List of top Questions asked in JEE Main

A hemispherical vessel is completely filled with a liquid of refractive index $ \mu $. A small coin is kept at the lowest point $ O $ of the vessel as shown in the figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point $ E $ (at the level of the vessel) is:

A galvanometer having a coil of resistance 30 $ \Omega $ needs 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be $ X \, \Omega $, where $ X $ is:

Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B. The separation between the images of O, formed by each refracting surface is:

The output voltage in the following circuit is (Consider ideal diode case):

Assume a living cell with 0.9% ($w/w$) of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data up to first decimal place only) The cell will:

A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is 1727°C and power radiated by the wire is 94.2 W. Its emissivity is $ \frac{x}{8} $, where $ x = \ldots $

Which of the following circuits has the same output as that of the given circuit?

Let $ A(6,8) $, $ B(10\cos\alpha, -10\sin\alpha) $, and $ C(-10\sin\alpha, 10\cos\alpha) $ be the vertices of a triangle. If $ L(a,9) $ and $ G(h,k) $ be its orthocenter and centroid respectively, then $ 5a - 3h + 6k + 100\sin2\alpha $ is equal to _________.

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:

The variance of the numbers 8, 21, 34, 47, \dots, 320, is:

Let $ f : \mathbb{R} \setminus \{0\} \to (-\infty, 1) $ be a polynomial of degree 2, satisfying $ f(x)f\left( \frac{1}{x} \right) = f(x) + f\left( \frac{1}{x} \right) $. If $ f(K) = -2K $, then the sum of squares of all possible values of $ K $ is:

The integral \[ \int_0^\pi \frac{8x}{4\cos^2 x + \sin^2 x} \, dx \text{ is equal to:} \]

Let P be the foot of the perpendicular from the point $ (1, 2, 2) $ on the line \[ \frac{x-1}{1} = \frac{y + 1}{-1} = \frac{z - 2}{2} \] Let the line $ \mathbf{r} = (-\hat{i} + \hat{j} - 2\hat{k}) + \lambda (\hat{i} - \hat{j} + \hat{k})$, $ \lambda \in \mathbb{R} $, intersect the line $L$ at $Q$. Then $ 2(PQ)^2 $ is equal to:

The observed and normal molar masses of compound MX₂ are 65.6 and 164 respectively. The percent degree of ionisation of MX₂ is ________________% (Nearest integer).

Consider the following oxides:
V_2O_5, Cr_2O_3, Mn_2O_7, V_2O_3, VO_2
A number of oxides which are acidic is $ x $.
Consider the following complex compound:
[Co(NH_2CH_2CH_2NH_2)_3](SO_4)_3
The primary valency of the complex is $ y $.
What is the value of $ x + y $ is?

For positive integers $ n $, if $ 4 a_n = \frac{n^2 + 5n + 6}{4} $ and \[ S_n = \sum_{k=1}^{n} \left( \frac{1}{a_k} \right), \text{ then the value of } 507 S_{2025} \text{ is:} \]

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:

Two simple pendulums having lengths $l_{1}$ and $l_{2}$ with negligible string mass undergo angular displacements $\theta_{1}$ and $\theta_{2}$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

1 + 3 + $5^2$ + 7 + $9^2$ + $\ldots$ upto 40 terms is equal to

Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is:

If \[ \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{96x^2 \cos^2 x}{1 + e^x} dx = \pi(a\pi^2 + \beta), \quad a, \beta \in \mathbb{Z}, \] then $ (a + \beta)^2 $ equals:

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:

Let the triangle PQR be the image of the triangle with vertices $ (1, 3), (3, 1) $ and $ (2, 4) $ in the line $ x + 2y = 2 $. If the centroid of $ \Delta PQR $ is the point $ (\alpha, \beta) $, then $ 15(\alpha - \beta) $ is equal to :

An electron projected perpendicular to a uniform magnetic field $ B $ moves in a circle. If Bohr’s quantization is applicable, then the radius of the electronic orbit in the first excited state is:

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at the 40 cm mark. A mass of 400 g is suspended at the 10 cm mark. To maintain the balance of the rod, the mass to be suspended at the 90 cm mark is: