List of top Questions asked in JEE Main

The number of integral solutions of $ \log_2 \left( \frac{x - 7}{2x - 3} \right) \geq 0 $ is:

Let $x_1, x_2, \dots, x_{100}$ be in an arithmetic progression, with $x_1 = 2$ and their mean equal to 200. If $y_i = (i \cdot x_i)$, then the mean of $y_1, y_2, \dots, y_{100}$ is:

pH of 1 litre of HCL solution is 1. How much water (in litres) is added to make pH=2?

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

	Column I		Column II
(A).	Biodegradable	(P).	Polyacrylonitrie
(B).	Synthetic	(Q).	PHBV
(C).	Natural	(R).	Dacron
(D).	Polyester	(S).	Rubber

Let $ m $ and $ n $ be the numbers of real roots of the quadratic equations $ x^2 - 12x + [x] + 31 = 0 $ and $ x^2 - 5|x+2| - 4 = 0 $, respectively, where $ [x] $ denotes the greatest integer less than or equal to $ x $. Then $ m^2 + mn + n^2 $ is equal to ___________.

The negation of $ (p \land (\sim q)) \lor (\sim p) $ is equivalent to:

If the probability that the random variable $ X $ takes values $ x $ is given by $ P(X = x) = k(x + 1) 3^{-x}, x = 0, 1, 2, \dots $, where $ k $ is a constant, then $ P(X \geq 2) $ is equal to:

The area of the quadrilateral having vertices as (1,2), (5,6), (7,6), (-1,-6) is?

Let $ A = \{1, 2, 3, 4, 5, 6, 7\} $. Then the relation $ R = \{(x, y) \in A \times A : x + y = 7\} $ is:

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A): $Cu ^{2+}$ in water is more stable than $Cu ^{+}$
Reason (R): Enthalpy of hydration for $Cu ^{2+}$ is much less than that of $Cu ^{+}$
In the light of the above statements, choose the correct answer from the options given below :

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

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:

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:

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:

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)

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 $(\alpha, \beta, \gamma)$ $\text{ be the image of the point }$ $P(3, 3, 5) \text{ in the plane } 2x + y - 3z = 6$. $\text{ Then } \alpha + \beta + \gamma \text{ is equal to:}$

Let O be the origin and OP and OQ be the tangents to the circle $ x^2 + y^2 - 6x + 4y + 8 = 0 $ at the points P and Q on it. If the circumcircle of the triangle OPQ passes through the point $ \left( \alpha, \frac{1}{2} \right) $, then a value of $ \alpha $ is.

A bolt manufacturing factory has three products A, B and C. 50% and 30% of the products are A and B type respectively and remaining are C type. Then probability that the product A is defective is 4%, that of B is 3% and that of C is 2%. A product is picked randomly picked and found to be defective, then the probability that it is type C.

64 identical balls made of conducting material each having a potential of 10 mV are joined to form a bigger ball. The potential of a bigger ball is?

Which one of the following elements will remain as liquid inside pure boiling water?

A body of mass $ 5 \, \text{kg} $ is moving with a momentum of $ 10 \, \text{kg} \cdot \text{ms}^{-1} $. Now a force of $ 2 \, \text{N} $ acts on the body in the direction of its motion for $ 5 \, \text{s} $. The increase in the kinetic energy of the body is _____ J.

Consider the word INDEPENDENCE. The number of words such that all the vowels are together is?

The ratio of the wavelength of spectral lines $ H_\alpha $ and $ H_\beta $ in the Balmer series is $ \frac{x}{20} $. The value of $ x $ is _______.