List of top Questions asked in JEE Main

if f(x)= \(\frac{(tan1\degree)x+\log_e(123)}{x\log_e(1234)-(tan1\degree)},x>0\) , then the least value of \(f(f(x))+f(f(\frac{4}{x}))\)is

Let the complex number \( z = x + iy \) be such that \(\frac{2z - 3i}{2z + i}\) is purely imaginary. If \( x + y^2 = 0 \), then \( y^4 + y^2 - y \) is equal to

If I(x) = \(\int e^{sin^2x}\)\((cos \;x \;sin \;2x - sin \;x)dx\) and I (0) = 1, then \(I(π/3)\) is equal to

Let the ellipse \(E : x^2 + 9y^2 = 9\) intersect the positive x- and y-axes at the points A and B respectively Let the major axis of E be a diameter of the circle C. Let the line passing through A and B meet the circle C at the point P. If the area of the triangle which vertices A, P and the origin O is m/n , where m and n are coprime, then m – n is equal to 

Let two vertices of triangle ABC be (2, 4, 6) and (0, –2, –5), and its centroid be (2, 1, –1). If the image of third vertex in the plane x + 2y + 4z = 11 is (α, β, γ), then αβ + βγ + γα is equal to

Let P be the point of intersection of the line \(\frac{x+3}{3}=\frac{y+2}{1}=\frac{1-z}{2}\) and the plane x + y + z = 2. If the distance of the point P from the plane 3x – 4y + 12z = 32 is q, then q and 2q are the roots of the equation 

Let O be the origin and the position vector of the point P be \(\hat i-2\hat j+3\hat k\). If the position vectors of the points A, B and C are \(-2\hat i+\hat j-3\hat k,2\hat i+4\hat j-2\hat k\) and \(-4\hat i+2\hat j-\hat k\) respectively then the projection of the vector \(\overrightarrow{OP}\) on a vector perpendicular to the vectors \(\overrightarrow{ AB}\) and \(\overrightarrow {AC}\) is

The shortest distance between the lines \(\frac{x+2}{1}=\frac{y}{-2}=\frac{z-5}{2}\) and \(\frac{x-4}{1}=\frac{y-1}{2}=\frac{z+3}{0}\) is

An arc PQ of a circle subtends a right angle at its centre O. The mid point of the arc PQ is R. If OP = μ, OR=v and OQ=αv+βv, then α, β² are the roots of the equation

\(96\cos\frac{π}{33}\cos \frac{2π}{33}\cos\frac{4π}{33}\cos\frac{8π}{33}\cos\frac{16π}{33}\) is equal to

Let a, b, c be three distinct positive real numbers such that (2a)^log_ea = (bc)^log_eb and b^log_e2 = a^log_ec. Then 6a + 5bc is equal to _____.

Let f : (-2, 2) → IR be defined by \(f(x) =   \begin{cases}     x[x]       & \quad -2<x<0\\     (x-1)[x],  & \quad 0\leq x<2   \end{cases}\)
Where [x] denotes the greatest integer function. If m and n respectively are the number of points in (-2, 2) at which y = |f(x)| is not continuous and not differentiable, then m + n is equal to ______.

Let y = p(x) be the parabola passing through the points (–1, 0), (0, 1) and (1, 0). If the area of the region \(\{x,y):(x+1)^2+(y-1)^2≤1,y≤p(x)\}\) is A, then 12(π-4A) is equal to__.

Let a common tangent to the curves y² = 4x and (x – 4)² + y² = 16 touch the curves at the points P and Q. Then (PQ)² is equal to ________.

The distance between two plates of a capacitor is \(d\) and its capacitance is \(C_1\), when air is the medium between the plates. If a metal sheet of thickness \(\frac {2d}{3}\) and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes \(C_2\). The ratio \(\frac {C_2}{C_1}\) is

A gas is compressed adiabatically, which one of the follwing statement is NOT true.

Given below are two statement:
statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g).
statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum.
In the light of the above statements , choose the correct answer from the options given below

The time period of a satellite revolving above earth's surface at a height equal to R will be
(given: \(g= \pi^2 \ m/s^2\), R= radius of earth)

Two projectiles are projected at 30° and 60° with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is :

A rectangular block of mass 5 kg attached to an horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3.14s. The maximum force exerted by spring on block is _____N.

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section 2.0 cm². The area of cross section at the oulet is 10 mm². If the piston is pushed at a speed of 4 cm s^-1, the speed of outgoing fluid is ______ cm s^-1.

A force of \(-P\hat k \) acts on the origin of the coordinate system. The torque about the point \((2, -3)\) is \(P(a\hat i+b\hat j)\), The ratio of \(\frac ab\) is \(\frac x2\). The value of x is -

If the maximum load carried by an elevator is 1400 kg (600 kg - Passengers + 800 kg- elevator), which is moving up with a uniform speed of 3 ms^-1 and the frictional force acting on it is 2000 N, then the maximum power used by the motor is ____ kW. (g=10 m/s²)

An electron revolves around an infinite cylindrical wire having uniform linear charge density \(2×10^{–8}\ Cm^{-1}\) in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ____ \(\times 10^6 ms^{-1}\). Given mass of electron = \(9\times10^{-31}\) kg.

If 917 Å be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be _____ Å.