Download App

12. limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS12. limits1 Mark
MCQ
$\mathop {\lim }\limits_{x \to 0} \,\frac{{{{\sin }^2}\,x}}{{\sqrt 2  - \sqrt {1 + \cos \,x} }}$ equals
  • A
    $\sqrt 2 $
  • ✓
    $4\sqrt 2 $
  • C
    $4$
  • D
    $2\sqrt 2 $
✓

Answer

Correct option: B.
$4\sqrt 2 $
b
$\mathop {\lim }\limits_{x \to 0} \frac{{\left( {\frac{{{{\sin }^2}x}}{{{x^2}}}} \right)\left( {\sqrt 2  + \sqrt {1 + \cos x} } \right)}}{{\left( {\frac{{1 - \cos x}}{{{x^2}}}} \right)}}$

$ = \frac{{{{\left( 1 \right)}^2}.\left( {2\sqrt 2 } \right)}}{{\frac{1}{2}}} = 4\sqrt 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

More "MCQ" from 12. limits→12. limits — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Domain of the function $f(x) = {\left[ {{{\log }_{10}}\left( {\frac{{5x - {x^2}}}{4}} \right)} \right]^{1/2}}$ is
→
The number of integral values of $k$ for which the line, $3 x+4 y=k$ intersects the circle, $\mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{x}-4 \mathrm{y}+4=0$ at two distinct points is
→
If the equation $a| z |^{2}+\overline{\bar{\alpha} z +\alpha \overline{ z }}+ d =0$ represents $a$ circle where $a,d$ are real constants then which of the following condition is correct ?
→
The equations of two lines through $(0,\;a)$ which are at distance ‘$a$’ from the point $(2a,\;2a)$ are
→
If the area of the triangle whose one vertex is at the vertex of the parabola, ${y^2} + 4\,\left( {x - {a^2}} \right) = 0$ and the other two vertices are the points of intersection of the parabola and $y -$ axis, is $250\, sq$. units, then a value of $‘a’$ is
→
The equation of the tangent to the conic ${x^2} - {y^2} - 8x + 2y + 11 = 0$ at $(2, 1)$ is
→
Which is the correct order for a given number $\alpha $in increasing order
→
If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is
→
The points $(at_1^2,2a{t_1}),(at_2^2,2a{t_2})$and $(a,0)$will be collinear, if
→
A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomwise, the probability that it is black or red ball is:
→