2020

A surveyor walks 500m up a hill which slopes at an angle of 30o. Calculate the vertical height through which he rises

A surveyor walks 500m up a hill which slopes at an angle of 30o. Calculate the vertical height through which he rises
A. 252m
B. 500m
C. 250m
D. 255m
Correct Option: Answer is C
Solution:

h 500

h/500 = sin 30o
= 500 sin 30o
= 500 x 1/2
= 250m

A surveyor walks 500m up a hill which slopes at an angle of 30o. Calculate the vertical height through which he rises Read More »

The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group.

The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group.
A. 7
B. 9
C. 15
D. 42

Correct Option: Answer is B
Solution:

Mean (x)= (∑▒x)/N
15= (∑▒x)/N
15N = ∑▒x
When the age of a teacher 45 yrs is added,
18 =(15N+45)/(N+1) ; 18(N+1) =15N+45
=18N + 18 = 15N + 45; 18N-15N=45-18
3N=27; N = 9

The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group. Read More »

The sum of the interior angle of pentagon is 6x + 6y. Find y in terms of x.

The sum of the interior angle of pentagon is 6x + 6y. Find y in terms of x.
A. y = 6 – x
B. y = 90 – x
C. y = 120 – x
D. y = 150 – x

Correct Option: Answer is B
Solution:

Sum of interior angles = (2n – 4) 90o
For pentagon, n = 5
Sum of interior angles = 6 x 90o = 540o
6x + 6y = 540o
6(x + y) = 540o
x + y = 540/6 = 90o
y = 90o
y = 90 – x

The sum of the interior angle of pentagon is 6x + 6y. Find y in terms of x. Read More »

In a class of 40 students, 32 offer mathematics, 24 offer physics and 4 offer neither mathematics nor physics. How many offers both mathematics and physics?

In a class of 40 students, 32 offer mathematics, 24 offer physics and 4 offer neither mathematics nor physics. How many offers both mathematics and physics?
A. 4
B. 8
C. 16
D. 20

Correct Option: Answer is D
Solution:
40

40 = 32 – x + x + 24 + 4
40 = 60 – x
x = 60 – 40
x = 20

In a class of 40 students, 32 offer mathematics, 24 offer physics and 4 offer neither mathematics nor physics. How many offers both mathematics and physics? Read More »

Three consecutive terms of a geometric progression are given as n – 2, n and n + 3. Find the common ratio

Three consecutive terms of a geometric progression are given as n – 2, n and n + 3. Find the common ratio
A. 3/2
B. 2/3
C. 1/2
D. 1/4

Correct Option: Answer is A
Solution:
=n/(n-2) = (n+3)/n
n2 = (n + 3) (n – 2)
n2 = n2 + n – 6
n2 + n – 6 – n2 = 0
n – 6 = 0
n = 6
Common ratio: n/(n-2)= 6/(6-2) = 3/2

Three consecutive terms of a geometric progression are given as n – 2, n and n + 3. Find the common ratio Read More »

The acres for rice, pineapple, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector of cassava in a pie chart?

The acres for rice, pineapple, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector of cassava in a pie chart?
A. 180o
B. 36o
C. 60o
D. 108o

Correct Option: Answer is B
Solution:
Acres for rice =2,
Acres for pineapple =5
Acres for cassava =3
Acres for cocoa =11
Acres for palm oil =9

Total number of acres = 2 + 5 + 3 + 11 + 9 = 30
Total angle in a pie chart = 360o
therefore, angle of the sector for cassava in a pie chart
= 3/30 x 360=36o

The acres for rice, pineapple, cassava, cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What is the angle of the sector of cassava in a pie chart? Read More »

A cylindrical tank has a capacity of 3080m3. What is the depth of the tank if the diameter of its base is 14m?

A cylindrical tank has a capacity of 3080m3. What is the depth of the tank if the diameter of its base is 14m?
A. 25m
B. 23m
C. 22m
D. 20m
Correct Option: Answer is D
Solution:

V=πr2h
V=3080m3
h=?

r=14/2=7m
3080 =22/7 x 7 x 7 x h
3080 = 154h; h= 3080/154 = 20m

A cylindrical tank has a capacity of 3080m3. What is the depth of the tank if the diameter of its base is 14m? Read More »

A sector of circle of radius 7.2cm which subtends an angle of 300o at the centre is used to form a cone. What is the radius of the base of the cone?

A sector of circle of radius 7.2cm which subtends an angle of 300o at the centre is used to form a cone. What is the radius of the base of the cone?
A. 8cm
B. 9cm
C. 6cm
D. 7cm

Correct Option: Answer is C
Solution:

l=7.2cm
r=? ; θ=300
Base circumference =length of an arc
2πr = θ/360 x 2πl
r = θ/360 x l
r= 300/360 x 7.2 =6cm

A sector of circle of radius 7.2cm which subtends an angle of 300o at the centre is used to form a cone. What is the radius of the base of the cone? Read More »

The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST

The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST
A. πr/3
B. πr/2
C. πr/12
D. πr/6

Correct Option: Answer is A
Solution:

r/(r/2) Sin θ = 1/2
θ = sin−1 (1/2) = 30o = 60o
Length of arc (minor)
ST = θ/360 x 2πr
60/360 ×2π×r= π/3

The chord ST of a circle is equal to the radius r of the circle. Find the length of arc ST Read More »

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