#TNPSC - #VAO (JUNE 2014) MATHS QUESTIONS(SOLVED):

1. If the SIMPLE interest for an amount at 4% per annum for 3 years is Rs.1200. Find the COMPOUND interest at the same rate for the same amount for 2 years.
A. Rs.10116
B. Rs.10720
C. Rs.10616
D. Rs.816

Ans: D
Explanation:
S.I for 3 years =1200
S.I for 1 year =1200/3=400
C.I for 2 years =400+[400+400*(4/100)]
=400+416=816

2. Which of the following is/are true?
(i) ax=bx-->a=b
(ii) x/a=x/b-->a=b
(iii) a=b-->ax=bx
(iv) a+x=b+x-->a=b

A. (i),(ii),(iii),(iv)
B. (i),(ii) and (iv) only
C. (i) and (iv) only
D. (iii) and (iv) only

Ans: D
Explanation:
(i) and (ii) are false if x=0(zero)

3. If + means *, - means +, * means /, / means - then the value of 84*28+8/10-9=
A. 23
B. 22
C. 30
D. 26

Ans: A
Explanation:
84/28*8-10+9 = 3*8-10+9 = 24-10+9=23

4. If the ratio of the ages of son and father in 2014 and 2022 are 1:4 and 3:8 respectively, then the SUM of the ages of son and father in 2010 is
A. 42
B. 43
C. 50
D. 45

Ans: A
Explanation:
2022-2014=8
1x+8 / 4x+8= 3x/8x
x+8/4x+8=3/8
8*(x+8)=3*(4x+8)
8x+64=12x+24
12x-8x=64-24
4x=40
x=10
There for SUM of ages of son and father in 2014 is X+4X=10+40=50
SUM of ages of son and father in "2010" is 50-(4+4)=42

5. Fine the volume of a largest sphere inscribed from the right circular cylindrical wood whose radius is 1 cm and height is 5 cm 
A. 4/3 pi cm3
B. 5/16 pi cm3
C. 5 pi cm3
D. 8 pi cm3

Ans: A
Explanation:
The radius of largest sphere inscribed from the cylinder of radius 1 cm is also 1cm.
Therefore Volume = 4/3 pi r3
= 4/3 pi (1*1*1) cm3
=4/3 pi cm 3 

6. The average of five numbers is 20. If we eliminate one number from it, the average will be reduced by 5. What is the number eliminated?
A.5
B. 40
C. 20
D. 15

Ans:B
Explanation:
5*20=100
4*15=60
100-60=40

7. The average of 50 students in 10th std class is 15 years. 10 more students are admitted afresh in the class and average age is increased by 0.5 years. The average age of newly joined students is
A. 15
B. 16
C. 17
D. 18

Ans: D
Explanation:
50*15=750
50+10 * 15*0.5=60*15.5=930
930-750=180
180/10=18

8. What percentage of students does not like computer science?
Subject - No. of students
Mathematics - 6
Physics - 12
Chemistry - 15
Biology - 8
Computer Science - 9
A. 91%
B. 9%
C. 82%
D. 18%

Ans: C
Explanation:
6+12+15+8+9=50
50-9=41
(41/50)*100=82%

9. In a set of first 'x' natural numbers there are 30 prime numbers. Find the number of composite numbers in the above set.
A. x-30
B. 30-x
C. x-29
D. x-31

Ans: D
Explanation:
Number of remaining numbers=x-30
BUT '1' IS NEITHER PRIME NOR COMPOSITE.
Therefore,
No of composite numbers = x-(30+1)=x-31

10. A number when divided by 2,3,4,5 and 6 leaves remainder, it is divisible by 7, the least possible number is
A. 117
B. 119
C. 113
D. 121

Ans: B
Clue: 119 is the only number which is divisible by 7.

11. A man saves Rs. 3000 per month from his total salary of Rs. 20000. The percentage of his savings is
A. 5%
B. 10%
C. 15%
D. 20%

Ans: C
Explanation:
(3000/20000) * 100=15

12. A seller says the cost of an item at a profit of 3%. Then he gives a discount of 3%. The he sells the item at
A. a profit of 0.09%
B. a loss of 0.09%
C. a profit of 9%
D. no loss or no profit

Ans: B
Explanation:
If both profit and discount are same then the result is loss.
Loss%= x2/100=(3*3)/100=9/100=0.09%

13. Find the sum of all natural numbers between 300 and 500 which are divisible by 11.
A.7337
B.7227
C.7447
D.7557

Ans: B
Explanation:
It makes an arithmetic progression.
Sum =1/2 n (a+l) 
a- first term
l- last term
n- no of terms

In this case a=308 , b=495 
( The smallest and largest numbers between 300-500 which are exactly divisible by 11)

To find n:
500-300=200
200/11 = 18 (Don't mind about remainder)
Therefore n=18

Substituting the values in the formula,
1/2 18 (308+495)=9*803=7227

14. Babu has 540 cakes. He wants to distribute then equally to some persons. IF THE NUMBER OF CAKES IS EQUAL TO 15% OF THE NUMBER OF PERSONS, find the number of cakes given to each person.
A.60
B.20
C.9
D.54

Ans: C
Explanation:
x= no of cakes, y= no of persons
540/x=y
but x=(15/100)y
540/ (15/100)y=y
y2=(540*100)/15=3600
y=60
x=540/60=9

Quick method:
Go with options:
(15/100)*60=9