List of top Questions asked in JEE Main

Height of tower AB is 30 m where B is foot of tower. Angle of elevation from a point C on level ground to top of tower is 60° and angle of elevation of A from a point D x m above C is 15° then find the area of quadrilateral ABCD.

If $f(x) + f(\pi-x) = \pi^{2}$ then $_{0}\int^{\pi}f(x) sinx dx$ ?

Find the sum of series: $2*2^2 - 2*3^2 + 2*4^2 +$ $….(20 \,terms)$

Let the number of elements in sets $A$ and $B$ be five and two respectively. Then the number of subsets of $A \times B$ each having at least 3 and at most 6 elements is:

Let S = $\{z \in C-\{i,2i\}:\frac{z^2+8iz-15}{z^2-3iz-2}\in R\}$ if $\alpha-\frac{13}{11}i\in S, a \in R-{0}$, then $242\alpha^2$ is equal to ____.

If all the particles have same kinetic energy, The relation between the wavelengths of alpha particle, electron and proton is:

Let the shortest distance between the lines $L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0$ and $L_1: x+1=y-1=4-z$ be $2 \sqrt{6}$ If $(\alpha, \beta, \gamma)$ lies on $L$, then which of the following is NOT possible?

The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by $50 \%$ The percentage change in voltage sensitivity of the galvanometer will be:

Given below are two statements :
Statement I : In a typical transistor, all three regions emitter, base and collector have same doping level.
Statement II : In a transistor, collector is the thickest and base is the thinnest segment.
In the light of the above statements, choose the most appropriate answer from the options given below.

If the functions $f(x)=\frac{x^3}{3}+2 b x+\frac{a x^2}{2}$ and $g(x)=\frac{x^3}{3}+a x+b x^2, a \neq 2 b$ have a common extreme point, then $a+2 b+7$ is equal to:

Let $a,b,c>1,a^3,b^3 \text{ and } c^3$ be in A.P., and $log_ab, log_ca \text{ and } log_bc$ be in G.P. If the sum of first 20 terms of an A.P., whose first term is $\frac{a+4b+c}{3}$ and the common difference is $\frac{a−8b+c}{10}$ is −444, then abc is equal to:

Let $N$ denote the number that turns up when a fair die is rolled If the probability that the system of equations$ x+y+z=1 $ $ 2 x + Ny +2 z=2 $ $ 3 x +3 y+ N z=3$ has unique solution is $\frac{k}{6}$, then the sum of value of $k$ and all possible values of $N$ is

Choose the correct representation of conductometric titration of benzoic acid vs sodium hydroxide

For an object placed at a distance $24\, m$ from a lens, a sharp focused image is observed on a screen placed at a distance $12\, cm$ from the lens A glass plate of refractive index $15$ and thickness $1 \,cm$ is introduced between lens and screen such that the glass plate plane faces parallel to the screen By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

Let $P$ be the plane, passing through the point $(1,-1,-5)$ and perpendicular to the line joining the points $(4,1,-3)$ and $(2,4,3)$. Then the distance of $P$ from the point $(3,-2,2)$ is

Electron beam used in an electron microscope, when accelerated by a voltage of $20 kV$, has a de-Broglie wavelength of $\lambda_0$. If the voltage is increased to $40 kV$, then the de-Broglie wavelength associated with the electron beam would be:

As shown in the figure a block of mass $10\, kg$ lying on a horizontal surface is pulled by a force $F$acting at an angle $30^{\circ}$, with horizontal For $\mu_{ s }=0.25$, the block will just start to move for the value of $F$ : [Given g=10ms^-2]

For the system of linear equations$\alpha x+y+z=1, x+\alpha y+z=1, x+y+\alpha z=\beta$ which one of the following statements is NOT correct ?

The tangents at the point $A (1,3)$ and $B (1,-1)$ on the parabola $y^2-2 x-2 y=1$ meet at the point $P$ Then the area (in unit $^2$ ) of $\triangle PAB$ is :-

A body of mass 200 g is tied to a spring of spring constant 12.5 N/m, while the other end of the spring is fixed at point $ O $. If the body moves about $ O $ in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s, then the ratio of extension in the spring to its natural length will be:

Let αx=exp(x^βy^γ) be the solution of the differential equation 2x²ydy−(1−xy²) dx = 0, x>0 , y(2)=$\sqrt {log_e2}$. Then α+β−γ equals :

If $A=\frac{1}{2}\begin{bmatrix}1 & \sqrt{3} \\ -\sqrt{3} & 1\end{bmatrix}$, then :

An organic compound $[ A ]\left( C _4 H _{11} N \right)$, shows optical activity and gives $N _2$ gas on treatment with The structure of $A$ is :

In the wet tests for identification of various cations by precipitation, which transition element cation doesn't belong to group IV in qualitative inorganic analysis ?

Element not present in Nessler’s reagent is