List of practice Questions

If \( \int x^x (1 + \log x) \, dx = k x^x + c \), then \( k = \)

A particle moves according to the law \( s = t^3 - 6t^2 + 9t + 25 \). The displacement of the particle at the time when its acceleration is zero is

If the population grows at the rate of \( 8% \) per year, then the time taken for the population to be doubled is \([ \log 2 = 0.6912 ]\)

Which among the following compounds is obtained when calcium formate is dry distilled alone?

A solution is \(0.25%\) by mass. What is the weight of solvent containing \(1.25~\text{g}\) solute?

What is the IUPAC name of 3–chloropropyl ethyl ether?

Which of the following can form a colloidal sol with water?

The area of the region bounded by the curve \( y = \log x \), x-axis and the lines \( x = 1 \), \( x = e \) is

The measure of the acute angle between the lines given by the equation \( 3x^2 - 4\sqrt{3}xy + 3y^2 = 0 \) is

Which of the following halogens combine with dihydrogen at the lowest temperature?

Identify product ‘C’ in the following reaction:
\[ \text{Propylene dibromide} \xrightarrow[\text{Alcohol}]{\text{Zn},\,\Delta} A \xrightarrow{\text{HBr}} B \xrightarrow[\text{ether}]{\text{Na}} C \]

Which of the following oxides is NOT volatile?

The edge length of an fcc type unit cell of copper having atomic radius \(127.6~\text{pm}\) is equal to

Which among the following is a cross-linked polymer?

Energy required to dissociate \(16\,\text{g}\) of \(\text{O}_2(g)\) into free atoms is \(x\,\text{kJ}\). The value of bond enthalpy of \(\text{O}=\text{O}\) bond is

What is the mass percentage of carbon in urea? (Molar mass of urea = \(60\,\text{g mol}^{-1}\))

Which is true for heat and temperature?

Which of the following is used as an antiseptic in soap?

Which statement from the following is true for a complex hexammine cobalt(III) chloride?

Caesium is used in

How many optical isomers are possible for a compound having four asymmetric carbon atoms?

Which among the following is true for Balz–Schiemann reaction?

Which among the following compounds contains phantom atom?

The rate law for the reaction \(A + B + C \rightarrow \text{Product}\) is expressed as \[ \text{Rate} = k[A]^2[B]^1[C]^0 \] What is the overall order of the reaction?

What is the number of atoms present per unit cell of aluminium having edge length \(4~\text{\AA}\)? (Given: Density of Al = \(2.7~\text{g cm}^{-3}\), Atomic mass of Al = 27)