RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

Rajasthan Board RBSE Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

Question 1.
The value of
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise is:
(A) 1/3
(B) -1/3
(C) 1
(D) – 1
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (B) is correct.

Question 2.
The value of
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
(A) 0
(B) ∞
(C) 1
(D) – 1
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (A) is correct.

Question 3.
The value of
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
(A) 2/3
(B) 1/3
(C) 1/2
(D) 3/2
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

Hence, option (D) is correct.

Question 4.
The value of
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
(A) 3
(B) 2
(C) 1
(D) – 1
Solution:

Hence, option (C) is correct.

Question 5.
The value of RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
(A) π/4
(B) π/2
(C) 0
(D) ∞
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (A) is correct.

Question 6.
The value of RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
(A) 0
(B) 1
(C) loge (ab)
(D) loge (a/b)
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (D) is correct.

Question 7.
The value of RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
(A) 0
(B) 1
(C) π/180
(D) π
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (C) is correct.

Question 8.
The value of RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
(A) 0
(B) 1/2
(C) -1/2
(D) -1
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (B) is correct.

Question 9.
The value of RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
(A) 0
(B) 81
(C) 4
(D) 1
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (B) is correct.

Question 10.
The value of
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
(A) 0
(B) ∞
(C) – 1
(D) 1
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (C) is correct.

Question 11.
If y is function of x, then derivative of y with respect to x is :
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
y = ax2 + bx + c (Let)
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (C) is correct.

Question 12.
Derivative of xn is :
(A) xn – 1
(B) (n – 1)xn – 2
(C) nxn – 1
(D) xn + 1/n + 1
Solution:
Let y = xn
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (C) is correct.

Question 13.
Derivative of \(\frac { 1 }{ \sqrt { x } } \) is:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (B) is correct.

Question 14.
\(\frac { d }{ dx }\)(5x) is equal to :
(A) 5x
(B) 10x
(C) 10x loge 5
(D) 5x loge 5
Solution:
\(\frac { d }{ dx }\) (5x) = 5x loge5 ( ∵\(\frac { d }{ dx }\) (ax .log a)
Hence, option (D) is correct.

Question 15.
\(\frac { d }{ dx }\) (loga x) is equal to :
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (A) is correct.

Question 16.
If f(x) = x3 + 6x2 – 5 then f'(1) is equal to :
(A) 0
(B) 9
(C) 4
(D) 15
Solution:
f(x) = x3 + 6x2 – 5
⇒ f'(x)= 3x2 + 12x – 0
⇒ f'(x)= 3x2 + 12x
⇒ f'(1)= 3(1)2 + 12(1)
⇒ f'(1)= 3 + 12 = 15
Hence, option (D) is correct

Question 17.
Derivative of sec x° is :
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (C) is correct.

Question 18.
Derivative of logx a is :
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (B) is correct.

Question 19.
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise and f'(0) = 0, then value of c is :
(A) 0
(B) 1
(C) 2
(D) -2
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (D) is correct.

Question 20.
Derivative of loge√x is :
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Hence, option (A) is correct

Question 21.
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
then find the value of a, b and c.
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

Question 22.
Evaluate
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

Question 23.
Evaluate RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

Question 24.
Evaluate
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

Question 25.
Evaluate RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

Question 26.
Evaluate RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

Question 27.
EvaluateRBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

Question 28.
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
Solution:
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

Question 29.
If y = x3. ex sin x, then find \(\frac { dy }{ dx }\).
Solution:
Given, y = x3. ex sin x
On differentiating
RBSE Solutions for Class 11 Maths Chapter 10 Limits and Derivatives Miscellaneous Exercise

RBSE Solutions for Class 11 Maths