Mathmetics
ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams
Q1.  The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, then what would be the difference of the larger and smaller numbers ? 
1)  2  2)  3 
3)  4  4)  6 
5)  None of these 
Answer : 4
Explanation : Let, the larger and smaller numbers are x and y respectively.
Explanation : Let, the larger and smaller numbers are x and y respectively.
x^{2} + y^{2} = 208  (i)
x^{2} = 18y
or x^{2}  18y = 0  (ii)
Equating from both equation,we get
y^{2} +18y  208 = 0
or y^{2} + 26y  8y  208 = 0
or y (y+26)  8 (y + 26) = 0
or y = 8 so, x = 12
Therefore, xy = 12  8 = 4
View Answer
Q2.  What is the remainder when 13^{5}+14^{5} + 15^{5} + 16^{5} is divided by 29 ? 
1)  0  2)  3 
3)  5  4)  8 
5)  None of these 
Answer : 0
View Answer
Q3.  What should be the remainder when 2 ^{100} is divided by 101 ? 
1)  1  2)  11 
3)  99  4)  100 
5)  None of these 
Answer : 99
View Answer
Q4. 

1)  3  2)  5 
3)  9  4)  11 
5)  None of these 
Answer : 11
Explanation :
Explanation :
Let, the ten's digit be x and unit's digit be y.
Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y), which is divisible by 11.
View Answer
Q5. 

1)  184  2)  192 
3)  196  4)  212 
5)  None of these 
Answer : 192
Explanation :
Explanation :
(x + y)^{2} = (x  y)^{2} + 4xy
or x + y = 28, x  y = 4
or 4xy = (28)^{2}  (4)^{2}
or 4xy = (28 + 4) (28  4)
or xy = = 32 x 6 = 192
View Answer
Q6. 

1)  (2^16 + 1)  2)  (2^16  1) 
3)  (7 x 2^23)  4)  (2^96 + 1) 
5)  None of these 
Answer : (2^96 + 1)
Explanation :
Explanation :
Let, 2^{32} = x. Then, (2^{32} + 1) = (x + 1).
Let, (x + 1) be completely divisible by the natural number N.
Then, (2^{96} + 1) = [(2^{32})^{3} + 1] = (x^{3} + 1) = (x + 1)(x^{2}  x + 1), which is completely divisible by N, since (x + 1) is divisible by N.
View Answer
Q7.  Twofifth of a number is two more than onethird another number.If the sum of the two numbers is 16,what is their product ? 
1)  40  2)  48 
3)  54  4)  60 
5)  None of these 
Answer : 60
Explanation : Let, two numbers are x and y respectively.
Explanation : Let, two numbers are x and y respectively.
According to the questions, x + y = 16  (I) and 2x/5  y/3 = 2  (II)
or 6x 5y = 30
Solving both equations , we get x = 10 and y = 6
So, their product = 10 X 6 = 60
View Answer
Q8. 

1)  2825  2)  2975 
3)  3025  4)  3775 
5)  None of these 
Answer : 3775
Explanation :
Explanation :
We know that,S_{n} = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100)/2  (1 + 2 + 3 + ... + 50)/2
= 100 x (1 + 100)  50 x (1 + 50) = (50 x 101)  (25 x 51)
= (5050  1275) = 3775.
View Answer
Q9. 

1)  8  2)  9 
3)  10  4)  12 
5)  None of these 
Answer : 10
Explanation :
Explanation :
4 a 3 
9 8 4 } ==> a + 8 = b ==> b  a = 8
13 b 7 
Also, 13 b7 is divisible by 11 (7 + 3)  (b + 1) = (9  b)
(9  b) = 0
or b = 9 (b = 9 and a = 1)
So, (a + b) = 10.
View Answer
Q10. 

1)  1  2)  2 
3)  3  4)  4 
5)  None of these 
Answer : 4
Explanation :
Explanation :
We, know that , Dividend = (divisor x Quotient )+Reminder
D = 5Q + 3
or D^{2} = (5Q + 3)^{2} = (25Q^{2} + 30Q + 9) = 5(5Q^{2} + 6Q + 1) + 4
On dividing D^{2} by 5, we get 4 as remainder.
View Answer