List of top Questions asked in JEE Main

The number of common tangents, to the circles $ x^2 + y^2 - 18x - 15y + 131 = 0 $ and $ x^2 + y^2 - 6x - 6y - 7 = 0 $, is

Let the foot of perpendicular of the point P(3, -2, -9) on the plane passing through the points (-1, -2, -3), (9, 3, 4), (9, -2, 1) be Q(α, β, γ). Then the distance of Q from the origin is

Let S be the set of all values of λ, for which the shortest distance between the lines x-λ/0 =y-3/4 = z+6/1 and x+λ/3 = y/-4 = z-6/0 is 13. Then 8 | $ \sum_{ λ∈S} λ| is $

Let S be the set of all (λ, μ) for which the vectors $ λ {i}ˆ-jˆ+kˆ, iˆ +2jˆ+µkˆ and 3iˆ -4jˆ +5kˆ, where λ-μ = 5, are coplanar, then $$ \sum_{(λ, μ) εs}80(λ^2, μ^2) $ is equal to

Let ABCD be a quadrilateral. If E and F are the mid points of the diagonals AC and BD respectively and $ (\vec{AB}-\vec{BC})+(\vec{AD}-\vec{DC})=k \vec{FE} $, then k is equal to

Negation of $ p \land (q \land \neg (p \land q)) $ is:}

Let A = {1, 2, 3, 4} and R be a relation on the set AxA defined by R = {((a, b), (c, d)): 2a+3b = 4c +5d}. Then the number of elements in R is

A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is

If the sum of the series $\left(\frac{1}{2}-\frac{1}{3}\right) + \left(\frac{1}{2^2}-\frac{1}{2·3} + \frac{1}{3^2}\right) + \left(\frac{1}{2^2}-\frac{1}{2^2·3} + \frac{1}{2·3^2} - \frac{1}{3^3}\right) + \left(\frac{1}{2^4}-\frac{1}{2^3·3} + \frac{1}{2^2·3^2} - \frac{1}{2·3^3} + \frac{1}{3^4}\right) + ........ $
is $\frac{α}{β}$ , where α and β are co-prime, then α+3β is equal to ________

Let an ellipse with centre (1, 0) and latus rectum of length $\frac{1}{2}$ have its major axis along x-axis. If its minor axis subtends an angle 60° at the foci, then the square of the sum of the lengths of its minor and major axes is equal to

Let the plane P contain the line 2x+y-z-3=0=5x-3y+4z+9 and be parallel to the line $\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}$. Then the distance of the point
A(8, -1, -19) from the plane P measured parallel to the line $\frac{x}{-3}=\frac{y-5}{4}=\frac{2-z}{-12}$ is equal to ___________.

If the line x = y = z intersects the line
xsinA+ysinB+zsinC-18=0=xsin2A+ysin2B+zsin2C-9,
where A, B, C are the angles of a triangle ABC, then 80$\left( sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2} \right)$ is equal to ________.

A thermodynamic system is taken through cyclic process. The total work done in the process is:

A vector in x-y plane makes an angle of 30º with y-axis. The magnitude of y-component of vector is $2\sqrt3$. The magnitude of x -component of the vector will be :

The speed of a wave produced in water is given by v=$λ^ag^bρ^c$. Where λ,g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are:

The position vector of a particle related to time t is given by $\vec{r}=(10t\hat{i}+15t^2\hat{j}+7\hat{k})m$
The direction of net force experienced by the particle is :

A single slit of width a is illuminated by a monochromatic light of wavelength 600 nm. The value of 'a' for which first minimum appears at θ=30° on the screen will be :

Given below are two statements:
Statement I : The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination.
Statement II : The resistivity of the material is independent of temperature.
In the light of the above statements, choose the correct answer from the options given below :

The fundamental frequency of vibration of a string stretched between two rigid support is 50 Hz. The mass of the string is 18 g and its linear mass density is 20 g/m. The speed of the transverse waves so produced in the string is_______ ms^-1.

There is an air bubble of radius 1 mm in a liquid of surface tension 0.075 N/m and density 1000 kg/m3. The bubble is at a depth of 10 cm below the free surface. By what amount is the pressure inside the bubble greater than the atmospheric pressure is ___pa(g-10 ms^-2).

As per given figure A, B and C are the first, second and third excited energy level of hydrogen atom respectively. If the ratio of the two wavelengths (ie. $\frac{λ_1}{λ_2}$) is $\frac{7}{4n}$ , then the value of n will be____.

The refractive index of a transparent liquid filled in an equilateral hollow prism is √2. The angle of minimum deviation for the liquid will be____.

A 20 cm long metallic rod is rotated with 210 rpm about an axis normal to the rod passing through its one end. The order end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field 0.2T parallel to the axis exists everywhere. The emf developed between the centre and the ring is ____ mV.

An electron in a hydrogen atom revolves around its nucleus with a speed of 6.76 × 106 ms-1 in an orbit of radius 0.52 A°. The magnetic field produced at the nucleus of the hydrogen atom is _______T.

A network of four resistances is connected to 9V battery, as shown in figure. The magnitude of voltage difference between the points A and B is ______V.