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Important Questions for CBSE Class 11 Maths Chapter 13 – Limits and Derivatives

 


Important Questions for CBSE Class 11 Maths Chapter 13 - Limits and Derivatives

CBSE Class 11 Maths Chapter-13 Important Questions - Free PDF Download

1 Marks Questions

1. Evaluate 

Ans. 


2. Evaluate 

Ans.

=


3. Find derivative of 

Ans. Let 


4. Find derivative of 

Ans.


5. Evaluate 

Ans.


6. What is the value of  

Ans.


7. Differentiate 

Ans.


8. If  find 

Ans.


9. Evaluate 

Ans.

=

=


10. Differentiate sinwith respect to 

Ans.

=


11. Evaluate 

Ans.


12. Evaluate 

Ans.

=

=

=


13. Find

 

Ans.


14. Evaluate 

Ans.


15. Find derivative of 

Ans.


16. Find derivative of 

Ans.


17. The value of 

Ans.


18. Evaluate 

Ans.


19. find the value of ‘a

Ans.


20. Differentiate 

Ans.


4 Marks Questions

1. Prove that 

Ans. We have

=


2. Evaluate 

Ans. 

=


3. Evaluate 

Ans.


4. It . Show that 

Ans. 

Hence proved


5. Differentiate 

Ans. Let 


6. Let  and if  What are the possible value of a and b ?

Ans. Given (1) =4

By eq. 

  


7. If  find 

Ans. 


8. Differentiate 

Ans. 


9. Differentiate 

Ans. (i)

(ii) 


10. Evaluate 

Ans. 


11. Evaluate 

Ans. 


12. Evaluate 

Ans. 


13. Find the derivative of at 

Ans. 

At 

=

=


14. Find the derivative of with respect to using product rule

Ans. let


15. Find the derivative of with respect to 

Ans. let

=

=

=

=


16. Find 

when 

Ans. 

We know that 

L. H. L. 

R. H. L. 

L. H. L. R. H. L does not exist


17. Find the derivative of the function at Also show that 

Ans. 

At 

 Hence proved


18. Evaluate 

Ans. 

=


19. Find derivative of  by first principle

Ans. 


20. Evaluate 

Ans. 


21. Evaluate (if it exist)

Ans. 


22. For what integers  and does both

Ans.

For all real number exist

For 

 all integral values of exist


23. If 

Ans. 

Differentiating w. r. t. we gill


24. Evaluate 

Ans. 


25. Differentiate the function with respect to 

Ans. 


26. Find 

Ans. 

27. Find 

Ans. 

28. Find derivative of by first principle

Ans. 

29. Find derivative of 

Ans. 

30. Find derivative of 
Ans.
 




6 Marks Questions

1. Differentiate tanfrom first principle.

Ans. 

=

=

=

=

=


2. Differentiate From first principle.

Ans. let 

=

=

=

=


3. Find derivative of cosec  by first principle

Ans. 


4. Find the derivatives of the following fuchsias:

Ans. (i)

(ii)


5. If for what Values of ‘a’ does  exist

Ans.given 

a=0

L.H.L.

=

R.H.L. 

exist

At  exist


6. Find the derivative of sin with respect to from first principle.

Ans. let 

=

=

=

=

=


7. Find the derivative of from first principle

Ans.


8. Find derivative of

Ans. (i)

(ii)


9. Evaluate 

Ans.


10. Differentiate

Ans. (i)

(ii)

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