# Kerala PSC GK | Practice/Model Maths Questions - 6

1. Find out the value of x and y if x+y=7 and 3x-2=11
[a] 4,3
[b] 5,2
[c] 3,4
[d] 2,5

x+y = 7, x=7-y
3x-2y=11, 3(7-y) - 2y = 11
21-3y-2y = 11
21-5y = 11, 5y =10, y=2
x+y =7, x+2 = 7, x = 5

2. Find the value of (√7 - √3) (√7 +√3) is:
[a] 2√3
[b] 3√7
[c] 4
[d] 3

(√7 - √3) (√7 +√3)
7 - 3 = 4

3. The total number of prime factors in 620 x 1615 x 2112
[a] 47
[b] 124
[c] 134
[d] 110

620 x 1615 x 2112
(3x2)20 x (24)15x (7x3)12
320 x 220 x 260 x 712 x 312
332 x 280 x 712
32+80+12 = 124

4. The value of 60.75 x 70.75 x (42)0.25
[a] 55
[b] 49
[c] 46
[d] 42

60.75 x 70.75 x (42)0.25
(6x7)0.75 x 420.25
420.75 x 420.25
420.75 + 0.25 = 421 = 42

5. The average weight of 30 students of a class is 12 and the average weight of 20 students in a class is 15. What is the average of 50 students of both classes.
[a] 13
[b] 13.2
[c] 14
[d] 14.2

Total weight of 30 students = 30 x 12 = 360
Total weight of 20 students = 20 x 15 = 300
Total weight = 360 + 300 = 660
Total students = 30 + 20 = 50
Average = 660/50 = 13.2

6. Average of 15 person is 24 years later a boy is included in to this group then average become 23 years. The age of the boy will be:
[a] 22
[b] 8
[c] 18
[d] 12

24-16 x 1
24-16 = 8

7. The average age of 24 boys and one teacher is 15 years. When the teacher's age is excluded the average decreases by one. What is the age of teacher.
[a] 39 years
[b] 38 years
[c] 40 years
[d] 36 years

Let the age of teacher be 'x'
The sum of the ages of teacher and students
= 25 x 15 = 375
Average = 375-x/24 = 14
375 - x = 24 x 14 = 336
x = 375 - 336 = 39 years

8. There are 30 students in a class. One student weighing 25 kg goes away and a new student joins the class. If the average weight is then increased by 200 grams. What is the weight of new student.
[a] 32 kg
[b] 31 kg
[c] 30 kg
[d] 29 kg

Increased weight = 200/1000 x 30 = 6kg
Weight of new student
= 25 + 6 = 31 kg

9. The average weight of 10 men decrease by 3 kg when one man, who weighs 85 kg is replaced by a new man. Find the weight of the new man?
[a] 48 kg
[b] 49 kg
[c] 52 kg
[d] 55 kg

Weight of New man
= 85 - 3 x 10
= 85 - 30 = 55 kg

10. The average age of 29 boys in the class is 14 years. When the age of class teacher is included the average becomes 15 years. The age of the class teacher is:
[a] 44
[b] 42
[c] 46
[d] 40

Total age of 29 boys = 14 x 29 = 406
Total age of 30 person = 15 x 30 = 450
Age of Class teacher = 450 - 406 = 44 years