List of top Questions asked in JEE Main- 2021

Match List - I with List - II.

	List - I		List - II
(I)	Mehrangarh Fort	(a)	Hyderabad
(II)	Siri Fort	(b)	Kolkata
(III)	Golconda Fort	(c)	Delhi
(IV)	Fort William	(d)	Jodhpur

Choose the correct answer from options given below :

If the sum of mean and variance of a binomial distribution is 15 and the sum of their squares is 117, then the number of independent trials is equal to ________.

Let \(A_{1}, A_{2}, A_{3}, \ldots \ldots\) be an increasing geometric progression. If \(\frac{1}{A_{4}}+\frac{1}{A_{8}}=\frac{10}{63}\) and \(A_{5} A_{7}=441\), then \(3\left(A_{2}+A_{4}\right)\) is equal to ________.

Let the equation of the plane passing through the points \((1,2,6),(2,5,7)\) and perpendicular to the plane \(4x-y+z=15\) be \(ax+by+cz+d=0\). If \(a, b, c, d \in \mathbf{Z}\) with \(\gcd(|a|,|b|,|c|)=1\), then \(|a+b+c+d|\) is equal to ________.

The number of real solutions in the interval \(\left[-\frac{3\pi}{2}, \frac{7\pi}{2}\right]\) of the equation \(4\sin^{2}x-8\sin x+3=0\) is ________.

Match List - I with List - II.

List - I

(I) Hall of Nation

(II) Falling Water, Pennsylvania

(III) Petronas Tower

(IV) Secretariat

List - II

Which among the following is the full form of the 'UNESCO' ?

\(x^{2}+y^{2}-4x-2y-11=0\) is a circle to which tangents are drawn from the point \((4,5)\) which form a quadrilateral with a pair of radii. The area of this quadrilateral in square units is ________.

If \(x^{2}+x+1=0\), then \(-\left\{\left(x-\frac{1}{x}\right)^{2}+\left(x^{2}-\frac{1}{x^{2}}\right)^{2}+\left(x^{3}-\frac{1}{x^{3}}\right)^{2}\right\}\) is ________.

The length of the perpendicular from the point \((1,2,3)\) to the line \(\frac{-x+6}{-3}=\frac{y-7}{2}=\frac{z-7}{-2}\) is ________.

The values of \(x\), for which the vectors \(\vec{a}=\left(x^{2}-16\right) \hat{i}+4\hat{j}-\left(x^{2}-25\right) \hat{k}\) make acute angles with the (positive directions of) coordinate axes lie in :

The minimum value of \(9\tan^{2}\theta+4\cot^{2}\theta\) is ________.

\(\int_{0}^{\pi} \sqrt{\frac{1+\cos 2x}{2}}\, \mathrm{d}x\) is ________.

Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three vectors such that \(|\vec{a}|=|\vec{b}|=\frac{|\vec{c}|}{2}=1\). If \(\vec{a} \times(\vec{a} \times \vec{c})+\vec{b}=\overrightarrow{0}\), then the acute angle between \(\vec{a}\) and \(\vec{c}\) is :

Solution of the differential equation \(\left(1+y^{2}\right) \mathrm{d}x=\left(\tan^{-1}y-x\right) \mathrm{d}y\) is :
(where \(c\) is an arbitrary constant)

Equation of the circle, which is the mirror image of the circle \(x^{2}+y^{2}-2x=0\) with respect to the line \(x+y=2\), is :

If \(A=\begin{bmatrix}1&a\\0&1\end{bmatrix}\), then \(A^{k}\ (k\in\mathbf{N})\) is :

If the equation of a line which divides the line segment joining the points \((1,0)\) and \((3,0)\) in the ratio \(2:1\) and is also perpendicular to it, is \(ax=7\), then the value of \(a\) is equal to :

Derivative of \(\tan^{-1}\left(\frac{2x}{1-x^{2}}\right)\) with respect to \(\sin^{-1}\left(\frac{2x}{1+x^{2}}\right)\) in \((1, \infty)\), is :

The values of \(s\) and \(t\), for which the system of equations
\(x_{1}+x_{2}+x_{3}=5\)
\(x_{1}+2x_{2}+3x_{3}=9\)
\(x_{1}+3x_{2}+sx_{3}=t\)
has no solution, are :

Equations of the common tangent of the ellipse \(\frac{(x+1)^{2}}{2^{2}}+\frac{(y-1)^{2}}{3^{2}}=1\) and the circle \((x+1)^{2}+(y-1)^{2}=4\) are :

The probability of solving a problem in Mathematics by two students X and Y are \(\frac{1}{4}\) and \(\frac{1}{5}\) respectively. If both of them try to solve the problem independently, then the probability that the problem will be solved by exactly one of them is equal to :

Draw a scene of a Kite festival by using colors.

OR

Draw a Harmonic three dimensional composition with the following two types of objects.
(i) CUBOID A : SIZE \(2\) cm \(\times\) \(2\) cm \(\times\) \(2\) cm, 5 Nos.
(ii) CUBOID B : SIZE \(5\) cm \(\times\) \(2\) cm \(\times\) \(2\) cm, 4 Nos.

Use 'Cool Colorscheme' for composition.

Draw a proportionate sketch of given reference image by using any black and white rendering techniques of your own choice.

OR

Decode image and prepare balanced composition in a frame of your choice by using any black and white rendering techniques.

The polar form of the complex number \(\frac{1+i}{1-i}\) is equal to :