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MATHEMATICS (New)

Inter Part-II

(Fresh/Reappear)

Note: Time allowed for Section - B and Section - C is 2 Hours and 40 minutes.

Section - B
Marks: 50

Q-ll) Answer any TEN parts. Each part carries FIVE marks.
1- Find the composite function f [ g (x) ] and g [ f (x) ] for the functions f(x) =

2 - Evaluate

3- Use first principle rule to determine the derivative of f(x) =

4. Use any suitable rule to perform for the function y=

5. Find an equation of the tangent line to the curve x² + y²= 13 at(2, -3)

6. Find F^// ( θ) if F (θ ) =Sin² θi + cos 2 θj + θ²k

7- Evaluate the integral

8. Evaluate

9 Find the equation of the line that passes through the pair of points A(3,4) and B(—5, 5)
10. Find the condition at which the line ax + by + c = O touches the circle x ²+ y² + 2gx + 2fY+ c = 0
11. Find the points of intersection in between the line 2x —y + 1 = O and the parabola y²= 9x dy Y t2

12. Solve the differential equation

13. Verify Euler's theorem for the homogeneous function u = f(x,y) - -ax² + 2hxy + b^y

Section - C
Marks: 30

Note : Attempt any THREE questions. Each question carries equal marks.
QIII) - (a) Find iterate of Newton - Raphson iterative method for the function f(x) = x³ —1,x₀=1
(b) For what value of C the line y = x + c will touch the hyperbola

Q-IV ) (a) Find the equation of the circle, which contains the points (0,0), (0,3) and (- 4 0)
(b)Find the area of the triangular region whose vertices are A(2,4) B(-2, 2) & C(0,0)
Q-V) (a) Find the critical values of the function f(x) = 2x³ - 3x²-60x +5

(b) Find for the parametric functions x(z), y(z), when x=4z² + 1, y=6z³

Q-VI) (a) Evaluate

(b) Find when x² y² +2y³ =x² +2 implicitly