Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main202529 Jan 2025Morning ShiftMathematicsLimitsActual

Let [t] be the greatest integer less than or equal to t. Then the least value of ( p N ) for which ( _ x 0⁺ (x ( [ 1 x ]+ [ 2 x ]+ + [ p x ] )-x^2 ( [ 1 x^2 ]+ [ 2^2 x^2 ]+ + [ 9^2 x^2 ] ) ) 1 ) is equal to ________.

Correct answer

0

Step-by-step solution

aligned & _ x 0⁺ (x ( [ 1 x ]+ [ 2 x ]+ . .+ [ p x ] )-x^2 ( [ 1 x^2 ]+ [ 2^2 x^2 ]+ [ 9^2 x^2 ] ) ) 1 & (1+2+ +p)- (1^2+2^2+ 9^2 ) 1 aligned aligned & p(p+1) 2 - 9.10 .19 6 1 & p(p+1) 572 aligned Least natural value of p is 24

Practice Limits on Quantrex Academy →

More from Limits

Let _ x 2 ( (x-2))(rx^2 + (p-2)x - 2p) (x-2)^2 = 5 for some r, p R . If the set of all possible values of q , such that the roots of the equation rx^2 - px + q = 0 lie in (0, 2) , 2026The value of _ x 0 ( x^2 ^2 x x^2 - ^2 x ) is: 2026Let f(x) = _ y 0 (1 - (xy)) (xy) y^3 . Then the number of solutions of the equation f(x) = x , x R is : 2026The product of all possible values of , for which _ x 0 ( 1 - ( x) (( +1)x) (( +2)x) ^2(( +1)x) ) = 2 , is: 2026If _ x 2 (x^3 - 5x^2 + ax + b) ( x-1 - 1) _e(x-1) = m , then a + b + m is equal to : 2026The value of _ x 0 _ e ( (e x) (e² x ) (e¹⁰ x ) ) e²-e^ 2 x is equal to 2026If _ x 0 e ^ ( a -1) x +2 ~b x+( c -2) e ^ -x x x- _ e (1+x) =2 , then a ²+ b ²+ c ² is equal to : 2026Let [ ] denote the greatest integer function and f(x)= _ n 1 n ³ _ k =1 ^ n [ k ² 3^ x ] . Then 12 _ j =1 ^ f( j ) is equal to _ _ _ _ . 2026 Full Limits list All JEE Main PYQs