List of top Questions asked in JEE Main

Let for A = \(\begin{bmatrix} 1 & 2 & 3 \\ \alpha & 3 & 1 \\ 1 & 1 & 2 \end{bmatrix}\), |A| = 2. If |2adj (2adj (2A))| = 32ⁿ , then 3n + α is equal to

Let for a triangle ABC,
\(\vec{AB}=-2\hat{i}+\hat{j}+3\hat{k} \)
\(\vec{CB}=α\hat{i}+β\hat{j}+γ\hat{k} \)
\(\vec{CA}=4\hat{i}+3\hat{j}+δ\hat{k} \)
If \(δ>0\) and the area of the triangle ABC is \(5\sqrt6\), then \(\vec{CB}.\vec{CA}\) is equal to

The plane, passing through the points (0, -1, 2) and (-1, 2, 1) and parellel to the line passing through (5,1,-7) and (1,-1,-1), also passes through the point

The line, that is coplanar to the line \(\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}\) is

The correct order of basicity of oxides of vanadium is

If \(\lim\limits_{x\rightarrow0}\frac{e^{ax}-\cos(bx)-\frac{cxe^{-ce}}{2}}{1-\cos(2x)}=17\) ,then 5a² + b² is equal to

The area of the region \(\left\{(x,y):x^2≤y≤|x^2-4|,y≥1\right\}\) is

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.

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 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.

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____.

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____.

If the total charge stored in capacitors is equal to 100μc, then find the value of x. (10V)

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).

A person driving car at a constant speed of 15 m/s is approaching a vertical wall. The person notices a change of 40 Hz in the frequency of his car’s horn upon reflection from the wall. The frequency of horn is ____ Hz.

Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is __________ \(× 10^{-3} \)kg-\(m^2\)

A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric constant K = 4. The thickness of the dielectric material is x, where x < d. Let C1 and C2 be the capacitance of the system for \(x =\) \(\frac{1}{3}d\) and \(x=\frac{2}{3}d\), respectively. If C₁ = 2μF, the value of C₂is _______ μF.

An ideal transformer with purely resistive load operates at 12 kV on the primary side. It supplies electrical energy to a number of nearby houses at 120 V. The average rate of energy consumption in the houses served by the transformer is 60 kW. The value of resistive load (Rs) required in the secondary circuit will be ________ mΩ.

A particle of mass 10 g moves in a straight line with retardation 2x, where x is the displacement in SI units. Its loss of kinetic energy for above displacement is \((10/x)^{-n}\)J. The value of n will be ____________

The radius of fifth orbit of the Li++ is __________ × 10^-12 m.
Take : radius of hydrogen atom = 0.51 Å

The length of a metallic wire is increased by 20% and its area of cross section is reduced by 4%. The percentage change in resistance of the metallic wire is ______

A steel rod bas a radius of 20 mm and a length of 2.0 m. A force of 62.8 kN stretches it along its length. Young's modulus of steel is 2.0 × 10^{11} N/m^2 . The longitudinal strain produced in the wire is _______ × 10^{-5}

Two identical circular wires of radius 20 cm and carrying current \(\sqrt2 \)A are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wires is _________ × 10^{-8} T.

The induced emf can be produced in a coil by
A. moving the coil with uniform speed inside uniform magnetic field
B. moving the coil with non uniform speed inside uniform magnetic field
C. rotating the coil inside the uniform magnetic field
D. changing the area of the coil inside the uniform magnetic field
Choose the correct answer from the options given below :

A monochromatic light wave with wavelength λ₁ and frequency ν₁, in air, enters another medium. If the angle of incidence and angle of refraction at the interface are 45° and 30° respectively, then the wavelength λ₂ and frequency ν₂of the refracted wave are: