# AP Inter 2nd Year Maths 2B Model Paper Set 2 with Solutions

Access to a variety of AP Inter 2nd Year Maths 2B Model Papers Set 2 allows students to familiarize themselves with different question patterns.

## AP Inter 2nd Year Maths 2B Model Paper Set 2 with Solutions

Time : 3 Hours
Max. Marks : 75

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

Section – A

I. Very Short Answer Type Questions.

1. Attempt all questions.
2. Each question carries two marks.

1. Find the value of k, if the circles x2 + y2 + 4x + 8 = 0 and x2 + y2 – 16y + k = 0 are orthogonal.

2. If the circle x2 + y2 – 4x + 6y + a = 0 has radius 4, then find a.

3. Obtain the parametric equations of the circle
(x – 3)2 + (y – 4)2 = 82.

4. Find the co-ordinates of the points on the parabola y2 = 8x whose focal distance is 10.

5. If the eccentricity of a hyperbola is $$\frac{5}{4}$$, then find the eccentricity of its conjugate hyperbola.

6. Evaluate $$\int \frac{d x}{\cosh x+\sinh x}$$ on R.

7. Evaluate $$\int \frac{x^8}{1+x^{18}}$$ on R.

8. Find $$\int_{-\pi / 2}^{\pi / 2}$$sin2cos4x dx.

9. Evaluate $$\int_0^\pi \sqrt{2+2 \cos \theta}$$ dθ.

10. Find the order and degree of the differential equation
$$\left[\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3\right]^{6 / 5}$$ = 6y.

Section – B
(5 × 4 = 20)

1. Attempt any five questions.
2. Each question carries four marks.

11. Find the pole of 3x + 4y- 45 = 0 with respect to the circle x2 + y2 – 6x – 8y + 5 = 0.

12. Find the equation of the circle which cuts the circles x2 + y2 – 4x – 6y + 11 = 0 and x2 + y2 – 10x – 4y + 21 = 0 orthogonally and has the diameter along the straight line 2x + 3y = 7.

13. Show that the points of intersection of the perpendicular tangents to an ellipse lie on a circle.

14. Find the value of k if 4x + y + k = 0 is a tangent to the ellipse x2 + 3y2 = 3.

15. Find the center, foci, eccentricity, equation of directrices to the hyperbola x2 – 4y2 = 4.

16. Evaluate $$\int_0^{\pi / 2} \frac{d x}{4+5 \cos x}$$

17. Solve the differential equation (1 + x2)$$\frac{d y}{d x}$$ + y = $$\mathrm{e}^{\tan ^{-1} x}$$

Section – C

1. Attempt any five questions.
2. Each question carries seven marks.

18. Find the equation of a circle which passes through (4, 1), (6, 5) and having the center on 4x + 3y – 24 = 0.

19. Show that the circles x2 + y2 – 6x – 2y + 1 = 0, x2 + y2 + 2x – 8y + 13 = 0 touch each other. Find the point of contact and the equation of common tangent at their point of contact.

20. Show that the common tangent to the parabola y2 = 4ax and x2 = 4by is xa1/3 + yb1/3 + a2/3b2/3 = 0.

21. Evaluate $$\int \frac{2 \sin x+3 \cos x+4}{3 \sin x+4 \cos x+5} d x \text {. }$$

22. Obtain the reduction formula for In = ∫cotn x dx, n being a positive integer, n ≥ 2 and deduce the value of ∫cot4 x dx.

23. Evaluate $$\int_0^{\pi / 4}$$log(1 + tan x)dx.

24. Solve the differential equation (x2 + y2) dx = 2xy dy.