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Let S be the set of all ordered pairs (x, y) of positive integers satisfying the condition x2-y2=12345678. Then

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Important Questions on Prime Time

HARD
For a real number r let r denote the largest integer less than or equal to r. Let a>1 a real number which is not an integer and k be the smallest positive integer such that ak>ak Then which of the following statement is always true?
MEDIUM
The number of digits in the decimal expansion of 165516 is
HARD
For a real number r we denote by r the largest integer less than or equal to r. If x, y are real numbers with x, y 1 then which of the following statements is always true?
MEDIUM
A number of two digits is equal to 'k' times to the sum of these digits. If the places of these digits are mutually exchanged. the newly formed number is equal to the sum of these digits multiplied by which one of the following options ?
MEDIUM
The number of positive integers n in the set 2,3,..,200 such that 1n has a terminating decimal expansion is
EASY

The sum of three consecutive numbers is 126. Find the highest number-

1. 41
2. 42
3. 43
4. 44

HARD
The function f :NI defined by fx=x-5x5 , where N is the set of natural numbers and x denotes the greatest integer less than or equal to x, is:
EASY

1 USD = Rs. 67.89. A money changer adds a margin of Rs. 1.11. What will be the cost of 150 USD ? 

1. Rs. 10,183
2. Rs. 10,350
3. Rs. 10,330
4. Rs. 10,450

MEDIUM
The number of distinct primes dividing 12!+13!+14! Is
HARD
Let n>1 be an integer. Which of the following sets of numbers necessarily contains a multiple of 3?
EASY

Twice the difference between two numbers is equal to their sum. If one number is 15, Find the other number.

1. 15
2. 10
3. 5
4. 20 

MEDIUM

Consider the following statements: For any integer n, 

I.. n2+3 is never divisible by 17 .

II.. n2+4 is never divisible by 17. Then

 

MEDIUM
P and Q are two examination halls. If 10 examinees are sent from P into Q, the number of examinees becomes equal in both the halls. If 20 examinees are transferred from Q into P, the number of examinees becomes double in P in comparison with Q. What is the number of examinees in each P and Q separately ?
EASY

How many times does the number 3 occur in unit's place for numbers ranging from 1 to 100?

1. 20
2. 11
3. 10
4. 19

EASY

B has 32 pens, 24 pencils and 16 erasers. How many sets of these three items can B make without any left over? 

1. 6
2. 7
3. 8
4. 9

EASY
The difference of the cubes of two consecutive numbers is 127. What are the numbers?
MEDIUM
If 59 is added to a square of a number, the result is 900. What is the number?
MEDIUM
The largest non-negative integer k such that 24k divides 13! is
MEDIUM
There are exactly twelve Sundays in the period from January 1 to March 31 in a certain year. Then, the day corresponding to February 15 in that year is
MEDIUM
How many natural numbers n are there such that n!+10 is a perfect square ?