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MCQ (Previous Year Questions) - Limit (Competition Level 1) - JEE MCQ


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18 Questions MCQ Test - MCQ (Previous Year Questions) - Limit (Competition Level 1)

MCQ (Previous Year Questions) - Limit (Competition Level 1) for JEE 2024 is part of JEE preparation. The MCQ (Previous Year Questions) - Limit (Competition Level 1) questions and answers have been prepared according to the JEE exam syllabus.The MCQ (Previous Year Questions) - Limit (Competition Level 1) MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ (Previous Year Questions) - Limit (Competition Level 1) below.
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MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 1

If f(1) = 1, f' (1) = 2, then 

 [AIEEE 2002]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 1

By -Hospital Rule

MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 2

The value of 

  [AIEEE 2002]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 2



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MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 3

[AIEEE 2002]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 3



MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 4

 (where [x] denotes greatest integer less than or equal to x)

 [AIEEE-2002]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 4

MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 5

If  the value of k is -

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 5


Using L'Hospital's rule

MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 6

Let f(a) = g(a) = k and their nth derivatives f n (a), gn(a) exist and are not equal for some n. Further if  then the value of k is-  

[AIEEE 2003]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 6


Appliying L'Hospital’s

MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 7

  [AIEEE 2003]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 7






= 1/32

MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 8

 then the values of a and b, are-  

[AIEEE 2004]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 8





⇒ e2a = e2 ⇒ a = 1 and b ∈ R

MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 9

Let α and β be the distinct roots of ax2 + bx + c = 0, then   is equal to -

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 9





MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 10

 

 [AIEEE-2011]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 10











∴ Limit does not exist.

MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 11

[JEE 2000 (Scr.)]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 11


The format is 1-, so, given limit = e


so.e-5

MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 12

 [JEE 2001 (Scr.)]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 12




MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 13

The integer n for which    is a finite non-zero number is          

[JEE 2002 (Scr.)]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 13


so clearly the value of n must be '3'

MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 14

If = 0 (n > 0)then the value of ‘a’ is equal to

[JEE 2003 (Scr.)]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 14




MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 15

For x > 0, 

 [JEE  2006, 3]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 15





⇒ In y = 0 ⇒ y = e0 ⇒ y = 1

*Multiple options can be correct
MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 16

Let L = a > 0, If L is finite, then

  [JEE 2009, 4]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 16





Far ‘L’ to the finite, 
a = 2, 

MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 17

If  [1 + x In (1+b2)]1/x = 2b sin2 θ, b > 0 and θ ∈ (-π, π]. Then the value of θ is      

 [JEE 2011, 3]

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 17

1 + b2 = 2b sine2 θ
b2 - 2bsin2θ+1 = 0
D = 4 sin4 θ - 4
=4(sin4θ - 1) < 0
If D < 0 then no solution
∴ D = 0
∴ sinθ = ±1 

MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 18

Detailed Solution for MCQ (Previous Year Questions) - Limit (Competition Level 1) - Question 18


1 - a = 0 ⇒ a = 1
1 - b - a = 4
b = -4

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