Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...

Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...

Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added...

Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$
The distance of the point...

Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$
The shortest distance between $\mathrm{L}_1$...

Consider the lines $$ \begin{aligned} & L_1: \frac{x+1}{3}=\frac{y+2}{1}=\frac{z+1}{2} \\ & L_2: \frac{x-2}{1}=\frac{y+2}{2}=\frac{z-3}{3} \end{aligned} $$
The unit vector perpendicular to...

Suppose four distinct positive numbers $\mathrm{a}_1, \mathrm{a}_2, \mathrm{a}_3, \mathrm{a}_4$ are in G.P. Let $\mathrm{b}_1=\mathrm{a}_1, \mathrm{~b}_2=\mathrm{b}_1+\mathrm{a}_2, \mathrm{~b}_3=\mathrm{b}_2+ \mathrm{a}_3$ and $\mathrm{b}_4=\mathrm{b}_3+\mathrm{a}_4$. STATEMENT-1:...

There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...

Match the statements given in Column I with the intervals/union of intervals given in Column II

Match the statements given in Column I with the values given in Column II

Let a solution $y=y(x)$ of the differential equation $x \sqrt{x^2-1} d y-y \sqrt{y^2-1} d x=0$ satisfy $y(2)=\frac{2}{\sqrt{3}}$. STATEMENT-1 : $...

There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...

Consider $$ \begin{aligned} & L_1: 2 x+3 y+p-3=0 \\ & L_2: 2 x+3 y+p+3=0 \end{aligned} $$ where $p$ is a...

There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult...

Let M be a $3 \times 3$ matrix satisfying $$ \mathbf{M}\left[\begin{array}{l} 0 \\ 1 \\ 0 \end{array}\right]=\left[\begin{array}{c} -1 \\ 2...

Let $y^{\prime}(x)+y(x) g^{\prime}(x)=g(x) g^{\prime}(x), y(0)=0, x \in \mathbb{R}$, where $f^{\prime}(x)$ denotes $\frac{d f(x)}{d x}$ and $g(x)$ is a given nonconstant...

Let $a, b, c, p, q$ be real numbers. Suppose $\alpha, \beta$ are the roots of the equation $...

STATEMENT-1: $\quad \mathrm{Pb}^{4+}$ compounds are stronger oxidizing agents than $\mathrm{Sn}^{4+}$ compounds. and STATEMENT-2: The higher oxidation states for the group...