New Technology

MATHEMATICS

1. How many arbitrary constants does the
general equation of a quadratic cone with a
given condition have?
a. 3
b. 4
c. 5
d. None of the above
e. b

2. What is the equation of a cylinder whose
generators are parallel to the axis of z and
which passes through the circle whose
centre is (a, 0, 0) and radius a and lying in
the xy-plane?
a. x2 ! y2 " 2ax # 0
b. 2 2 x ! y "3ax # 0
c. 2 2 x ! y " 4ax # 0
d. 2 2 x ! y " ax # 0
e. a

3. Let a # iˆ ! 2 ˆj ! 3kˆ!, b # iˆ " 3 ˆj ! 2kˆ!
and c # ˆj " kˆ!. What is x! equal to which is orthogonal to a! and satisfies
x $b # b $c
! ! ! !?
a. 3iˆ " kˆ
b. "3iˆ ! kˆ
c. "iˆ ! 2 ˆj " kˆ
d. iˆ " 2 ˆj ! kˆ
e. c

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