4 1 + 2 - 3 = - Vidyadip

MCQ

${4 \over {1 + \sqrt 2 - \sqrt 3 }} = $

✓
$2 + \sqrt 2 + \sqrt 6 $
B
$1 + \sqrt 2 + \sqrt 3 $
C
$3 + \sqrt 2 + \sqrt 3 $
D
None of these

✓

Answer

Correct option: A.

$2 + \sqrt 2 + \sqrt 6 $

a
(a) ${4 \over {1 + \sqrt 2 - \sqrt 3 }} = {{4\,(1 + \sqrt 2 + \sqrt 3 )} \over {{{(1 + \sqrt 2 )}^2} - 3}}$

$ = {{4(1 + \sqrt 2 + \sqrt 3 )} \over {3 + 2\sqrt 2 - 3}} + {{\sqrt 6 (\sqrt 3 - \sqrt 2 )} \over {3 - 2}}$

$ = \sqrt 2 (1 + \sqrt 2 + \sqrt 3 ) = 2 + \sqrt 2 + \sqrt 6 $.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $cos A = {3\over 4} , $ then $32\sin \left( {\frac{A}{2}} \right)\sin \left( {\frac{{5A}}{2}} \right) = $

The sum of the solutions of the equation $\left| {\sqrt x - 2} \right| + \sqrt x \left( {\sqrt x - 4} \right) + 2 = 0\left( {x > 0} \right)$ is equal to

If $z_1 , z_2$ and $z_3, z_4$ are $2$ pairs of complex conjugate numbers, then $\arg \left( {\frac{{{z_1}}}{{{z_4}}}} \right) + \arg \left( {\frac{{{z_2}}}{{{z_3}}}} \right)$ equals

In the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$, the equation of diameter conjugate to the diameter $y = \frac{b}{a}x$, is

If ${(1 + x)^n} = {C_0} + {C_1}x + {C_2}{x^2} + .... + {C_n}{x^n}$, then the value of ${C_0} + 2{C_1} + 3{C_2} + .... + (n + 1){C_n}$ will be

Let $A =\left[ a _{ ij }\right]$ be a $3 \times 3$ matrix such that $A \left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], A \left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right]=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]$ and $A \left[\begin{array}{l}2 \\ 1 \\ 2\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$, then $a _{23}$ equals:

Given $A =$$\left[ {\begin{array}{*{20}{c}}1&3\\2&2\end{array}} \right]$ ; $I =$$\left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$ . $If A - \lambda I$ is a singular matrix then

For a differentiable function $\mathrm{f}: I R \rightarrow I R$, suppose $f^{\prime}(\mathrm{x})=3 f(\mathrm{x})+\alpha$, where $\alpha \in \operatorname{IR}, f(0)=1$ and $\lim _{x \rightarrow-\infty} f(x)=7$. Then $9 \mathrm{f}\left(-\log _{\mathrm{e}} 3\right)$ is equal to ............

Let the line of the shortest distance between the lines $L_1: \vec{r}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})$ and $L_2: \vec{r}=(4 \hat{i}+5 \hat{j}+6 \hat{k})+\mu(\hat{i}+\hat{j}-\hat{k})$ intersect $\mathrm{L}_1$ and $\mathrm{L}_2$ at $\mathrm{P}$ and $\mathrm{Q}$ respectively. If $(\alpha, \beta, \gamma)$ is the midpoint of the line segment $PQ$, then $2(\alpha+\beta+\gamma)$ is equal to____.

Consider the equation ${x^2} + \alpha x + \beta = 0$ having roots $\alpha ,\beta $ such that $\alpha \ne \beta $ .Also consider the inequality $\left| {\left| {y - \beta } \right| - \alpha } \right| < \alpha $ ,then