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
is:
(A) 1/3
(B) -1/3
(C) 1
(D) – 1
Solution:

Hence, option (B) is correct.

Question 2.
The value of

(A) 0
(B) ∞
(C) 1
(D) – 1
Solution:

Hence, option (A) is correct.

Question 3.
The value of

(A) 2/3
(B) 1/3
(C) 1/2
(D) 3/2
Solution:

Hence, option (D) is correct.

Question 4.
The value of

(A) 3
(B) 2
(C) 1
(D) – 1
Solution:

Hence, option (C) is correct.

Question 5.
The value of
(A) π/4
(B) π/2
(C) 0
(D) ∞
Solution:

Hence, option (A) is correct.

Question 6.
The value of
(A) 0
(B) 1
(C) log_e (ab)
(D) log_e (a/b)
Solution:

Hence, option (D) is correct.

Question 7.
The value of
(A) 0
(B) 1
(C) π/180
(D) π
Solution:

Hence, option (C) is correct.

Question 8.
The value of
(A) 0
(B) 1/2
(C) -1/2
(D) -1
Solution:

Hence, option (B) is correct.

Question 9.
The value of
(A) 0
(B) 81
(C) 4
(D) 1
Solution:

Hence, option (B) is correct.

Question 10.
The value of

(A) 0
(B) ∞
(C) – 1
(D) 1
Solution:

Hence, option (C) is correct.

Question 11.
If y is function of x, then derivative of y with respect to x is :

Solution:
y = ax² + bx + c (Let)

Hence, option (C) is correct.

Question 12.
Derivative of xⁿ is :
(A) x^{n – 1}
(B) (n – 1)x^{n – 2}
(C) nx^{n – 1}
(D) x^{n + 1}/n + 1
Solution:
Let y = xⁿ

Hence, option (C) is correct.

Question 13.
Derivative of \(\frac { 1 }{ \sqrt { x } } \) is:

Solution:

Hence, option (B) is correct.

Question 14.
\(\frac { d }{ dx }\)(5^x) is equal to :
(A) 5^x
(B) 10^x
(C) 10^x log_e 5
(D) 5^x log_e 5
Solution:
\(\frac { d }{ dx }\) (5^x) = 5^x log_e5 ( ∵\(\frac { d }{ dx }\) (a^x .log a)
Hence, option (D) is correct.

Question 15.
\(\frac { d }{ dx }\) (log_a x) is equal to :

Solution:

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