# TS Inter 2nd Year Maths 2B Question Paper March 2023

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## TS Inter 2nd Year Maths 2B Question Paper March 2023

Time : 3 Hours
Max. Marks : 75

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 with center C = (-1, 2) and radius r = 5.

2. Find the equation of the normal at P = (3, 5) of the circle
S ≡ x2 + y2 – 10x – 2y + 6 = 0.

3. Find the equation of the radical axis of the following circles :
x2 + y2 – 3x – 4y +5 = 0, 3(x2 + y2) – 7x + 8y – 11 = 0.

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

5. If 3x – 4y + k = 0 is a tangent to x2 – 4y2 = 5, find the value of k.

6. Evaluate ∫$$\sqrt{1-\cos 2 x}$$ dx on I ⊂ [2nπ, (2n + 1) π], n ∈ Z.

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

8. Evaluate $$\int_2^3 \frac{2 x}{1+x^2}$$dx.

9. Find $$\int_0^{\pi / 2}$$ cos8x dx.

10. Find the order and degree of
$$\left[\frac{\mathrm{d}^3 y}{\mathrm{~d} x^3}\right]^2$$ – 3$$\left[\frac{\mathrm{d} y}{\mathrm{~d} x}\right]^2$$ – ex = 4

Section – B

1. Attempt ANY FIVE questions.
2. Each question carries FOUR marks.

11. Find the length of the chord formed by x2 + y2 = a2 on the line x cos a + y sin a = R

12. Find the equation of the circle which cuts orthogonally the circle x2 + y2 – 4x + 2y – 7 = 0 and having the center at (2, 3).

13. Find the eccentricity, coordinates of foci, length of latus rec¬tum and equations of directrices of the following ellipse :
9x2 + 16y2 – 36x + 32y – 92 = 0.

14. Find the condition for the line lx + my + n = 0 to be a tangent to the ellipse $$\frac{x^2}{\mathrm{a}^2}+\frac{y^2}{\mathrm{~b}^2}$$ = 1.

15. Find the equations of the tangents to the hyperbola 3x2 – 4y2 = 12 which are

1. parallel and
2. perpendicular to the line y = x – 7.

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

17. Solve the differential equation
$$\frac{d y}{d x}$$ = $$\frac{x y+y}{x y+x}$$

Section – C
(5 × 7 = 35)

2. Each question carries SEVEN marks.

18. Find the equation of circle passing through (3, 4), (3, 2), (1, 4).

19. Find the equation of circle with center (-2, 3) cutting a chord length 2 units on 3x + 4y + 4 = 0.

20. Derive the equation of the parabola in standard form.

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

22. Evaluate $$\int \frac{d x}{x(x+1)(x+2)}$$

23. Evaluate $$\int_{\pi / 6}^{\pi / 3} \frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}$$dx

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