List of top Questions asked in JEE Main- 2024

Among the following, total number of meta directing functional groups is (Integer based) \(−OCH_3​, −NO_2​, −CN, −CH_3​, −NHCOCH_3​, −COR, −OH, −COOH, −Cl\).

3-Methylhex-2-ene on reaction with HBr in presence of peroxide forms an addition product (A). The number of possible stereoisomers for 'A' is ______.

If three moles of an ideal gas at 300 K expand isothermally from 30 dm³ to 45 dm³ against a constant opposing pressure of 80 kPa, then the amount of heat transferred is ______ J.

Mass of methane required to produce 22 g of CO₂​ after complete combustion is ______ g.
(Given Molar mass in g mol⁻¹: C=12.0, H=1.0, O=16.0).

The correct statement regarding nucleophilic substitution reaction in a chiral alkyl halide is:

Given below are two statements:
Statement (I): Aqueous solution of ammonium carbonate is basic.
Statement (II): Acidic/basic nature of salt solution of a salt of weak acid and weak base depends on \( K_a \) and \( K_b \) value of acid and the base forming it.
In the light of the above statements, choose the most appropriate answer from the options given below:

Yellow compound of lead chromate gets dissolved on treatment with hot NaOH solution. The product of lead formed is a:

Given below are two statements:
Statement (I): The 4f and 5f-series of elements are placed separately in the Periodic table to preserve the principle of classification.
Statement (II): s-block elements can be found in pure form in nature.
In the light of the above statements, choose the most appropriate answer from the options given below:

Consider the following complex ions:
P = \([FeF_6]^{3-}\) 
Q = \([V(H_2O)_6]^{2+}\) 
R = \([Fe(H_2O)_6]^{2+}\) 
The correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.) is:

Which of the following electronic configurations would be associated with the highest magnetic moment?

If the average depth of an ocean is 4000 m and the bulk modulus of water is \( 2 \times 10^9 \, \text{N/m}^2 \), then the fractional compression \( \frac{\Delta V}{V} \) of water at the bottom of the ocean is \( \alpha \times 10^{-2} \). The value of \( \alpha \) is ______ (Given \( g = 10 \, \text{m/s}^2 \), \( p = 1000 \, \text{kg/m}^3 \)).

Two immiscible liquids of refractive indices \( \frac{8}{5} \) and \( \frac{3}{2} \) respectively are put in a beaker as shown in the figure. The height of each column is 6 cm. A coin is placed at the bottom of the beaker. For near-normal vision, the apparent depth of the coin is \( \frac{\alpha}{4} \) cm. The value of \( \alpha \) is ______.

A thin metallic wire having a cross-sectional area of \( 10^{-4} \, \text{m}^2 \) is used to make a ring of radius 30 cm. A positive charge of \( 2\pi \, C \) is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the center of the ring. The tension in the ring is ______ N; provided that the ring does not deform (neglect the influence of gravity).
(Given, \(\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{SI units}\))

A particle starts from origin at \( t = 0 \) with a velocity \( 5\hat{i} \, \text{m/s} \) and moves in the \( x\)-\( y \) plane under the action of a force that produces a constant acceleration of \( (3\hat{i} + 2\hat{j}) \, \text{m/s}^2 \). If the \( x \)-coordinate of the particle at that instant is 84 m, then the speed of the particle at this time is \( \sqrt{\alpha} \, \text{m/s} \). The value of \( \alpha \) is ______.

The average kinetic energy of a monatomic molecule is 0.414 eV at temperature: (Use \( k_B = 1.38 \times 10^{-23} \, \text{J/mol-K} \))

A convex lens of focal length 40 cm forms an image of an extended source of light on a photo-electric cell. A current \( I \) is produced. The lens is replaced by another convex lens having the same diameter but focal length 20 cm. The photoelectric current now is:

Which of the following circuits is reverse-biased?

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If \( \vec{E} \) and \( \vec{B} \) represent the electric and magnetic fields respectively, then the region of space may have:
(A) \( \vec{E} = 0, \vec{B} = 0 \) 
(B) \( \vec{E} = 0, \vec{B} \neq 0 \) 
(C) \( \vec{E} \neq 0, \vec{B} = 0 \) 
(D) \( \vec{E} \neq 0, \vec{B} \neq 0 \) 
Choose the most appropriate answer from the options given below:

Position of an ant \( S \) (in meters) moving in the Y-Z plane is given by \( S = 2t \hat{j} + 5t \hat{k} \) (where \( t \) is in seconds). The magnitude and direction of velocity of the ant at \( t = 1 \, s \) will be:

Let \( f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3) \), \( x \in \mathbb{R} \). Then \( f'(10) \) is equal to ______.

Let the set of all \( a \in \mathbb{R} \) such that the equation \(\cos 2x + a \sin x = 2a - 7\) has a solution be \([p, q]\) and \( r = \tan 9^\circ - \tan 27^\circ - \frac{1}{\cot 63^\circ + \tan 81^\circ} \), then \( pqr \) is equal to ______.

If \( 8 = 3 + \frac{1}{4}(3 + p) + \frac{1}{4^2}(3 + 2p) + \frac{1}{4^3}(3 + 3p) + \ldots \infty \), then the value of \( p \) is ______.

Let the area of the region \(\{(x, y) : x - 2y + 4 \geq 0, x + 2y^2 \geq 0, x + 4y^2 \leq 8, y \geq 0\}\) be \(\frac{m}{n}\), where \( m \) and \( n \) are coprime numbers. Then \( m + n \) is equal to ______.

If the solution of the differential equation \((2x + 3y - 2) \, dx + (4x + 6y - 7) \, dy = 0, \quad y(0) = 3,\) is  \(\alpha x + \beta y + 3 \log_e |2x + 3y - \gamma| = 6,\) then \(\alpha + 2\beta + 3\gamma\) is equal to ____.

Let for a differentiable function \(f : (0, \infty) \rightarrow \mathbb{R}\), \(f(x) - f(y) \geq \log_e \left( \frac{x}{y} \right) + x - y, \quad \forall \; x, y \in (0, \infty).\) 
Then \(\sum_{n=1}^{20} f'\left(\frac{1}{n^2}\right)\) is equal to ____.