ramanujans contest

By
Test1 and 2
Pattern-

Questions 
Level 1
(Proposed)
Donot publish proposed questions

1)If 
$(x, y)$ is a solution for the system of equations below, find the maximum value of $x^2+y^2$.\begin{align} 2x^2+5xy+3y^2&=2 \\ 6x^2+8xy+4y^2&=3 \end{align}

2)The area of square $ABCD$ is 256 sq.cm
. Point $E$ is inside the square, at the same distances from points $D$ and $C$, and such that $m \angle DEC = 150^{\circ}$. What is the perimeter of $\triangle ABE$ equal to? Prove your answer is correct.

FINALISED QUESTIONS (level 1)


1)Let x be the number of zeros when the expression  22!12!20!20!26!4!19!20!1887!
Is divided by 10 
Find the closest integral value of x

Answer: 50

2)let ABCD be a parallelogram with vertices A(21,37) , B(37,23) C(43,69) . Let a line passing through the origin divides the parallelogram into two congruent figures. Let m/n be the slope of the line where m and n are relatively prime positive integers find m+n

Ans:85


3)What is the sum of the digits of the square of 111111111?
Ans: 81


4)Given four congruent circles are externally tangential to each other and are internally tangential to the larger circle, if the area of the larger circle is 17.48 find the area of a smaller circle to the nearest integer. 

Ans: 3


5) 2)If positive numbers a, b, c satisfy abc = 1, and the value of x is m/n where m,n are relatively prime integers find m+n

Ans=3




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