Part 2 and final part of the AA3 question collection set for HSC +2 Mathematics. Part 1 of the Question Paper Set contained questions from 1-20. In this set, we provide the questions from 21-40.
21) Real and imaginary parts of $ 4-i\sqrt{3} $ are:
a) $ 4, \;\sqrt{3} $ b) $ 4, \;-\sqrt{3} $ c) $ -\sqrt{3}, \; 4 $ d) $ \sqrt{3}, \; 4 $
22) If a+ib = (8-6i)-(2i-7) then the values of a and b are:
a) 8, –15 b) 8, 15 c) 15, 9 d) 15, –8
23) Which of the following are correct? (i) $ Re(z)\leq |z| $ (ii) $ Im(z) \geq |z| $ (iii) $ |\overline{z}|=|z| $ (iv) $ (\overline{z^{n}})=(\overline{z})^{n} $
a) (i), (ii) b) (ii), (iii) c) (ii), (iii), and (iv) d) (i), (iii) and (iv)
24) The principal value of arg z lies in the interval:
a) $ [0, \; \frac{\pi}{2}] $ b) $ [-\pi, \; \pi] $ c) $ [0, \; \pi] $ d) $ [-\pi, \; 0] $
25) The fourth roots of unity form the vertices of:
a) an equilateral triangle b) a square c) a hexagon d) a rectangle
26) The value of $ e^{i\Theta}+e^{-i\Theta} $ is:
a) $ 2\; cos \Theta $ b) $ \; cos \Theta $ c) $ 2\; sin \Theta $ d) $ \; sin \Theta $
27) Identify the correct statement:
a) Sum of moduli of two complex numbers is equal to their modulus of the sum
b) Modulus of the product of the complex numbers is equal to sum of their moduli
c) Arguments of the product of two complex numbers is the product of their arguments
d) Argument of the product of two complex numbers is equal to sum of their arguments
28) If $ z_{1} $ and $ z_{2} $ are complex numbers then which of the following is meaningful?
a) $ z_{1} < z_{2} $ b) $ z_{1} > z_{2} $ c) $ z_{1} \geq z_{2} $ d) z_{1} \neq z_{2}
29) The vertex of the parabola $ x^2=-4y $ is: a) (0, 1) b) (0, –1) c) (1, 0) d) (0, 0)
30) The equation of the L.R. of $ x^2=-4y $ is: a) x=-1 b) y=-1 c) x=1 d) y=1
31) The length of the major and minor axes of $ 4x^2+3y^2=12 $ are:
a) $ 4, \; 2\sqrt{3} $ b) $ 2, \; \sqrt{3} $ c) $ 2\sqrt{3}, \; 4 $ d) $ \sqrt{3}, \; 2$
32) The length of the L.R. of $ \frac{x^2}{16}+\frac{y^2}{9}=1 $ are:
a) $ \frac{9}{2} $ b) $ \frac{2}{9} $ c) $ \frac{9}{16} $ d) $ \frac{16}{9} $
33) If the centre of the ellipse is (4, –2) and one of the foci is (4, 2), then the other focus is:
a) (4, 6) b) (6, –4) c) (4, –6) d) (6,4)
34) The eccentricity of the hyperbola $ \frac{y^2}{9}-\frac{x^2}{25}=1 $ is:
a) $ \frac{34}{3} $ b) $ \frac{5}{3} $ c) $ \frac{\sqrt{34}}{3} $ d) $ \frac{\sqrt{34}}{5} $
35) The equations of transverse and conjugate axes of the hyperbola $ \frac{x^2}{9}-\frac{y^2}{4}=1 $ are:
a) x=2; y=3 b) y=0; x=0 c) x=3; y=2 d) x=0; y=0
36) The point of contact of the tangent y=mx+c and the parabola $ y^2=4ax $ is:
a) $ (\frac{a}{m^2}, \; \frac{2a}{m}) $ b) $ (\frac{2a}{m^2}, \; \frac{a}{m}) $
c) $ (\frac{a}{m}, \; \frac{2a}{m^2}) $ d) $ (\frac{-a}{m^2}, \; \frac{-2a}{m}) $
37) If $ t_{1}, \; t_{2} $ are the extremities of any focal chord of a parabola $ y^2=4ax $ then $ t_{1} t_{2} $ is:
a) –1 b) 0 c) $ \pm 1 $ d) $ \frac{1}{2} $
38) The condition that the line lx+my+n=0 may be a normal to the hyperbola $ \frac{x^2}{a^2}-\frac{y^2}{b^2}=1 $ is:
a) $ al^3+2alm^2+m^2n=0 $ b) $ \frac{a^2}{l^2}+ \frac{b^2}{m^2}=\frac{(a^2+b^2)^2}{n^2} $
c) $ \frac{a^2}{l^2}+ \frac{b^2}{m^2}=\frac{(a^2-b^2)^2}{n^2} $
d) $ \frac{a^2}{l^2}- \frac{b^2}{m^2}=\frac{(a^2+b^2)^2}{n^2} $
39) The chord of contact of tangents from any point on the directrix of the parabola $ y^2=4ax $ passes through its:
a) vertex b) focus c) directrix d) latus rectum
40) The locus of the point of intersection of perpendicular tangents to the parabola $ y^2=4ax $ is:
a) latus rectum b) directrix c) tangent at the vertex d) axis of the parabola
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