Sector – 18 A, Dwarka, New Delhi – 110 CLASS - XII ENGLISH Q1. Write a Book Review in a file Wells, as per the format given be S. No. 1 Summary and 2 Character ske 3 Evaluation of 4 Conclusion MATHS Complete the following assignme 1. If tan -1 1 + tan -1 (1/2) = tan 2. Let f : R – { - 4/3} → R be 3. Evaluate Sin [ π– sin -1 (-1) 4. Prove that cos 2 (tan -1 2)+si 5. If a binary operation * is value of (2*3)*4. 6. Find the principal value o 7. Evaluate sin{ 1/2 cos -1 (4/ 8. If : R → R ,a,b,c,d є R such function. 9. Evaluate : Cos (π/3- sin -1 ( 10. Show that the function f: 11. If f(x) = e x and g(x) = log e x 0075 www.Sa SUMMER HOLIDAY HOMEWORK e/folder on “The Invisible Man” by HG elow: CONTENT d analysis etch- 5 Main characters Plot and structure ent in Maths notebook n -1 α, find α. a funcon defined as f(x) = 4x / 3x+4. Find the i )]. in 2 (cot -1 3) = 3/10. defined on the set Z of integers as a*b = 3a –b, of tan -1 [sin(sin -1 x+cos -1 x)] , x ε [ -1,1] . /5) }. h that (a,b) *(c,d) = (ac, b + ad) Find the identity (-√3/2)). : R → R such that f(x) = x 2 is neither one –one no x , find fog and gof. Is fog = gof ? achdevaGlobal.in K inverse of f. then find the y element of the or onto.
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Sector – 18 A, Dwarka, New Delhi – 110075
CLASS - XII
ENGLISH
Q1. Write a Book Review in a file/folder on “The Invisible Man” by HG
Wells, as per the format given below:
S. No.
1 Summary and analysis
2 Character sketch
3 Evaluation of Plot and structure
4 Conclusion
MATHS
Complete the following assignment in Maths notebook
1. If tan-1
1 + tan-1
(1/2) = tan
2. Let f : R – { - 4/3} → R be a func@on defined as f(x) = 4x / 3x+4. Find the inverse of f.
3. Evaluate Sin [ π– sin-1
(-1)].
4. Prove that cos2(tan
-12)+sin
5. If a binary operation * is defined on the set Z of integers a
value of (2*3)*4.
6. Find the principal value of tan
7. Evaluate sin{ 1/2 cos-1
(4/5) }.
8. If : R → R ,a,b,c,d є R such that (a,b) *(c,d) = (ac, b + ad) Find the identity element of the
function.
9. Evaluate : Cos (π/3- sin-1
(
10. Show that the function f: R
11. If f(x) = ex and g(x) = logex , find fog and gof. Is fog = gof ?
110075 www.SachdevaGlobal.in
SUMMER HOLIDAY HOMEWORK
Q1. Write a Book Review in a file/folder on “The Invisible Man” by HG
below:
CONTENT
ummary and analysis
Character sketch- 5 Main characters
Evaluation of Plot and structure
Complete the following assignment in Maths notebook
(1/2) = tan-1
α, find α.
→ R be a func@on defined as f(x) = 4x / 3x+4. Find the inverse of f.
1)].
2)+sin2(cot
-13) = 3/10.
If a binary operation * is defined on the set Z of integers as a*b = 3a –b, then find the
Find the principal value of tan-1
[sin(sin-1
x+cos-1
x)] , x ε [ -1,1] .
(4/5) }.
є R such that (a,b) *(c,d) = (ac, b + ad) Find the identity element of the
(-√3/2)).
Show that the function f: R → R such that f(x) = x2 is neither one –one nor onto.
x , find fog and gof. Is fog = gof ?
www.SachdevaGlobal.in
SUMMER HOLIDAY HOMEWORK
→ R be a func@on defined as f(x) = 4x / 3x+4. Find the inverse of f.
b, then find the
є R such that (a,b) *(c,d) = (ac, b + ad) Find the identity element of the
one nor onto.
Sector – 18 A, Dwarka, New Delhi – 110075 www.SachdevaGlobal.in
12. Prove that:
13. Prove: 2 tan-1
(1/2) + tan-1
(1/7) = tan-1
(31/17)
14. Solve for x: tan-1
2x + tan-13x = π/4
15. Prove that the function f: R →R defined as f(x) = 2x-3 is invertible and find f-1
(x)
16. Show that sin-1
12 /13 + cos-1
4/5 + tan-1
63/16 = π .
17. Show that the relation are in the set a = {x : x є w, x ≤10}given by
is an equivalence relation , find the elements related to 3.
18. Examine if the following are binary operations
(i) a*b =a+b/2,a,b є N
(ii) a*b=a+b/2, a,b є Q .
19. Prove that
.
20. Prove: 2 tan-1
1/2) + tan-1
(1/7) = tan-1
(31/17).
21. Solve for x: tan-1
2x + tan-1
3x = π/4.
22. Prove that tan -1
(1/5) + tan -1
(1/7) + tan -1
(1/3) + tan -1
(1/8) = 1.
23. Prove that .
24. Prove that .
25. Prove that .
26. Write in simplest form: .
27. If A =�4 32 1� and B = �2 45 1� , verify (AB)−1
= B −1
A−1
.
Sector – 18 A, Dwarka, New Delhi – 110075 www.SachdevaGlobal.in
28. Split matrix �3 1 12 3 41 0 1 in two matrices, one of which is symmetric and the other is skew
– symmetric.
29. If A = � 3 1−1 2� verify � - 5A + 7I = 0, hence find ���.
30. Find the inverse of A = �2 3 11 4 12 1 0 , using elementary row transformation.
31. If A' = �−2 31 2� , B = �−1 01 2� find (A +2B)'.
32. If A = �−1 43 −7� , verify that (A2)' = (A')
2.
33. If A' = � 3 4−1 20 1 and B = �−1 2 11 2 3� then verify that
(A + B)' = A' + B' (ii) (A – B)' = A' - B'
34. For the matrix A = �1 56 7�, verify that
(i) (A + A') is a symmetric matrix. (ii) (A – A') is a skew – symmetric matrix.
35. Using elementary column transformations, find the inverse of the following matrices: