Question types

PART - 2 CH - 12 Limits and Derivatives question types

76 questions across 7 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

76
Questions
7
Question groups
5
Question types
Sample Questions

PART - 2 CH - 12 Limits and Derivatives questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

$\frac{d}{d x}\left(\log _a x\right)$ is equal to :
  • $\frac{1}{x \cdot \log _e a}$
  • B
    $\frac{\log _e a}{x}$
  • C
    $\frac{1}{x}$
  • D
    $\frac{x}{\log _e a}$

Answer: A.

View full solution
If $\lim _{x \rightarrow 0}\left(1+\frac{a}{x}+\frac{b}{x^2}\right)^{2 x}=e^2$, then values of $a$ and $b$ are equal to :
  • A
    $a \in R , b=2$
  • $a=1, b \in R$
  • C
    $a \in R , b \in R$
  • D
    $a=1, b=2$

Answer: B.

View full solution
If $f(x)=\left\{\begin{array}{cc}2 x+b, & x<\alpha \\ x+d, & x \geq \alpha\end{array}\right.$ is such that $\lim _{x \rightarrow \alpha} f(x)=l$, then $l$ is equal to :
  • $2 d-b$
  • B
    $2 b-d$
  • C
    $2 d+b$
  • D
    $b-2 d$

Answer: A.

View full solution
Part (A)Part (B)
1. $\frac{d}{d x}(\sin \sqrt{x})$(a) $\frac{e^{\sqrt{2 x}}}{\sqrt{2 x}}$
2. $\frac{d}{d x}(x+2)^3$(b) $\frac{\sec ^2 \sqrt{x}}{2 \sqrt{x}}$
3. $\frac{d}{d x}\left(\frac{1}{\sqrt{x}}\right)$(c) $3(x+2)^2$
4. $\frac{d}{d x} e^{\sqrt{2 x}}$(d) $\frac{\cos \sqrt{x}}{2 \sqrt{x}}$
5. $\frac{d}{d x} \tan \sqrt{x}$(e) $-\frac{1}{2} x^{-3 / 2}$
View full solution
Part (A)Part (B)
1. $\frac{d}{d x}\left(\log _e x\right)$(a) $-\frac{2}{x^3}$
2. $\frac{d}{d x}\left(\log _a x\right)$(b) $(x+1) e^x$
3. $\frac{d}{d x}\left(\frac{1}{x^2}\right)$(c) $\frac{1}{x}$
4. $\frac{d}{d x} \sqrt{a x+b}$(d) $\frac{a}{2 \sqrt{a x+b}}$
5. $\frac{d}{d x}\left(x e^x\right)$(e) $\frac{1}{x \log _e a}$
View full solution

Generate a PART - 2 CH - 12 Limits and Derivatives paper free

Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.

Download App