List of top Questions asked in JEE Main

The length of a seconds pendulum at a height h=2R from earth surface will be :
(Given : R= Radius of earth and acceleration due to gravity at the surface of earth g=π²ms⁻²)

Let 5 digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers Then the serial number of the number 42923 is

A light ray emits from the origin making an angle \(30\degree\) with the positive x-axis. After getting reflected by the line \(x + y = 1\), if this ray intersects x-axis at Q, then the abscissa of Q is

If the sum of the series \(\left(\frac{1}{2}-\frac{1}{3}\right) + \left(\frac{1}{2^2}-\frac{1}{2·3} + \frac{1}{3^2}\right) + \left(\frac{1}{2^2}-\frac{1}{2^2·3} + \frac{1}{2·3^2} - \frac{1}{3^3}\right) + \left(\frac{1}{2^4}-\frac{1}{2^3·3} + \frac{1}{2^2·3^2} - \frac{1}{2·3^3} + \frac{1}{3^4}\right) + ........ \)
is \(\frac{α}{β}\) , where α and β are co-prime, then α+3β is equal to ________

Let a_n be the n^th term of the series 5 + 8 + 14 + 23 + 35 + 50 +.... and Sn = \(\displaystyle\sum_{k=1}^{n} a_k.\) Then S³⁰ - a⁴⁰ is equal to

Match List I with List II

List I (Complex)		List II (Hybridization)
A.	Ni(CO)4	I.	sp3
B.	[Cu(NH3)4]2+	II.	dsp2
C.	[Fe(NH3)6]2+	III.	sp3d2
D.	[Fe(H2O)6]2+	IV.	d2sp3

Choose the correct answer from the options given below:

What is the center of gravity of a semi-circular disc of radius (R)?

A $100\, m$ long wire having cross-sectional area $625 \times 10^{-4} \, m ^2$ and Young's modulus is $10^{10} Nm ^{-2}$ is subjected to a load of $250 \, N$, then the elongation in the wire will be:

For certain chemical reaction X 🡢 Y, the rate of formation of product is plotted against the time as shown in the figure. The number of correct statement/s from the following is______.
(A) Over all order of this reaction is one
(B) Order of this reaction can't be determined 
(C) In region I and III, the reaction is of first and zero order respectively 
(D) In region-II, the reaction is of first order 
(E) In region-II, the order of reaction is in the range of 0.1 to 0.9.

A block is fastened to a horizontal spring. The block is pulled to a distance \(x=10\ cm\) from its equilibrium position (at $x=0$ ) on a frictionless surface from rest. The energy of the block at $x=5$ $cm$ is $025 J$. The spring constant of the spring is _____$Nm ^{-1}$.

The primary and secondary valencies of cobalt respectively in \([ Co(NH_3)_5Cl]Cl_2\) are :

Let $f$ be a twice differentiable function on $R$. 
If $f ^{\prime}(0)=4$ and $f(x)+\int\limits_0^x(x-t) f^{\prime}(t) d t=\left(e^{2 x}+e^{-2 x}\right) \cos 2 x+\frac{2}{a} x,$ 
then $(2 a+1)^5 a^2$ is equal to ______.

Let a₁, a₂, a₃, …. be a G.P. of increasing positive numbers. Let the sum of its 6^th and 8^th terms be 2 and the product of its 3rd and 5th terms be \(\frac{1}{9}\) .Then 6 (a₂ + a₄) (a₄ + a₆) is equal to

On a temperature scale X, the boiling point of water is 65° X and the freezing point is 15° X. Assume that the X scale is linear. The equivalent temperature corresponding to 95° X on the Fahrenheit scale would be:

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$
Assertion A: Steel is used in the construction of buildings and bridges.
Reason R: Steel is more elastic and its elastic limit is high.
In the light of above statements, choose the most appropriate answer from the options given below:

Match List I with List II :

	List I		List II
A	3 Translational degrees of freedom	I	Monoatomic gases
B	3 Translational, 2 rotational degrees of freedoms	II	Polyatomic gases
C	3 Translational, 2 rotational and 1 vibrational degrees of freedom	III	Rigid diatomic gases
D	3 Translational, 3 rotational and more than one vibrational degrees of freedom	IV	Nonrigid diatomic gases

Choose the correct answer from the options given below:

If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$, then $3(\alpha+\beta+\gamma)$ is equal to

Let $A = \begin{bmatrix} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{bmatrix}, a , b \in R$. 
If for some $n \in N , A ^{ n }=\begin{bmatrix}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{bmatrix}$ 
then $n + a + b$ is equal to _________.

A particle of mass 100 g is projected at time \(𝑡=0\) with a speed \(20\,ms^{−1}\) at an angle \(45°\) to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time \(𝑡=2 s\) is found to be \(\sqrt{K}\  kgm^2/s.\) The value of \(K\) is ________. (Take \(g=10\) \(ms^{−2}\))

Let be a sequence such that a1+a₂+....+ a_n=\(\frac{n^2+3n}{ (n+1 ) (n+2)}\). If  \(28∑^{10}_{k=1}\frac{1}{a_k} =\) P₁P₂P₃ . . . P_m ,  where p1, p2, …..p_m are the first m prime numbers, then m is equal to

A plane $E$ is perpendicular to the two planes $2 x-2 y+z=0$ and $x-y+2 z=4$, and passes through the point $P (1,-1,1)$ If the distance of the plane $E$ from the point $Q(a, a, 2)$ is $3 \sqrt{2}$, then $( PQ )^2$ is equal to

The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :