Final part of the Question Paper set AA2 on StateBoard/ HSC Mathematics. You may wish to refer to Part 1 of the Question Paper Series before attempting this part. Again, if you know the answers, share it
21) The complex number form of $ 3-\sqrt{-7} $ is:
a) $ -3+i\sqrt{7} $ b) $ –3-i\sqrt{7} $
c) $ 3-i7 $ d) $ 3+i7 $
22) Real and imaginary parts of $ \frac{3}{2i} $ are:
a) $ 0, \;\frac{3}{2} $ b) $ \frac{3}{2}, \;0 $
c) 2, 3 d) 3,2
23) The standard form (a+ ib) of 3+2i+(-7-i) is:
a) 4-i b) -4+i c) 4+i d) 4+4i
24) The modulus values of -2+2i and 2-3i are:
a) $ \sqrt{5}, \;5 $ b) $ 2\sqrt{5}, \;\sqrt{13} $
c) 2\sqrt{2}, \;\sqrt{13} d) –4, 1
25) The cube roots of unit are:
a) In G.P. with common ratio $ \omega $
b) In G.P. with common difference $ \omega^{2} $
c) In A.P. with common difference $ \omega $
d) In A.P. with common difference $ \omega^{2} $
26) Which of the following statements is correct?
a) Negative complex numbers exist b) order relation does not exist in real numbers
c) order relation exist in complex numbers d) (1+i) > (3-2i) is meaningless
27) The value of $ z\overline{z} $ is:
a) $ |z| $ b) $ |z|^2 $ c) $ 2|z| $ d) $ 2|z|^2 $
28) If $ |z-z_{1}| = |z-z_{2}| $ then the locus of z is:
a) A circle with centre at the origin b) A circle with centre at $ z_{1} $
c) A straight line passing through the origin d) Is a perpendicular bisector of the line joining $ z_{1} $ and $ z_{2} $
29) The axis of the parabola $ y^2=4x $ is:
a) x=0 b) y=9 c) x=1 d) y=1
30) The equation of the latus rectum of $ y^2=4x $ is:
a) x=1 b) y=1 c) x=4 d) y=-1
31) The equations of the major and minor axes of $ \frac{x^2}{9}\;+\;\frac{y^2}{4}=1 $ are:
a) x=3, y=2 b) x=-3, y=-2 c) x=0, y=0 d) y=0, x=0
32) The equations of the minor and major axes of $ \frac{x^2}{9}\;+\;\frac{y^2}{4}=1 $ are:
a) 6, 4 b) 3, 2 c) 4,6 d) 2, 3
33) The equation of the latus rectum of $ \frac{x^2}{16}\;+\;\frac{y^2}{9}=1 $ are:
a) $ y= \pm \sqrt{7} $ b) $ x= \pm \sqrt{7} $
c) $ x= \pm 7 $ d) $ y= \pm 7 $
34) The eccentricity of the ellipse $ 16x^2+25y^2=400 $ is:
a) $ \frac{4}{5} $ b) $ \frac{3}{5} $
c) $ \frac{3}{4} $ d) $ \frac{2}{5} $
35) The equation of the tangent at (-3, 1) to the parabola $ x^2=9y $ is:
a) 3x-2y-3=0 b) 2x-3y+3=0 c) 2x+3y+3=0 d) 3x+2y+3=0
36) The equations of the directrices of the hyperbola $ \frac{x^2}{9}\;-\;\frac{y^2}{4}=1 $ are:
a) $ y=\pm \frac{9}{\sqrt{13}} $ b) $ x=\pm \frac{13}{9} $
c) $ y=\pm \frac{\sqrt{13}}{9} $ d) $ x=\pm \frac{9}{\sqrt{13}} $
37) The vertices of the hyperbola $ 25x^2-16y^2=400 $ are:
a) $ (0, \; \pm4) $ b) $ (\pm4, \;0) $ c) $ (0, \; \pm5) $ d) $ (\pm5, \;0) $
38) The equation of chord of contact of tangents from (2, 4) to the ellipse $ 2x^2+5y^2=20 $ is:
a) x-5y+5=0 b) 5x-y+5=0 c) x+5y-5=0 d) 5x-y-5=0
39) Find the angle between the asymptotes of the hyperbola $ 24x^2-8y^2=27 $ is:
a) $ \frac{\pi}{3} $ b) $ \frac{\pi}{3} $ or $ \frac{2\pi}{3} $
c) $ \frac{2\pi}{3} $ d) $ \frac{-2\pi}{3} $
40) The point of contact of the tangent y=mx+c and the hyperbola $ \frac{x^2}{a^2}\;-\;\frac{y^2}{b^2}=1 $ is:
a) $ (\frac{am^2}{c},\; \frac{b^2}{c}) $ b) $ (\frac{a^2m}{c},\; \frac{b^2}{c}) $
c) $ (\frac{-a^2m}{c},\; \frac{-b^2}{c}) $ d) $ (\frac{-am^2}{c},\; \frac{-b^2}{c}) $
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