Download OU Intermediate 2018 Core Subjects 0293 Mathematics Question Paper

Total No. of Questions—24

Total No. of Printed Pages—8 Regd. No.

Part III

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MATHEMATICS Paper - II(B)

(English Version)

Time : 3 Hours] [Max. Marks : 75

Note :— This question paper consists of THREE sections A, B and C.

SECTION A 10x2= 20

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I. Very short answer type questions :

Attempt ALL questions

Each question carries TWO marks

1. Find the equation of the circle whose centre is (—1, 2) and which passes through (5, 6).
2. If the length of the tangent from (2, 5) to the circle x² + y² — 5x + 4y + k=0 is √37, then find k.

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3. If the angle between the circles x² + y² - 12x - 6y + 41 =0 and x² + y² + kx + 6y - 59 = 0 is 45°, find k.
4. Find the equation of the parabola, whose vertex is (3, -2) and focus is (3, -5).
5. If 3x —4y +k=0 is a tangent to x² — 4y² = 5, find the value of k.
6. Evaluate : ∫ sin²x dx
7. Evaluate : ∫ cos³ x sinx dx

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8. Evaluate : ∫₀² |1-x|dx.
9. Evaluate : ∫₀^π/2 xsinx dx.
10. Find the general solution of dy/dx = e^x+y

SECTION B 5x4=20

II. Short answer type questions :

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Attempt ANY FIVE questions.

Each question carries FOUR marks.

11. Find the area of the triangle formed by the normal at (3, —4) to the circle x² + y² - 2x — 4y + 25 = 0 with the coordinate axes.
12. Find the equation and length of the common chord of the two circles : x² + y² +3x + 5y +4 =0 and x² + y² + 5x + 3y +4 =0
13. Find the equation of the ellipse referred to its major and minor axes as the coordinate axes X, Y respectively with latus rectum of length 4, and distance between foci 4√2.

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14. Find the eccentricity, length of latus rectum, foci and the equations of directrices of the ellipse : 9x² + 16y² — 36x + 32y - 92 = 0.
15. Show that angle between the two asymptotes of a hyperbola x²/a² - y²/b² =1 is 2tan^-1(b/a) (or) 2 sec^-1 (e).
16. Find the area bounded between the curves y = x², y = √x.
17. Solve : dy/dx +1 = e^x+y.

SECTION C 5x7=35

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III. Long answer type questions :

Attempt ANY FIVE questions.

Each question carries SEVEN marks.

18. Find the equation of a circle which passes through (4, 1), (6, 5) and having the centre on 4x + 3y — 24 =0.
19. Show that the circles, x²+ y² — 6x — 9y + 13 =0, x²+y²—2x—16y=0 touch each other. Find the point of contact and the equation of common tangent at their point of contact.

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20. Derive the equation of parabola in the standard form, that is y² = 4ax.
21. Evaluate : ∫_a^b √(b - x)(x - a) dx
22. Evaluate : ∫ cos⁵ x sinx dx
23. Evaluate : ∫₀² |1-x|dx.
24. Evaluate : ∫₀^π/2 xsinx dx.

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25. Find the general solution of dy/dx = e^x+y

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