JEE Advanced Model Paper 18 with solutions for online practice

A)

0

∫

−1

(x - 1) x (x + 1) (x + 2) (x + 3) dx =

1

∫

−1

(x - 2) (x - 1) x (x + 1) (x + 2) dx = 0
B) If f (x) = 0 has two pairs of equal roots than y = f (x) has 1 point where it is notdifferentiable .
C) L =

lim

x→1

8

1−x5

-

4

1−x4

..... (1)
L =

lim

x→1

−8x8

1−x8

+

4x4

1−x4

..... (2)
(1) + (2)
2L = 8 - 4 = 4 ⇒ L = 2
D) 60 = 2 . 2 . 3 . 5 ⇒ x4+zx3+bx2 + cx + 60 = (x - 2) (x - 2) (x - 3) (x - 5)
⇒ 1 + a + b + c + 60 = 8 = 23