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Limits and Derivatives

JEE Main 2024 (Online) 27th January Morning ShiftMCQMedium📈 Topic in 14% papers+4−1
Ques. 1JEE Main 2024, 27 January (Morning Shift)

If a= x 0 1+ 1+x4- 2x4 and b= x 0 2x 2- 1+ x, then the value of ab3 is :

  1. 36
  2. 25
  3. 32
  4. 30

Answer

(3) 32

Solution

Rationalise twice:

a= x 0 1+x4-1x4 ( 1+ 1+x4+ 2 )

= x 0 1 ( 1+ 1+x4+ 2 ) ( 1+x4+1 )

= 12 2 2= 14 2

b= x 0 2x ( 2+ 1+ x )1- x

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

b= x 0(1+ x) ( 2+ 1+ x )

=2 2 2=4 2

ab3= (4 2)34 2=(4 2)2=32

Answer: (3)

Keep practising — Limits and Derivatives

Ques. 2JEE Main 2024, 27 January (Evening Shift)

If x 0 3+ x+ x+ e(1-x)3 2x= 13, then 2 - is equal to :

  1. 2
  2. 1
  3. 5
  4. 7

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