List of top Questions asked in JEE Main

Let a line pass through two distinct points $ P(-2, -1, 3) $ and $ Q $, and be parallel to the vector $ 3\hat{i} + 2\hat{j} + 2\hat{k} $. If the distance of the point $ Q $ from the point $ R(1, 3, 3) $ is 5, then the square of the area of $ \triangle PQR $ is equal to:

Given below are two statements:
Statement (I): $\textit{An element in the extreme left of the periodic table forms acidic oxides.}$
Statement (II):$ \textit{Acid is formed during the reaction between water and oxide of a reactive element present in the extreme right of the periodic table.} In the light of the above statements, choose the correct answer from the options given below:$

A ring and a solid sphere are released from rest from the same height on enough rough inclined surface. The ratio of their speed when they reach the bottom is $ \sqrt{\frac{7}{x}} $ m/s, then $ x $ is ______.

Mean free path for an ideal gas is observed to be 20 μm while the average speed of molecules of gas is observed to be 600 m/s, then the frequency of collision is near?

In a resonance tube closed at one end. Resonance is obtained at lengths $ l_1 = 120 \, \text{cm} $ and $ l_2 = 200 \, \text{cm} $. If $ v_s = 340 \, \text{m/s} $, find the frequency of sound.

The sum of squares of roots of $ |x - 2|^2 - |x - 2| - 2 = 0 $ and $ x^2 - 2|x - 3| - 5 = 0 $ equals to:

Let the area of the bounded region $ \{(x, y) : 0 \leq 9x \leq y^2, y \geq 3x - 6 \ be $ A $. Then 6A is equal to:

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:

A rod of linear mass density $ \lambda $ and length $ L $ is bent to form a ring of radius $ R $. Moment of inertia of the ring about any of its diameter is:

A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of $25\pi$ Nm for 40s, the speed increases to 2100 rpm. The diameter of the disk is ______ m.

Choose the correct option for structures of A and B, respectively:

Which of the following binary mixture does not show the behavior of minimum boiling azeotropes?

A metal complex with a formula MC$\ell_4$3NH$_3$ is involved in sp$^3$d$^2$ hybridisation. It upon reaction with excess of AgNO$_3$ solution gives ‘x’ moles of AgCl. Consider ‘x’ is equal to the number of lone pairs of electron present in central atom of BrF$_5$. Then the number of geometrical isomers exhibited by the complex is ________

Match the List-I with List-II.

Choose the correct answer from the options given below:

If the number of seven-digit numbers, such that the sum of their digits is even, is $ m \cdot n \cdot 10^a $; $ m, n \in \{1, 2, 3, ..., 9\} $, then $ m + n $ is equal to

In the following reactions, which one is NOT correct?

If $\lim_{x \to 1} \frac{(x-1)(6+\lambda \cos(x-1)) + \mu \sin(1-x)}{(x-1)^3} = -1$, where $\lambda, \mu \in \mathbb{R}$, then $\lambda + \mu$ is equal to

The pH of a 0.01 M weak acid $\mathrm{HX}\left(\mathrm{K}_{\mathrm{a}}=4 \times 10^{-10}\right)$ is found to be 5 . Now the acid solution is diluted with excess of water so that the pH of the solution changes to 6 . The new concentration of the diluted weak acid is given as $\mathrm{x} \times 10^{-4} \mathrm{M}$. The value of x is _______ (nearest integer).

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	Boltzmann constant	I.	$ \text{ML}^2\text{T}^{-1} $
B.	Coefficient of viscosity	II.	$ \text{MLT}^{-3}\text{K}^{-1} $
C.	Planck's constant	III.	$ \text{ML}^2\text{T}^{-2}\text{K}^{-1} $
D.	Thermal conductivity	IV.	$ \text{ML}^{-1}\text{T}^{-1} $

Choose the correct answer from the options given below :

"P" is an optically active compound with molecular formula $ C_6H_{12}O $. When "P" is treated with 2,4-dinitrophenylhydrazine, it gives a positive test. However, in presence of Tollens reagent, "P" gives a negative test. Predict the structure of "P".

For $ \alpha, \beta, \gamma \in \mathbb{R} $, if \[ \lim_{x \to 0} \frac{x^2 \sin(\alpha x) + (\gamma - 1)e^{x^2}}{\sin(2x - \beta x)} = 3, \] then $ \beta + \gamma - \alpha $ is equal to:

The equation for real gas is given by $ \left( P + \frac{a}{V^2} \right)(V - b) = RT $, where $ P $, $ V $, $ T $, and $ R $ are the pressure, volume, temperature and gas constant, respectively. The dimension of $ ab $ is equivalent to that of:

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of $ 100 \, \text{cm}^2 $ with hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density $ 1.5 \times 10^3 \, \text{kg/m}^3 $. What force one needs to apply on the hinged door so that it does not open?

Consider the above reaction, what mass of CaCl₂ will be formed if 250 ml of 0.76 M HCl reacts with 1000 g of CaCO₃?

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at $ x = 0 $ at $ t = 0 $ sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave?