List of top Questions asked in JEE Main

A company has two plants A and B to manufacture motorcycles. 60% motorcycles are manufactured at plant A and the remaining are manufactured at plant B. 80% of the motorcycles manufactured at plant A are rated of the standard quality, while 90% of the motorcycles manufactured at plant B are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If p is the probability that it was manufactured at plant B, then 126p is

Let PQR be a triangle with R (-1,4, 2). Suppose M(2, 1, 2) is the mid point of PQ. The distance of the centroid of \(\triangle PQR\) from the point of intersection of the line\(\frac{x-2}{0}=\frac{y}{2}=\frac{z+3}{-1}\) and \(\frac{x-1}{1}=\frac{y+3}{-3}=\frac{z+1}{1}\) is

Let $\beta(m, n) = \int_{0}^{1}x^{m-1}(1-x)^{n-1}dx$, $m, n > 0$. If $\int_{0}^{1}(1-x^{10})^{20}dx = a\beta(b,c)$, then $100(a+b+x)$ equals

Let \( f(x) = x^5 + 2x^3 + 3x + 1 \), \( x \in \mathbb{R} \), and \( g(x) \) be a function such that \( g(f(x)) = x \) for all \( x \in \mathbb{R} \). Then \( \frac{g(7)}{g'(7)} \) is equal to:

Evaluate the integral  \(\int_{0}^{1} \frac{1}{\sqrt{3+x} + \sqrt{1+x}} \, dx\) Given that the integral can be expressed in the form \(a + b\sqrt{2} + c\sqrt{3}\), where \(a, b, c\) are rational numbers, find the value of \(2a + 3b - 4c\).

The probability that Ajay will not go to office is \(\frac{1}{5}\) and probability that Ajay and Vijay will not go to the office is \(\frac{2}{7}\), if their visits to office is independent of each other, then find the probability that Ajay will go to the office, but Vijay will not go, is

Let \( C: x^2 + y^2 = 4 \) and \( C': x^2 + y^2 - 4\lambda x + 9 = 0 \) be two circles. If the set of all values of \( \lambda \) such that the circles \( C \) and \( C' \) intersect at two distinct points is \( R = [a, b] \), then the point \( (8a + 12, 16b - 20) \) lies on the curve:

Given below are two statements:
Statement I : Picric acid is 2, 4, 6-trinitrotoluene.
Statement II : Phenol-2, 4-disulphuric acid is treated with conc. HNO₃ to get picric acid.
In the light of the above statement, choose the most appropriate answer from the options given below:

Given below are two statements:
Statement I: \( \text{S}_8 \) solid undergoes disproportionation reaction under alkaline conditions to form \( \text{S}^{2-} \) and \( \text{S}_2\text{O}_3^{2-} \). 
Statement II: \( \text{ClO}_4^- \) can undergo disproportionation reaction under acidic condition.
In the light of the above statements, choose the most appropriate answer from the options given below:

Highest enol content will be shown by:

Which of the following has highly acidic hydrogen?

Which is following compound is easily attacked by electrophile?

According to IUPAC system, the compound

Which of the following complex is homoleptic?

Diamagnetic Lanthanoid ions are:

Consider the above reactions, identify product B and product C.

What is the effect that occurs between lone pair and pi bond?

Which of the following is least iconic

Given below are two statements :
Statement I: In group 13, the stability of +1 oxidation state increases down the group.
Statement II: The atomic size of gallium is greater than that of aluminium. In the light of the above statements.
Choose the most appropriate answer from the options given below:

An octahedral complex with the formula \(\text{CoCl}_3n\text{NH}_3\) upon reaction with excess of \(\text{AgNO}_3\) solution gives 2 moles of \(\text{AgCl}\). Consider the oxidation state of Co in the complex is \(x\). The value of "x + n" is ______.

The following reaction occurs in the Blast furnace where iron ore is reduced to iron metal:
\(\text{Fe}_2\text{O}_3(s) + 3\text{CO}(g) \rightleftharpoons 2\text{Fe}(l) + 3\text{CO}_2(g)\)
Using Le Chatelier's principle, predict which one of the following will not disturb the equilibrium.

The molar conductivity for electrolytes A and B are plotted against C^1/2 as shown below. Electrolytes A and B respectively are :

Given below are two statements:
Statement I: On passing HCl$_{(g)}$ through a saturated solution of BaCl$_2$, at room temperature white turbidity appears.
Statement II: When HCl gas is passed through a saturated solution of NaCl, sodium chloride is precipitated due to common ion effect.
In the light of the above statements, choose the most appropriate answer from the options given below:

The product A formed in the following reaction is:

Methods used for purification of organic compounds are based on :