An arc of a circle of length 22 cm subtends an angle of 3x° at the center of the circle. Find the value of x if the diameter of the circle is 14 cm
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(A)
60o
2
Find the value of α\(^2\) + β\(^2\) if α + β = 2 and the distance between points (1, α) and (β, 1) is 3 units
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(D)
11
3
The sum of the interior angles of a pentagon is 6x + 6y. Find y in the terms of x
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(A)
y = 90 - x
4
In the diagram above, PQ = 4 cm and TS = 6 cm. If the area of parallelogram PQTU is 32 cm\(^2\), find the area of the trapezium PQRU
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(B)
72 cm2
5
Find the midpoint of the line joining P(-3, 5) and Q(5, -3).
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(A)
(1, 1)
6
Determine the locus of a point inside a square PQRS which is eqidistant from PQ and QR
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(A)
The diagonal QS
7
Find the value of x in the figure above
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(D)
5\(\sqrt{6}\)
8
P, R and S lie on a circle center as shown above while Q lies outside the circle. Find ∠PSO
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(C)
35o
9
The locus of a point which is 5 cm from the line LM is a
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(B)
pair of line on opposite sides of LM and parallel to it, each distance 5 cm from LM
10
If y = 3 cos(\(\frac{x}{3}\)), find \(\frac{dy}{dx}\) when x = (\(\frac{3π}{2}\))
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(D)
-1
11
Find the derivatives of (2 + 3x)(1 - x) with respect to x
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(C)
1 - 6x
12
What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2?
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(A)
8π
13
Find the derivatives of the function y = 2x\(^2\)(2x - 1) at the point x = -1?
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(B)
16
14
Evaluate \(\int_{1}^{3}(x^2 - 1)dx\)
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(D)
\(6\frac{2}{3}\)
15
Some white balls put in a basket containing twelve red balls and sixteen black balls. If the probability of picking a white ball from the baskets is \(\frac{3}{7}\), how many white balls were introduced?
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(B)
21
16
find the mean deviation of 1, 2, 3 and 4
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(C)
1.0
17
An unbiased die is rolled 100 times and the outcome is tabulated above.
What is the probability of obtaining a 5?
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(A)
1/5
18
The pie chart above shows the distribution of the crops harvested from a farmland in a year. If 3000 tonnes of millet is harvested, what amount of beans is harvested
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(C)
1200 tonnes
19
In how many ways can 2 students be selected from a group of 5 students in a debating competition?
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(B)
10 ways
20
The mean age of a group of students is 15 years. When the age of a teacher, 45 years old, is added to the age of the students, the mean of their ages becomes 18 years. Find the number of the students in the group
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(A)
9
21
A container has 30 gold medals, 22 silver medals and 18 bronze medals. If one medals is selected at the random from the container, what is the probability that it is not a gold medal?
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(C)
4/7
22
A committee of six is to be formed by a state governor from nine state commissioners and three members of the state house of assembly. In how many ways can the members of the committee be chosen so as to include one member of the house of Assembly
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(A)
378 ways
23
The weight of 10 pupils in a class are 15 kg, 16 kg, 17 kg, 18 kg, 16 kg, 17 kg, 17 kg, 17 kg, 18 kg, and 16 kg. What is the range of this distribution?
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(B)
3
24
I. Rectangular bars of equal width
II. The height of each rectangular bar is proportional to the frequency of the corresponding class interval.
III. Rectangular bars have common sides with no gaps in between
A histogram is described completely by
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(A)
I, II and III
25
y is inversely proportional to x and y = 4 when x = 1/2. Find x when y = 10.
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(C)
1/5
26
What are the integer values of x which satisfy the inequality -1 < 3 -2x \(\leq\) 5?
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(D)
-1, 0, 1
27
Given that the first and forth terms of G.P are 6 and 162 respectively, find the sum of the first three terms of the progression
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(C)
78
28
If the operation * on the set of integers is defined by P * Q = \(\sqrt{PQ}\), find the value of 4 * ( 8 * 32).
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(A)
8
29
Find the remainder when 3x3 + 5x2 - 11x + 4 is divided by x + 3
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(C)
1
30
The nth term of two sequences are Qn = 3 . 2n - 2 and Um = 3 . 22m - 3. Find the product of Q2 and U2.
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(A)
18
31
Factorize completely ac - 2bc - a\(^2\) + 4b\(^2\)
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(A)
(a - 2b)(c - a - 2b)
32
Find the sum to infinity of the series 1/2 , 1/6, 1/18, .....
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(C)
3/4
33
The length L of a simple pendulum varies directly as the square of its period T. If a pendulum with period 4 sec. is 64 cm long, find the length of pendulum whose period is 9 sec
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(B)
324 cm
34
Three teachers shared a packet of chalk. The first teacher got 2/5 of the chalk and the second teacher received 2/15 of the remainder. What fraction did the third teacher receive?
Simplify \(\frac{1}{\sqrt{3}+2}\) in the form \(a+b\sqrt{3}\)
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(A)
2 -√3
41
A farmer planted 5000 grains of maize and harvested 5000 cobs, each bearing 500 grains. What is the ratio of the number of grains sowed to the number harvested?
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(C)
1 : 500
42
The shadow of a pole 5√3m high is 5m. Find the angle of elevation of the sun.
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(D)
60o
43
The shaded area in the diagram above is represented by
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(B)
{(x,y) : y + 3x < 6}
44
PQRSTV is a regular polygon of side 7 cm inscribed in a circle. Find the circumference of the circle PQRSTV.
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(D)
44 cm
45
The graph above shows the cumulative frequency curve of the distribution of marks in a class test. What percentage of the students scored more than 20 marks?
