Download App

STD 12 - 10. vector algebra — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 10. vector algebra4 Marks
MCQ
If $|a|\, = a$ and $|b|\, = b,$ then ${\left( {\frac{a}{{{a^2}}} - \frac{b}{{{b^2}}}} \right)^2} = $
  • A
    ${\left( {\frac{{a + b}}{{ab}}} \right)^2}$
  • B
    $\frac{{{{(a - b)}^2}}}{{ab}}$
  • ✓
    ${\left( {\frac{{a - b}}{{ab}}} \right)^2}$
  • D
    $\frac{{{{(a + b)}^2}}}{{ab}}$
✓

Answer

Correct option: C.
${\left( {\frac{{a - b}}{{ab}}} \right)^2}$
c
(c) ${\left( {\frac{a}{{{a^2}}} - \frac{b}{{{b^2}}}} \right)^2} = \frac{{{a^2}}}{{{a^4}}} + \frac{{{b^2}}}{{{b^4}}} - \frac{{2a\,.\,b}}{{{a^2}{b^2}}}$,{$\because $ $a^2 = a^2$ etc.}

$ = \frac{{{a^2} + {b^2} - 2a\,.\,b}}{{{a^2}{b^2}}} = {\left( {\frac{{a - b}}{{ab}}} \right)^2}.$

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 $\left( {\frac{1}{2},\frac{1}{3},n} \right)$ are the direction cosines of a line, then the value of $n$ is
→
The number of solution of the given equation $a\sin x + b\cos x = c$ , where $|c|\, > \,\sqrt {{a^2} + {b^2}} ,$ is
→
Consider the following two statements:
Statement $I$ : For any two non $-$ zero complex numbers $z_1, z_2$ 
$\left(\left|z_1\right|+\left|z_2\right|\right)\left|\frac{z_1}{\left|z_1\right|}+\frac{z_2}{\left|z_2\right|}\right| \leq 2\left(\left|z_1\right|+\left|z_2\right|\right)$ 
Statement $II$ : If $x, y, z$ are three distinct complex numbers and $a, b, c$ are three positive real numbers
such that $\frac{a}{|y-z|}=\frac{b}{|z-x|}=\frac{c}{|x-y|}$ then
$\frac{a^2}{y-z}+\frac{b^2}{z-x}+\frac{c^2}{x-y}=1$
→
If the system of equation $3x - 2y + z = 0$, $\lambda x - 14y + 15z = 0$, $x + 2y + 3z = 0$ have a non-trivial solution, then $\lambda = $
→
If $\sqrt 3 + i = (a + ib)(c + id)$, then ${\tan ^{ - 1}}\left( {\frac{b}{a}} \right) + $ ${\tan ^{ - 1}}\left( {\frac{d}{c}} \right)$ has the value
→
The line passes through $(1, 0)$ and $( - \;2,\;\sqrt 3 )$ makes an angle of ...... with $x$-axis ......$^o$
→
The sum of $\left(1^2-1+1\right)(1 !)+\left(2^2-2+1\right)(2 !)$ $+\ldots+\left(n^2-n+1\right)(n !)$ is
→
$\int_{}^{} {\frac{{dx}}{{2 + \cos x}} = } $
→
The maximum value of the function $f(x)=2 x^3-15 x^2+36 x-48$ on the set $A=\left\{x \mid x^2+20 \leq 9 x\right\}$ is
→
Numbers are to be formed between $1000$ and $3000$, which are divisible by $4$, using the digits $1,2,3,4,5$ and $6$ without repetition of digits. Then the total number of such numbers is.
→