List of practice Questions

The rate at which the metal cools in moving air is proportional to the difference of temperatures between the metal and air. If the air temperature is 290K and the metal temperature drops from 370K to 330K in 10 minutes, then the time required to drop the temperature up to 295K is

Evaluate \[ \int_{\frac{\pi}{5}}^{\frac{3\pi}{10}} \frac{\tan x}{\tan x + \cot x} \, dx \]

The micro-organisms double themselves in 3 hours. Assuming that the quantity increases at a rate proportional to itself, then the number of times it multiplies itself in 18 years is

The points A \( (-a, -b) \), B \( (0, 0) \), C \( (a, b) \) and D \( (a^2, ab) \) are

The cosine of the angle included between the lines \[ \vec{r_1} = (2i + j - 2k) + \lambda (i - 2j - 2k) \quad \text{and} \quad \vec{r_2} = (i + j + 3k) + \mu (3i + 2j - 6k) \] where \( \lambda, \mu \in \mathbb{R} \) is

The value of \[ \tan^{-1} \left( \frac{1}{3} \right) + \tan^{-1} \left( \frac{1}{5} \right) + \tan^{-1} \left( \frac{1}{7} \right) + \tan^{-1} \left( \frac{1}{8} \right) \] is

The maximum value of \( z = 3x + 5y \), subject to \( 3x + 2y \leq 18 \), \( x \leq 4 \), \( y \leq 6 \), \( x, y \geq 0 \) is

Which among the following compounds is obtained when glucose reacts with hydrogen cyanide?

For any non-zero vectors \( \vec{a} \) and \( \vec{b} \), \( \left| \vec{b} \times (\vec{a} \times \vec{b}) \right| = \)

Evaluate the integral \[ \int \frac{1 + 2e^{-x}}{1 - 2e^{-x}} \, dx \]

If \( \sin(x + y) + \cos(x + y) = \sin \left[ \cos^{-1} \left( \frac{1}{3} \right) \right] \), then \[ \frac{dy}{dx} = \]

The area included between the parabolas \( y^2 = 5x \) and \( x^2 = 5y \) is

Identify the hydrocarbon compound from the following containing carbon atoms in the range of C\(_6\) to C\(_7\)?

If 2 moles of an ideal gas at 546 K has a volume of 44.8 L, then what will be its pressure?

Which of the following reaction of diazonium salt involves retention of diazonium group?

Which of the following is obtained by catalytic oxidation of ammonia?

The volume of oxygen required for complete combustion of 0.25 mole of methane at S.T.P. is

What is the product obtained when Br\(_2\) water reacts with glucose?

What is the value of rate constant of first-order reaction, if it takes 15 minutes for consumption of 20% of reactants?

What is the correct order of C-X bond strength in CH\(_3\)-X?

Number of oxygen atoms present in salicylaldehyde are

Identify compound ‘B’ in following series of reactions?

How many numbers of P-OH and P-O-P bonds are present in pyrophosphoric acid respectively?

The common name of 1-Chloro-2, 2-dimethyl propane is

Which polymer from the following is used as synthetic leather?