2020

Find the non-zero positive value of x which satisfies the equation â– (x&1&0@1&x&1@0&1&x) = 0

Find the non-zero positive value of x which satisfies the equation

â– (x&1&0@1&x&1@0&1&x) = 0

A. 2
B. âˆš3
C. âˆš2
D. 1

Solution:
x(x2 â€“ 1)-1(x â€“ 0)+0(1-0) =0
x3-x-x+0+0=0
x3-2x+0=0; x3=2x
x2=2; x = âˆš2

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
Solution:

h 500

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

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

Solution:

Mean (x)= (âˆ‘â–’x)/N
15= (âˆ‘â–’x)/N
15N = âˆ‘â–’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 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 â€“ x
B. y = 90 â€“ x
C. y = 120 â€“ x
D. y = 150 â€“ x

Solution:

Sum of interior angles = (2n â€“ 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 â€“ x

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

Solution:
40

40 = 32 â€“ x + x + 24 + 4
40 = 60 â€“ x
x = 60 â€“ 40
x = 20

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

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

Solution:
=n/(n-2) = (n+3)/n
n2 = (n + 3) (n â€“ 2)
n2 = n2 + n â€“ 6
n2 + n â€“ 6 â€“ n2 = 0
n â€“ 6 = 0
n = 6
Common ratio: n/(n-2)= 6/(6-2) = 3/2

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

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

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
Solution:

V=Ï€r2h
V=3080m3
h=?

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

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

Solution:

l=7.2cm
r=? ; Î¸=300
Base circumference =length of an arc
2Ï€r = Î¸/360 x 2Ï€l
r = Î¸/360 x l
r= 300/360 x 7.2 =6cm

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. Ï€r/3
B. Ï€r/2
C. Ï€r/12
D. Ï€r/6