List of top Questions asked in JEE Main

The following system of linear equations
\(7x + 6y - 2z = 0\)
\(3x + 4y + 2z = 0\)
\(x - 2y - 6z = 0\), has

In the expansion of \(\left(\frac{x}{\cos\theta} + \frac{1}{x\sin\theta}\right)^{16}\), if \(\ell_1\) is the least value of the term independent of x when \(\frac{\pi}{8} \le \theta \le \frac{\pi}{4}\) and \(\ell_2\) is the least value of the term independent of x when \(\frac{\pi}{16} \le \theta \le \frac{\pi}{8}\), then the ratio \(\ell_2 : \ell_1\) is equal to :

Let a, b \(\in\) R, a \(\ne\) 0 be such that the equation, \(ax^2 - 2bx + 5 = 0\) has a repeated root \(\alpha\), which is also a root of the equation, \(x^2 - 2bx - 10 = 0\). If \(\beta\) is the other root of this equation, then \(\alpha^2 + \beta^2\) is equal to :

The molarity of \(\mathrm{HNO_3}\) in a sample which has density 1.4 g/mL and mass percentage of 63% is _____.
(Molecular Weight of \(\mathrm{HNO_3}\) = 63)

The hardness of a water sample containing \(10^{-3}\) M \(\mathrm{MgSO_4}\) expressed as \(\mathrm{CaCO_3}\) equivalents (in ppm) is ______.
(molar mass of \(\mathrm{MgSO_4}\) is 120.37 g/mol)

A chemist has 4 samples of artificial sweetener A, B, C and D. To identify these samples, he performed certain experiments and noted the following observations :
(i) A and D both form blue-violet colour with ninhydrin.
(ii) Lassaigne extract of C gives positive \(\mathrm{AgNO_3}\) test and negative \(\mathrm{Fe_4[Fe(CN)_6]_3}\) test.
(iii) Lassaigne extract of B and D gives positive sodium nitroprusside test
Based on these observations which option is correct ?

The acidic, basic and amphoteric oxides, respectively, are :

The compound that cannot act both as oxidising and reducing agent is :

\([\mathrm{Pd(F)(Cl)(Br)(I)}]^{2-}\) has n number of geometrical isomers. Then, the spin-only magnetic moment and crystal field stabilisation energy [CFSE] of \([\mathrm{Fe(CN)_6}]^{n-6}\), respectively, are:
[Note : Ignore the pairing energy]

The \(K_{sp}\) for the following dissociation is \(1.6 \times 10^{-5}\)
\(\mathrm{PbCl_{2(s)} \rightleftharpoons Pb^{2+}_{(aq)} + 2Cl^-_{(aq)}}\)
Which of the following choices is correct for a mixture of 300 mL 0.134 M \(\mathrm{Pb(NO_3)_2}\) and 100 mL 0.4 M NaCl ?

B has a smaller first ionization enthalpy than Be. Consider the following statements :
(I) It is easier to remove 2p electron than 2s electron
(II) 2p electron of B is more shielded from the nucleus by the inner core of electrons than the 2s electrons of Be.
(III) 2s electron has more penetration power than 2p electron.
(IV) atomic radius of B is more than Be (Atomic number B = 5, Be = 4)
The correct statements are :

If the magnetic moment of a dioxygen species is 1.73 B.M, it may be :

The distance \(x\) covered by a particle in one dimensional motion varies with time \(t\) as \(x^2 = at^2 + 2bt + c\). If the acceleration of the particle depends on \(x\) as \(x^{-n}\), where \(n\) is an integer, the value of \(n\) is __________

A body of mass \(m=10\) kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s^-1) with which it can be rotated about its other end in space station is : (Breaking stress of wire \(=4.8\times10^{7}\ \mathrm{N\,m^{-2}}\) and area of cross-section of the wire \(=10^{-2}\ \mathrm{cm^2}\)) is:

In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be ________.

A quantity \(f\) is given by \(f=\sqrt{\frac{hc^5}{G}}\) where \(c\) is speed of light, \(G\) universal gravitational constant and \(h\) is the Planck's constant. Dimension of \(f\) is that of :

The electric fields of two plane electromagnetic plane waves in vacuum are given by
\(\vec{E_1}=E_0\hat{j}\cos(\omega t-kx)\) and
\(\vec{E_2}=E_0\hat{k}\cos(\omega t-ky)\)
At \(t=0\), a particle of charge \(q\) is at origin with a velocity \(\vec{v}=0.8c\,\hat{j}\) (\(c\) is the speed of light in vacuum). The instantaneous force experienced by the particle is :

Radiation, with wavelength \(6561\,\mathrm{\AA}\) falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of \(3\times10^{-4}\) T. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :

A body A of mass \(m\) is moving in a circular orbit of radius \(R\) about a planet. Another body B of mass \(\frac{m}{2}\) collides with A with a velocity which is half \(\left(\frac{\vec{v}}{2}\right)\) the instantaneous velocity \(\vec{v}\) of A. The collision is completely inelastic. Then, the combined body :

Three harmonic waves having equal frequency \(\nu\) and same intensity \(I_0\), have phase angles 0, \(\frac{\pi}{4}\) and \(-\frac{\pi}{4}\) respectively. When they are superimposed the intensity of the resultant wave is close to :

If the vectors, \(\vec{p} = (a+1)\hat{i} + a\hat{j} + a\hat{k}\), \(\vec{q} = a\hat{i} + (a+1)\hat{j} + a\hat{k}\) and \(\vec{r} = a\hat{i} + a\hat{j} + (a+1)\hat{k}\) \((a \in R)\) are coplanar and \(3(\vec{p}\cdot\vec{q})^2 - \lambda|\vec{r}\times\vec{q}|^2 = 0\), then the value of \(\lambda\) is ______.

The product \(2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdots\) to \(\infty\) is equal to :

The number of distinct solutions of the equation \(\log_{\frac{1}{2}}|\sin x| = 2 - \log_{\frac{1}{2}}|\cos x|\) in the interval \([0, 2\pi]\), is ____.

Negation of the statement :
\(\sqrt{5}\) is an integer or 5 is an irrational is :

The coefficient of \(x^4\) is the expansion of \((1 + x + x^2)^{10}\) is _____.