Assignment

1. MATHS ASSIGNMENT (CHAPTER :- 1 – 8) CLASS – XII
4 MARKS
1. y = , show (x2
+ 1)2
y2 + 2x (x2
+ 1)2
y1 = 2.
2. Prove using properties :-
+ + +
+ + +
+ + +
= .
3. Evaluate :- ∫ ( )( )
dx
4. If (cos x)y
= (cos y)x
, find .
5. Prove :- = − .
6. A = R – {3}, B = R – {1}. f : A → B. f(x) = . Show that f is one – one & onto.
7. Prove :- ∫ √ + √ = √ .
8. If a + b + c ≠ 0 & = 0. Prove a = b = c
9. Evaluate :- ∫( − )√ − − dx.
10. Differentiate :- log (xsinx
+ cot2
x), w.r.t. x
11. Evaluate :- ∫ ( )( )
dx
12. Prove :- y = ( )
- x is an increasing function of x in [0, ]
13. Evaluate :- ∫ .
14. Differentiate :- tan w.r.t. x
15. If x + + √ + = . = ( )
.
16. If A =
−
, find k : A2
= 8A + kI .
17. If f(x) =
| |
≠
=
. check the continuity at x = 0.
18. If y = ecos x
, prove y2 + sin x y1+ y cos x = 0.
19. Evaluate :- ∫ dx.
20. Prove :-
( + )
( + )
( + )
= 2abc (a + b + c)3
.
21. If + + = , Prove x2
+ y2
+ z2
+ 2xyz = 1.
22. Find equation of tangent to the curve x2
+ 3y = 3 which is 11 to line y – 4x + 5 = 0.
23. Find x :
−
−
=
− − −

2. 24. Evaluate :- ∫ dx.
25. Prove : ∫ = .
26. Using property of determine. Prove :
+ + − −
− + + −
− − + +
= 2 (a + b) (b + c) ( c + a)
27. Solve for x : + =
28. Evaluate :- ∫ .
29. Prove : √ − + sin = √ − .
30. Show that the relation R in set R of real numbers, defined as R = {(a, b): a ≤ b2
} is neither reflexive nor
symmetric nor transitive.
31. Using elementary operation find A-1
, A = .
32. Show that the curve 2x = y2
& 2xy = k cut at right angles if k2
= 8.
33. Find if y =
–
.
34. Evaluate : ∫ ( ) , ( ) = | | + | + | + | + | .
35. Find the intervals in which f(x) = sin x + cos x, 0 ≤ ≤ is strictly increasing or decreasing.
36. Show that the relation R on z defined by (a, b) ∈ R  a – b is divisible by 5 is an equivalence relation.
37. Solve by matrix method :- x + 2y + 5z = 10, x – y – z = -2, 2x + 3y – z = -11.
38. Evaluate :- ∫ .
39. If y = Aemx
+ Benx
, show that y2
– (m + n) y1 + mny = 0.
40. Evaluate : ∫ + as limit of sum.