List of top Questions asked in JEE Main

Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options

An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be
[If, g = 10 ms^–2 and radius of earth = 6400 km]

If \(z = 2 + 3i\), then \(z^5 + (\overline{z})^5\) is equal to:

1.80 g of solute A was dissolved in 62.5 cm³ of ethanol and freezing point of the solution was found to be 155.1 K. The molar mass of solute A is ____ g mol^–1.
[Given : Freezing point of ethanol is 156.0 K, Density of ethanol is 0.80 g cm^–3, Freezing point depression constant of ethanol is 2.00 K kg mol^–1]

Let A and B be two \(3 × 3\) non-zero real matrices such that AB is a zero matrix. Then

A ball is released from a height h. If t₁ and t₂ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between t₁ and t_2..

If \(\frac{1}{(20-a)(40-a)} + \frac{1}{(40-a)(60-a)} + \ldots + \frac{1}{(180-a)(200-a)} = \frac{1}{256}\), then the maximum value of a is :

For the curve
\(\begin{array}{l}C : \left(x^2 + y^2 – 3\right) + \left(x^2 – y^2 – 1\right)^5 = 0, \end{array}\)

\((α, α), α > 0\), on C is equal to ________.

For a cell, \(Cu(s)|Cu^{2+}(0.001M)||Ag^+(0.01M)|Ag(s)\)
the cell potential is found to be \(0.43 V\) at \(298 K\). The magnitude of standard electrode potential for \(Cu^{2+}/{Cu}\) is ____ \(× 10^{–2}\) V.
[Given: \(E_{Ag^+/Ag^⊖}=0.80\) V and \(\frac {2.303RT}{F}=0.06 V\)]

Let S be the set containing all 3 × 3 matrices with entries from {-1, 0, 1}. The total number of matrices A ∈ S such that the sum of all the diagonal elements of A^T A is 6 is ________.

If the length of the latus rectum of the ellipse x² + 4y² + 2x + 8y – λ = 0 is 4, and l is the length of its major axis, then λ + l is equal to ________.

Which of the following matrices can NOT be obtained from the matrix \(\begin{bmatrix} -1 &2 \\  1 & -1 \end{bmatrix}\) by a single elementary row operation?

The vertical component of the earth’s magnetic field is 6 × 10^–5 T at any place where the angle of dip is 37°. The earth’s resultant magnetic field at that place will be (Given tan 37° = ¾)

Sum of oxidation state (magnitude) and coordination number of cobalt in \(Na[Co(bpy)Cl_4]\) is____ .
(Given : bpy =)

If \(\lim_{{x \to 0}} \frac{\alpha e^x + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \frac{2}{3}\), where \(\alpha, \beta, \gamma \in \mathbb{R}\) then which of the following is NOT correct?

Consider the following sulphur based oxoacids.
\(H_2SO_3,H_2SO_4,H_2S_2O_8 \)and \(H_2S_2O_7\)
Amongst these oxoacids, the number of those with peroxo (O–O) bonds is_____.

The reaction of zinc with excess of aqueous alkali, evolves hydrogen gas and gives:

Lithium nitrate and sodium nitrate, when heated separately, respectively, give :

The integral \(\int_0^{\frac{\pi}{2}} \frac{1}{3 + 2\sin x + \cos x} \, dx\) is equal to

As shown in the figure, a potentiometer wire of resistance 20 Ω and length 300 cm is connected with resistance box (R.B.) and a standard cell of emf 4 V. For a resistance ‘R‘ of resistance box introduced into the circuit, the null point for a cell of 20 mV is found to be 60 cm. The value of ‘R ‘ is Ω.

A 1.84 mg sample of polyhydric alcoholic compound ‘X’ of molar mass 92.0 g/mol gave 1.344 mL of H₂ gas at STP. The number of alcoholic hydrogens present in compound ‘X’ is____.

Number of lone pairs of electrons in the central atom of SCl₂, O₃, CIF₃ and SF₆, respectively, are: