List of top Questions asked in JEE Main- 2021

If \((2021)^{3762}\) is divided by 17, then the remainder is __________.

The area of the triangle with vertices \(A(z)\), \(B(iz)\) and \(C(z + iz)\) is :

The line \(2x - y + 1 = 0\) is a tangent to the circle at the point \((2, 5)\) and the centre of the circle lies on \(x - 2y = 4\). Then, the radius of the circle is :

Team 'A' consists of 7 boys and \(n\) girls and Team 'B' has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then \(n\) is equal to :

If the Boolean expression \((p \Rightarrow q) \Leftrightarrow (q * (\sim p))\) is a tautology, then the boolean expression \((p * (\sim q))\) is equivalent to :

If \(A = \begin{pmatrix} 0 & \sin\alpha \\ \sin\alpha & 0 \end{pmatrix}\) and \(\det\left(A^2 - \frac{1}{2}I\right) = 0\), then a possible value of \(\alpha\) is :

In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement?

If the fourth term in the expansion of \((x + x^{\log_2 x})^7\) is 4480, then the value of \(x\) where \(x \in N\) is equal to :

If \(\cot^{-1}(\alpha) = \cot^{-1}2 + \cot^{-1}8 + \cot^{-1}18 + \cot^{-1}32 + \cdots\) upto 100 terms, then \(\alpha\) is :

Two dies are rolled. If both dices have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is :

The system of equations \(kx + y + z = 1\), \(x + ky + z = k\) and \(x + y + zk = k^2\) has no solution if \(k\) is equal to :

The value of
\(4 + \dfrac{1}{5 + \dfrac{1}{4 + \dfrac{1}{5 + \dfrac{1}{4 + \cdots \infty}}}}\) is :

Which of the following is true for \(y(x)\) that satisfies the differential equation
\(\dfrac{dy}{dx} = xy - 1 + x - y\); \(y(0) = 0\) :

Which of the following statements is correct for the function \(g(\alpha)\) for \(\alpha \in R\) such that
\(g(\alpha) = \int_{\pi/6}^{\pi/3} \dfrac{\sin^{\alpha}x}{\cos^{\alpha}x + \sin^{\alpha}x}\,dx\)

The sum of possible values of \(x\) for
\(\tan^{-1}(x + 1) + \cot^{-1}\left(\dfrac{1}{x - 1}\right) = \tan^{-1}\left(\dfrac{8}{31}\right)\) is :

In a triangle PQR, the co-ordinates of the points P and Q are \((-2, 4)\) and \((4, -2)\) respectively. If the equation of the perpendicular bisector of PR is \(2x - y + 2 = 0\), then the centre of the circumcircle of the \(\Delta\)PQR is :

The value of
\(\lim_{x \to 0^+} \dfrac{\cos^{-1}(x - [x]^2) \cdot \sin^{-1}(x - [x]^2)}{x - x^3}\), where \([x]\) denotes the greatest integer \(\le x\) is :

Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is __________ \(\times\) \(10^{21}\). (Round off to the Nearest Integer). [Given : \(\mathrm{N_A}\) = 6.023 \(\times\) \(10^{23}\)]

At 363 K, the vapour pressure of A is 21 kPa and that of B is 18 kPa. One mole of A and 2 moles of B are mixed. Assuming that this solution is ideal, the vapour pressure of the mixture is ___________ kPa. (Round off to the Nearest Integer).

In Duma's method of estimation of nitrogen, 0.1840 g of an organic compound gave 30 mL of nitrogen collected at 287 K and 758 mm of Hg pressure. The percentage composition of nitrogen in the compound is __________. (Round off to the Nearest Integer). [Given : Aqueous tension at 287 K = 14 mm of Hg]

When 35 mL of 0.15 M lead nitrate solution is mixed with 20 mL of 0.12 M chromic sulphate solution, _________ \(\times\) \(10^{-5}\) moles of lead sulphate precipitate out. (Round off to the Nearest Integer).

The INCORRECT statements below regarding colloidal solutions is :

Sulphurous acid (\(\mathrm{H_2SO_3}\)) has \(\mathrm{Ka_1}\) = 1.7 \(\times\) \(10^{-2}\) and \(\mathrm{Ka_2}\) = 6.4 \(\times\) \(10^{-8}\). The pH of 0.588 M \(\mathrm{H_2SO_3}\) is __________. (Round off to the Nearest Integer).

At 25\(^\circ\)C, 50 g of iron reacts with HCl to form \(\mathrm{FeCl_2}\). The evolved hydrogen gas expands against a constant pressure of 1 bar. The work done by the gas during this expansion is _________ J. (Round off to the Nearest Integer).

[Given : R = 8.314 J mol\(^{-1}\) K\(^{-1}\). Assume, hydrogen is an ideal gas] [Atomic mass of Fe is 55.85 u]

A and B decompose via first order kinetics with half-lives 54.0 min and 18.0 min respectively. Starting from an equimolar non reactive mixture of A and B, the time taken for the concentration of A to become 16 times that of B is _________ min. (Round off to the Nearest Integer).