List of top Questions asked in JEE Main

If G be the gravitational constant and u be thee nergy density then which of the following quantity have the dimension as that the \(\sqrt{UG}\)

Suppose AB is a focal chord of the parabola \( y^2 = 12x \) of length \( l \) and slope \( m<\sqrt{3} \). If the distance of the chord AB from the origin is \( d \), then \( ld^2 \) is equal to _________.

The number of distinct real roots of the equation \[ |x| \, |x + 2| - 5|x + 1| - 1 = 0 \] is _________.

Let \( a_1, a_2, a_3, \dots \) be in an arithmetic progression of positive terms.
Let \( A_k = a_1^2 - a_2^2 + a_3^2 - a_4^2 + \dots + a_{2k-1}^2 - a_{2k}^2 \).  
If \( A_3 = -153 \), \( A_5 = -435 \), and \( a_1^2 + a_2^2 + a_3^2 = 66 \), then \( a_{17} - A_7 \) is equal to _________.

Let \( f \) be a differentiable function in the interval \( (0, \infty) \) such that \( f(1) = 1 \) and \(\lim_{t \to x} \frac{t^2 f(x) - x^2 f(t)}{t - x} = 1\) for each \( x > 0 \).
Then \( 2f(2) + 3f(3) \) is equal to _________.

If the constant term in the expansion of \((1 + 2x - 3x^3) \left(\frac{3}{2}x^2 - \frac{1}{3x}\right)^9\) is \( p \), then \( 108p \) is equal to _________.

From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable \( X \) denote the number of defective items in the sample. If the variance of \( X \) is \( \sigma^2 \), then \( 96\sigma^2 \) is equal to _________.

If the line \(\frac{2 - x}{3} = \frac{3y - 2}{4\lambda + 1} = 4 - z\) makes a right angle with the line  \(\frac{x + 3}{3\mu} = \frac{1 - 2y}{6} = \frac{5 - z}{7},\) then \( 4\lambda + 9\mu \) is equal to:

The value of \(\int_{-\pi}^{\pi} \frac{2y(1 + \sin y)}{1 + \cos^2 y} \, dy\)

If \(\frac{1}{\sqrt{1} + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \dots + \frac{1}{\sqrt{99} + \sqrt{100}} = m\) and  \(\frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \dots + \frac{1}{99 \cdot 100} = n,\) then the point \( (m, n) \) lies on the line

Suppose \( \theta \in \left[ 0, \frac{\pi}{4} \right] \) is a solution of \( 4 \cos \theta - 3 \sin \theta = 1 \). Then \( \cos \theta \) is equal to:

Let the line 2x + 3y – k = 0, k > 0, intersect the x-axis and y-axis at the points A and B, respectively. If the equation of the circle having the line segment AB as a diameter is x² + y² – 3x – 2y = 0 and the length of the latus rectum of the ellipse x² + 9y² = k² is m n , where m and n are coprime, then 2m + n is equal to

Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point (3, 2) and parallel to the coordinate axes touch it. Then the shortest distance of the circle C from the point (5, 5) is :

Let \( A \) and \( B \) be two square matrices of order 3 such that \( |A| = 3 \) and \( |B| = 2 \). Then \(|A^\top A (\text{adj}(2A))^{-1} (\text{adj}(4B)) (\text{adj}(AB))^{-1} A A^\top|\) is equal to:

The integral \(\int_{0}^{\pi/4} \frac{136 \sin x}{3 \sin x + 5 \cos x} \, dx\) is equal to

If the function \(f(x) = \frac{\sin 3x + \alpha \sin x - \beta \cos 3x}{x^3},\) \(x \in \mathbb{R} \), is continuous at \( x = 0 \), then \( f(0) \) is equal to:

If the system of equations \(11x + y + \lambda z = -5,\) \(2x + 3y + 5z = 3,\) \(8x - 19y - 39z = \mu\) has infinitely many solutions, then \( \lambda^4 - \mu \) is equal to:

For the function \(f(x) = \sin x + 3x - \frac{2}{\pi}(x^2 + x), \quad x \in \left[0, \frac{\pi}{2}\right],\)consider the following two statements:  
1. \( f \) is increasing in \( \left(0, \frac{\pi}{2}\right) \).  
2. \( f' \) is decreasing in \( \left(0, \frac{\pi}{2}\right) \).  
Between the above two statements

Let two straight lines drawn from the origin \( O \) intersect the line \(3x + 4y = 12\) at the points \( P \) and \( Q \) such that \( \triangle OPQ \) is an isosceles triangle and \( \angle POQ = 90^\circ \).  If \( l = OP^2 + PQ^2 + QO^2 \), then the greatest integer less than or equal to \( l \) is:

Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on the sides of the rectangle PQRS. Let a and b be the sides of the rectangle PQRS when its area is maximum. Then (a + b)² is equal to :

Let \( d \) be the distance of the point of intersection of the lines \(\frac{x+6}{3} = \frac{y}{2} = \frac{z+1}{1}\) and \(\frac{x-7}{4} = \frac{y-9}{3} = \frac{z-4}{2}\) from the point \((7, 8, 9)\). Then \( d^2 + 6 \) is equal to:

Two resistances of 100Ω and 200Ω are connected in series with a battery of 4V and negligible internal resistance. A voltmeter is used to measure voltage across the 100Ω resistance, which gives a reading of 1V. The resistance of the voltmeter must be _____ Ω.

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m, then the time period of small oscillations will be _____ s. [take \( g = \pi^2 \, m/s^2 \)]

Number of molecules/species from the following having one unpaired electron is ________.
\( \text{O}_2, \, \text{O}_2^{1-}, \, \text{NO}, \, \text{CN}^{1-}, \, \text{O}_2^{2-} \)

The number of different chain isomers for \( \text{C}_7\text{H}_{16} \) is ______.