# +2 Mathematics - Sample Model Questions - HSC

Practice questions 17-24 are provided in this section. Refer here for questions 1-8 and 9-16. Prepare the questions well and send your answers through the comments section of this post..

17) If the point of intersection of the tangents at $t_{1}=t$ and $t_{2}=3t$ to the parabola $y^2=8x$ is:

a) $(6t^2, 8t)$

b) $(8t, 6t^3)$

c) $(t^2, 4t)$

d) $(4t, t^2)$

18) The straight line 2x-y+c = 0 is a tangent to the ellipse $4x^2+8y^2=32$, if c is:

a) $\pm 2\sqrt3$

b) $\pm 6$

c) 36

d) $\pm 4$

19) The angle between the curves $\frac{x^2}{25}+\frac{y^2}{9}=1$ and $\frac{x^2}{8}-\frac{y^2}{8}=1$ is:

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

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

c) $\frac{\pi}{6}$

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

20) The least possible perimeter of a rectangle of area $100m^2$ is:

a) 10

b) 20

c) 40

d) 60

21) The curve $y=ax^3+bx^2+cx+d$ has a point of inflexion at x = 1, then

a) 3a+b = 0

b) 3a+b = 1

c) a+b = 0

d) a+3b = 0

22) If $s=t^3-4t^2+7$, the velocity when the acceleration is zero is:

a) $\frac{-16}{3} m/Sec$

b) $\frac{32}{3} m/Sec$

c) $\frac{16}{3} m/Sec$

d) $\frac{-32}{3} m/Sec$

23) If u = y sinx, then $\frac{\partial^2 u}{\partial x\partial y}=$

a) cos x

b) cos y

c) sin x

d) 0

24) The curve $a^2y^2 = x^2(a^2-x^2)$ has

a) one loop between x = 0 and x = a

b) two loops between x = 0 and x = a

c) two loops between x = –a and x = a

d) no loop