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???

Conjurer

4)

Since roots are imaginary, the functions do not cut the x axis.It lies either above the axis(if a/A > 0) or below the axis (if a/A <0).In either case f(x)/a + g(x)/A >0

jw

please someone try
the other Questions

ananth_patri

for 3) is the answer k=6??

ananth_patri

well the process is this way... write 23²³ as 23(23)²² and now

=23(529)¹¹ =23(530-1)^{11 ,....}all the binomail exp tyerms will be in the form 53k ....the last 2 terms are ¹¹C₁₀ 530 - ¹¹C₁₁ ... so this will make as ...23(53k-1)/53 which ...thus we get it as n - 23/53.....now we can get it as 30/53 on makin the left term positive....thus remainder is 30 which is 5*K thus K=6.. hope u got it ...rate if useful....

ankitagg

ananth will u please tell me what does [ ] this mean in his question.

dream

@ankitagg
it is nothing
it is just a symbol that it is square root , ie, to the power 1/2

anchitsaini

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