The oxides of nitrogen obtained by the reaction of nitric acid with
(i) \(\mathrm{P}_4 \mathrm{O}_{10}\), (ii) \(\mathrm{P}_4\) respectively are

Two thin circular discs $A$ and $B$ of radii $2 \mathrm{cm}$ and $4 \mathrm{cm}$ are in a liquid at the same depth. $T_A$ is the thrust on $A$ and $T_B$ thrust on $B$. Then $T_A:T_B=$

In Ellingham diagram, the plot is drawn between

Which of the following statements is correct about the cathode rays?
1. These rays start from anode and move towards cathode.
2. They are visible with human eye.
3. In presence of electric and magnetic fields, they behave like positively charged particles.
4. Their characteristic does not depend on the nature of material at electrode.

Match the item given in Column-I (method used for determining colligative property) and Column-II (for the corresponding colligative property) and find the correct order.
\(\begin{array}{|c|c|c|}
\hline & \text { Column I } & \text { Column II } \\
\hline \text { A. } & \text { Beckmann method } & \text { 1. Osmotic pressure } \\
\hline \text { B. } & \begin{array}{l}
\text { Ostwald-Walker method }
\end{array} & \text { 2. Elevation in B.P } \\
\hline \text { C. } & \begin{array}{l}
\text { Berkeley-Hartley method }
\end{array} & \text { 3. Depression in F.P. } \\
\hline \text { D. } & \text { Landsberger method } & \begin{array}{l}
\text { 4. Relative lowering of vapour pressure }
\end{array} \\
\hline
\end{array}\)

Least reactive alkyl chloride in a \(\mathrm{S}_{\mathrm{N}} 2\) reaction is

Assertion (A) Molality of a solution increases with temperature.
Reason (R) Molality expression does not involve any volume term.

If \(a, b, c\) and \(d \in R\) such that \(a^2+b^2=4\) and \(c^2+d^2=2\) and if \((a+i b)^2=(c+i d)^2(x+i y)\), then \(x^2+y^2\) is equal to

\(P, Q, R\) and \(S\) are four points with the position vectors \(3 \mathbf{i}-4 \mathbf{j}+5 \mathbf{k},-4 \mathbf{i}+5 \mathbf{j}+\mathbf{k}\) and \(-3 \mathbf{i}+4 \mathbf{j}+3 \mathbf{k}\), respectively. Then, the line \(P Q\) meets the line \(R S\) at the point

If the circle \(x^2+y^2+2 g x+2 f y+c=0(c>0)\) touches both the coordinate axes and lies in the third quadrant, then the length of the chord intercepted by the circle on the line \(x+y+\sqrt{c}=0\) is

The direction cosines of a line are \(\left\langle\frac{-9}{11}, \frac{6}{11}, \frac{-2}{11}\right\rangle\) respectively. Then its direction ratios are

If \(\sin x \cosh y=\cos \theta\) and \(\cos x \sinh y=\sin \theta\), then \(\sin ^2 x+\cosh ^2 y=\)

The particular solution of the differential equation \(\left(1+y^2\right) d x-x y d y=0, y(1)=0\) represents