JEE (Advanced) 2019 Paper-1

Among $$B_2H_6, B_3N_3H_6, N_2O, N_2O_4, H_2S_2O_3 and H_2S_2O_8$$, the total number of molecules containing covalent bond between two atoms of the same kind is ___________

At 143 K,the reaction of $$XeF_4$$ with $$O_2F_2$$ produces a xenon compound Y. The total number of lone pair(s) of electrons present on the whole molecule of Y is

For the following reaction, the equilibrium constant $$K_$$ at 298 K is $$1.6 \times 10^{17}$$
$$Fe^{2+} (aq) + S^{2-} (aq) \rightleftharpoons FeS (s)$$
When equal volumes of 0.06 M $$Fe^{2+}$$ (aq) and $$0.2 M S^{2-}(aq)$$ solutions are mixed, the equilibrium concentration of $$Fe^{2+}$$ (aq) is found to be $$Y \times 10^{-17} M$$. The value of Y is _________ .

On dissolving 0.5 g of a non-volatile non-ionic solute to 39 g of benzene, its vapor pressure decreases from 650 mm Hg to 640 mm Hg. The depression of freezing point of benzene (in K) upon addition of the solute is ___________ .
(Given data: Molar mass and the molal freezing point depression constant of benzene are $$78 g mol^{-1} and 5.12 K kg mol^{-1}$$ respectively)

Consider the kinetic data given in the following table for the reaction A + B + C $$\rightarrow$$ Product.

The rate of the reaction for $$[A] = 0.15 mol dm^{-3}, [B] = 0.25 mol dm^{-3} and [C] = 0.15 mol dm^{-3}$$ is found to be $$Y \times 10^{-5} mol dm^{-3} s^{-1}$$. The value of Y is _______ .

Schemes 1 and 2 describe the conversion of P to Q and to S, respectively. Scheme 3 describes the synthesis of T from Q and S. The total number of Br atoms in a molecule of T is _________ .

Let S be the set of all complex numbers z satisfying $$|z - 2 + i | \geq \sqrt 5$$ If the complex number $$Z_0$$ is such that $$\frac{1}{|z_0 - 1|}$$ is the maximum of the set $$\left\{\frac{1}{|z - 1|}: z \in S\right\}$$ then the principal argument of $$\frac{4 - z_0 - \overline{z_0}}{z_0 - \overline{z_0} + 2i}$$ is

Let
$$M = \begin{bmatrix}\sin^4\theta & -1-\sin^2\theta \\1 + \cos^2\theta & \cos^4\theta \end{bmatrix} = \alpha I + \beta M^{-1}$$
where $$\alpha = \alpha (\theta) and \beta = \beta (\theta)$$ are real numbers, and I is the $$2 \times 2$$ identity matrix. If
$$\alpha^*$$ is the minimum of the set $$\left\{\alpha (\theta): \theta \in [0, 2\pi)\right\}$$ and
$$\beta^*$$ is the minimum of the set $$\left\{\beta (\theta): \theta \in [0, 2\pi)\right\}$$,
then the value of $$\alpha^* + \beta^*$$ is

A line y = mx + intersects the circle $$(x — 3)^2 + (y + 2)^2 = 25$$ at the points P and Q. If the midpoint of the line segment PQ has x-coordinate $$-\frac{3}{5},$$ then which one of the following options is correct?

The area of the region $${(x,y): xy \leq 8, 1 \leq y \leq x^2}$$ is