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Test: Limit (Competition Level) - 4 - JEE MCQ


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30 Questions MCQ Test Additional Study Material for JEE - Test: Limit (Competition Level) - 4

Test: Limit (Competition Level) - 4 for JEE 2024 is part of Additional Study Material for JEE preparation. The Test: Limit (Competition Level) - 4 questions and answers have been prepared according to the JEE exam syllabus.The Test: Limit (Competition Level) - 4 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Limit (Competition Level) - 4 below.
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Test: Limit (Competition Level) - 4 - Question 1

Test: Limit (Competition Level) - 4 - Question 2

The value of 

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 2


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Test: Limit (Competition Level) - 4 - Question 3

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 3


secx > 1, when x is near o
sin–1 (secx) is underfixed  (sec x) does not exists

Test: Limit (Competition Level) - 4 - Question 4

greatest integer function is

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 4



Test: Limit (Competition Level) - 4 - Question 5

If α and β be the roots of ax2 + bx + c = 0, 

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 5



= ea(α - β)

Test: Limit (Competition Level) - 4 - Question 6

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 6

Given limit =

Test: Limit (Competition Level) - 4 - Question 7

Let x > 0 then 

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Test: Limit (Competition Level) - 4 - Question 8

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 8

 





= log2. 

Test: Limit (Competition Level) - 4 - Question 9

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 9

Then we get the following
lim(n→∞) (n!)1/n / n
= lim(n→∞) π1/(2n)(2n)1/(2n) (1/e)
= 1·1·1/e
= 1/e

Test: Limit (Competition Level) - 4 - Question 10

Let f : R → R be such that f(1) = 3, f1(1) = 6 then 

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Test: Limit (Competition Level) - 4 - Question 11

Let un  and L= 

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Test: Limit (Competition Level) - 4 - Question 12

The value of  denotes greatest integer function, is 

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 12

f(x) = x2 - sinx tanx
f(x) = 2x - sinx (sec2 x + 1)
f''(x) = 2 - (sinx + cosx) - 2secx tan2
secx + cosx > 2
∴ f''(x) < 0 ⇒ f'(x) is decreasing 
f'(x) < f(0), as x > 0
f'(x) < 0 ⇒ f(x) is decreasing if x > 0
∴ f(x) < f(0) 

Test: Limit (Competition Level) - 4 - Question 13

If a1 = 1 and an = n(1 + an–1 then the limit 

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Test: Limit (Competition Level) - 4 - Question 14

If f(n+1) =  n∈N & f(n) > 0 for all n∈N then f(n) is equal to 

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Test: Limit (Competition Level) - 4 - Question 15

Let f(x) =  Then the set of values of x for which f (x) = 0 , is :

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Test: Limit (Competition Level) - 4 - Question 16

 where n is a non zero real number then a is equal to

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Test: Limit (Competition Level) - 4 - Question 17

The value of 

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 17

lim x-->0 [(2x+3)/(3x+5)]1|x|
lim x-->0 [(2(0) + 3)/(3(0) + 5)]1\|0|
lim x-->0 [3/5]
= doesn’t exist

Test: Limit (Competition Level) - 4 - Question 18

Let f(x) =  then  is equal, (where [.] denotes greatest integer function and {.} fractional part) 

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 18








(i) becomes,


∴ (C) is the correct answer.

Test: Limit (Competition Level) - 4 - Question 19

 then m + n is equal to 

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 19

Put x – 1 = y  


Test: Limit (Competition Level) - 4 - Question 20

 represents fractional part function)

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 20



Test: Limit (Competition Level) - 4 - Question 21

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 21


=
= 1/12
 

Test: Limit (Competition Level) - 4 - Question 22

 (where [.] denotes the greatest integer function) is equal to  

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 22



Test: Limit (Competition Level) - 4 - Question 23

 then the constants a and b are (where a > 0) 

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 23



 = limit is finite. So b = 1

Test: Limit (Competition Level) - 4 - Question 24

The value of 

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Test: Limit (Competition Level) - 4 - Question 25

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 25

Applying  L’Hospital rule



= 1/8

Test: Limit (Competition Level) - 4 - Question 26

If f(n+1) =  n ∈ N and f(n) > 0 for all n ∈ N then 

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 26




Test: Limit (Competition Level) - 4 - Question 27

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 27

Let f(n) = 

Test: Limit (Competition Level) - 4 - Question 28

The value of where [.] represents greatest integral function, is 

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 28

We know that


Test: Limit (Competition Level) - 4 - Question 29

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 29


By L Hospital’s Rule 

Test: Limit (Competition Level) - 4 - Question 30

Detailed Solution for Test: Limit (Competition Level) - 4 - Question 30

The given limit is 

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