These Limits And Derivatives Class 11 NCERT Questions and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Limits And Derivatives Class 11 NCERT Questions and Answers will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.
Limits And Derivatives Class 11 NCERT Questions and Answers
1. Limy→∞ {(x + 6)/(x + 1)}(x+4) equals
(A) e
(B) e³
(C) e5
(D) e6
Answer: e5
2. The value of Limn→∞ {1² + 2² + 3² + …… + n²}/n³ is
(A) 0
(B) 1
(C) -1
(D) n
Answer: 0
3. The value of Limx→0 (1/x) × sin-1 {2x/(1 + x²) is
(A) 0
(B) 1
(C) 2
(D) -2
Answer: 2
4. Limx→0 sin (ax)/bx is
(A) 0
(B) v
(C) a/b
(D) b/a
Answer: a/b
5. Limx→0 log(1 – x) is equals to
(A) 0
(B) 1
(C) 1/2
(D) None of these
Answer: 0
6. Limx->0 {(ax – bx )/ x} is equal to
(A) log a
(B) log b
(C) log (a/b)
(D) log (a*b)
Answer: log (a/b)
7. The value of Limx->∞ (sin x/x) is
(A) 0
(B) 1
(C) -1
(D) None of these
Answer: 0
8. Limx->-1 [1 + x + x2 + ……….+ x10 ] is
(A) 0
(B) 1
(C) -1
(D) 2
Answer: 1
9. The value of Limx->a (a*sin x – x*sin a)/(ax2 – xa2 ) is
(A) (a*cos a + sin a)/a2
(B) (a*cos a – sin a)/a2
(C) (a*cos a + sin a)/a
(D) (a*cos a – sin a)/a
Answer: (a*cos a – sin a)/a2
10. The value of Limx->0 (sin ax/sin bx) is
(A) a+b
(B) a-b
(C) a*b
(D) a/b
Answer: a/b
11. The value of Limx->0 (1 + x)n is equal to
(A) 0
(B) 1
(C) 1/2
(D) None of these
Answer: 1
12. The value of the limit Limn->0 (1 + an)b/n is
(A) ea
(B) eb
(C) eab
(D) ea/b
Answer: eab
13. The expansion of ax is
(A) ax = 1 + x/1! * (log a) + x2 /2! * (log a)2 + x3 /3! * (log a)3 + ………..
(B) ax = 1 – x/1! * (log a) + x2 /2! * (log a)2 – x3 /3! * (log a)3 + ………..
(C) ax = 1 + x/1 * (log a) + x2 /2 * (log a)2 + x3 /3 * (log a)3 + ………..
(D) ax = 1 – x/1 * (log a) + x2 /2 * (log a)2 – x3 /3 * (log a)3 + ………..
Answer: ax = 1 + x/1! * (log a) + x2 /2! * (log a)2 + x3 /3! * (log a)3 + ………..
14. Limx->∞ {(x + 6)/(x + 1)}(x + 4) equals
(A) e
(B) e3
(C) e5
(D) e6
Answer: e5
15. Limx->0 (1 – cos x)/x is
(A) 0
(B) 1
(C) 1/2
(D) Limit does not exist
Answer: 0
16. Limx->0 sin (ax)/bx is
(A) 0
(B) 1
(C) a/b
(D) b/a
Answer: a/b
17. Then value of Limx->0 {ex – (1 + x)}/x2 is
(A) 0
(B) 2
(C) 1/2
(D) e
Answer: 1/2
18. The value of the limit Limn->∞ (1 + 1/n)n+5 is
(A) 0
(B) 1
(C) e
(D) 1/e
Answer: e
19. The value of the limit Limx->0 {log(1 + ax)}/x is
(A) 0
(B) 1
(C) a
(D) 1/a
Answer: a
20. 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: -2/(x-1)2
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