Maths Doubt Clarification

A person forgot his 5 digit pin code, but he remembers some hints. 1. 1st digit is square of 2nd digit. 2. Sum of 2nd and 3rd digit makes 10. 3. 4th digit is 2nd digit + 1. 4. Sum of 5th and 3rd digit makes 14. 5. Sum of all 5 digits = 30. Tell the pin code.

I give you 4 tablets which contain 2 for fever and 2 for cold. All 4 have same size, shape, taste, weight and color, No cover. You have to take 1 cold and 1 fever tablet right now. How will you choose correctly?

If m denotes the number of 5-digit numbers such that their digits are in strictly descending order of magnitude and n is the corresponding figure when the digits are in strictly ascending order of magnitude. Then, (m-n) has the value?

In a unique hockey series between India and Pakistan, they decide to play on till a team wins 5 matches.The number of ways in which the series can be won by India, if no match ends in a draw is?

Determine whether Even or Odd: f(x+y) + f(x-y) = 2f(x).f(y); where f(0) is not zero and x, y belongs to set of real numbers.

Find the exponent of 12 in 50!

Find integral solutions to the equation [x] [y] = x + y.Show that all integral solutions lie on two lines. Determine these lines , where [.] denotes greatest integer function.

Let a,b,c,d be real nos. such that sigma lower limit k=1 and upper limit n(ak^3+bk^2+ck+d) = n^4 for every natural no. "n". Then |a| + |b| + |c| + |d| = ?

Given x/a + y/b = 1 and ax + by = 1 are two variable lines, a,b being the parameters connected by relation a^2 + b^2 = ab. The locus of the point of the intersection has the equation lx^2 + my^2 + nxy - 1 = 0 then (l+m+n) is?

Find the range of (x^2+x+1) / (x^2-x+1).

_ + _ + _ + _ + _ = 30. Fill the boxes using (1, 3, 5, 7, 9, 11, 13, 15).

x = 3 + 2*sqrt(2). Find x^(1/2) + x^(-1/2)