List of top Questions asked in JEE Main- 2024

Number of amine compounds from the following giving solids which are soluble in NaOH upon reaction with Hinsberg's reagent is _____.

Let A(-1, 1) and B(2, 3) be two points and P be a variable point above the line AB such that the area of $\triangle APB$ is 10. If the locus of P is $ax + by = 15$, then $5a + 2b$ is:

A capacitor of reactance \( 4 \sqrt{3} \, \Omega \) and a resistor of resistance \( 4 \, \Omega \) are connected in series with an AC source of peak value \( 8 \sqrt{2} \, \text{V} \). The power dissipation in the circuit is ___________ W.

A galvanometer (G) of $2 \, \Omega$ resistance is connected in the given circuit. The ratio of charge stored in $C_1$ and $C_2$ is:

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^\text{th}$ division coincides exactly with a certain division on the main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm, then how many main scale divisions are there in 1 cm?

Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure

The tensions T1 and T2 in the string are respectively:

The electron affinity values are negative for:
A. Be → Be⁻
B. N → N⁻
C. O → O²⁻
D. Na → Na⁻
E. Al → Al⁻
Choose the most appropriate answer from the options given below:

Consider the following elements.

Which of the following is/are true about A',B',C'andD' ? A. Order of atomic radii: \( B' < A' < D' < C' \)
B. Order of metallic character: \( B' < A' < D' < C' \)
C. Size of the element: \( D' < C' < B' < A' \)
D. Order of ionic radii: \( B^{+} < A^{+} < D^{+} < C^{+} \)
Choose the correct answer from the options given below:

A clock has a 75 cm long second hand and a 60 cm long minute hand, respectively. In 30 minutes duration, the tip of the second hand will travel \(x\) distance more than the tip of the minute hand. The value of \(x\) in meters is nearly (Take \(\pi = 3.14\)):

A planet at distance r from the sun takes 200 days to complete one revolution around the sun. What will be the time period for a planet at distance \(\frac{r}{4}\) from the sun?

A bob of mass \( m \) is suspended by a light string of length \( L \). It is imparted a minimum horizontal velocity at the lowest point \( A \) such that it just completes a half circle, reaching the topmost position \( B \). The ratio of kinetic energies \( \frac{(\text{K.E.})_A}{(\text{K.E.})_B} \) is:

If \(E = \frac{(A-x^2)}{Bt}\) where \(E\) is energy, \(x\) is displacement and \(t\) is time. Find dimensions of \(AB\)

A particle connected with light thread is performing vertical circular motion. Speed at point B (Lowermost point) is sufficient, so that it is able to complete its circular motion. Ignoring air friction, find the ratio of kinetic energy at A to that at B. (A being top-most point)

A string is wrapped around the rim of a wheel of moment of inertia $0.40 \, \text{kgm}^2$ and radius $10 \, \text{cm}$. The wheel is free to rotate about its axis. Initially, the wheel is at rest. The string is now pulled by a force of $40 \, \text{N}$. The angular velocity of the wheel after $10 \, \text{s}$ is $x \, \text{rad/s}$, where $x$ is ______.

For a \(1-D\) motion, relation between position x and time \(t\) is \(t = αx^2 + βx\) Find the relation between velocity \(v\) and acceleration \(a\).

A circular table is rotating with an angular velocity of \( \omega \, \text{rad/s} \) about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of \( 1 \, \text{m} \) on the groove. All the surfaces are smooth. If the radius of the table is \( 3 \, \text{m} \), the radial velocity of the ball with respect to the table at the time the ball leaves the table is \( x\sqrt{2}\omega \, \text{m/s} \), where the value of \( x \) is \(\dots\).

Two identical conducting spheres P and S with charge Q on each, repel each other with a force 16N. A third identical uncharged conducting sphere R is successively brought in contact with the two spheres. The new force of repulsion between P and S is :

The value of unknown resistance (x) for which the potential difference between B and D will be zero in the arrangement shown, is :

Let \( a, ar, ar^2, \dots \) be an infinite G.P. If $$ \sum_{n=0}^\infty ar^n = 57 \quad \text{and} \quad \sum_{n=0}^\infty a^3 r^{3n} = 9747, $$ then \( a + 18r \) is equal to: 

If \[ \left( \frac{1}{\alpha + 1} + \frac{1}{\alpha + 2} + \dots + \frac{1}{\alpha + 1012} \right) - \left( \frac{1}{2 \cdot 1} + \frac{1}{4 \cdot 3} + \frac{1}{6 \cdot 5} + \dots + \frac{1}{2024 \cdot 2023} \right) \]

Let \( A = \{2, 3, 6, 7\} \) and \( B = \{4, 5, 6, 8\} \). Let \( R \) be a relation defined on \( A \times B \) by \((a_1, b_1) R (a_2, b_2)\) if and only if \(a_1 + a_2 = b_1 + b_2\). Then the number of elements in \( R \) is __________.

Let \( A \) be a \( 3 \times 3 \) matrix of non-negative real elements such that \[A \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} = 3 \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}.\]Then the maximum value of \( \det(A) \) is _____