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

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

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

II. Short Answer Type Questions.

  1. Answer any FIVE questions.
  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

III. Long Answer Type Questions.

  1. Answer ANY FIVE questions,
  2. Each Question carries SEVEN marks.

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

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

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 \(\frac{\mathrm{dy}}{\mathrm{dx}}\) = \(\frac{x^2+y^2}{2 x^2}\).

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