
1.

A rational number between 
3 
and 
3 
is 
4 
8 

Answer: Option
D
Explanation:
3 
= 
3 × 4 
= 
12 
4 
4 × 4 
16 
∴ 
6 
, 
7 
, 
8 
, 
9 
, 
10 
, 
11 
, 
12 

16 
16 
16 
16 
16 
16 
16 
∴ Required rational number = 
9 

16 


2.

Find the largest number, which exactly divides every number of the form (n^{3} – n) (n – 2) where n is a natural number greater than 2.

Answer: Option
C
Explanation:
(n ^{3} – n)(n – 2)
= n(n – 1)(n + 1)(n – 2)
When n = 3,
Number = 3 × 2 × 4 = 24.


3.

The least number, which is to be added to the greatest number of 4 digits so that the sum may be divisible by 345, is

Answer: Option
B
Explanation:
The largest 4digit number = 9999
345 
) 
9999 
( 
28 


690 




3099 




2760 




339 


∴ Required number = 345 – 339 = 6.


4.

If a = 4011 and b = 3989 then value of ab = ?

A.

1,59,99,879

B.

1,58,99,879

C.

1,59,89,979

D.

1,59,98,879

Answer: Option
A
Explanation:
a = 4011, b = 3989
∴ ab = 4011 × 3989
= (4000 + 11)(4000 – 11)
= (4000) ^{2} – (11) ^{2}
= 16000000 – 121
= 1,59,99,879.


5.

For any integral value of n, 3^{2n} + 9n + 5 when divided by 3 will leave the remainder

Answer: Option
B
Explanation:
Expression = 3 ^{2n} + 9n + 5
= (3 ^{2n} + 9n + 3) + 2
= 3(3 ^{2n – 1} + 3n + 1) + 2
Clearly, remainder = 2.

