JEE (Advanced) 2020 Paper-1

5.00 mL of 0.10 M oxalic acid solution taken in a conical flask is titrated against NaOH from a burette using phenolphthalein indicator. The volume of NaOH required for the appearance of permanent faint pink color is tabulated below for five experiments. What is the concentration, in molarity, of the NaOH solution?

Consider the reaction A $$\rightleftharpoons$$ B at 1000 K. At time t’, the temperature of the system was increased to 2000 K and the system was allowed to reach equilibrium. Throughout this experiment the partial pressure of A was maintained at 1 bar. Given below is the plot of the partial pressure of B with time.
What is the ratio of the standard Gibbs energy of the reaction at 1000 K to that at 2000 K?

Consider a 70% efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and
298 K. Its cell reaction is
$$H_{2} (g) + \frac{1}{2}O_{2}(g) \rightarrow H_{2}O (l)$$

The work derived from the cell on the consumption of $$1.0 \times 10^{−3}$$ mol of $$H_{2}$$(g) is used to compress
1.00 mol of a monoatomic ideal gas in a thermally insulated container. What is the change in the
temperature (in K) of the ideal gas?

The standard reduction potentials for the two half-cells are given below.
$$O_{2}(g) + 4H^{+} (aq) + 4e^{-} \rightarrow 2 H_{2}O (l), E^{0} = 1.23 V$$,

$$2H^{+} (aq) + 2e^{-} \rightarrow H_{2} (g), E^{0} = 0.00 V$$.

Use $$𝐹 = 96500 C mol^{−1},𝑅 = 8.314 J mol^{−1} K^{−1}$$.

Aluminium reacts with sulfuric acid to form aluminium sulfate and hydrogen. What is the volume of hydrogen gas in liters (L) produced at 300 K and 1.0 atm pressure, when 5.4 g of aluminium and 50.0 mL of 5.0 M sulfuric acid are combined for the reaction?
(Use molar mass of aluminium as $$27.0 g mol^{−1}, 𝑅 = 0.082 atm L mol^{−1} K^{−1}$$)

$$^{238}_{92}U$$ is known to undergo radioactive decay to form $$^{206}_{82}Pb$$ by emitting alpha and beta particles. A rock initially contained $$68 \times 10^{−6}$$ g of $$^{238}_{92}U$$ If the number of alpha particles that it would emit during its radioactive decay of $$^{238}_{92}U$$ to $$^{206}_{82}Pb$$ in three half-lives is Z \times 10^{18}, then what is the value of Z?

In the following reaction, compound Q is obtained from compound P via an ionic intermediate.

What is the degree of unsaturation of Q?

Suppose a, b denote the distinct real roots of the quadratic polynomial $$x^{2} + 20x − 2020$$ and
suppose c, d denote the distinct complex roots of the quadratic polynomial $$x^{2} − 20x + 2020$$. Then the value of
ac(a - c) + ad(a - d) + bc(b - c) + bd(b + d)
is

If the function $$f: R \rightarrow R$$ is defined by $$f(x) = |x|(x − \sin x)$$, then which of the following statements is TRUE?

Let the functions $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ be defined by
$$f(x) = e^{x - 1} - e^{-|x - 1|}$$ and $$g(x) = \frac{1}{2}(e^{x - 1} + e^{1 - x})$$.
Then the area of the region in the first quadrant bounded by the curves $$y = f(x), y = g(x)$$ and $$x = 0$$ is

Let 𝑎, 𝑏 and $$\lambda$$ be positive real numbers. Suppose 𝑃 is an end point of the latus rectum of the parabola $$y^{2} = 4\lambda x$$, and suppose the ellipse $$\frac{x^{2}}{a^{2}} +\frac{y^{2}} {b^{2}} = 1$$ passes through the point 𝑃. If the tangents to the parabola and the ellipse at the point 𝑃 are perpendicular to each other, then the eccentricity of the ellipse is