For 'invert sugar', the correct statement(s) is (are)
(Given: specific rotations of $\left(+\right)-$sucrose, $\left(+\right)-$maltose, $\mathrm{L}-\left(-\right)-$glucose and $\mathrm{L}-\left(+\right)-$fructose in aqueous solution are $+\mathrm{ }{66}^{°},\mathrm{ }+{140}^{°},\mathrm{ }–{52}^{°}$ and $+\mathrm{ }{92}^{°}$, respectively)

Match the chemical substance in Column I with type of polymers/type of bond in Column II. Indicate your answer by darkening the appropriate bubbles of \(4 \times 4\) matrix given in the ORS.

Column I	Column II
A. Cellulose	p. Natural polymer
B. Nylon-6,6	q. Synthetic polymer
C. Protein	r. Amide linkage
D. Sucrose	s. Glycoside linkage

When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a temperature increase of ${5.7}^{\mathrm{o}}\mathrm{C}$ was measured for the beaker and its contents (Expt.1). Because the enthalpy of neutralization of a strong acid with a strong base is a constant $(-57.0\mathrm{ }\mathrm{k}\mathrm{J}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1})$ , this experiment could be used to measure the calorimeter constant. In a second experiment (Expt. 2), 100 mL of 2.0 M acetic acid $({\mathrm{K}}_{\mathrm{a}}=2.0\times {10}^{-5})$ was mixed with 100 mL of 1.0 M NaOH (under identical conditions to Expt. 1) where a temperature rise of ${5.6}^{\mathrm{o}}\mathrm{C}$ was measured. (Consider heat capacity of all solutions as $4.2\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{g}}^{-1}\mathrm{ }{\mathrm{K}}^{-1}$ and density of all solutions as $1.0\mathrm{ }\mathrm{g}\mathrm{ }\mathrm{m}{\mathrm{L}}^{-1}$ )
The pH of the solution after Expt. 2 is

An ideal gas is expanded from $({\mathrm{p}}_1\mathrm{ },\mathrm{ }{\mathrm{V}}_1\mathrm{ },\mathrm{ }{\mathrm{T}}_1)\mathrm{ }\mathrm{to}\mathrm{ }({\mathrm{p}}_2\mathrm{ },\mathrm{ }{\mathrm{V}}_2\mathrm{ },\mathrm{ }{\mathrm{T}}_2)$ under different conditions. The correct statement(s) among the following is(are)

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The hydrogen-like species \(\mathrm{Li}^{2+}\) is in a spherically symmetric state \(S_1\) with one radial node. Upon absorbing light the ion undergoes transition to a state \(S_2\). The state \(S_2\) has one radial node and its energy is equal to the ground state energy of the hydrogen atom.
Question:
The state \(S_1\) is

A student performs a titration with different burettes and finds titre values of \(25.2 \mathrm{~mL}, 25.25 \mathrm{~mL}\), and \(25.0 \mathrm{~mL}\).
The number of significant figures in the average titre value is

The acidic hydrolysis of ether (X) shown below is fastest when

For any $3\times 3$ matrix $M$, let $\left|M\right|$ denote the determinant of $M$. Let $E=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\\ 8& 13& 18\end{array}\right], P=\left[\begin{array}{lll}1& 0& 0\\ 0& 0& 1\\ 0& 1& 0\end{array}\right] \& F=\left[\begin{array}{ccc}1& 3& 2\\ 8& 18& 13\\ 2& 4& 3\end{array}\right]$ If $Q$ is a nonsingular matrix of order $3\times 3$, then which of the following statements is (are) TRUE ?

A series \(R\) - \(C\) circuit is connected to \(A C\) voltage source. Consider two cases; \((A)\) when \(C\) is without a dielectric medium and \((B)\) when \(C\) is filled with dielectric of constant 4. The current \(I_R\) through the resistor and voltage \(V_C\) across the capacitor are compared in the two cases. Which of the following is/are true?

Which of the given statement(s) about \(\mathbf{N}, \mathbf{O}, \mathbf{P}\) and \(\mathbf{Q}\) with respect to \(\mathbf{M}\) is (are) correct?

A projectile is thrown from a point \(\mathrm{O}\) on the ground at an angle \(45^{\circ}\) from the vertical and with a speed \(5 \sqrt{2} \mathrm{~m} / \mathrm{s}\). The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, \(0.5 \mathrm{~s}\) after the splitting. The other part, \(t\) seconds after the splitting, falls to the ground at a distance \(x\) meters from the point O. The acceleration due to gravity \(g=10 \mathrm{~m} / \mathrm{s}^{2}\).
The value of $t$ is _________.

Column I gives some devices and Column II gives some processes on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the \(4 \times 4\) matrix given in the ORS.

\(\mathrm{MgSO}_4\) on reaction with \(\mathrm{NH}_4 \mathrm{OH}\) and \(\mathrm{Na}_2 \mathrm{HPO}_4\) forms a white crystalline precipitate. What is its formula?