please see( more than one choice)

1.. √1-x² + √1-y² = a(x-y) then dy/dx is

a) (1-x²)/(1-y²) b) (1-y²)/ (1-x²) c) (√1-x²)/(1-y²) d) √1-y²)/ (1-x²)

2. If y= cosec x (cot^–1x) thendy/dx
a. x/√1-x² b) -x/√1+x²
c) x/√1+x² d) None

3. The tangents to the circle x² + y² = 25 which is parallel to line 2x-y+1 = 0 are

a) y=2x+4√5 b) y=2x-4√5 c) y=2x+5√5 d) y=2x-5√5

4. ∫1/sin²x+cos²xdx =
a) -2cot2x+c b) tanx-cotx+c c) 9+(sec²x)/2 d) 3-tan²x/2 e) (3-sec²x)/2 f) (tan²x/2)-5

5. lim 0 to pi/4∫tanⁿ xdx , n belongs to I (more than one choice)
a) I_n+I_n-2=1/n-1
b) I_n+I_n-2=1/n
c) I1 = I3 + 2I5
d) None
6. At x=3/2 the value is real for (more tahn one choice)
(a) cos^–1 2x (b) cosec^–1 x (c) tan^–1 x (d) None