List of top Questions asked in JEE Main- 2021

The 3D figure shows the view of an object. Identify the correct view looking in the direction of arrow, from the answer figure's.

The 3D figure shows the view of an object. Identify the correct view looking in the direction of arrow, from the given answer figure's.

Let \(f(x)=\max\left\{x^{2},x^{3}\right\}\) for all \(x\in\mathbf{R}\). Then which of the following is NOT true ?

\(\lim_{x\to 0}\frac{1}{x^{2}}\left(\mathrm{e}^{x^{2}}-\cos\frac{x}{2}\right)\) is equal to :

The 3D figure shows view of an object, looking in the direction of arrow, identify the correct elevation from the answer figures.

If \(\int\sqrt{\frac{\cos(x-\theta)}{\cos(x+\theta)}}\,\mathrm{d}x=\alpha\sin^{-1}\left(\frac{\sin x}{\cos\theta}\right)+\beta\log_{\mathrm e}\left|\cos x+\sqrt{\cos^{2}x-\sin^{2}\theta}\right|+\mathrm{C}\),
where C is a constant of integration and \(\frac{\pi}{6}<\theta<\frac{\pi}{4}\), then \(\alpha\sin\theta+\beta\cos\theta\) is equal to :

The sum of the series
\(\frac{1}{6}+\frac{5}{6^{2}}+\frac{19}{6^{3}}+\ldots+\frac{3^{10}-2^{10}}{3^{10}\cdot 2^{10}}\) is :

Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation \(x^{2}+\sqrt{3}\,x+1=0\). Then \(\alpha^{2022}+\beta^{2022}\) is equal to :

The sum of all values of \(\lambda\), for which the system of equations
\(x+y+z=1\)
\(x+2y+4z=\lambda\)
\(x+4y+10z=\lambda^{2}\)
has infinitely many solutions, is :

If \(A=\begin{pmatrix}0&0&2\\1&0&0\\0&-1&0\end{pmatrix}\), then :

The domain of the function, \(f(x)=\sqrt{\frac{\log_{0.6}|x-2|}{|x|}}\) is :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Over the last two decades collective attention span is decreasing.
Reason R : Quick availability and rapid access to large amount of information leads to loss of interest in one topic very quickly.
In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R :
Assertion A : In past two decades, rate of divorce has increased in India.
Reason R : Increasing number of married couples do not want to have children.
In the light of the above statements, choose the correct answer from the options given below :

Hundreds of Shanty towns line the river banks, train tracks, and garbage dumps in the Filipino capital. Around a quarter of its 12 million are considered “informal settlers”. Manila is starkly representative of a global problem. According to the United Nations, about a quarter of the World’s urban population lives in slums.

Slum tourism takes outsiders through their most impoverished marginalized districts. Slum tourism sparks considerable debate around an uncomfortable moral dilemma. Many consider the practice little more than slack-jawed privileged people gawking at those less fortunate. Others argue they raise awareness and provide numerous examples of giving back to the local communities.

The nearest meaning of “Gawking” in this paragraph would be :

Population of city A, B and C from 1981–2011.

Choose the correct statement :

In a survey, the speeds of 100 vehicles were observed. The following table gives the distribution of vehicle speed and the corresponding number of vehicles.

Vehicle Speed (km hr-1)	No. of Vehicles
20	6
25	20
28	24
29	28
33	15
38	4
40	2
45	1

The median speed of the vehicles is :

Hundreds of Shanty towns line the river banks, train tracks, and garbage dumps in the Filipino capital. Around a quarter of its 12 million are considered ‘informal settlers’. Manila is starkly representative of a global problem. According to the United Nations, about a quarter of the World’s urban population lives in slums.

Slum tourism takes outsiders through their most impoverished marginalized districts. Slum tourism sparks considerable debate around an uncomfortable moral dilemma. Many consider the practice little more than slack-jawed privileged people gawking at those less fortunate. Others argue they raise awareness and provide numerous examples of giving back to the local communities.

Which of the following best justify ‘Slum Tourism’ in the above paragraph ?

The surface area of earth is 510 million km². The land area is thirty percent of total surface. Urban land is three percent of total land surface. World population is 7.8 billion and fifty five percent is urban population. Find the closest correct answer.

The following pie-charts show the distribution of students enrolled in higher secondary and in college education, with respect to the household income of their families.

The ratio between the number of students from LIG household category studying at higher secondary to those in college is :

Map Reading.

In the given diagram, water body is located at a level :

As per 73^rd amendment act (73^rd CAA) 1992 first time one third (1/3) reservation for women was provided in which of the following ?

Map Reading.

In the given diagram, for a person to travel from railway station to temple, one will have to move in ________ direction.

Map Reading.

With reference to the diagram, choose the correct statement.

Which one of the following south Indian states has the highest ground water utilization (in percent) of its total groundwater potential ?

Which of these schemes / programmes by Government of India is linked to heritage cities ?