List of practice Questions

If the percentage error in the radius of a circle is 3, then the percentage error in its area is:

The equation of the tangent to the curve \[ y = x^3 - 2x + 7 \] at the point $ (1,6) $ is:

The distance $ s $ traveled by a particle in time $ t $ is given by: \[ s = 4t^2 + 2t + 3. \] The velocity of the particle when $ t = 3 $ seconds is:

Evaluate the limit: \[ \lim_{x \to 0} \frac{\sin(\pi \cos^2 x)}{x^2}. \]

If the function \[ f(x) = \frac{\sqrt{1+x} - 1}{x} \] is continuous at $ x = 0 $, then $ f(0) $ is:

If \[ 3f(x) - 2f\left(\frac{1}{x}\right) = x, \] then $ f'(2) $ is:

A pair of isosteric compounds is

If $ \mathbf{a} = 4\hat{i} + 5\hat{j} - 3\hat{k} $ and $ \mathbf{b} = 6\hat{i} - 2\hat{j} - 2\hat{k} $ are two vectors, then the magnitude of the component of $ \mathbf{b} $ parallel to $ \mathbf{a} $ is:

The value of $\lim_{𝑥→3}\frac{(𝑥^2 −9)}{(𝑥^2−4𝑥+3 )} $ is (rounded off to the nearest integer).

The half-lives of two radioactive materials A and B are respectively $ T $ and $ 2T $. If the ratio of the initial masses of the materials A and B is 8:1, then the time after which the ratio of the masses of the materials A and B becomes 4:1 is:

What are X and Y respectively in the following reactions?

Which of the following sequence of reagents convert propene to 1-chloropropane?

What are A and B in the following reaction sequence?

Styrene on reaction with reagent X gave Y, which on hydrolysis followed by oxidation gave Z. Z gives positive 2,4-DNP test but does not give iodoform test. What are X and Z respectively?

The product of which of the following reactions undergo hydrolysis by SN1 mechanism?

Which of the following are general methods for the preparation of 1-iodopropane?

Which of the following sweeteners use is limited to soft drinks?

Which of the following amino acids possess two chiral centres?

Which of the following represents the simplified version of nucleoside?

Which of the following polymerisation leads to the formation of neoprene?

The ratio of Xe: $ \text{F}_2 $ required in the above reaction is: \[ \text{Xe}(g) + 2\text{F}_2(g) \xrightarrow{873 \, K, 7 \, \text{bar}} \text{XeF}_4(s) \]

The type of iron obtained from the Blast furnace in the extraction of iron is:

Which of the following general reactions is an example for heterogeneous catalysis?

At 298 K, the value of $ -\frac{d[Br^-]}{dt} $ for the reaction \[ 5Br^- (aq) + BrO_3^- (aq) + 6H^+ (aq) \rightarrow 3Br_2 (aq) + 3H_2O (l) \] is $ x $ mol $ L^{-1} $ min$^{-1}$. What is the rate (in mol $ L^{-1} $ min$^{-1}$) of this reaction?

A non-volatile solute is dissolved in water. The $\Delta T_f$ of the resultant solution is 0.052 K. What is the freezing point of the solution (in K)?
(Given: $ K_b $ of water = 0.52 K kg mol$^{-1}$, $ K_f $ of water = 1.86 K kg mol$^{-1}$, Freezing point of water = 273 K)