99 Percentile Qs Bank for JEE MainMathematicsLimits

_ x 0 ( 4 ! x^8 (1- x^2 3 - x^2 4 + x^2 3 x^2 4 ) )=

Options

A8
B1 6
C1 24
D2 3

Correct answer

C. 1 24

Step-by-step solution

aligned & _ x 0 ( 4 ! x^8 (1- x^2 3 - x^2 4 + x^2 3 x^2 4 ) ) & _ x 0 ( 4 ! x^8 (1- x^2 3 ) (1- x^2 4 ) ) & = _ x 0 ( 4 ! x^8 (1-1+2 ^2 x^2 6 ) (1-1+2- ^2 x^2 8 ) ) & .=4 ! [ _ x 0 x^2 6 x^2 6 ) 2 36 [ _ x 0 x^2 8 x^2 8 )^2 2 64 ] & =4 3 2 [1 2 36 1 2 64 ]= 1 24 aligned

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) , 2026 The value of _ x 0 ( x^2 ^2 x x^2 - ^2 x ) is: 2026 Let f(x) = _ y 0 (1 - (xy)) (xy) y^3 . Then the number of solutions of the equation f(x) = x , x R is : 2026 The product of all possible values of , for which _ x 0 ( 1 - ( x) (( +1)x) (( +2)x) ^2(( +1)x) ) = 2 , is: 2026 If _ x 2 (x^3 - 5x^2 + ax + b) ( x-1 - 1) _e(x-1) = m , then a + b + m is equal to : 2026 The value of _ x 0 _ e ( (e x) (e² x ) (e¹⁰ x ) ) e²-e^ 2 x is equal to 2026 If _ 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 : 2026 Let [ ] 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 99 Percentile Qs Bank for JEE Main PYQs