List of top Questions asked in JEE Main

Match List I with List II

Choose the correct answer from the options given below :

The heat absorbed by a system in going through the given cyclic process is :

Let $P$ be a point on the ellipse \[\frac{x^2}{9} + \frac{y^2}{4} = 1.\]Let the line passing through $P$ and parallel to the $y$-axis meet the circle \[x^2 + y^2 = 9\]at point $Q$ such that $P$ and $Q$ are on the same side of the $x$-axis. Then, the eccentricity of the locus of the point $R$ on $PQ$ such that $PR : RQ = 4 : 3$ as $P$ moves on the ellipse, is:

Two cells are connected in opposition as shown. Cell \( E_1 \) is of 8 V emf and 2 \( \Omega \) internal resistance; the cell \( E_2 \) is of 2 V emf and 4 \( \Omega \) internal resistance. The terminal potential difference of cell \( E_2 \) is:

Force F depends on distance \(x\) and time \(t\) as \(F = ax^ 2 + bt\;\frac{1}{2}\) . Final dimension of \(\frac{b^2}{a}\) is

solid sphere is rolling purely with speed v on horizontal surface. It rolls up an incline surface and stops at height h. Then height h is [g is the acceleration due to gravity]:

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s, 4.632 s, 4.6 s and 4.64 s. The arithmetic mean of these reading in correct significant figure is.

Given below are two statements : one is labelled as Assertion(A) and the other is labelled as Reason (R).
Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. 
Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. 
In the light of the above statements, choose the correct answer from the options given below :

The specific heat at constant pressure of a real gas obeying \( PV^2 = RT \) equation is:

The work function of a substance is 3.0 eV. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately:

Four identical particles of mass \( m \) are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \[ \left( \frac{2 \sqrt{2} + 1}{32} \right) \frac{G m^2}{L^2}, \] the length of the sides of the square is:

A force is represented by \( F = ax^2 + b t^{1/2} \) Where \( x = \) distance and \( t = \) time. The dimensions of \( \frac{b^2}{a} \) are:

In an ac circuit, the instantaneous current is zero,when the instantaneous voltage is maximum. In this case, the source may be connected to :
A. pure inductor.
B. pure capacitor.
C. pure resistor.
D. combination of an inductor and capacitor.
Choose the correct answer from the options given below :

In the truth table of the above circuit the value of X and Y are

A cricket player catches a ball of mass 120 g moving with 25 m/s speed. If the catching process is completed in 0.1 s then the magnitude of force exerted by the ball on the hand of player will be (in SI unit):

A line passing through the point \( A(9, 0) \) makes an angle of \( 30^\circ \) with the positive direction of the x-axis. If this line is rotated about \( A \) through an angle of \( 15^\circ \) in the clockwise direction, then its equation in the new position is:

For \(0 < \theta < \frac{pi}{2}\), if the eccentricity of the hyperbola \( x^2 - y^2 \csc^2 \theta = 5 \) is \( \sqrt{7} \) times the eccentricity of the ellipse \( x^2 \csc^2 \theta + y^2 = 5 \), then the value of \( \theta \) is:

Why does oxygen show anomalous behavior ?

Give below are two statements:
Statement-I : Noble gases have very high boiling points. 
Statement-II: Noble gases are monoatomic gases. They are held together by strong dispersion forces. Because of this they are liquefied at very low temperature. Hence, they have very high boiling points. 
In the light of the above statements, choose the correct answer from the options given below.

Evaluate the following statements related to group 14 elements for their correctness.
(A) Covalent radius decreases down the group from C to Pb in a regular manner.
(B) Electronegativity decreases from C to Pb down the group gradually.
(C) Maximum covalence of C is 4 whereas other elements can expand their covalence due to presence of d orbitals.
(D) Heavier elements do not form ppi-ppi bonds.
(E) Carbon can exhibit negative oxidation states.
Choose the correct answer from the options given below:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Melting point of Boron (2453 K) is unusually high in group 13 elements.
Reason (R): Solid Boron has a very strong crystalline lattice. 
In the light of the above statements, choose the most appropriate answer from the options given below:

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of \(\frac{1}{ \theta}\) vs the resistance (R) of the resistance box is shown in the figure. The figure of merit of the galvanometer is .............. ×10^–1 A/division. [The source has emf 2V]

Resistance of a wire at \(0^\circ C\), \(100^\circ C\) and \(t^\circ C\) is found to be \(10 \, \Omega\), \(10.2 \, \Omega\) and \(10.95 \, \Omega\) respectively. The temperature \(t\) in Kelvin scale is ______.

Let\(f(x) = |2x^2 + 5|x - 3|, x \in \mathbb{R}\). If \(m\) and \(n\) denote the number of points were \(f\)is not continuous and not differentiable respectively, then\(m + n\)is equal to:

Let $\alpha$ be a non-zero real number. Suppose $f : \mathbb{R} \to \mathbb{R}$ is a differentiable function such that $f(0) = 2$ and \[\lim_{x \to \infty} f(x) = 1.\]If $f'(x) = \alpha f(x) + 3$, for all $x \in \mathbb{R}$, then $f(-\log 2)$ is equal to ________ .