Question 1 :
If a 6-sided dice is rolled twice, then the probability for a sum of 2 or 12 is.
(A) 1/18 (B) 1/15 (C) 1/16
Solution :
Sample space n(S) = 36
Let A be the event of getting the sum 2 or 12.
A = { (1, 1) (6, 6)}
n(A) = 2
p(A) = n(A) / n(S)
p(A) = 2/36
p(A) = 18
Question 2 :
The two angles of a triangle are complementary, Then, the measure of the third angle is
(A) 20 (B) 40 (C) 90
Solution :
If two angles are complementary, then sum of those angles will be 90. Then the other angle is also 90, because the sum of interior angles of a triangle is 180.
Question 3 :
There are 9 soup cans in a row and 8 are stacked on top, then 7, then 6 and so forth until there is only 1 can stacked on the very top. How many soup cans were used to form this arrangement ?
(A) 14 (B) 52 (C) 45
Solution :
By writing the number of soup cans in each row as sequence, we get
9, 8, 7, .......1
To find the number of soup cans in total, we should find the sum of the above sequence.
Number of terms in the sequence is 9.
= n(n + 1) / 2
= 9(9 + 1) / 2
= 9 (5)
= 45
Hence there are 45 soup cans are in the arrangement.
Question 4 :
How many positive single digit prime numbers greater than one is there?
(A) 2 (B) 4 (C) 1
Solution :
Prime numbers are 2, 3, 5, 7.
So, we have 4 one digit prime numbers are there.
Question 5 :
How many positive even prime numbers are there?
(A) 2 (B) 1 (C) 5
Solution :
There is only one even prime number is there. That is 2.
Question 6 :
If the product of 3 and x² is 48, then the value of “x” is
(A) 4 (B) 5 (C) 8
Solution :
3x² = 48
x² = 16
x = √16
x = 4
Question 7 :
The sum of the Interior and exterior angles of a triangle is
(A) 180 (B) 360 (C) 540
Solution :
The sum of interior angle of the triangle is 180 and the sum of exterior angle of triangle is 180.
Question 8 :
If the radius and height of a right circular cylinder are 8 and 5 respectively, then the volume of the cylinder is
(A) 320π (B) 420π (C) 360π
Solution :
Radius (r) = 8 and height (h) = 5
Volume of cylinder = πr^{2}h
= π ⋅ 8^{2 }⋅ 5
= 320π
Volume of cylinder is 320π.
Question 9 :
A group of 2000 bees can make 7 jars of honey in one year. How long will it take for 5000 bees to make 70 jars of honey (in years) ?
(A) 6 (B) 7 (C) 4
Solution :
A group of 2000 bees can make 7 jars of honey in one year.
2000 ⋅ 70 ⋅ 1 = 5000 ⋅ 7 ⋅ x
x = (2000 ⋅ 70) / (5000 ⋅ 7)
x = 4
Then the required number of years is 4.
Question 10 :
The radius and height of a cone is 7/2 and 12 respectively, calculate the volume of the cone?
(A) 18π (B) 49π (C) 25π
Solution :
Radius (r) = 7/2 and height (h) = 12
Volume of cone = (1/3) πr^{2}h
= (1/3) π (7/2)^{2}(12)
= 49π
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