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Guess paper proof
A
17 – 03 – 2015
Part – III
MATHEMATICS, Paper – II (B)
(Coordinate Geometry and Calculus)
Time: 3 hours
Max. Marks: 75
Section – A
Very short answer types questions.
i)
Answer all questions
ii)
Each questions carries two marks
1. If the length of the tangent from (5, 4) to the circle x2+y2+2ky=0 is 1 then find k.
(Q.NO:15, direct problem)
2. Find the equation of the polar of (1, -2) with respect to the circle x2+y2-10x-10y +
25=0.
(Method, Q.NO:18)
3. Find the angle between the circles x2 + y2 – 12x – 6y + 41 = 0 and x2 + y2 + 4x + 6y –
59 = 0
(Q.NO:24, direct problem)
4. Find the equation of the parabola whose focus is S(1, -7), vertex is A(1, -2).
(Q.NO:45, direct problem)
5. If the eccentricity of a hyperbola is , then find the eccentricity of its conjugate
hyperbola.
(Q.NO:68, direct problem)
6. Evaluate ∫
Sol:
on
(Method)
let log (1+x) = t
Diff w.r.t “x” on both sides
[
]
=∫
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=∫
=∫
=
+c
=
7. Evaluate ∫
8. Evaluate ∫
Sol:
(Q.NO:102, direct problem)
√
=∫
√
=[
]
=3–1
=2
9. Find ∫–
(Q.NO:126, direct problem)
10. Find the order and degree of
⁄
⁄
[
(Q.NO:150, direct problem)
]
Section – B
Short answer types questions.
(i) Attempt any five questions
(ii) Each questions carries four marks
11. Find the equation of the circle whose centre lies on the X-axis and passing through
(-2, 3) and (4, 5).
12. Show that circles S
(Q.NO:272, direct problem)
x2 + y2 – 2x – 4y – 20 = 0, S1
x2 + y2 + 6x + 2y – 90 = 0 touch
each other internally. Find their point of contact.
(Method, Q.NO:264)
13. Find the equation of the ellipse in the standard form whose distance between foci is
4(A) -2nd prob
2 and the length of latus rectum is
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14. Find the eccentricity, coordinates of foci, lengths of latus rectum and the equation of
directrix of the ellipse 9x2 + 16y2 – 36x + 32y – 92 = 0 (Q.NO:196, direct problem)
15. Find the equation of the tangents to the hyperbola x2 – 4y2 = 4 which are Method
a. Parallel
Q.NO: 65
b. Perpendicular to the line x + 2y = 0
Q.NO:67
16. Find the reduction formula for ∫
⁄
for an integer n
(Q.NO:234, direct
problem)
17. Solve
(Q.NO:258, direct problem)
Section – C
Long answer types questions.
a. Attempt any five questions
b. Each questions carries seven marks
18. Find the values of “c” if the points (2, 0), (0, 1), (4, 5), (0, c) are concyclic. (Q.NO:275, direct
problem)
19. Find the direct common tangents of the circles x2+y2+22x-4y-100=0 and
(Q.NO:267, direct problem)
20. Prove that the area of the triangle formed by the tangents at (x1, y1), (x2, y2) and (x3, y3) to
the parabola y2 = 4ax (a>0) is
| sq. units
|
21. Evaluate ∫
22. Evaluate ∫
(Method, Q.NO:290)
9th example prob-6(D)
√
2M /4M actually
23. Evaluate ∫
(Q.NO:298, direct problem)
24. Solve the differential equation (2x + y + 1(dx + (4x + 2y – 1) dy = 0. (Method, Q.NO:320,
321,322)
Direct problems - total scoring
Method problems - total scoring
: 14 + 16 + 21=51
:4+4+14 = 22
Plus academy guess paper
Total Scoring: 51+ 22 =
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2B IPE 2015 Question paper
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