end{array}$then L is equal to _____.

$\begin{array}{l}\text{Let}~\vec{a} = \alpha \hat{i} + \hat{j} + \beta \hat{k}~\text{and}~ \vec{b} = 3 \hat{i} + 5\hat{j} + 4 \hat{k}~ \text{be two vectors, such that }\vec{a} \times \vec{b} = -\hat{i} + 9\hat{j} + 12 \hat{k}.\end{array}$
$\begin{array}{l}~\text{Then the projection of } \vec{b}-2\vec{a} ~\text{on}~ \vec{b}+ \vec{a}~\text {is equal to}\end{array}$