List of top Questions asked in JEE Main

Which of the following statements is false?

A power transmission line feeds input power at $2300\, V$ to a step down transformer with its primary windings having $4000$ turns, giving the output power at $230\, V$. If the current in the primary of the transformer is $5\, A$, and its efficiency is $90\%$, the output current would be :

In a screw gauge, $5$ complete rotations of the screw cause it to move a linear distance of $0.25\, cm$. There are $100$ circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading of $4$ main scale divisions and $30$ circular scale divisions. Assuming negligible zero error, the thickness of the wire is :

When metal ? $M$ ? is treated with $NaOH$, a white gelatinous precipitate ?$X$? is obtained, which is soluble in excess of $NaOH$. Compound ?$X$? when heated strongly gives an oxide which is used in chromatography as an adsorbent. The metal ?$M$? is :

If the length of the latus rectum of an ellipse is $4$ units and the distance between a focus and its nearest vertex on the major axis is $\frac{3}{2}$ units, then its eccentricity is :

In \(XeO_3F_2\), the number of bond pair(s), \(\pi\)-bond(s) and lone pair(s) on \(Xe\) atom respectively are :

Which of the following best describes the diagram below of a molecular orbital ?

Which of the following arrangements shows the schematic alignment of magnetic moments of antiferromagnetic substance ?

A group 13 element 'X' reacts with chlorine gas to produce a compound $XCl _{3} . XCl _{3}$ is electron deficient and easily reacts with $NH _{3}$ to form $Cl _{3} X \leftarrow NH _{3}$ adduct; however, $XCl _{3}$ does not dimerise. $X$ is

A sinusoidal voltage of peak value $283\, V$ and angular frequency $320/s$ is applied to a series $LCR$ circuit. Given that $R = 5 \, \Omega , L = 25 \, mH $ and $C=1000 \, \mu F$. The total impedance, and phase difference between the voltage across the source and the current will respectively be :

What is the conductivity of a semiconductor sample having electron concentration of $5 \times 10^{18} \, m^{-3}$, hole concentration of $5 \times 10^{19} \, m^{-3} $ , electron mobility of $2.0 \, m^2 \, V^{-1} \, s^{-1}$ and hole mobility of $0.01 \, m^2 \, V^{-1} \, s^{-1}$ ? (Take charge of electron as $1.6 \times 10^{-19} C$)

A physical quantity $P$ is described by the relation $P = a^{1/2} b^2 c^3 d^{-4} $ If the relative errors in the measurement of $a, b, c$ and $d$ respectively, are $2\%, 1\%, 3\%$ and $5\%$, then the relative error in $P$ will be :

Two particles $A$ and $B$ of equal mass $M$ are moving with the same speed $v$ as shown in the figure. They collide completely inelastically and move as a single particle $C$. The angle $\theta$ that the path of $C$ makes with the $X-axis$ is given by :

An external pressure \(P\) is applied on a cube at \(0^{\circ}C\) so that it is equally compressed from all sides.\(K\) is the bulk modulus of the material of the cube and \(\alpha\) is its coefficient of linear expansion.Suppose we want to bring the cube to its original size by heating it. The temperature should be raised by :

The integral $\int\limits^{\frac{3\, \pi}{4}}_{\frac{\pi}{4}} \frac{dx}{ 1 + \cos \, x}$ is equal to :

$\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{\left(\pi - 2x\right)^{3}} $ equals :

The current gain of a common emitter amplifier is $69$ . If the emitter current is $7.0 \,mA$, collector current is :

The energy stored in the electric field produced by a metal sphere is $4.5\, J$. If the sphere contains $ 4 \, \mu C$ charge, its radius will be : [Take : $\frac{1}{4 \pi \epsilon_o } = 9 \times 10^{9} \, N - m^2 / C^2$ ]

The value of $(^{21}C_{1} - ^{10}C_{1}) + (^{21}C_{2} - ^{10}C_{2}) + (^{21}C_{3} - ^{10}C_{3}) +(^{21}C_{4} - ^{10}C_{4}) +....+(^{21}C_{10} - ^{10}C_{10})$ is :

The group having triangular planar structures is :

$2$ moles of an ideal monatomic gas is carried from a state $(P_0, V_0)$ to a state $(2P_0, 2V_0)$ along a straight line path in a P-V diagram. The amount of heat absorbed by the gas in the process is given by

If two different numbers are taken from the set $\{0,1,2,3, \ldots \ldots, 10\}$then the probability that their sum as well as absolute difference are both multiple of $4$, is :

Let $l_n = \int \tan^{n} x \, dx , (n > 1) . l_4 + l_6 = a \, \, \tan^5 \, x + bx^5 + C$, where $C$ is a constant of integration, then the ordered pair $(a, b)$ is equal to :

Let $S_{n} = \frac{1}{1^{3}} + \frac{1+2}{1^{3} + 2^{3}} + \frac{1+2+3}{1^{3} + 2^{3} + 3^{3}} + ...... + \frac{1+2+...+n}{1^{3} + 2^{3} +.... +n^{3}} . $ . If $100 \, S_n = n , $ then $n$ is equal to :