Limits and Derivatives - CBSE STD 11 Science Maths Questions

Q 1M.C.Q (1 Marks)1 Mark

If $f(x) = x^{100} + x^{99} ....... + x + 1,$ then $f(1)$ is equal to:

✓
$5050$
B
$5049$
C
$5051$
D
$50051$

Answer: A.

View full solution →

Q 2M.C.Q (1 Marks)1 Mark

$ \lim\limits_{\text{x} \rightarrow 0}\frac{\tan2\text{x}-\text{x}}{3\text{x}-\sin\text{x}}$ is equal to:

A
$2$
✓
$\frac{1}{2}$
C
$-\frac{1}{2}$
D
$\frac{1}{4}$

Answer: B.

View full solution →

Q 3M.C.Q (1 Marks)1 Mark

$\lim\limits_{\text{x} \rightarrow0}\frac{(1+\text{x})^{\text{n}}-1}{\text{x}}$ is equal to:

✓
$\text{n}$
B
$1 $
C
$-\text{n}$
D
$0$

Answer: A.

View full solution →

Q 4M.C.Q (1 Marks)1 Mark

$\lim\limits_{\text{x} \rightarrow0}\frac{\text{cosec}-\cot\text{x}}{\text{x}}$ is equal to:

A
$-\frac{1}{2}$
B
$1$
✓
$\frac{1}{2}$
D
$-1$

Answer: C.

View full solution →

Q 5M.C.Q (1 Marks)1 Mark

If $\text{y}=\frac{1+\frac{1}{\text{x}^{2}}}{1-\frac{1}{\text{x}^{2}}}$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:

✓
$\frac{-4\text{x}}{(\text{x}^{2}-1)^{2}}$
B
$\frac{-4\text{x}}{(\text{x}^{2}-1)^{2}}$
C
$\frac{1-\text{x}^{2}}{4\text{x}}$
D
$\frac{4\text{x}}{\text{x}^{2}-1}$

Answer: A.

View full solution →

Q 62 Marks Questions2 Marks

Evaluate:
$\lim\limits _{\text{x} \rightarrow 3}\frac{\text{x}^{2}-9}{\text{x}-3}$

View full solution →

Q 72 Marks Questions2 Marks

Evaluate:
$\lim\limits_{\text{x} \rightarrow 0}\frac{\sin^{2}2\text{x}}{\sin^{2}4\text{x}}$

View full solution →

Q 82 Marks Questions2 Marks

Differentiate the following functions.
$(\text{ax}^{2}+\cot\text{x})(\text{p}+\text{q}\cos\text{x})$

View full solution →

Q 92 Marks Questions2 Marks

Differentiate the following functions.
$\frac{1}{\text{ax}^{2}+\text{bx}+\text{c}}$

View full solution →

Q 102 Marks Questions2 Marks

Differentiate the following functions.
$\Big(\text{x}+\frac{1}{\text{x}}\Big)^{3}$

View full solution →

Q 113 Marks Question3 Marks

Differentiate the following functions.
$(\sin\text{x}+\cos\text{x})^{2}$

View full solution →

Q 123 Marks Question3 Marks

Differentiate the following functions.
$\frac{\text{x}^{2}\cos\frac{\pi}{4}}{\sin\text{x}}$

View full solution →

Q 133 Marks Question3 Marks

Evaluate:
$\lim\limits _{\text{x} \rightarrow \frac{1}{2}}\frac{4\text{x}^{2}-1}{2\text{x}-1}$

View full solution →

Q 143 Marks Question3 Marks

Evaluate:
$\lim\limits_{\text{x} \rightarrow\frac{\pi}{6}}\frac{\sqrt{3}\sin\text{x}-\cos\text{x}}{\text{x}-\frac{\pi}{6}}$

View full solution →

Q 153 Marks Question3 Marks

Differentiate the following functions.
$\sin^{3}\text{x}\cos^{3}\text{x}$

View full solution →

Q 16Fill In The Blanks[1 Marks ]1 Mark

If $\text{y}=1+\frac{\text{x}}{1!}+\frac{\text{x}^{2}}{2!}+\frac{\text{x}^{3}}{3!}+....$ then ____________.

View full solution →

Q 17Fill In The Blanks[1 Marks ]1 Mark

$\lim\limits_{\pi \rightarrow 0}\Big(\sin\text{mx}\cot\frac{\text{x}}{\sqrt{3}}\Big)=2$ then ___________.

View full solution →

Q 18Fill In The Blanks[1 Marks ]1 Mark

$\lim\limits_{\text{x} \rightarrow 3^{+}}\frac{\text{x}}{[\text{x}]}=$ ___________.

View full solution →

Q 19Fill In The Blanks[1 Marks ]1 Mark

If $\text{f}(\text{x})=\frac{\tan\text{x}}{\text{x}-\pi}$ then $\lim\limits_{\text{x} \rightarrow \pi}\text{f}(\text{x})=$ ____________.

View full solution →

Q 205 Marks Questions5 Marks

Evaluate:
$\lim\limits_{\text{x} \rightarrow 0}\frac{2\sin\text{x}-\sin2\text{x}}{\text{x}^{3}}$

View full solution →

Q 215 Marks Questions5 Marks

Differentiate the functions with respect to 'x'.
$\text{x}\cos\text{x}$

View full solution →

Q 225 Marks Questions5 Marks

Evaluate:
$\lim\limits_{\text{x} \rightarrow0}\frac{\sin2\text{x}+3\text{x}}{2\text{x}+\tan3\text{x}}$

View full solution →

Q 235 Marks Questions5 Marks

Evaluate:
$\lim\limits_{\text{x} \rightarrow0}\frac{\sqrt{2}-\sqrt{1+\cos\text{x}}}{\sin^{2}\text{x}}$

View full solution →

Q 245 Marks Questions5 Marks

Evaluate the following limits.
Let $\begin{cases}\frac{\text{k}\cos\text{x}}{\pi-{2}\text{x}}, \\3,\text{x}=\frac{\pi}{2}\text{and } \text{f}(\text{x})=\text{f}\big(\frac{\pi}{2}\big)\end{cases}$ Find the value of k.

View full solution →

Limits and Derivatives question types

Limits and Derivatives questions

Generate a Limits and Derivatives paper free

Limits and Derivatives Maths - Limits and Derivatives

Limits and Derivatives question types

Limits and Derivatives questions

Generate a Limits and Derivatives paper free