HSC Maths Sample Question Paper- Part 2 - AA2

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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