Guess paper proof - intermediate guess papers

Guess paper proof - intermediate guess papers

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Guess paper proof
B
13 – 03 – 2015
Part – III
MATHEMATICS, Paper – I (A)
(English version)
Time: 3 hours
Max. Marks: 75
Section – A
Very short answer types questions.
i)
ii)
Answer all questions
Each questions carries two marks
1. f:
defined by
, then this function is injection or not? Justify.
concept
2. Find the range of the real valued function
. plus academy – guess
√
problem -Method
3. Construct a
matric, whose elements are defined by
4. Find the rank of the matrix [
|
|
] plus academy – guess problem -Method
5. A = 2i+5j+k and b=4i+mj+nk are collinear vectors, then find m and n. plus academy
– guess problem -direct
6. OABC is a parallelogram. If OA = a and OC = c find the vector equation of the side
BC. plus academy – guess problem -direct
7. Find the angle between the planes r.(2i-j+2k)=3 and r(3i+6j+k)=4. plus academy –
guess problem -Method
8. Find the period of tan(x+4x+9x+…….n2x), where n is any positive integer. plus
academy – guess problem -Method
9. If
, where
, evaluate
. Concept
)n=
10. Prove that (
, for any n R. plus academy
– guess problem -direct
Junior Intermediate
|
1A IPE 2015 Question paper
|
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Section – B
Short answer types questions.
(i) Attempt any five questions
(ii) Each questions carries four marks
11. Examine whether the following system of equations are consistent or inconsistent
and if consistent, find the complete solution x+y+z=1, 2x+y+z=2, x+2y+2z=1. plus
academy – guess problem -direct
12. A,b,c are non-coplanar vectors. Prove that the following four points are coplanar
6a+6b-c, 2a-b+3c, -a+2b-4c, -12a-b-3c. plus academy – guess problem -Method
13. Find the volume of the tetrahedron, whose vertices are (1, 2, 1), (3, 2, 5), (2, -, 0) and
(-1, 0, 1)
14. Of
and
, then find the value of
tan2A. plus academy – guess problem -method
15. If
are solutions of the equation
, then find the value of (i) Tan
(ii) ) Tan
. plus academy – guess problem -direct
16. Prove that
17. Prove that
+2
+
= plus academy – guess problem -direct
+
=
plus academy – guess problem -direct
Section – C
Long answer types questions.
(i) Attempt any five questions
(ii) Each questions carries seven marks
18. Let f={(1, a), (2, c), (4, d), (3, b)} and g-1 = {(2, a), (4, b), (3, d)}, then show that
(gof)-1 = f-1og-1. plus academy – guess problem -Method
19. Using the principle of finite mathematical induction prove that
1.2.3+2.3.4+3.4.5+…………up to n terms =
,
plus academy –
guess problem -direct
x  2 2 x  3 3x  4
20. Find the value of x if x  4 2 x  9 3x  16  0 plus academy – guess problem –
x  8 2 x  27 3x  64
direct
Junior Intermediate
|
1A IPE 2015 Question paper
|
[email protected]
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21. Solve the following system of equations by using Cramer’s rule
x-y+3z = 5, 4x + 2y – z = 0, -x + 3y + z = 5. plus academy – guess problem -direct
22. If ̅
̅
compute | ̅
̅, ̅
̅
̅
̅
̅
̅
̅, ̅
̅
̅
̅ and ̅
̅
̅
̅ then
̅ |.
23. If A+B+C = , then show that
(
)
plus academy – guess problem -direct
24. If r1=2, r2=3, r3=6 and r=1then show that a=3, b=4, c=5. plus academy – guess
problem -direct
Direct problems total scoring
Method problems total scoring
: 57
: 23
Plus academy guess paper
Total Scoring: 57 + 23 = 80/97
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Junior Intermediate
|
1A IPE 2015 Question paper
|
[email protected]