List of top Questions asked in JEE Main

Two balls with the same mass and initial velocity are projected at different angles in such a way that the maximum height reached by the first ball is 8 times higher than that of the second ball. $ T_1 $ and $ T_2 $ are the total flying times of the first and second ball, respectively, then the ratio of $ T_1 $ and $ T_2 $ is:

Let the range of the function \[ f(x) = 6 + 16 \cos x \cdot \cos\left(\frac{\pi}{3} - x\right) \cdot \cos\left(\frac{\pi}{3} + x\right) \cdot \sin 3x \cdot \cos 6x, \quad x \in R \text{ be } [\alpha, \beta]. \] Then the distance of the point $(\alpha, \beta)$ from the line $3x + 4y + 12 = 0$ is:

Identify the correct statement among the following:

The motion of an airplane is represented by the velocity-time graph as shown below. The distance covered by the airplane in the first 30.5 seconds is km.

The value of $ \cot^{-1} \left( \frac{\sqrt{1 + \tan^2(2)} - 1}{\tan(2)} \right) - \cot^{-1} \left( \frac{\sqrt{1 + \tan^2 \left( \frac{1}{2} \right)} + 1}{\tan \left( \frac{1}{2} \right)} \right) $ is equal to:

Let $ |z_1 - 8 - 2i| \leq 1 $ and $ |z_2 - 2 + 6i| \leq 2 $, where $ z_1, z_2 \in \mathbb{C} $. Then the minimum value of $ |z_1 - z_2| $ is:

Density of 3 M NaCl solution is 1.25 g/mL. The molality of the solution is:

For an experimental expression $ y = \frac{32.3 \times 1125}{27.4} $, where all the digits are significant. Then to report the value of $ y $, we should write:

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ‘M’, is :

Suppose that the number of terms in an A.P. is $ 2k, k \in \mathbb{N} $. If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55, and the last term of the A.P. exceeds the first term by 27, then $ k $ is equal to:

A point particle of charge $ Q $ is located at $ P $ along the axis of an electric dipole 1 at a distance $ r $ as shown in the figure. The point $ P $ is also on the equatorial plane of a second electric dipole 2 at a distance $ r $. The dipoles are made of opposite charge $ q $ separated by a distance $ 2a $. For the charge particle at $ P $ not to experience any net force, which of the following correctly describes the situation?

The expression given below shows the variation of velocity $ v $ with time $ t $: \[ v = At^2 + \frac{Bt}{C + t}. \] The dimension of $ ABC $ is:

A small rigid spherical ball of mass $ M $ is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider $ g $ as acceleration due to gravity):

Consider the following electrochemical cell at standard condition. $$ \text{Au(s) | QH}_2\text{ | QH}_X(0.01 M) \, \text{| Ag(1M) | Ag(s) } \, E_{\text{cell}} = +0.4V $$ The couple QH/Q represents quinhydrone electrode, the half cell reaction is given below: $$ \text{QH}_2 \rightarrow \text{Q} + 2e^- + 2H^+ \, E^\circ_{\text{QH}/\text{Q}} = +0.7V $$

The number of singular matrices of order 2, whose elements are from the set $ \{2, 3, 6, 9\} $ is:

Three infinitely long wires with linear charge density $ \lambda $ are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?

The elemental composition of a compound is 54.2%C, 9.2%H, and 36.6%O. If the molar mass of the compound is 132 g/mol, the molecular formula of the compound is:

To obtain the given truth table, the following logic gate should be placed at G

In a measurement, it is asked to find the modulus of elasticity per unit torque applied on the system. The measured quantity has the dimension of $ [M^a L^b T^c] $. If $ b = 3 $, the value of $ c $ is:

Let a circle C pass through the points (4, 2) and (0, 2), and its centre lie on $3x + 2y + 2 = 0$. Then the length of the chord of the circle C, whose midpoint is (1, 2), is:

Given below are two statements:

Statement (I):
are isomeric compounds.

Statement (II):
are functional group isomers.

In the light of the above statements, choose the correct answer from the options given below:

Concentrated nitric acid is labelled as 75%by mass. The volume in mL of the solution which contains 30 g of nitric acid is: Given: Density of nitric acid solution is 1.25 g/mL.

Let $ \hat{a} $ be a unit vector perpendicular to the vectors \[ \mathbf{b} = \hat{i} - 2\hat{j} + 3\hat{k} \quad \text{and} \quad \mathbf{c} = 2\hat{i} + 3\hat{j} - \hat{k}, \] $\text{and makes an angle of}$ $ \cos\left( -\frac{1}{3} \right) $ $\text{with the vector}$ $ \hat{i} + \alpha \hat{j} + \hat{k} $. $\text{If}$ $ \hat{a} $ $\text{makes an angle of}$ $ \frac{\pi}{3} $ $\text{with the vector}$ $ \hat{i} + \alpha \hat{j} + \hat{k} $, then the value of $ \alpha $ $\text{is:}$

Find the IUPAC name of the compound.

A convex lens made of glass (refractive index = 1.5) has a focal length of 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to: