List of practice Questions

If \[ y = \tan^{-1}\left( \frac{\sqrt{1 + \cos \frac{x}{2}}}{\sqrt{1 - \cos \frac{x}{2}}} \right) \] then \( \frac{dy}{dx} \) is
The maximum value of \[ Z = 3x + 5y, \] subject to \[ x + 4y \leq 24, \quad y \leq 4, \quad x \geq 0, \quad y \geq 0 \] is
If \[ y = \tan^{-1}\left( \frac{\sqrt{1 + \cos \frac{x}{2}}}{\sqrt{1 - \cos \frac{x}{2}}} \right) \] then \( \frac{dy}{dx} \) is
Bacteria increases at the rate proportional to the number of bacteria present. If the original number \( N \) doubles in \( 4 \) hours, then the number of bacteria will be \( 4N \) in
If \( A = \begin{pmatrix} 1 & 0 & 2 \\ 2 & 1 & 3 \\ 0 & 3 & -5 \end{pmatrix} \) where \( A_{ij} \) is the cofactor of the element \( a_{ij} \) of matrix \( A \), then \( a_{21}A_{21} + a_{22}A_{22} + a_{23}A_{23} = \)
\( y = c^2 + \dfrac{c}{x} \) is the solution of the differential equation
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
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
Which is true for heat and temperature?
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?
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)
Which among the following is true for the value of Henry’s law constant \(K\)?
When \(\text{SO}_2\) is passed through acidified \(\text{K}_2\text{Cr}_2\text{O}_7\), the process that takes place is
Which among the following is a powerful bleaching and oxidising agent?