HSC +2 Maths Important Questions AA4 - Part 3

Part 3 of AA4, +2 Mathematics Practice questions set, containing questions from 17 to 24 are provided below. You may wish to refer to the related post section at the bottom of this post to view other parts of this AA4 series.These questions are a random collection of questions and not aligned to the blue print format. However, they will give you a good practice from an examination angle and solving them would give you the cutting edge to your examinations.
Questions from 17-24 of 40 - AA4 Series
17) The eccentricity of the hyperbola with asymptotes x+2y-5+0, 2x-y+5=0 is:

a) 3          b) $\sqrt2$          c) $\sqrt3$          d) 2

18) The velocity v of a particle moving along a straight line when at a distance x from the origin is

given by $a+by^{2}=x^{2}$ where a and b are constants. Then the acceleration is:

a) $\frac{b}{x}$             b) $\frac{a}{x}$

c) $\frac{x}{b}$             d) $\frac{x}{a}$

19) The radius of a cylinder is increasing at the rate of 2cm/sec and its altitude is decreasing at the rate of

3cm/sec. The rate of change of volume when the radius is 3cm and the altitude is 5cm is:

a) $23\pi$        b) $33\pi$        c) $43\pi$

d) $53\pi$

20) The value of ‘a’ so that the curves $y=3e^{x}$ and $y=\frac{a}{3}e^{-x}$ intersect

orthogonally is:

a) –1           b) 1           c) 1/3           d) 3

21) If f(a) =2 ; f’(a)=1; g(a)=-1; g’(a)=2, then the value of $\underset{x\rightarrow a}{lim} \frac{g(x)f(a)-g(a)f(x)}{x-a}$

is:

a) 5           b) -5           c) 3           d) –3

22) If $u=x^{y}$, then $\frac{\partial u}{\partial x}$ is equal to:

a) $yx^{y-1}$           b) u logx           c) u logy           d) $xy^{x-1}$

23) If $x=r \: cos\Theta, \: y=r\: sin\Theta$, then $\frac{\partial r}{\partial x}$ is:

a) $sec\Theta$           b) $sin\Theta$

c) $cos\Theta$           d) $cosec\Theta$

24) If $u=log(\frac{x^2+y^2}{xy})$, then $x\frac{\partial u}{\partial x}+y\frac{\partial u}{\partial y}$ is:

a) 0           b) u           c) 2u           d) $u^{-1}$