CBSE Class 11 Mathematics Chapter 13 Limits and Derivatives Multiple Choice Questions with Answers. MCQ Class 11 Mathematics Limits and Derivatives with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 11 Mathematics Limits and Derivatives MCQs with Answers to know their preparation level.
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MCQ Class 11 Mathematics Limits and Derivatives with Answers - Set - 5
Question 1:
The value of Limx→0 cos x/(1 + sin x) is
(a) 0
(b) -1
(c) 1
(d) None of these
Correct Answer – (C)
Given, Limx→0 cos x/(1 + sin x)
= cos 0/(1 + sin 0)
= 1/(1 + 0)
= 1/1
= 1
Question 2 :
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 + ………..
Correct Answer – (A)
Question 3 :
The value of limy→0 {(x + y) × sec (x + y) – x × sec x}/y is
(a) x × tan x × sec x
(b) x × tan x × sec x + x × sec x
(c) tan x × sec x + sec x
(d) x × tan x × sec x + sec x
Correct Answer – (D)
Given, limy→0 {(x + y) × sec (x + y) – x × sec x}/y
= limy→0 {x sec (x + y) + y sec (x + y) – x × sec x}/y
= limy→0 [x{ sec (x + y) – sec x} + y sec (x + y)]/y
= limy→0 x{ sec (x + y) – sec x}/y + limy→0 {y sec (x + y)}/y
= limy→0 x{1/cos (x + y) – 1/cos x}/y + limy→0 {y sec (x + y)}/y
= limy→0 [{cos x – cos (x + y)} × x/{y × cos (x + y) × cos x}] + limy→0 {y sec (x + y)}/y
= limy→0 [{2sin (x + y/2) × sin(y/2)} × 2x/{2y × cos (x + y) × cos x}] + limy→0 {y sec (x + y)}/y
= limy→0 {sin (x + y/2) × limy→0 {sin(y/2)/(2y/2)} × limy→0 { x/{y × cos (x + y) × cos x}] + sec x
= sin x × 1 × x/cos² x + sec x
= x × tan x × sec x + sec x
So, limy→0 {(x + y) × sec (x + y) – x × sec x}/y = x × tan x × sec x + sec x
Question 4 :
The value of the limit Limx→0 (cos x)cot² x is
(a) 1
(b) e
(c) e1/2
(d) e-1/2
Correct Answer – (D)
Given, Limx→0 (cos x)cot² x
= Limx→0 (1 + cos x – 1)cot² x
= eLimx→0 (cos x – 1) × cot² x
= eLimx→0 (cos x – 1)/tan² x
= e-1/2
Question 5 :
Limx→-1 [1 + x + x² + ……….+ x10] is
(a) 0
(b) 1
(c) -1
(d) 2
Correct Answer – (B)
Given, Limx→-1 [1 + x + x² + ……….+ x10]
= 1 + (-1) + (-1)² + ……….+ (-1)10
= 1 – 1 + 1 – ……. + 1
= 1
MCQ Class 11 Mathematics Limits and Derivatives with Answers
Question 6 :
The value of the limit Limn→0 (1 + an)b/n is
(a) ea
(b) eb
(c) eab
(d) ea/b
Correct Answer – (C)
Given, Limn→0 (1 + an)b/n
= eLimn→0(an × b/n)
= eLimn→0(ab)
= eab
Question 7 :
Limx→0 (ex² – cos x)/x² is equals to
(a) 0
(b) 1
(c) 2/3
(d) 3/2
Correct Answer – (D)
Given, Limx→0 (ex² – cos x)/x²
= Limx→0 (ex² – cos x – 1 + 1)/x²
= Limx→0 {(ex² – 1)/x² + (1 – cos x)}/x²
= Limx→0 {(ex² – 1)/x² + Limx→0 (1 – cos x)}/x²
= 1 + 1/2
= (2 + 1)/2
= 3/2
Question 8 :
Then value of Limx→1 (1 + log x – x)}/(1 – 2x + x²) is
(a) 0
(b) 1
(c) 1/2
(d) -1/2
Correct Answer – (D)
Given, Limx→1 (1 + log x – x)}/(1 – 2x + x²)
= Limx→1 (1/x – 1)}/(-2 + 2x) {Using L. Hospital Rule}
= Limx→1 (1 – x)/{2x(x – 1)}
= Limx→1 (-1/2x)
= -1/2
Question 9 :
The value of the limit Limx→0 {log(1 + ax)}/x is
(a) 0
(b) 1
(c) a
(d) 1/a
Correct Answer – (C)
Given, Limx→0 {log(1 + ax)}/x
= Limx→0 {ax – (ax)² /2 + (ax)³ /3 – (ax)4 /4 + …….}/x
= Limx→0 {ax – a² x² /2 + a³ x³ /3 – a4 x4 /4 + …….}/x
= Limx→0 {a – a² x /2 + a³ x² /3 – a4 x³ /4 + …….}
= a – 0
= a
Question 10 :
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
Correct Answer – (B)
Given,
Limx→a (a × sin x – x × sin a)/(ax² – xa²)
When we put x = a in the expression, we get 0/0 form.
Now apply L. Hospital rule, we get
Limx→a (a × cos x – sin a)/(2ax – a²)
= (a × cos a – sin a)/(2a × a – a²)
= (a × cos a – sin a)/(2a² – a²)
= (a × cos a – sin a)/a²
So, Limx→a (a × sin x – x × sin a)/(ax² – xa²) = (a × cos a – sin a)/a²
- NCERT Solutions Class 11 Mathematics Limits and Derivatives with Answers : Exercise 13.1
- NCERT Solutions Class 11 Mathematics Limits and Derivatives with Answers : Exercise 13.2
- NCERT Solutions Class 11 Mathematics Limits and Derivatives with Answers : Exercise 13 Misc
- NCERT Solutions Class 11 Mathematics Textbook download
