List of top Questions asked in JEE Main

Let $ \vec{a} = 2\hat{i} - \hat{j} + \hat{k} $ and $ \vec{b} = \lambda \hat{j} + 2\hat{k} $, where $ \lambda \in \mathbb{Z} $, be two vectors. Let $ \vec{c} = \vec{a} \times \vec{b} $ and $ \vec{d} $ be a vector of magnitude $2$ in the $yz$-plane. If $ |\vec{c}| = \sqrt{53} $, then the maximum possible value of $ (\vec{c}\cdot\vec{d})^2 $ is equal to

The wavelength of photon 'A' is 400 nm. The frequency of photon 'B' is $10^{16}\,\text{s}^{-1}$. The wave number of photon 'C' is $10^{5}\,\text{cm}^{-1}$. The correct order of energy of these photons is:

The final product [B] is:

The value of \[ \sum_{k=1}^{\infty} (-1)^{k+1}\left(\frac{k(k+1)}{k!}\right) \] is:

Let $\alpha, \beta$ be the roots of the quadratic equation \[ 12x^2 - 20x + 3\lambda = 0,\ \lambda \in \mathbb{Z}. \] If \[ \frac{1}{2} \le |\beta-\alpha| \le \frac{3}{2}, \] then the sum of all possible values of $\lambda$ is

A biconvex lens is formed by using two plano-convex lenses as shown in the figure. The refractive index and radius of curvature of surfaces are also mentioned. When an object is placed on the left side of the lens at a distance of $30\,\text{cm}$, the magnification of the image will be:

The area of the region \[ A = \{(x,y) : 4x^2 + y^2 \le 8 \;\text{and}\; y^2 \le 4x\} \] is

Let a circle of radius $4$ pass through the origin $O$, the points $A(-\sqrt{3}a,0)$ and $B(0,-\sqrt{2}b)$, where $a$ and $b$ are real parameters and $ab\neq0$. Then the locus of the centroid of $\triangle OAB$ is a circle of radius

If the chord joining the points $ P_1(x_1, y_1) $ and $ P_2(x_2, y_2) $ on the parabola $ y^2 = 12x $ subtends a right angle at the vertex of the parabola, then $ x_1x_2 - y_1y_2 $ is equal to

The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are $ 2, 3, 5, 10, 11, 13, 15, 21 $, then the mean deviation about the median of all the 10 observations is:

An atom $ ^8_3X $ is bombarded by a shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleus is recorded by:

Given below are two statements:
Statement I: Sucrose is dextrorotatory. However, sucrose upon hydrolysis gives a solution having mixture of products. This solution shows laevorotation.
Statement II: Hydrolysis of sucrose gives glucose and fructose. Since the laevorotation of glucose is more than the dextrorotation of fructose, the resulting solution becomes laevorotatory.
In the light of the above statements, choose the correct answer from the options given below.

A thin prism with angle 5° of refractive index 1.72 is combined with another prism of refractive index 1.9 to produce dispersion without deviation. The angle of second prism is :

Let \[ A=\{z\in\mathbb{C}:|z-2|\le 4\} \quad\text{and}\quad B=\{z\in\mathbb{C}:|z-2|+|z+2|=5\}. \] Then the maximum value of $|z_1-z_2|$, where $z_1\in A$ and $z_2\in B$, is:

The formal charges on the atoms marked as (1) to (4) in the Lewis representation of $ \mathrm{HNO_3} $ molecule respectively are

Let $a_1,a_2,a_3,a_4$ be an A.P. of four terms such that each term of the A.P. and its common difference are integers. If $a_1+a_2+a_3+a_4=48$ and $a_1^2a_2a_3a_4+1^4=361$, then the largest term of the A.P. is equal to

Given below are two statements: Statement I: The increasing order of boiling point of hydrogen halides is HCl<HBr<HI<HF. Statement II: The increasing order of melting point of hydrogen halides is HCl<HBr<HF<HI. In the light of the above statements, choose the correct answer from the options given below:

A student is given one compound among the following compounds that gives positive test with Tollen's reagent. The compound is:

The heat generated in 1 minute between points A and B in the given circuit, when a battery of 9 V with internal resistance of 1 $\Omega$ is connected across these points is ______ J.

Let \[ f(x)=\int \frac{dx}{2\left(\frac{3}{2}\right)^x+2x\left(\frac12\right)^x} \] such that $f(0)=-26+24\log_e(2)$. If $f(1)=a+b\log_e(3)$, where $a,b\in\mathbb{Z}$, then $a+b$ is equal to:

For some $\alpha, \beta \in R$, let $A = \begin{pmatrix} \alpha & 2 \\1 & 2 \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 1 \\ \beta & 1 \end{pmatrix}$ be such that $A^2-4A+2I-B^2-3B+I=O$. Then $(\det(\text{adj}(A^3-B^3)))^2$ is equal to:

Initially a satellite of 100 kg is in a circular orbit of radius 1.5$R_E$. This satellite can be moved to a circular orbit of radius 3$R_E$ by supplying $a \times 10^6$ J of energy. The value of a is_________ . (Take Radius of Earth $R_E = 6 \times 10^6$ m and g = 10 m/s$^2$).

If \[ \int e^x \left( \frac{x^2 - 2}{\sqrt{1 + x(1 - x)^{3/2}}} \right) \, dx = f(x) + c \quad \text{and} \quad f(0) = 1 \] find $ f\left( \frac{1}{2} \right) $:

Let $R$ be a relation defined on the set $\{1,2,3,4\times\{1,2,3,4\}$ by \[ R=\{((a,b),(c,d)) : 2a+3b=3c+4d\} \] Then the number of elements in $R$ is

By usual analysis, 1.00 g of compound (X) gave 1.79 g of magnesium pyrophosphate. The percentage of phosphorus in compound (X) is : _________ (nearest integer)
(Given, molar mass in g mol$^{-1}$ ; O = 16, Mg = 24, P = 31)}