If sin y = x sin(a+y), then $\frac{dy}{dx}$ is equal to

A) $\frac{\sin\sqrt{a}}{\sin\left(a+y\right)}$

B) $\frac{\sin^{2} (a+y)}{\sin a}$

C) $\sin(a+y)$

D) None of these


The equation $y^{2}+3=2(2x+y)$ represents a parabola with the vertex at

A) (1/2,1) and axis parallel to y-axis

B) (1,1/2) and axis parallel to x-axis

C) (1/2,1) and focus at (3/2,1)

D) (1,1/2) and focus at (3/2,1)


The solution of sin x = $-\frac{\sqrt{3}}{2}$ is

A) $x = n\pi+ (-1)^{n}\frac{4\pi}{3}, n \epsilon Z$

B) x = n\pi+ (-1)^{n}\frac{2\pi}{3}, n \epsilon Z

C) $x = n\pi+ (-1)^{n}\frac{3\pi}{3}, n \epsilon Z$

D) None of these


 If a, b, c are in A. P, then the value of $\begin{vmatrix}x+1& x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c \end{vmatrix}$ is?

A) 3

B) -3

C) 0

D) Noneof these


The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder, in cm3/min, when the radius is 2 cm and the height is 3 cm is

A) $-2\pi$

B) -$\frac{-8\pi}{5}$

C) $\frac{-3\pi}{5}$

D) $\frac{2\pi}{5}$