Courses

# Test: Limit (Competition Level) - 4

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

Description
This mock test of Test: Limit (Competition Level) - 4 for JEE helps you for every JEE entrance exam. This contains 30 Multiple Choice Questions for JEE Test: Limit (Competition Level) - 4 (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Limit (Competition Level) - 4 quiz give you a good mix of easy questions and tough questions. JEE students definitely take this Test: Limit (Competition Level) - 4 exercise for a better result in the exam. You can find other Test: Limit (Competition Level) - 4 extra questions, long questions & short questions for JEE on EduRev as well by searching above.
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