List of top Questions asked in JEE Main

Let for $x \in R$ $f(x)=\frac{x+|x|}{2} \text { and } g(x)=\begin{cases}x, & x<0 \\x^2, & x \geq 0\end{cases} $ 

Then area bounded by the curve $y=(f \circ g)(x)$ and the lines $y=0,2 y-x=15$ is equal to

The product , which is not obtained during the electrolysis of brine solution is ____ .
The power radiated from a linear antenna of length \( l \) is proportional to: (Given, \( \lambda \) = Wavelength of wave):
Consider the following reaction that goes from A to B in three steps as shown
Consider the following reaction that goes from A to B in three steps as shown
below Choose the correct option:

Radius of the first orbit in H-atom is \(a_0\). Then, de Broglie wavelength of electron in the third orbit is.

Let \(\vec{a}\) = 2\(\widehat{i}\)+3\(\widehat{j}\)+4\(\widehat{k}\), \(\vec{b}\) = \(\widehat{i}\)-2\(\widehat{j}\)-2\(\widehat{k}\), \(\vec{c}\) = -\(\widehat{i}\)+4\(\widehat{j}\)+3\(\widehat{k}\) and \(\vec{d}\) is a vector perpendicular to \(\vec{b}\) and \(\vec{c}\),  \(\vec{a}\).\(\vec{d}\) = 18, then find |\(\vec{a}\)x\(\vec{d}\)|2
Given below are two statements:
Statement I: Area under velocity- time graph gives the distance travelled by the body in a given time.
Statement II: Area under acceleration-time graph is equal to the change in velocity- in the given time.
In the light of given statements, choose the correct answer from the options given below.
The volume of 0.02 M aqueous HBr required to neutralize 10.0 mL of 0.01 M aqueous Ba(OH)2 is ____ . (Assume complete neutralization)
From the top A of a vertical wall AB of height 30 m, the angles of depression of the top P and bottom Q of a vertical tower PQ are 15\(^\circ\) and 60\(^\circ\) respectively. B and Q are on the same horizontal level. If C is a point on AB such that CB = 15 m, then the area (in m$^2$) of the quadrilateral BCPQ is equal to : 
Match column I with column II and choose the correct option.
Column IColumn II
(I) Torque(a) M°LT-2
(II) stress(b) ML-1T-1
(III) Coefficient of viscosity(c) ML-IT-2
(IV) Potential gradient(d) ML27-2
The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be
A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of cross section of the cylinder carrying the load is 250 cm². The maximum pressure the smaller piston would have to bear is [Assume g = 10 m/s²]:

The sum of all values of \( \alpha \), for which the points whose position vectors are:

\[ \mathbf{r_1} = \hat{i} - 2\hat{j} + 3\hat{k}, \quad \mathbf{r_2} = 2\hat{i} - 3\hat{j} + 4\hat{k}, \quad \mathbf{r_3} = (\alpha+1)\hat{i} + 2\hat{k}, \quad \mathbf{r_4} = \hat{j} + 2\hat{k} \]

are coplanar, is equal to:

If the variance of the frequency distribution

xiFrequency ft
23
36
416
5\(\alpha\)
69
75
86

is 3 , then $\alpha$ is equal to

The number of real roots of the equation $\sqrt{x^2-4 x+3}+\sqrt{x^2-9}=\sqrt{4 x^2-14 x+6}$, is:

The value of tan 9°-tan27°-tan63°+tan81° is____.
Let A be the point (1, 2) and B be any point on the curve \( x^2 + y^2 = 16 \). If the centre of the locus of the point P, which divides the line segment AB in the ratio 3:2 is the point C (\( \alpha, \beta \)), then the length of the line segment AC is:
If the equation of the plane passing through the line of intersection of the planes 2x – y + z = 3, 4x– 3y +5z + 9 = 0 and parallel to the line  \(\frac{x+1}{−2} =\frac{ y+3}{4}= \frac{z−2}{5}\) is ax by+cz+6=0. then a + b + c is equal to 
Glycerine of density 1.25 × 103 kg m-3 is flowing through the conical section of pipe. The area of cross-section of the pipe at its ends is 10 cm2 and 5 cm2 and pressure drop across its length is 3 Nm-2. The rate of flow of glycerine through the pipe is x x10-5 m3 s-1. The value of x is____.
If the formula of borax is \(Na_2B_4Ox(OH)y.zH_2O\) , Find the value of x + y + z. 
Out of the following which has maximum CFSE? ( consider with sign)
The ratio of silica to alumina in cement is:
Which of the following is not ambidentate ligand
Which of the following can be represented as a meridional isomer?
Identify the correct statement about the compound GaAIC14