List of top Questions asked in JEE Main

Match the terms in Column-I with their description in Column-II and choose the correct option:

	Column 1(Type of hydride)		Column II
A.	Electron	1.	MgH₂
B.	Electron precise	2.	HF
C.	Electron rich	3.	CH₄
D.	Saline Hydride	4.	B₂H₆

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: In an Ellingham diagram, the oxidation of carbon to carbon monoxide shows a negative slope with respect to temperature.
Reason R: CO tends to get decomposed at higher temperature.
In the light of the above statements, choose the correct answer from the options given below

Two radioactive elements A and B initially have the same number of atoms. The half-life of A is the same as the average life of B. If \( \lambda_A \) and \( \lambda_B \) are the decay constants of A and B respectively, then choose the correct relation from the given options:

The density of the alkali metals is in the order:

Four gases A, B, C and D have critical temperatures 5.3, 33.2, 126.0 and 154.3K respectively. For their adsorption on fixed amount of charcoal, the correct order is :

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and the third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed (\( V_{\text{rms}} \)) and choose the correct answer from the options given below:

For lead storage battery pick the correct statements:
A. During charging of battery, PbSO₄ on anode is converted into PbO₂
B. During charging of battery, PbSO₄ on cathode is converted into PbO₂
C. lead storage battery consists of grid of lead packed with PbO₂ as anode
D. lead storage battery - 38% solution of sulphuric acid as an electrolyte
choose the correct answer from the options given below:

A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table is halved, it will just slip when placed at a distance of ----- from the centre:

The bond order and magnetic property of acetylide ion are same as that of

A metal chloride contains 55% by mass of chlorine. 100 mL of vapours gives 0.57 gm of chlorine at STP. Calculate the molecular mass of metal chloride. (Nearest integer)

The radii of two planets 'A' and 'B' are 'R' and '4R' and their densities are \( \rho \) and \( \frac{\rho}{3} \) respectively. The ratio of acceleration due to gravity at their surfaces (i.e. \( g_A : g_B \)) will be:

Let A = {1, 2, 3, 4,.....10} and B = {0, 1, 2, 3, 4}. The number of elements in the relation R = {(a, b) ∈ A × A: 2(a – b)2 + 3(a – b) ∈ B} is______.

Let S be the set of all values of θ Ε [-π, π] for which the system of linear equations
x+y+√3z=0
-x+(tanθ)y+ √7z=0
x+y+(tanθ)z = 0 has non-trivial solution.
Then 120/π ∑θ_θ∈s is equal to

The coefficient of \(x^{18}\) in the expansion of \(\left(x^4 - \frac{1}{x^3}\right)^{15}\) is ________

If α > β > 0 are the roots of the equation ax2 + bx + 1 = 0, and \(\lim\limits_{x \to \frac{1}{\alpha}}\left(\frac{1-cos(x^2+bx+a)}{2(1-ax)^2}\right)^{1/2}=\frac{1}{k}\left(\frac{1}{\beta}-\frac{1}{\alpha}\right),\) then k 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

A circle passing through the point P\(( \alpha , \beta )\) in the first quadrant touches the two coordinate axes at the points A and B. The point P is above the line AB. The point Q on the line segment AB is the foot of perpendicular from P on AB. If PQ is equal to 11 units, then value of \(( \alpha \beta )\) is ___

Let the mean and variance of 8 numbers \(x, y, 10, 12, 6, 12, 4, 8\) be \(9\) and \(9.25\) respectively. If \(x > y\), then \(3x - 2y\) is equal to:

Let \(\vec{a} = 6\hat{i} + 9\hat{j} + 12\hat{k}\), \(\vec{b} = a\hat{i} + 11\hat{j} - 2\hat{k}\), and \(\vec{c}\) be vectors such that \(\vec{a} \times \vec{c} = \vec{a} \times \vec{b}\). If \(\vec{a} \cdot \vec{c} = -12\) and \(\vec{c} \cdot (\hat{i} - 2\hat{j} + \hat{k}) = 5\), then \(\vec{c} \cdot (\hat{i} + \hat{j} + \hat{k})\) is equal to:

Let \(\lambda_1, \lambda_2\) be the values of \(\lambda\) for which the points \((1, \lambda, \frac{1}{2})\) and \((-2, 0, 1)\) are at equal distance from the plane \(2x + 3y - 6z + 7 = 0\). If \(\lambda_1 > \lambda_2\), then the distance of the point \((1 - \lambda_2, \lambda_2, \lambda_1)\) from the line \(\frac{x-5}{1} = \frac{y-1}{2} = \frac{z+7}{2}\) is:

Consider a circle \(C_1 : x^2 + y^2 - 4x - 2y = \alpha - 5\). Let its mirror image in the line \(y = 2x + 1\) be another circle \(C_2 : 5x^2 + 5y^2 - 10x - 10y + 36 = 0\). Let \(r\) be the radius of \(C_2\). Then \(\alpha + r\) is equal to:

If the solution curve of the differential equation \( (y - 2 \log x) dx + (x \log x^2) dy = 0 \) passes through the points \( \left( e^{4/3}, \alpha \right) \) and \( \left( e^4, \alpha \right) \), then \( \alpha \) is equal to:

Let [t] denote the greatest integer ≤t. Then \(\frac{2}{π} \int\limits_{\frac{\pi}{6}}^{\frac{5\pi}{6}} (8 [cosec x]-5[cot x]) dx\)is equal to ______.

If a_a is the greatest term in the sequence \(a_n=\frac{n^3}{n^4+147},n=1,2,3,...,\) then a is equal to______________.

A common example of alpha decay is