List of top Questions asked in JEE Main

If $\tan 15^{\circ}+\frac{1}{\tan 75^{\circ}}+\frac{1}{\tan 105^{\circ}}+\tan 195^{\circ}=2 a$, then the value of $\left(a+\frac{1}{a}\right)$ is :

If $[ t ]$ denotes the greatest integer $\leq t$, then the value of $\frac{3( e -1)}{ e } \int\limits_1^2 x^2 e^{[x]+\left[x^3\right]} dx$ is :

Let $y=x+2,4 y=3 x+6$ and $3 y=4 x+1$ be three tangent lines to the circle $(x-h)^2+(y- k )^2= r ^2$ Then $h + k$ is equal to :

If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is:

The coefficient of $x^{301}$ in $(1+x)^{500}+x(1+x)^{499}+x^2(1+x)^{498}+\ldots \ldots +x^{500}$ is :

If $a_n=\frac{-2}{4 n^2-16 n+15}$, then $a_1+a_2+\ldots \ldots+a_{25}$ is equal to:

The minimum number of elements that must be added to the relation $R=\{(a, b),(b, c)\}$ on the set $\{ a , b , c \}$ so that it becomes symmetric and transitive is :

If $P ( h , k )$ be a point on the parabola $x=4 y^2$, which is nearest to the point $Q (0,33)$, then the distance of $P$ from the directrix of the parabola $y^2=4(x+y)$ is equal to :

Let the system of linear equations $ x+y+ kz =2$ $ 2 x+3 y-z=1 $ $ 3 x+4 y +2 z= k$ have infinitely many solutions Then the system $ ( k +1) x+(2 k -1) y=7$ $ (2 k +1) x+( k +5) y=10$ has:

Let $A= \begin{pmatrix} m & n \\ p & q\end{pmatrix}, d=|A| \neq 0$ and $|A-d(\operatorname{Adj} A)|=0$ Then

Match List I with List II: 

List - I		List - II
A.	Torque	I.	kg m-1 s-2
B.	Energy Density	II.	kg ms-1
C.	Pressure gradient	III.	kg m-2 s-2
D.	Impulse	IV.	kg m2 s-2

Choose the correct answer from the options given below : 

As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $Q$ in three different regions I, II and III is given by: (I: r $<$ a, II: $a $<$ r $<$ b$, III: $r$>$b)$

An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth Its velocity when it strikes the earth's surface, ignoring air resistance, will be

A force is applied to a steel wire ' $A$ ', rigidly clamped at one end As a result elongation in the wire is $02\, mm$ If same force is applied to another steel wire ' $B$ ' of double the length and a diameter $24$ times that of the wire ' $A$ ', the elongation in the wire ' $B$ ' will be (wires having uniform circular cross sections)

A machine gun of mass $10\, kg$ fires $20 \,g$ bullets at the rate of $180$ bullets per minute with a speed of $100 \,m s ^{-1}$ each The recoil velocity of the gun is

A current carrying rectangular loop $P Q R S$ is made of uniform wire The length $P R=Q S=5 \,cm$ and $P Q=R S=100\, cm$ If ammeter current reading changes from $I$ to $2 I$, the ratio of magnetic forces per unit length on the wire $P Q$ due to wire $R S$ in the two cases respectively $\left(f_{P Q}^I: f_{P Q}^{2 I}\right)$ is:

As shown in the figure, a current of $2 A$ flowing in an equilateral triangle of side $4 \sqrt{3} cm$ The magnetic field at the centroid $O$ of the triangle is

 (Neglect the effect of earth's magnetic field)

A block of $\sqrt{3} kg$ is attached to a string whose other end is attached to the wall An unknown force $F$ is applied so that the string makes an angle of $30^{\circ}$ with the wall The tension $T$ is:(Given $g =10 \,ms ^{-2}$ )

The equivalent resistance between A and B is _________.

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $R$
Assertion A: Efficiency of a reversible heat engine will be highest at $-273^{\circ} C$ temperature of cold reservoir
Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as $n =\left(1-\frac{T_2}{T_1}\right)$
In the light of the above statements, choose the correct answer from the options given below

Match List I with List II: 

List I		List II
A.	Attenuation	I.	Combination of a receiver and transmitter
B.	Transducer	II.	Process of retrieval of information from the carrier wave at received
C.	Demodulation	III.	Converts one form of energy into another
D.	Repeater	IV.	Loss of strength of a signal while propagating through a medium

Choose the correct answer from the options given below :

In the given circuit, rms value of current $\left( I _{ rms }\right)$ through the resistor $R$ is:

A thin prism $P_1$ with an angle $6^{\circ}$ and made of glass of refractive index $154$ is combined with another prism $P_2$ made from glass of refractive index $172$ to produce dispersion without average deviation The angle of prism $P_2$ is