JEE Advanced 2016 (1)
r = 1 ∑ 2 5 ( 3 p r + 2 q r ) Find the value of above expression if p r , q r ( p r < q r ) are the roots of x 2 − r 2 ( r + 1 ) x + r 5 = 0 .
Try my set JEE ADVANCED 2016
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2 solutions
well calculations are generally to be done smartly. if you neglect NOT option which is generally not in IIT ques,you can just see the unit's digit or something like that instead of calculating the whole thing.
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That was with this question ! . The JEE People are not fools you can see some previous year problems they mostly give SAME Units digit to avoid this smart work.
My point is that they avoid giving such type of problems in which some or the other 3 digit number multiplication is involved
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yeah! but still! anyway there's no point in arguing. would you help me with problem 5 of this set i'm not getting 5 as the answer
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@Ayush Agarwal – Yeah right! :) . I Will try if i could solve it i will surely reply :)
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@Prakhar Bindal – I got range of latus rectum (0,4) but it nowhwere says integral.Tell me your procedure.
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@Ayush Agarwal – Yeah you are correct report the problem as i did not noticed it . it should be mentioned!
i too got exactly the same range
@Ayush Agarwal – Hey i have already solve it !. I Got length of latus rectum as 1,2,3 (integral values)
Roots are p r = r 2 and q r = r 3 .
Realise by inspection that roots of quadratic are r^3 and r^2. from the range of values of r it can be easily recognised q = r^3 and p = r^2 . Simply Apply summation formula of sum of cubes and squares of first n natural numbers.
Problem is nice but according to me JEE Does not gives this type of crazy calculations (especially in advanced)