# +2 Maths Model Questions in One Mark

Continuing our one mark questions for HSC Mathematics, questions from 25-32 are provided in this post. Check the following links for questions

25) The value of $\int_{0}^{\frac{\pi}{2}}\frac{cos^\frac{5}{3}x}{cos^\frac{5}{3}x+sin^\frac{5}{3}x}\;dx$ is

a) $\frac{\pi}{4}$

b) $\frac{\pi}{2}$

c) $\frac{\pi}{3}$

d) $\frac{2\pi}{3}$

26) The volume generated when the region bounded by y=x, y=1, x=0 is rotated about x-axis is:

a) $\frac{\pi}{3}$

b) $\frac{2\pi}{3}$

c) $\frac{\pi}{2}$

d) $\frac{\pi}{4}$

27) The C.S.A of a sphere of radius 5 intercepted between two parallel planes of distance 2 and 4 from the centre is:

a) $20\pi$

b) $40\pi$

c) $10\pi$

d) $30\pi$

28) The area between the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and its auxiliary circle is:

a) $\pi b(a-b)$

b) $2\pi a(a-b)$

c) $\pi a(a-b)$

d) $2\pi b(a-b)$

29) The differential equation of all circles with centre at the origin is:

a) xdy + ydx = 0

b) xdy – ydx = 0

c) xdx + ydy = 0

d) xdx – ydy = 0

30) If $\frac{\mathrm{dy} }{\mathrm{d} x}=\frac{x-y}{x+y}$ then

a) $2xy+y^2-x^2=c$

b) $x^2+y^2-x+y=c$

c) $x^2-y^2-2xy=c$

d) $x^2+y^2-2xy=c$

31) The P.I. of $(D^2+D)y=5e^{-x}$

a) $5e^{-x}$

b) $-5e^{-x}$

c) $5xe^{-x}$

d) $-5xe^{-x}$

32) The differential equation obtained by eliminating a and b from $y=ae^{3x}+be^{-3x}$ is:

a) $\frac{\mathrm{d^2}y }{\mathrm{d}x^2}+9y=0$

b) $\frac{\mathrm{d^2}y }{\mathrm{d}x^2}-9y=0$

c) $\frac{\mathrm{d^2}y }{\mathrm{d}x^2}-9\frac{\mathrm{d}y }{\mathrm{d}x}=0$

d) $\frac{\mathrm{d^2}y }{\mathrm{d}x^2}+9x=0$