Calculate the length of an arc of a circle of diameter 14cm, which subtends an angle of 90o at the centre of the circle
A
14\(\pi\) cm
B
7\(\pi\) cm
C
5\(\pi\) cm
D
4\(\pi\) cm
CORRECT OPTION:
d
Length of an arc \(\frac{\theta}{360^o}\pi d\)
= \(\frac{90^o}{360^o}\) x \(\pi\) x 4cm
= 4\(\pi\) cm
5
What is the value of k if the mid-point of the line joining (1 - k, -4) and (2, k - 1) is (-k, k)?
A
-4
B
-1
C
-2
D
-3
CORRECT OPTION:
d
The midpoint (-k, k) = (\(\frac{1 - k + 2}{2}, \frac{-4 + k + 1}{2}\))
\(\Rightarrow\) -k = \(\frac{3 - k}{2}\)
-2k = 3 - k
-2k + k = 3
k = -3
6
\(\begin{array}{c|c} \text{Age in years} & 10 & 11 & 12\\
\hline \text{No. of pupils} & 6 & 27 & 7\end{array}\)
the table above shows the number of pupil in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?
A
\(\frac{27}{40}\)
B
\(\frac{3}{30}\)
C
\(\frac{17}{20}\)
D
\(\frac{33}{40}\)
CORRECT OPTION:
c
Total number of pupils = 6 + 27 + 7 = 40
Number of pupils that are at least 11 years old = 27 + 7
= 34
therefore prob. (at least 11 years) = \(\frac{34}{17}\)
= \(\frac{17}{20}\)
7
If 5, 8, 6 and 2 occur with frequencies 3, 2, 4 and 1 respectively, find the product of the modal and the median number
A
40
B
30
C
48
D
36
CORRECT OPTION:
d
The mode = 6
therefore the array is 21, 53, 64, 82
The median = 6
The product = 6 x 6 = 36
8
In how many ways can 6 subjects be selected from 10 subjects for an examination?
in a basket, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or banana?
prob. (a grape or a banana) = \(\frac{1}{5}\) + \(\frac{11}{30}\)
= \(\frac{17}{30}\)
10
a senatorial candidate had planned to visit seven cities prior to a primary election. However, he could only visit four of the cities. How many different itineraries could be considered?
A
840
B
720
C
640
D
520
CORRECT OPTION:
a
No of ways = \(^{7}P_{4}\)
= 7 x 6 x 5 x 4
= 840
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