Test: Limit (Competition Level) - 4


30 Questions MCQ Test Mathematics for JEE Mains | Test: Limit (Competition Level) - 4


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QUESTION: 1

Solution:
QUESTION: 2

The value of 

Solution:


QUESTION: 3

Solution:


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

QUESTION: 4

greatest integer function is

Solution:



QUESTION: 5

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

Solution:



= ea(α - β)

QUESTION: 6

Solution:

Given limit =

QUESTION: 7

Let x > 0 then 

Solution:



QUESTION: 8

Solution:

 





= log2. 

QUESTION: 9

Solution:

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

QUESTION: 10

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

Solution:

QUESTION: 11

Let un  and L= 

Solution:









QUESTION: 12

The value of  denotes greatest integer function, is 

Solution:

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) 

QUESTION: 13

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

Solution:







QUESTION: 14

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

Solution:





QUESTION: 15

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

Solution:


QUESTION: 16

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

Solution:



QUESTION: 17

The value of 

Solution:

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

QUESTION: 18

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

Solution:








(i) becomes,


∴ (C) is the correct answer.

QUESTION: 19

 then m + n is equal to 

Solution:

Put x – 1 = y  


QUESTION: 20

 represents fractional part function)

Solution:



QUESTION: 21

Solution:


=
= 1/12
 

QUESTION: 22

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

Solution:



QUESTION: 23

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

Solution:



 = limit is finite. So b = 1

QUESTION: 24

The value of 

Solution:




QUESTION: 25

Solution:

Applying  L’Hospital rule



= 1/8

QUESTION: 26

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

Solution:




QUESTION: 27

Solution:

Let f(n) = 

QUESTION: 28

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

Solution:

We know that


QUESTION: 29

Solution:


By L Hospital’s Rule 

QUESTION: 30

Solution:

The given limit is 

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