Download App

Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives1 Mark
MCQ
$\mathop {\lim }\limits_{\text{x} \to 0} \frac{{\sin 5\text{x}}}{{\tan 3\text{x}}}$
  • A
    $-\frac{5}{3}$
  • ✓
    $\frac{5}{3}$
  • C
    $-\frac{7}{3}$
  • D
    $\text{None of these}$
✓

Answer

Correct option: B.
$\frac{5}{3}$
$\mathop {\lim }\limits_{\text{x} \to 0} \frac{{\sin 5\text{x}}}{{\tan 3\text{x}}}$
$=\mathop {\lim }\limits_{\text{x} \to 0} \frac{{\sin 5\text{x}}}{{5\text{x}}}\times\frac{\text{3x}}{\tan\text{x}}\times\frac{5}{3}$
we know that $ =\displaystyle \lim_{\text{x}\rightarrow 0}\frac {\sin 5\text{x}}{5\text{x}}=1$
$=\mathop {\lim }\limits_{\text{x} \to 0}\times\frac{\text{3x}}{\tan\text{x}}=1$
$= \text{L}=1\times 1\times \dfrac {5}{3}$
$= \displaystyle \lim_{\text{x}\rightarrow 0}\frac {\sin 5\text{x}}{5\text{x}}=\frac{5}{3}$

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 "M.C.Q (1 Marks)" from Limits and Derivatives→Limits and Derivatives — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

If in the expansion of $(1+\text{x})^{20},$ the coefficients of $r^{th}$ and $(r + 4)$ terms are equal, then $r$ is equal to:
→
If $A = {\sin ^2}\theta + {\cos ^4}\theta ,$ then for all real values of $\theta$
→
The ${n^{th}}$ term of an $A.P.$ is $3n - 1$.Choose from the following the sum of its first five terms
→
If $\tan\alpha=\frac{1-\cos\beta}{\sin\beta},$ then:
→
Let $A$ and $B$ be two sets such that $A ∩ B = ϕ.$ Find the value of $(A ∪ B′) =$
→
The value of $\frac{{3 + \cot {{76}^o}\cot {{16}^o}}}{{\cot {{76}^o} + \cot {{16}^o}}}$
→
Out of $30$ consecutive numbers, $2$ are chosen at random. The probability that their sum is odd, is
→
Consider the lines given by $ \mathrm{L}_1: \mathrm{x}+3 \mathrm{y}-5=0 $ $ \mathrm{~L}_2: 3 \mathrm{x}-\mathrm{ky}-1=0 $ $ \mathrm{~L}_3: 5 \mathrm{x}+2 \mathrm{y}-12=0$

Match the Statements / Expressions in Column $I$ with the Statements / Expressions in Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS.$

Column $I$ Column $II$
$(A)$ $ \mathrm{L}_1, \mathrm{~L}_2, \mathrm{~L}_3$ are concurrent, if $(p)$ $\mathrm{k}=-9$
$(B)$ One of $\mathrm{L}_1, \mathrm{~L}_2, \mathrm{~L}_3$ is parallel to at least one of the other two, if $(q)$ $\mathrm{k}=-\frac{6}{5}$
$(C)$ $\mathrm{L}_1, \mathrm{~L}_2, \mathrm{~L}_3$ form a triangle, if $(r)$ $\mathrm{k}=\frac{5}{6}$
$(D)$ $ \mathrm{L}_1, \mathrm{~L}_2, \mathrm{~L}_3$ do not form a triangle, if $(s)$ $\mathrm{k}=5$
→
Which of the following collections are sets?
→
A man wants to cut three lengths from a single piece of board of length $91 \ cm.$ The second length is to be $3 \ cm$ longer than the shortest and third length is to be twice as long as the shortest. What are the possible lengths for the shortest board if the third piece is to be at least $5 \ cm$ longer than the second?
→