If sin \(\theta\) = \(\frac{x}{y}\) and 0o < 90o then find \(\frac{1}{tan\theta}\)
\(\frac{x}{\sqrt{y^2 - x^2}}\)
\(\frac{y}{x}\)
\(\frac{\sqrt{y^2 + x^2}}{y^2 - x^2}\)
\(\frac{y^2 - x^2}{x}\)
Correct answer is D
\(\frac{1}{tan\theta}\) = \(\frac{cos\theta}{sin\theta}\)
sin\(\theta\) = \(\frac{x}{y}\)
cos\(\theta\) = \(\frac{\sqrt{y^2 - x^2}}{y}\)
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