Number System MCQs

If the symbol [x] denotes the greatest integer less than or equal to x, then the value of :
$$\left[ {\frac{1}{4}} \right]$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{1}{{50}}} \right]$$   $$ + $$ $$\left[ {\frac{1}{4} + \frac{2}{{50}}} \right]$$   $$ + $$ $$....$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{{49}}{{50}}} \right]$$

If the sum of digits of a two digit number is 10 and if the digits of two digits number is reversed, then the number is decreased by 36. Which of the following is correct regarding the number?
I. The difference of the digits is 4.
II. The value of number can be 84.
III. Number is always a composite number.

P is a prime number and (P² + 3) is also a prime number . The no. of numbers that P can assume is:

If 0 < x < 1, which of the following is greatest ?

When 'n' is divisible by 5 the remainder is 2. What is the remainder when n² is divided by 5 ?

The remainder , when (15²³ + 23²³) is divided by 19, is

Given n = 1 + x and x is the product of four consecutive integers. Then which of the following us true ?
I. n is an odd integer.
II. n is prime.
III. n is a perfect square

Which one of the following is the common factor of (47⁴³ + 43⁴³) and (47⁴⁷ + 43⁴⁷) = ?

What is the sum of all the common terms between the given series S₁ and S₂?
S₁ = 2, 9, 16, . . . . . ., 632
S₂ = 7, 11, 15, . . . . . ., 743