Limits - Maharashtra Board STD 11 Maths Questions

Q 1MCQ1 Mark

$\lim _{x \rightarrow \infty}\left[\frac{(2 x+3)^7(x-5)^3}{(2 x-5)^{10}}\right]=$

A
$\frac{3}{8}$
✓
$\frac{1}{8}$
C
$\frac{1}{6}$
D
$\frac{1}{4}$

Answer: B.

View full solution →

Q 2MCQ1 Mark

$
\lim _{x \rightarrow 3}\left[\frac{5^{x-3}-4^{x-3}}{\sin (x-3)}\right]=
$

A
$\log 5-4$
✓
$\log \frac{5}{4}$
C
$\frac{\log 5}{\log 4}$
D
$\frac{\log 5}{4}$

Answer: B.

View full solution →

Q 3MCQ1 Mark

$\lim _{x \rightarrow 0}\left[\frac{\left(3^{\sin x}-1\right)^3}{\left(3^x-1\right) \cdot \tan x \cdot \log (1+x)}\right]=$

A
$3 \log 3$
B
$2 \log 3$
✓
$(\log 3)^2$
D
$(\log 3)^3$

Answer: C.

View full solution →

Q 4MCQ1 Mark

$\lim _{x \rightarrow 0}\left[\frac{x \cdot \log (1+3 x)}{\left(e^{3 x}-1\right)^2}\right]=$

A
$\frac{1}{e^9}$
B
$\frac{1}{\mathrm{e}^3}$
C
$\frac{1}{9}$
✓
$\frac{1}{3}$

Answer: D.

View full solution →

Q 5MCQ1 Mark

$\lim _{x \rightarrow \frac{\pi}{2}}\left(\frac{3^{\cos x}-1}{\frac{\pi}{2}-x}\right)=$

A
$1$
✓
$\log 3$
C
$3^{\frac{\pi}{2}}$
D
$3 \log 3$

Answer: B.

View full solution →

Q 6Solve the following Question.(1 Marks)1 Mark

Evaluate the following limits:
$\lim _{\theta \rightarrow 0}\left[\frac{1-\cos 2 \theta}{\theta^2}\right]$

View full solution →

Q 7Solve the following Question.(1 Marks)1 Mark

Evaluate the following limits:
$\lim _{x \rightarrow 2}\left[\frac{x^3-4 x^2+4 x}{x^2-1}\right]$

View full solution →

Q 8Solve the following Question.(1 Marks)1 Mark

Evaluate the following limits : $\lim _{x \rightarrow 3}\left[\frac{x^2+2 x-15}{x^2-5 x+6}\right]$

View full solution →

Q 9Solve the following Question.(1 Marks)1 Mark

Evaluate the following limits : $\lim _{x \rightarrow-3}\left[\frac{x+3}{x^2+4 x+3}\right]$

View full solution →

Q 10Solve the following Question.(1 Marks)1 Mark

Evaluate the following limits : $\lim _{z \rightarrow 2}\left[\frac{z^2-5 z+6}{z^2-4}\right]$

View full solution →

Q 11Solve the Following Question.(2 Marks)2 Marks

Evaluate the following limits:
$\lim _{x \rightarrow 1}\left[\frac{4^{x-1}-2^x+1}{(x-1)^2}\right]$

View full solution →

Q 12Solve the Following Question.(2 Marks)2 Marks

Evaluate the following limits:
$\lim _{x \rightarrow 2}\left[\frac{\log x-\log 2}{x-2}\right]$

View full solution →

Q 13Solve the Following Question.(2 Marks)2 Marks

Evaluate the following limits:

Given that $7 \mathrm{x} \leq \mathrm{f}(\mathrm{x}) \leq 3 \mathrm{x}^2-6$ for all $x$. Determine the value of $\lim _{x \rightarrow 3} f(x)$

View full solution →

Q 14Solve the Following Question.(2 Marks)2 Marks

Evaluate the following limits:

Find the limit of the function, if it exists, at $x=1$
$
f(x)=\left\{\begin{array}{lll}
7-4 x & \text { for } & x<1 \\
x^2+2 & \text { for } & x \geq 1
\end{array}\right.
$

View full solution →

Q 15Solve the Following Question.(2 Marks)2 Marks

Evaluate the following limits:
If $f(r)=\pi r^2$ then find $\lim _{h \rightarrow 0}\left[\frac{f(r+h)-f(r)}{h}\right]$

View full solution →

Q 16Solve the Following Question.(3 Marks)3 Marks

Evaluate the following limits: $\lim _{x \rightarrow 1}\left[\frac{\sqrt{x}-1}{\log x}\right]$

View full solution →

Q 17Solve the Following Question.(3 Marks)3 Marks

Evaluate the following limits: $\lim _{x \rightarrow 1}\left[\frac{2^{2 x-2}-2^x+1}{\sin ^2(x-1)}\right]$

View full solution →

Q 18Solve the Following Question.(3 Marks)3 Marks

Evaluate the following limits:
$\lim _{x \rightarrow \infty}\left[\frac{(2 x+1)^2(7 x-3)^3}{(5 x+2)^5}\right]$

View full solution →

Q 19Solve the Following Question.(3 Marks)3 Marks

Evaluate the following limits:
$\lim _{x \rightarrow 0}\left[\frac{\left(5^x-1\right)^2}{\left(2^x-1\right) \log (1+x)}\right]$

View full solution →

Q 20Solve the Following Question.(3 Marks)3 Marks

Evaluate the following limits:

$
\lim _{x \rightarrow 1}\left[\frac{a b^x-a^x b}{x^2-1}\right]
$

View full solution →

Q 21Solve the Following Question.(4 Marks)4 Marks

Evaluate the following limits: $\lim _{x \rightarrow \infty}\left(\frac{8 x^2+5 x+3}{2 x^2-7 x-5}\right)^{\frac{4 x+3}{8 x-1}}$

View full solution →

Q 22Solve the Following Question.(4 Marks)4 Marks

Evaluate the following limits:
$\lim _{x \rightarrow 0} \frac{1}{x^{12}}\left[1-\cos \left(\frac{x^2}{2}\right)-\cos \left(\frac{x^4}{4}\right)+\cos \left(\frac{x^2}{2}\right) \cdot \cos \left(\frac{x^4}{4}\right)\right]$

View full solution →

Q 23Solve the Following Question.(4 Marks)4 Marks

Evaluate the following limits:$\lim _{x \rightarrow 0}\left(\frac{\sqrt{1-\cos x}}{x}\right)$

View full solution →

Q 24Solve the Following Question.(4 Marks)4 Marks

Evaluate the following limits:
$\lim _{x \rightarrow 0}\left[\frac{a^{3 x}-a^{2 x}-a^x+1}{x \cdot \tan x}\right]$

View full solution →

Q 25Solve the Following Question.(4 Marks)4 Marks

Evaluate the following limits: $\lim _{x \rightarrow 0}\left[\frac{x\left(6^x-3^x\right)}{\cos (6 x)-\cos (4 x)}\right]$

View full solution →

Q 26Solve the Following Question.(5 Marks)5 Marks

Evaluate the following limits:
$\lim _{x \rightarrow 1}\left(\frac{x+3 x^2+5 x^3+\cdots \cdots \cdots \cdots \cdots+(2 n-1) x^n-n^2}{x-1}\right)$

View full solution →

Q 27Solve the Following Question.(5 Marks)5 Marks

Evaluate the following limits: $\lim _{x \rightarrow \frac{\pi}{4}}\left[\frac{(\sin x-\cos x)^2}{\sqrt{2}-\sin x-\cos x}\right]$

View full solution →

Q 28Solve the Following Question.(5 Marks)5 Marks

Evaluate the following limits: $\lim _{x \rightarrow a}\left[\frac{x \cos a-a \cos x}{x-a}\right]$

View full solution →

Q 29Solve the Following Question.(5 Marks)5 Marks

Evaluate the following limits: $\lim _{x \rightarrow \infty}\left[\frac{\sqrt{x^2+5}-\sqrt{x^2-3}}{\sqrt{x^2+3}-\sqrt{x^2+1}}\right]$

View full solution →

Q 30Solve the Following Question.(5 Marks)5 Marks

Evaluate the following limits:
$\lim _{x \rightarrow \frac{\pi}{6}}\left[\frac{2-\sqrt{3} \cos x-\sin x}{(6 x-\pi)^2}\right]$

View full solution →

Limits question types

Limits questions

Generate a Limits paper free

Limits Maths - Limits

Limits question types

Limits questions

Generate a Limits paper free