Instructions

For the following questions answer them individually

Instructions

The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.

Question 32

The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is the sameas its molality. Density of this solution at 298 K is 2.0 gcm$$^{-3}$$. Theratio of the molecular weights of the solute and solvent, $$\left(\frac{MW_{solute}}{MW_{solvent}}\right)$$, is

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Question 33

The diffusion coefficient of an ideal gas is proportional to its mean free path and meanspeed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases x times. The value of x is

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Question 34

In neutral or faintly alkaline solution, 8 moles of permanganate anion quantitatively oxidize thiosulphate anions to produce X moles of a sulphur containing product. The magnitude of X is

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Question 35

The number of geometric isomers possible for the complex $$[CoL_2Cl_2]^- (L = H_2NCH_2CH_2O^-)$$ is

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Question 36

In the following monobromination reaction, the number of possible chiral products is

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Instructions

For the following questions answer them individually

Question 37

Let $$-\frac{\pi}{6} < \theta < \frac{\pi}{12}$$ Suppose $$\alpha_1$$ and $$\beta_1$$ are the roots of the equation $$x^2 - 2x \sec \theta + 1$$ and $$\alpha_2$$ and $$\beta_2$$ are the roots of the equation $$x^2 + 2x \tan \theta - 1 = 0$$. If $$\alpha_1 > \beta_1$$ and $$\alpha_2 > \beta_2$$ then $$\alpha_1 + \beta_2$$ equals

Question 38

A debate club consists of 6 girls and 4 boys. A team of 4 membersis to be selected from this club including the selection of a captain (from among these 4 members) for the team.If the team hasto include at most one boy, then the numberof waysof selecting the team is

Question 39

Let $$ S = \left\{x \epsilon (-\pi, \pi): x \neq 0, \pm \frac{\pi}{2}\right\}$$ The sum of all distinct solutions of the equation $$\sqrt{3} \sec x + \cosec x + 2(\tan x - \cot x) = 0$$ in the set S is equal to

Question 40

A computer producing factory has only two plants $$T_1$$ and $$T_2$$ Plant $$T_1$$ produces 20% and plant $$T_2$$ produces 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective given that it is produced in plant $$T_1$$) = 10P (computer turns out to be defective given that it is produced in plant $$T_2$$), where P(E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is producedin plant $$T_2$$ is