List of top Questions asked in JEE Main

An acidic buffer is obtained on mixing :

Of the species, NO, NO⁺, NO²⁺ and NO^- , the one with minimum bond strength is :

The electronic spectrum of \([\mathrm{Ti(H_2O)_6}]^{3+}\) shows a single broad peak with a maximum at 20,300 cm^-1 . The crystal field stabilization energy (CFSE) of the complex ion, in kJ mol^-1, is :

It is true that :

Henry's constant (in kbar) for four gases \(\alpha, \beta, \gamma\) and \(\delta\) in water at 298 K is given below :

	\(\alpha\)	\(\beta\)	\(\gamma\)	\(\delta\)
\(K_H\)	50	2	\(2\times10^{-5}\)	0.5

(density of water = \(10^3\ \mathrm{kg\,m^{-3}}\) at 298 K)
This table implies that :

Let C_NaCl and C_BaSO4 be the conductances (in S) measured for saturated aqueous solutions of NaCl and BaSO₄, respectively, at a temperature T. Which of the following is false?

The complex that can show optical activity is :

A person of 80 kg mass is standing on the rim of a circular platform of mass 200 kg rotating about its axis at 5 revolutions per minute (rpm). The person now starts moving towards the centre of the platform. What will be the rotational speed (in rpm) of the platform when the person reaches its centre ________.

When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to \(0^\circ\), the surface tension of the liquid, in milliNewton \(\mathrm{m^{-1}}\), is [\(\rho_{\mathrm{(liquid)}} = 900\ \mathrm{kg\,m^{-3}}\), \(g = 10\ \mathrm{m\,s^{-2}}\)]
(Give answer in closest integer) ________.

The atomic number of the element unnilennium is :

A bakelite beaker has volume capacity of 500 cc at \(30^\circ\)C. When it is partially filled with \(V_m\) volume (at \(30^\circ\)C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If \(\gamma_{\mathrm{(beaker)}} = 6\times10^{-6}\ {}^\circ\mathrm{C^{-1}}\) and \(\gamma_{\mathrm{(mercury)}} = 1.5\times10^{-4}\ {}^\circ\mathrm{C^{-1}}\), where \(\gamma\) is the coefficient of volume expansion, then \(V_m\) (in cc) is close to ________.

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is :

The magnetic field of a plane electromagnetic wave is
\(\vec{B} = 3\times 10^{-8}\sin\left[200\pi (y+ct)\right]\hat{i}\) T
where \(c = 3\times 10^{8}\ \mathrm{ms^{-1}}\) is the speed of light. The corresponding electric field is :

When the wavelength of radiation falling on a metal is changed from 500 nm to 200 nm, the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :

A balloon filled with helium (\(32^\circ\)C and 1.7 atm.) bursts. Immediately afterwards the expansion of helium can be considered as

Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of the cylinder is \(I = M\left(\frac{R^2}{4} + \frac{L^2}{12}\right)\). If such a cylinder is to be made for a given mass of a material, the ratio \(\frac{L}{R}\) for it to have minimum possible I is

In a Young's double slit experiment, light of 500 nm is used to produce an interference pattern. When the distance between the slits is 0.05 mm, the angular width (in degree) of the fringes formed on the distance screen is close to

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wavetrain of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wavetrain (in cm) when it reaches the top of the rope ?

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of \(\frac{\mu_0 I}{\pi}\) is :

A charged particle carrying charge \(1\ \mu\)C is moving with velocity \((2\hat i + 3\hat j + 4\hat k)\) ms\(^{-1}\). If an external magnetic field of \((5\hat i + 3\hat j - 6\hat k) \times 10^{-3}\) T exists in the region where the particle is moving then the force on the particle is \(\vec F \times 10^{-9}\) N. The vector \(\vec F\) is :

The value of \((0.16)^{\log_{2.5}\left(\frac{1}{3} + \frac{1}{3^2} + \ldots \text{to } \infty\right)}\) is equal to _______ .

When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is

If \(\lim_{x \to 0}\left\{\frac{1}{x^8}\left(1 - \cos\frac{x^2}{2} - \cos\frac{x^2}{4} + \cos\frac{x^2}{2}\cos\frac{x^2}{4}\right)\right\} = 2^{-k}\), then the value of k is _______ .

If \(\left(\frac{1+i}{1-i}\right)^{\frac{m}{2}} = \left(\frac{1+i}{1-i}\right)^{\frac{n}{3}} = 1\), \((m, n \in N)\) then the greatest common divisor of the least values of \(m\) and \(n\) is _______ .

Let \(A = \begin{bmatrix} x & 1 \\ 1 & 0 \end{bmatrix}\), \(x \in \mathbb{R}\) and \(A^4 = [a_{ij}]\). If \(a_{11} = 109\), then \(a_{22}\) is equal to _______ .