List of top Questions asked in JEE Main

In the given reaction,
\( \begin{array}{l}X+Y+3Z\rightleftharpoons XYZ_3\end{array}\)
if one mole of each of X and Y with 0.05 mol of Z gives compound XYZ3. (Given : Atomic masses of X, Y and Z are 10, 20 and 30 amu, respectively.) the yield of XYZ3 is _______ g. (Nearest integer)
Among the following marked proton of which compound shows lowest  \(pK_a\) value ?

A common tangent T to the curves
\(C_1:\frac{x^2}{4}+\frac{y^2}{9} = 1\)
and
\(C_2:\frac{x^2}{4^2}\frac{-y^2}{143} = 1\)
does not pass through the fourth quadrant. If T touches C1 at (x1, y1) and C2 at (x2, y2), then |2x1 + x2| is equal to ______.

Identify the major products A and B for the below given reaction sequence.
Identify the major products A and B for the below given reaction sequence.

 

Match the List I  with List II

List I

 

List II

AIAnti-depressant
BII550 times sweeter than cane sugar
CIIINarcotic analgesic
DIVAntiseptic

Choose the correct answer from the options given below:

If \(t = \sqrt{x} + 4\), then \(\left.\frac{dx}{dt}\right|_{t=4}\) is

Match List I with List II.
 

List-IList-II
A. Benzene sulphonyl chlorideI. Test for primary amines
B. Hoffmann bromamide reactionII. Anti Saytzeff
C. Carbylamine reactionIII. Hinsberg reagent
D. Hoffmann orientationIV. Known reaction of Isocyamates

Choose the correct answer from the options given below:

The kinetic energy of emitted electron is E when the light incident on the metal has wavelength λ. To double the kinetic energy, the incident light must have wavelength :

2sin(\(\frac{\pi}{22}\))sin(\(\frac{3\pi}{22}\))sin(\(\frac{5\pi}{22}\))sin(\(\frac{7\pi}{22}\))sin(\(\frac{9\pi}{22}\)) is equal to

According to MO theory, number of species/ions from the following having identical bond order is ___.
CN-, NO+, O2, O+2, O2+2
An object is projected in the air with initial velocity u at an angle θ. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be ______ degree.
If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth \(\alpha h \ (h \ll Re)\) from the earth surface. The value of α will be ________.
(Use Re=6400 km)
The conductivity of a solution of complex with formula CoCl3(NH3)4 corresponds to 1 : 1 electrolyte, then the primary valency of central metal ion is ______.
The pressure P1 and density d1 of diatomic gas \(\gamma = \frac{7}{5}\) changes suddenly to \(P_2 > P_1\) and d2 respectively during an adiabatic process. The temperature of the gas increases and becomes _____ times of its initial temperature.
(Given \(\frac{d_2}{d_1} = 32\))

The statement 
\((p⇒q)∨(p⇒r) \)
is NOT equivalent to

Let
\(\vec{a}\) and \(\vec{b}\) be two vectors such that 
\(|\vec{a} + \vec{b}|^2 = |\vec{a}|^2 + 2|\vec{b}|^2,\  \vec{a} \cdot \vec{b} = 3\) and \(|\vec{a} \times \vec{b}|^2 = 75\)
Then \(|\vec{a}|^2\) is equal to _____.

In the given reaction

Fig. 

the number of sp2 hybridised carbon(s) in compound ‘X’ is _____.

Let the tangents at the points P and Q on the ellipse
\(\begin{array}{l} \frac{x^2}{2}+\frac{y^2}{4}=1\ \text{meet at the point}\ R\left(\sqrt{2},2\sqrt{2}-2\right).\end{array}\)
If S is the focus of the ellipse on its negative major axis, then SP2 + SQ2 is equal to ________.
At 30ºC, the half life for the decomposition of \(AB_2\) is 200 s and is independent of the initial concentration of \(AB_2\). The time required for 80% of the \(AB_2\) to decompose is(Given : \(log\; 2 = 0.30,\; log \;3 = 0.48\))

A body of mass 10 kg is projected at an angle of 45° with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time t = T/√2, is _________.
[Take g = 10m/s2]

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is \(\frac{\alpha^2}{4}\) RJ/mol k; then the value of α will be _______.
(Assume that the given diatomic gas has no vibrational mode).

Let y = y1(x) and y = y2(x) be two distinct solution of the differential equation
\(\frac{dy}{dx} = x+y,\)
with y1(0) = 0 and y2(0) = 1 respectively. Then, the number of points of intersection of y = y1 (x) and y = y2(x) is

Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is π. The difference of resultant intensities, at the point A and B, will be_______I.
Let α→ = \(2\^{i}-\^{j}+5\^{k} and b→= α\^{i}+β\^{j}+2\^{k}. If ((α→×b→)×\^{i}).\^{k} \)=\(\frac{ 23}{2}\),then \(|b→×2\^{j}\| \)is equal to
The X–Y plane be taken as the boundary between two transparent media M1 and M2.M1 in Z 0 has a refractive index of \(\sqrt2\) and M2 with \(Z<0\) has a refractive index of \(\sqrt3\). A ray of light travelling in M1 along the direction given by the vector \(\mathbf{\overrightarrow{P}} = 4\sqrt{3}\mathbf{\hat{i}} - 3\sqrt{3}\mathbf{\hat{j}} - 5\hat{k}\), is incident on the plane of separation. The value of difference between the angle of incident in M1 and the angle of refraction in M2 will be ______ degree.