IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry - few Ds Rates awaiting...`pls........salutes assured

jw

1) if sum of 84 members first of the series
(4+^{[ ]}

3 / 1 + ^{[ ]}

3 ) + (8+

15 /

3 +

5 ) + ( 12 + ^{[ ]}

35 / ^{[ ]}

5 + ^{[ ]}

7 ) +......

is????????

2) if x and y are real nos satisfing x^2 + y^2 - 6x + 8y + 24 = 0
the gretest value of 16/5 cos^2 (^{[ ]}

(x^2 + y^2) ) - 24/5 sin (^{[ ]}

(x^2 + y^2) ) is???

3) when 23²³is divided by 53 the reminder is 5k.
k is??

4) let f(x) = ax^2 + bx + c and g(x) = Ax^2 + bx +K where a

0 A not equal to 0
a, b c A k is R

roots of f(x) =0 and g(x) =0 are imaginary then

f(x)/a + g(x) /A >0 for all x belongs to R

how???