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JEE Exam  >  JEE Tests  >  Test: Limit (Competition Level) - 4 - JEE MCQ

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


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30 Questions MCQ Test - Test: Limit (Competition Level) - 4

Test: Limit (Competition Level) - 4 for JEE 2024 is part of 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.
Solutions of Test: Limit (Competition Level) - 4 questions in English are available as part of our course for JEE & Test: Limit (Competition Level) - 4 solutions in Hindi for JEE course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Limit (Competition Level) - 4 | 30 questions in 60 minutes | Mock test for JEE preparation | Free important questions MCQ to study for JEE Exam | Download free PDF with solutions
Test: Limit (Competition Level) - 4 - Question 1
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Test: Limit (Competition Level) - 4 - Question 2
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The value of 

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Test: Limit (Competition Level) - 4 - Question 3
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secx > 1, when x is near o
sin–1 (secx) is underfixed  (sec x) does not exists

Test: Limit (Competition Level) - 4 - Question 4
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greatest integer function is
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Test: Limit (Competition Level) - 4 - Question 5
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If α and β be the roots of ax2 + bx + c = 0, 
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= ea(α - β)

Test: Limit (Competition Level) - 4 - Question 6
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Given limit =

Test: Limit (Competition Level) - 4 - Question 7
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Let x > 0 then 
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Test: Limit (Competition Level) - 4 - Question 8
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= log2. 

Test: Limit (Competition Level) - 4 - Question 9
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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
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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
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Let un  and L= 
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Test: Limit (Competition Level) - 4 - Question 12
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The value of  denotes greatest integer function, is 
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f(x) = x2 - sinx tanx
f(x) = 2x - sinx (sec2 x + 1)
f''(x) = 2 - (sinx + cosx) - 2secx tan2x 
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
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If a1 = 1 and an = n(1 + an–1)  then the limit 
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Test: Limit (Competition Level) - 4 - Question 14
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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
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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
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 where n is a non zero real number then a is equal to
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Test: Limit (Competition Level) - 4 - Question 17
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The value of 
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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
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Let f(x) =  then  is equal, (where [.] denotes greatest integer function and {.} fractional part) 
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(i) becomes,


∴ (C) is the correct answer.

Test: Limit (Competition Level) - 4 - Question 19
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 then m + n is equal to 
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Put x – 1 = y  


Test: Limit (Competition Level) - 4 - Question 20
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 represents fractional part function)
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Test: Limit (Competition Level) - 4 - Question 21
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=
= 1/12
 

Test: Limit (Competition Level) - 4 - Question 22
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 (where [.] denotes the greatest integer function) is equal to  
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Test: Limit (Competition Level) - 4 - Question 23
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 then the constants a and b are (where a > 0) 
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 = limit is finite. So b = 1

Test: Limit (Competition Level) - 4 - Question 24
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The value of 
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Test: Limit (Competition Level) - 4 - Question 25
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Applying  L’Hospital rule



= 1/8

Test: Limit (Competition Level) - 4 - Question 26
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If f(n+1) =  n ∈ N and f(n) > 0 for all n ∈ N then 
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Test: Limit (Competition Level) - 4 - Question 27
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Let f(n) = 

Test: Limit (Competition Level) - 4 - Question 28
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The value of where [.] represents greatest integral function, is 
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We know that


Test: Limit (Competition Level) - 4 - Question 29
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By L Hospital’s Rule 

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

The given limit is 

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