**MCQs Questions for Class 11 Maths Chapter 13 Limits and Derivatives**

In this 21^{st} century, Multiple Choice Questions (MCQs) play a vital role to prepare for a competitive examination. CBSE board has also brought a major change in its board exam patterns. Now-a-days, a total of 10 MCQs questions are asked in the class 10 board examination.

In most of the competitive examinations, only MCQ questions are asked. So, for getting ready for the competitive examinations, we have to practice for MCQs questions to solve. It strengthens the critical thinking and problem solving skills.

In future, if you want to prepare for competitive examination and to crack it, then you should more focus on the MCQ questions. Thus, from the board examinations point of view and competitive examinations point of view, you should practice more on multiple choice questions.

Thus, let’s solve these MCQs Questions to make our foundation very strong.

**MCQs Questions for Class 11
Maths Chapter 13 Limits and Derivatives**

**1.** The value of Lim_{x→0} {sin
(a + x) – sin (a – x)}/x is

(a) 0

(b) 1

(c) 2 cos a

(d) 2 sin a

**Answer: c**

**2. **Find the derivative of e^{x2}.

(a) e^{x2}

(b) 2x

(c) 2e^{x2}

(d) 2xe^{x2}

**Answer: d**

**3. **The
value of Lim_{x→-1} [1 + x + x² +
……….+ x^{10}] is

(a) 0

(b) 1

(c) -1

(d) 2

**Answer: b**

**4. **What is the value of d/dx (sin x tan x)?

(a) sin x + tan x sec x

(b) cos x + tan x sec x

(c) sin x + tan x

(d) sin x + tan x sec^{2 }x

**Answer: a**

**5. **The
value of** **Lim_{x→0} log(1 – x) is equal to

(a) 0

(b) 1

(c) 1/2

(d) None of these

**Answer: a**

**6. **What is the value of d/dx (e^{x} tan x) at x
= 0?

(a) 0

(b) 1

(c) -1

(d) 2

**Answer: b**

**7. **The derivative of [1 + (1/x)] /[1 - (1/x)] is

(a) 1/(x – 1)²

(b) -1/(x – 1)²

(c) 2/(x – 1)²

(d) -2/(x – 1)²

**Answer: d**

**8. **What is the number of critical points of f(x) = |x^{2} – 1| / x^{2}?

(a) 0

(b) 1

(c) 2

(d) 3

**Answer: c**

**9. **The expansion of log(1 – x) is

(a) x – x²/2 + x³/3 – ……..

(b) x + x²/2 + x³/3 + ……..

(c) -x + x²/2 – x³/3 + ……..

(d) -x – x²/2 – x³/3 – ……..

**Answer: d**

**10. **What will be the value of dy/dx if x = a sec^{2 }Î¸ and y = a tan^{3 }Î¸ at Î¸ = Ï€/4?

(a) 1/2

(b) 3/4

(c) 3/2

(d) 1/4

**Answer: c**

**11. **The value of Lim_{n→∞} (sin
x/x) is

(a) 0

(b) 1

(c) -1

(d) None of these

**Answer: a**

**12. **If y = (3x – 4)/(x + 2), then what is the value of dy/dx?

(a) dy/dx

(b) y

(c) 1/(dy/dx)

(d) A constant

**Answer: c**

**13. **The
value of Lim_{x→0} sin
(ax)/(bx) is

(a) 0

(b) 1

(c) a/b

(d) b/a

**Answer: c**

**14. **If y = 1/(1 + x + x^{2} + x^{3}), then what is the value of y’ at x = 0?

(a) 0

(b) 1

(c) -1

(d) ½

**Answer: c**

**15. **The value of Lim_{x→0} {log(1
+ ax)}/x is

(a) 0

(b) 1

(c) a

(d) 1/a

**Answer: c**