List of top Questions asked in JEE Main

The largest natural number $n$ such that $3^n$ divides $66!$ is:

$5 \,g$ of $NaOH$ was dissolved in deionized water to prepare a $450 \,mL$ stock solution What volume (in $mL$ ) of this solution would be required to prepare $500 \,mL$ of $01\, M$ solution? Given: Molar Mass of $Na, O$ and $H$ is 23,16 and $1 \,g\, mol ^{-1}$ respectively

Correct order of strength of H-bond in the following -:
(A) Liquid water
(B) Ice
(C) Impure water

$K_2Cr_2O_7$ paper acidified with dil. $H_2SO_4$ turns green when exposed to :

Let $S$ denote the set of all real values of $\lambda$ such that the system of equations
$ \lambda x+y+z=1 $
$x+\lambda y+z=1 $
$x+y+\lambda z=1$
is inconsistent, then $\displaystyle \sum_{\lambda \in S}\left(|\lambda|^2+|\lambda|\right)$ is equal to

If the velocity of light $c$, universal gravitational constant $G$ and Planck's constant $h$ are chosen as fundamental quantities The dimensions of mass in the new system is :

A Carnot engine operating between two reservoirs has efficiency $\frac{1}{3}$ When the temperature of cold reservoir raised by $x$, its efficiency decreases to $\frac{1}{6}$ The value of $x$, if the temperature of hot reservoir is $99^{\circ} C$, will be :

Two polaroide $A$ and $B$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other Now, another polaroid $C$ is placed between $A$ and $B$ bisecting angle between them If intensity of unpolarized light is $I _0$ then intensity of transmitted light after passing through polaroid $B$ will be:

Considering a group of positive charges, which of the following statements is correct ?

Let $H$ be the hyperbola, whose foci are $(1 \pm \sqrt{2}, 0)$ and eccentricity is $\sqrt{2}$. Then the length of its latus rectum is _____

If a point $P (\alpha, \beta, \gamma)$ satisfying $(\alpha\,\, \beta\,\, \gamma) \begin{pmatrix} 2 & 10 & 8 \\9 & 3 & 8 \\8 & 4 & 8\end{pmatrix}=(0\,\,0\,\,0) $ lies on the plane $2 x+4 y+3 z=5$, then $6 \alpha+9 \beta+7 \gamma$ is equal to :

Benzyl isocyanide can be obtained by : Choose the correct answer from the options given below :

In the extraction of copper, its sulphide ore is heated in a reverberatory furnace after mixing with silica to:

To inhibit the growth of tumours, identify the compounds used from the following : A EDTA B Coordination Compounds of Pt C D-Penicillamine D Cis - Platin Choose the correct answer from the option given below:

The number of points on the curve $y=54 x^5-135 x^4-70 x^3+180 x^2+210 x$ at which the normal lines are parallel $to x+90 y+2=0$ is

If the four points, whose position vectors are $3 \hat{i}-4 j+2 \hat{k}, l+2 j-\hat{k}_4-2 \hat{k}-j+3 \hat{k}$ and $5 \hat{i}-2 \alpha \hat{j}+4 \hat{k}$ are coplanar, then a is equal to

If two charges $q _1$ and $q _2$ are separated with distance ' $d$ ' and placed in a medium of dielectric constant $K$ What will be the equivalent distance between charges in air for the same electrostatic force?

Let $\alpha$ be a root of the equation $(a-c) x^2+(b-a) x+(c-b)=0$where $a , b , c$ are distinct real numbers such that the matrix $\begin{bmatrix}\alpha^2 & \alpha & 1 \\ 1 & 1 & 1 \\ a & b & c\end{bmatrix}$is singular Then, the value of $\frac{(a-c)^2}{(b-a)(c-b)}+\frac{(b-a)^2}{(a-c)(c-b)}+\frac{(c-b)^2}{(a-c)(b-a)}$ is

The correct order in aqueous medium of basic strength in case of methyl substituted amines is :

Let $y (x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)\left(1+x^{16}\right)$ Then $y^{\prime}-y^{\prime \prime}$ at $x=-1$ is equal to :

Every planet revolves around the sun in an elliptical orbit:-
A. The force acting on a planet is inversely proportional to square of distance from sun
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun
C. The Centripetal force acting on the planet is directed away from the sun
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit
Choose the correct answer from the options given below:

Given below are two statements:
Statement I : In froth floatation method a rotating paddle agitates the mixture to drive air out of it.
Statement II : Iron pyrites are generally avoided for extraction of iron due to environmental reasons.
In the light of the above statements, choose the correct answer from the options given below:

Consider the lines $L_1$ and $L_2$ given by

$L_1: \frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2} $

$ L_2: \frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3}$

A line $L_3$ having direction ratios $1,-1,-2$, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively Then the length of line segment $P Q$ is

The points of intersection of the line $a x+b y=0,(a \neq b)$ and the circle $x^2+y^2-2 x=0$ are $A (\alpha, 0)$ and $B (1, \beta)$ The image of the circle with $AB$ as a diameter in the line $x+y+2=0$ is :

Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$, be in AP and $a_1+a_3=10$ If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$, then $8 \sigma^2$ is equal to :