The larger value of y for which (y - 1)2 = 4y - 7 is
2
4
6
7
8
Correct answer is B
(y - 1)2 = 4y - 7
y2 - 2xy + 1 = 4y - 7
y2 - 6y + 8 = 0
(y - 4)(y - 2)
y = 4 or 2 = 4
Two fair dice are rolled. What is the probability that both show up the same number of points.
\(\frac{1}{36}\)
\(\frac{7}{36}\)
\(\frac{1}{2}\)
\(\frac{1}{3}\)
\(\frac{1}{6}\)
Correct answer is E
A dice has 6 faces, 2 dice has 6 x 6 = 36 combined face
Prob. of both showing the same number of points
= \(\frac{6}{36}\)
= \(\frac{1}{6}\)
A right circular cone has a base radius r cm and a vertical angle 2yo. The height of the cone is
r tan yo cm
r sin yo cm
r cot yo cm
r cos yo cm
r cosec yo cm
Correct answer is C
\(\frac{r}{h}\) = tan yo
h = \(\frac{r}{tan y^o}\)
= r cot yo
30
32
55
62
92
Correct answer is E
If y = cf(x)
cf(5) = 30 + 32 + 30
= 92
If pq + 1 = q2 and t = \(\frac{1}{p}\) - \(\frac{1}{pq}\) express t in terms of q
\(\frac{1}{p - q}\)
\(\frac{1}{q - 1}\)
\(\frac{1}{q + 1}\)
1 + 0
\(\frac{1}{1 - q}\)
Correct answer is C
Pq + 1 = q2......(i)
t = \(\frac{1}{p}\) - \(\frac{1}{pq}\).........(ii)
p = \(\frac{q^2 - 1}{q}\)
Sub for p in equation (ii)
t = \(\frac{1}{q^2 - \frac{1}{q}}\) - \(\frac{1}{\frac{q^2 - 1}{q} \times q}\)
t = \(\frac{q}{q^2 - 1}\) - \(\frac{1}{q^2 - 1}\)
t = \(\frac{q - 1}{q^2 - 1}\)
= \(\frac{q - 1}{(q + 1)(q - 1)}\)
= \(\frac{1}{q + 1}\)