List of top Questions asked in JEE Main

Match Column-I with Column-II : Choose the correct answer from the options given below:

If the gravitational field in the space is given as $\left(-\frac{K}{r^2}\right)$ Taking the reference point to be at $r =2\, cm$ with gravitational potential $V =10 \,J / kg$ Find the gravitational potential at $r =3\, cm$ in SI unit (Given, that $K =6 \,Jcm / kg$)

A sinusoidal carrier voltage is amplitude modulated The resultant amplitude modulated wave has maximum and minimum amplitude of $120 \, V$ and $80\, V$ respectively The amplitude of each sideband is:

Solution of 12 g of non-electrolyte (A) prepared by dissolving it in 1000 mL of water exerts the same osmotic pressure as that of 0.05 M glucose solution at the same temperature. The empirical formula of A is CH₂O. The molecular mass of A is ____ g. (Nearest integer)

A₂+B₂→2AB. \(ΔH^0_f\)= -200 kJ mol^-1 AB, A2 and B2 are diatomic molecule. If the bond enthalpies of A₂, B₂ and AB are in the ratio 1:0.5:1, then the bond enthalpy of A₂ is ___ kJmol^-1 (Nearest integer)

Position-time graph for a particle is parabolic and is as shown:

Choose the corresponding v – t graph.

A circle with centre \((2,3) \) and radius \(4\) intersects the line \(𝑥+𝑦=3\) at the points \(𝑃\) and \(𝑄\). If the tangents at \(𝑃\) and \(𝑄\) intersect at the point \(S(α,β)\), then \(4α−7β\) is equal to _____ .

Heat is given to an ideal gas in an isothermal process
A Internal energy of the gas will decrease
B Internal energy of the gas will increase
C Internal energy of the gas will not change
D The gas will do positive work E The gas will do negative work
Choose the correct answer from the options given below:

A triangle is formed by the tangents at the point \((2,2)\) on the curves \(𝑦^2=2𝑥\) and \(𝑥^2+𝑦^2=4𝑥\), and the line \(𝑥+𝑦+2=0\). If \(𝑟\) is the radius of its circumcircle, then \(𝑟^2\) is equal to ____ .

Match List-I with List-II :

	List-I (Species)		List-II (Maximum allowed concentration in ppm in drinking water)
A	F-	I	< 50 ppm
B	\(SO^{2-}_4\)	II	< 5 ppm
C	\(NO^-_3\)	III	< 2 ppm
D	Zn	IV	< 500 ppm

Choose the correct answer from the options given below :

A certain quantity of real gas occupies a volume of 30.15 dm3 at 100 atm and 500 K when its compressibility factor is 1.07. Its volume at 300 atm and 300K (When its compressibility factor is 1.4) is _____ x 10-4 dm3 (Nearest integer)

The total number of 4-digit numbers whose greatest common divisor with 54 is 2 , is ____.

Let R be a relation defined on N as a ⁡R⁡b if 2a+3b is a multiple of 5 ,a , b∈N. Then R is

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is

Let \(𝑦=𝑦(𝑥)\) be the solution of the differential equation \(𝑥\;𝑙𝑜𝑔_𝑒⁡𝑥\frac{𝑑𝑦}{ 𝑑𝑥} +𝑦=𝑥^2𝑙𝑜𝑔_𝑒⁡𝑥,(𝑥>1)\).  If \(𝑦(2)=2\), then \(𝑦(𝑒)\) is equal to 

If the tangent at a point 𝑃 on the parabola \(𝑦^2=3𝑥\) is parallel to the line \(𝑥+2𝑦=1\) and the tangents at the points 𝑄 and 𝑅 on the ellipse \(\frac{𝑥^2}{ 4} +\frac{𝑦^2}{ 1} =1\) are perpendicular to the line 𝑥−𝑦=2, then the area of the triangle PQR is : 

KMnO₄ is titrated with ferrous ammonium sulphate hexahydrate in presence of dilute H₂SO₄. Number of water molecules produced for 2 molecules of KMnO₄ is______.

The value of the integral \(∫_{\frac 12}^2 \frac{tan^{-1}x}{x}dx\) is equal to

If the lines \(\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{1}\)  and \(\frac{x-a}{2}=\frac{y+2}{3}=\frac{z-3}{1}\) intersect at the point 𝑃, then the distance of the point 𝑃 from the plane 𝑧=𝑎 is : 

D-(+)- Glyceraldehyde  
The two products formed in above reaction are

Let \(\overrightarrow 𝑎 =4\hat 𝑖+3\hat 𝑗ˆ\) and \(\overrightarrow 𝑏 =3\hat 𝑖−4\hat 𝑗\)+\(5\hat 𝑘\). If \(\overrightarrow 𝑐\)  is a vector such that \(\overrightarrow 𝑐 ⋅(\overrightarrow 𝑎 ×\overrightarrow𝑏⃗ )+25=0\), \(\overrightarrow𝑐 ⋅(\hat𝑖+\hat𝑗+ \hat𝑘)=4\), and projection of \(\overrightarrow𝑐\)  on \(\overrightarrow𝑎\)  is \(1\) , then the projection of \(\overrightarrow 𝑐\)  on \(\overrightarrow 𝑏\) equals 

The plane \(2x−y+z=4\) intersects the line segment joining the points \(A(a,−2,4)\) and \(B(2,b,−3)\) at the point C in the ratio \(2:1\) and the distance of the point C from the origin is \(\sqrt5\). If \(ab<0 \) and \(P\) is the point \((a−b,b,2b−a)\). Then \(CP^2 \) is equal to

Match the following

Column-A	Column-B
Nylon 6	Natural Rubber
Vulcanized Rubber	Cross Linked
cis-1,4-polyisoprene	Caprolactam
Polychloroprene	Neoprene.

Choose the correct answer from option given below

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is