2020

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

■(x&1&0@1&x&1@0&1&x) = 0

A. 2
B. √3
C. √2
D. 1

Correct Option: Answer is C
Solution:
x(x2 – 1)-1(x – 0)+0(1-0) =0
x3-x-x+0+0=0
x3-2x+0=0; x3=2x
x2=2; x = √2

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

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 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

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

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

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

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 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

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