List of top Questions asked in JEE Main- 2021

When 10 mL of an aqueous solution of \(Fe^{2+}\) ions was titrated in the presence of dil \(H_2SO_4\) using diphenylamine indicator, 15 mL of 0.02 M solution of \(K_2Cr_2O_7\) was required to get the end point. The molarity of the solution containing \(Fe^{2+}\) ions is \(x \times 10^{-2}\) M. The value of \(x\) is ________. (Nearest integer)
A home owner uses \(4.00 \times 10^3 \text{ m}^3\) of methane (\(CH_4\)) gas, (assume \(CH_4\) is an ideal gas) in a year to heat his home. Under the pressure of 1.0 atm and 300 K, mass of gas used is \(x \times 10^5\) g. The value of \(x\) is ________. (Nearest integer) (Given R = 0.083 L atm \(K^{-1} mol^{-1}\))
A source of monochromatic radiation of wavelength 400 nm provides 1000 J of energy in 10 seconds. When this radiation falls on the surface of sodium, \(x \times 10^{20}\) electrons are ejected per second. Assume that wavelength 400 nm is sufficient for ejection of electron from the surface of sodium metal. The value of \(x\) is ________. (Nearest integer) (\(h = 6.626 \times 10^{-34} \text{ Js}\))
The number of sigma bonds in \(H_3C-CH=CH-C\equiv CH\) is ________.
At 298 K, the enthalpy of fusion of a solid (X) is 2.8 kJ \(mol^{-1}\) and the enthalpy of vaporisation of the liquid (X) is 98.2 kJ \(mol^{-1}\). The enthalpy of sublimation of the substance (X) in kJ \(mol^{-1}\) is ________. (in nearest integer)
\(CO_2\) gas is bubbled through water during a soft drink manufacturing process at 298 K. If \(CO_2\) exerts a partial pressure of 0.835 bar then \(x \text{ m mol}\) of \(CO_2\) would dissolve in 0.9 L of water. The value of \(x\) is ________. (Nearest integer) (Henry's law constant for \(CO_2\) at 298 K is \(1.67 \times 10^3\) bar)
For the reaction \(A + B \rightleftharpoons 2C\) the value of equilibrium constant is 100 at 298 K. If the initial concentration of all the three species is 1 M each, then the equilibrium concentration of C is \(x \times 10^{-1}\) M. The value of \(x\) is ________. (Nearest integer)
Consider the cell at \(25^{\circ}C\): \(Zn | Zn^{2+} (aq, 1 \text{ M}) || Fe^{3+} (aq), Fe^{2+} (aq) | Pt(s)\). The fraction of total iron present as \(Fe^{3+}\) ion at the cell potential of 1.500 V is \(x \times 10^{-2}\). The value of \(x\) is ________. (Nearest integer) (Given: \(E^0_{Fe^{3+}/Fe^{2+}} = 0.77 \text{ V}\), \(E^0_{Zn^{2+}/Zn} = -0.76 \text{ V}\))
Consider the complete combustion of butane, the amount of butane utilized to produce 72.0 g of water is ________ \(\times 10^{-1}\) g. (in nearest integer)
Three moles of AgCl get precipitated when one mole of an octahedral co-ordination compound with empirical formula \(CrCl_3 \cdot 3NH_3 \cdot 3H_2O\) reacts with excess of silver nitrate. The number of chloride ions satisfying the secondary valency of the metal ion is ________.
Let $y=y(x)$ be the solution of the differential equation $\frac{dy}{dx} = 1 + xe^{y-x}, -\sqrt{2}<x<\sqrt{2}, y(0) = 0$. Then, the minimum value of $y(x), x \in (-\sqrt{2}, \sqrt{2})$ is equal to :

Let $g: N \to N$ be defined as $g(3n+1) = 3n+2, g(3n+2) = 3n+3, g(3n+3) = 3n+1$, for all $n \ge 0$. Then which of the following statements is true ?
Let a parabola $P$ be such that its vertex and focus lie on the positive x-axis at a distance 2 and 4 units from the origin, respectively. If tangents are drawn from $O(0, 0)$ to the parabola $P$ which meet $P$ at $S$ and $R$, then the area (in sq. units) of $\Delta SOR$ is equal to :
If $b$ is very small as compared to the value of $a$, so that the cube and other higher powers of $\frac{b}{a}$ can be neglected in the identity $\frac{1}{a-b} + \frac{1}{a-2b} + \frac{1}{a-3b} + ....... + \frac{1}{a-nb} = \alpha n + \beta n^2 + \gamma n^3$, then the value of $\gamma$ is :
Let the vectors $(2 + a + b)\hat{i} + (a + 2b + c)\hat{j} - (b + c)\hat{k}$, $(1 + b)\hat{i} + 2\hat{j} - b\hat{k}$ and $(2 + b)\hat{i} + 2\hat{j} + (1 - b)\hat{k}$, $a, b, c \in \mathbb{R}$ be co-planar. Then which of the following is true ?
The number of real roots of the equation $e^{6x} - e^{4x} - 2e^{3x} - 12e^{2x} + e^x + 1 = 0$ is :
A spherical gas balloon of radius 16 meter subtends an angle $60^{\circ}$ at the eye of the observer A while the angle of elevation of its center from the eye of A is $75^{\circ}$. Then the height (in meter) of the top most point of the balloon from the level of the observer's eye is :
The locus of the centroid of the triangle formed by any point P on the hyperbola $16x^2 - 9y^2 + 32x + 36y - 164 = 0$, and its foci is :
Let $S_n$ be the sum of the first n terms of an arithmetic progression. If $S_{3n} = 3S_{2n}$, then the value of $\frac{S_{4n}}{S_{2n}}$ is :
The value of the definite integral $\int_{\pi/24}^{5\pi/24} \frac{dx}{1 + \sqrt[3]{\tan 2x}}$ is :
The sum of all values of $x$ in $[0, 2\pi]$, for which $\sin x + \sin 2x + \sin 3x + \sin 4x = 0$, is equal to :
The term independent of '\(x\)' in the expansion of \(\left( \frac{x+1}{x^{2/3}-x^{1/3}+1} - \frac{x-1}{x-x^{1/2}} \right)^{10}\), where \(x \neq 0, 1\) is equal to __________.
Let \(\vec{p} = 2\hat{i} + 3\hat{j} + \hat{k}\) and \(\vec{q} = \hat{i} + 2\hat{j} + \hat{k}\) be two vectors. If a vector \(\vec{r} = \alpha\hat{i} + \beta\hat{j} + \gamma\hat{k}\) is perpendicular to each of the vectors \((\vec{p} + \vec{q})\) and \((\vec{p} - \vec{q})\), and \(|\vec{r}| = \sqrt{3}\), then \(|\alpha| + |\beta| + |\gamma|\) is equal to __________.
The ratio of the coefficient of the middle term in the expansion of \((1+x)^{20}\) and the sum of the coefficients of two middle terms in expansion of \((1+x)^{19}\) is __________.