List of top Questions asked in JEE Main

The large difference between the melting and boiling points of oxygen and sulphur may be explained on the basis of

What is the time period of a simple pendulum of length \( L \) and acceleration due to gravity \( g \)?

An object of mass \( m \) is projected from the origin in a vertical \( xy \)-plane at an angle \( 45^\circ \) with the x-axis with an initial velocity \( v_0 \). The magnitude and direction of the angular momentum of the object with respect to the origin, when it reaches the maximum height, will be:

The carbohydrates “Ribose” present in DNA is
A. A pentose sugar
B. Present in pyranose form
C. In “D” configuration
D. A reducing sugar, when free
E. In \( \alpha \)-anomeric form

In \( I(m, n) = \int_0^1 x^{m-1} (1-x)^{n-1} \, dx \), where \( m, n > 0 \), then \( I(9, 14) + I(10, 13) \) is:

In the context of the photoelectric effect, what is the threshold frequency \( f_0 \) for a metal if the work function is \( \phi = 2 \, \text{eV} \)?

If \( \alpha \) and \( \beta \) are the roots of the equation \( 2z^2 - 3z - 2i = 0 \), where \( i = \sqrt{-1} \), then \[ 16 \cdot {Re} \left( \frac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{15} + \beta^{15}} \right) \cdot {Im} \left( \frac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{15} + \beta^{15}} \right) \] is equal to:

A thin plano-convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m. The radius of curvature of the curved surface of the lens is:

Let \( f(x) = \frac{2^{x+2} + 16}{2^{2x+1} + 2^{x+4} + 32} \). Then the value of \[ 8 \left( f\left( \frac{1}{15} \right) + f\left( \frac{2}{15} \right) + \dots + f\left( \frac{59}{15} \right) \right) \] is equal to:

The amount of work done to break a big water drop of radius \( R \) into 27 small drops of equal radius is 10 J. The work done required to break the same big drop into 64 small drops of equal radius will be:

Let in a \( \triangle ABC \), the length of the side AC is 6, the vertex B is \( (1, 2, 3) \) and the vertices A, C lie on the line \[ \frac{x - 6}{3} = \frac{y - 7}{2} = \frac{z - 7}{-2}. \] Then the area (in sq. units) of \( \triangle ABC \) is:

For the given cell: \[ {Fe}^{2+}(aq) + {Ag}^+(aq) \to {Fe}^{3+}(aq) + {Ag}(s) \] The standard cell potential of the above reaction is given. The standard reduction potentials are given as: \[ {Ag}^+ + e^- \to {Ag} \quad E^\circ = x \, {V} \] \[ {Fe}^{2+} + 2e^- \to {Fe} \quad E^\circ = y \, {V} \] \[ {Fe}^{3+} + 3e^- \to {Fe} \quad E^\circ = z \, {V} \] The correct answer is:

An alternating current is given by \[ I = I_A \sin \omega t + I_B \cos \omega t. \] The r.m.s. current will be:

A satellite is launched into a circular orbit of radius \( R \) around the earth. A second satellite is launched into an orbit of radius \( 1.03R \). The time period of revolution of the second satellite is larger than the first one approximately by:

A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8 before A throws a sum of 5. The probability that A wins if A makes the first throw is:

If the equation of a circle is \( 4x^2 + 4y^2 - 12x + 8y = 0 \), what is the radius of the circle?

Find the value of the integral \( \int_0^{\frac{\pi}{2}} \sin^2(x) \, dx \).

A uniform solid cylinder of mass \( m \) and radius \( r \) rolls along an inclined rough plane of inclination \( 45^\circ \). If it starts to roll from rest from the top of the plane, then the linear acceleration of the cylinder axis will be:

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg/m\(^3\). If the pressure inside the bubble is 2100 N/m\(^2\) greater than the atmospheric pressure, then the surface tension of the liquid in SI units is (use \(g = 10 \, {m/s}^2\)).

Given below are two statements I and II.
Statement I: Dumas method is used for estimation of "Nitrogen" in an organic compound.
Statement II: Dumas method involves the formation of ammonium sulfate by heating the organic compound with concentrated H\(_2\)SO\(_4\). In the light of the above statements, choose the correct answer from the options given below:

In the reaction \( 2A + B \rightarrow C \), if the rate law is \( \text{Rate} = k[A]^2[B] \), what is the overall order of the reaction?

A car of mass \( m \) moves on a banked road having radius \( r \) and banking angle \( \theta \). To avoid slipping from the banked road, the maximum permissible speed of the car is \( v_0 \). The coefficient of friction \( \mu \) between the wheels of the car and the banked road is:

Let \( D = \{a, b, c\} \). How many distinct ways can \( D \) be partitioned into non-empty subsets, representing equivalence relations?

In a sound wave, the displacement of the air particles follows the equation \( y = A \cos(kx - \omega t) \). What is the wave velocity?

Let \( y = y(x) \) be the solution of the differential equation \[ \left( xy - 5x^2 \sqrt{1 + x^2} \right) dx + (1 + x^2) dy = 0, \quad y(0) = 0. \] Then \( y(\sqrt{3}) \) is equal to: