# AP Inter 2nd Year Maths 2B Question Paper April 2022

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## AP Inter 2nd Year Maths 2B Question Paper April 2022

Time : 3 Hours
Max. Marks : 75

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

Section – A (10 × 2 = 20)

I. Very short answer type questions :

1. Attempt ALL questions.
2. Each question carries TWO marks.

1. Find the equation of circle whose extremities of a diameter are (1, 2) and (4, 5).

2. Locate the position of the point (2, 4) with respect to the circle x2 + y2 – 4x – 6y + 11 = 0.

3. Find the equation of the radical axis of the circles
S ≡ x2 + y2 – 5x + 6y + 12 = 0
S1 ≡ x2 + y2 + 6x – 4y – 14 = 0

4. Find the vertex and focus x2 – 6x – 6y + 6 = 0.

5. If e, e1 are the eccentricities of a hyperbola and its conjugate hyperbola PT. $$\frac{1}{e^2}$$ + $$\frac{1}{\mathrm{e}_1^2}$$ = 1

6. Evaluate ∫sec2 x cosec2xdx .

7. Evaluate ∫x log x dx on (0, ∞].

8. Evaluate ∫$$\int_0^\pi \sqrt{2+2 \cos \theta} d \theta$$

9. Evaluate $$\int_0^{\frac{\pi}{2}}$$cos7 x sin2 x dx.

10. Find the general solution of $$\frac{d y}{d x}$$ = ex+y

Section – B

2. Each Question carries FOUR marks.

11. Find the equations of the tangents to the circle x2 + y2 – 4x + 6y – 12 = 0 which are parallel to x + y – 8 = 0.

12. Find the equation of the circle passing through the points of intersection of the circles
x2 + y2 – 8x – 6y + 21 = 0
x2 + y2 – 2x – 15 = 0 and (1, 2)

13. Find the length of major axis, minor axis, latus rectum, eccentricity, coordinates of centre, foci and the equation of directrices of the ellipse x2 + 2y2 – 4x + 12y + 14 = 0.

14. Find the equation of the ellipse with focus at (1, -1), e = $$\frac{2}{3}$$ and directrix as x + y + 2 = 0.

15. Find the centre, foci, eccentricity, equation of the directrices, length of the latus rectum of the hyperbola 16y2 – 9x2 = 144.

16. Evaluate $$\int_0^{\frac{\pi}{2}} \frac{\cos ^{\frac{5}{2}} x}{\sin ^{\frac{5}{2}} x+\cos ^{\frac{5}{2}}}$$dx.

17. Solve (1 + x2)$$\frac{d y}{d x}$$ + 2xy – 4x2 = 0

Section – C

2. Each Question carries SEVEN marks.

18. If (2, 0), (0, 1), (4, 5) and (0, c) are concyclic then find c.

19. Show that x + y + 1 = 0 touches the circle x2 + y2 – 3x + 7y + 14 = 0 and find its point of contact.

20. Define parabola and derive its equation in standard form.

21. Evaluate $$\int \frac{1}{1+\sin x+\cos x} d x$$.

22. Obtain Reduction formula for ∫tanx dx and also evaluate ∫tan4xdx.

23. Evaluate $$\int_0^1 \frac{\log (1+x)}{1+x^2}$$dx.

24. Solve $$\frac{\mathrm{dy}}{\mathrm{dx}}$$ = $$\frac{x^2+y^2}{2 x^2}$$.