List of top Questions asked in JEE Main

The ratio of number of atoms present in a simple cubic, body centered cubic and face centered cubic structure are, respectively :
There are two long co-axial solenoids of same length $l$. the inner and outer coils have radii $r_1$ and $r_2$ and number of turns per unit length $n_1$ and $n_2$ respectively. The rate of mutual inductance to the self-inductance of the inner-coil is :
A student scores the following marks in five tests : $45,54,41,57,43$. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is
Let the equations of two sides of a triangle be $3x - 2y + 6 = 0$ and $4x + 5y - 20 = 0$. If the orthocentre of this triangle is at $(1, 1)$, then the equation of its third side is :
Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number beams is :
Temperature difference of \(120^{\circ}C\) is maintained between two ends of a uniform rod \(AB\) of length \(2L\). Another bent rod \(PQ\), of same cross section as \(AB\) and length \(\frac{3L}{2}\) , is connected across \(AB\) (See figure). In steady state, temperature difference between \(P\) and \(Q\) will be close to :
Another bent rod PQ, of same cross section as AB and length 3L/2, is connected across AB
The combination of plots which does not represent isothermal expansion of an ideal gas is:
The contrapositive of the statement "If you are born in India, then you are a citizen of India", is :
The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if $D_m$ is the angle of minimum deviation?
A circle cuts a chord of length $4a$ on the x-axis and passes through a point on the y-axis, distant $2b$ from the origin. Then the locus of the centre of this circle, is :
The energy required to take a satellite to a height $'h'$ above Earth surface (radius of Earth = $6.4 \times 10^3 \; km) $ is $E_1$ and kinetic energy required for the satellite to be in a circular orbit at this height is $E_2$. The value of $h$ for which $E_1 $ and $E_2$ are equal, is:
Two solids dissociate as follows $ {A(s) <=> B(g) + C(g) ; K_{p_1} = x \; atm^2}$ $ {D(s) <=> C(g) + E(g) ; K_{p_2} = y \; atm^2}$ The total pressure when both the solids dissociate simultaneously is :
In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :
In the cell ${Pt(s) | H_2(g , 1 bar | HCl(aq) | Ag(s) | Pt(s)} $ the cell potential is 0.92 when a $10^{-6}$ molal HCl solution is used. THe standard electrode potential of ${(AgCl/Ag,Cl^{-})}$ electrode is : $\left\{ \text{given} , \frac{2.303RT}{F} = 0.06 V \; at \; 298K\right\}$
The structures of beryllium chloride in the solid state and vapour, phase, respectively,are :
Three blocks $A, B$ and $C$ are lying on a smooth horizontal surface, as shown in the figure. $A$ and $B$ have equal masses, $m$ while $C$ has mass $M$. Block $A$ is given an brutal speed $v$ towards $B$ due to which it collides with $B$ perfectly inelastically. The combined mass collides with $C$, also perfectly inelastically $\frac{5}{6}$ th of the initial kinetic energy is lost in whole process. What is value of $M/m$ ?
Two blocks $A$ and $B$ of masses $m_A = 1 \; kg$ and $m_B = 3 \; kg$ are kept on the table as shown in figure. The coefficient of friction between $A$ and $B$ is $0.2$ and between $B$ and the surface of the table is also $0.2.$ The maximum force $F$ that can be applied on $B$ horizontally, so that the block $A$ does not slide over the block $B$ is : (Take $g = 10 \; m/s^2$)
Three Carnot engines operate in series between a heat source at a temperature $T_1$ and a heat sink at temperature $T_4$ (see figure). There are two other reservoirs at temperature $T_2$, and $T_3$, as shown, with $T_2 > T_2 > T_3 > T_4$ . The three engines are equally efficient if:
$ \lim\limits_{n \to \infty}$$\frac{3}{n}\left\{1+\sqrt{\frac{n}{n+3}}+\sqrt{\frac{n}{n+6}}+\sqrt{\frac{n}{n+9}}+....+\sqrt{\frac{n}{n+3\left(n-1\right)}}\right\}$
Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is $16$. The intensity of the waves are in the ratio:
The area of the region $A = [(x, y): 0 \leq y \leq x|x|+1$ and $-1 \leq x \leq 1]$ in s units is :
An urn contains $5$ red and $2$ green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :
The integral $ \int \frac{2x^{3} -1}{x^{4} +x} dx $ is equal to : (Here C is a constant of integration)
The integral $\int sec^{2/3} x cosec^{4/3}x\, dx$ is equal to (Hence $C$ is a constant of integration)
If in a parallelogram $ABDC$, the coordinates of $A, B$ and $C$ are respectively $(1, 2), (3, 4)$ and $(2, 5),$ then the equation of the diagonal $AD$ is :