CBSE CLASS XII
Q. 2. Differentiate w.r.t
Q. 3. Let and . Show that F(A)= 0 .Use this result to find out .
Q. 4. Without expanding show that :-
Q. 5. Show that is continuous both at x = 0 and x =1.
Q. 6. Differentiate with respect to
Q. 7. Show that .
Q. 8. Find if
Q. 9. Let the two matrices A and B be given by
Verify that AB=BA=6I , where I is a unit matrix of order 3 and hence solve the system of equations : x – y =3; 2 x + 3 y +4z =17; Y + 2z = 7
Q. 10. If , find and hence solve the system of equations:
Q. 11. Differentiate with respect to .
Q. 12. If verify that .
Q. 13. If , prove that
Q. 14. Find matrix X for which, where is cube root of unity.
Q. 15. Find X if
Q. 16. Find a and b so that the function f is given by is continuous at x=3 and x=5.
Q. 17. If x = sin t y = sin mt , prove that :
Q. 18. Find when y =
Q. 19. Show that the system of equations given below is consistent and hence solve them:
Q. 20. If , show that , hence show that the result holds good when
Q. 21. Find when
Show that :
Q. 22. is continuous at x=0.
Q. 23. Differentiate w .r. t.
Q. 24. If y = , find .
Q. 25. Prove that .
Q. 26. If then prove that
Q. 27. If ; prove that
Q. 28. For what values of a and b , the following system of equations is consistent?
Q. 29. If prove that
is a constant independent of a and b.
Q. 30. If y = ,than show that
Q. 31. Determine the value of ‘k’ so that the function:
is continuous at x =
Q. 32. If A = , find and show that .
. 33. If , find .
Q. 34. If , find .
Q. 35. If then at t = .
Q. 36. Prove , using properties of determinants that
Q. 37. If find .
Q. 38. If , find .
Paper By Mr. Ashok Khugshal