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Test: Limits And Continuity : Intuitive Approach - 3

40 Questions MCQ Test Quantitative Aptitude for CA CPT | Test: Limits And Continuity : Intuitive Approach - 3

Description

This mock test of Test: Limits And Continuity : Intuitive Approach - 3 for CA Foundation helps you for every CA Foundation entrance exam. This contains 40 Multiple Choice Questions for CA Foundation Test: Limits And Continuity : Intuitive Approach - 3 (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Limits And Continuity : Intuitive Approach - 3 quiz give you a good mix of easy questions and tough questions. CA Foundation students definitely take this Test: Limits And Continuity : Intuitive Approach - 3 exercise for a better result in the exam. You can find other Test: Limits And Continuity : Intuitive Approach - 3 extra questions, long questions & short questions for CA Foundation on EduRev as well by searching above.

QUESTION: 1

If f(x) = (x²-4)÷(x-2) for x<2, f(x)=4 for x=2 and f(x)=2 for x>2, then f(x) at x = 2 is

A.
Discontinuous
B.
Continuous
C.
Maxima
D.
Minima

Solution:

QUESTION: 2

f(x) = when x^o0, then f(x) is

A.
Discontinuous at x = 0
B.
Continuous at x = 0
C.
Maxima at x = 0
D.
Minima at x = 0

Solution:

QUESTION: 3

If = i, then which of the following is correct?

A.
a = 1, l = 2
B.
a = 2, l = 3
C.
a = -2, l = -1
D.
a = -2, l = 3

Solution:

QUESTION: 4

is equal to

A.
1/3
B.
-1/3
C.
1
D.
None of these.

Solution:

QUESTION: 5

If f(x) = x for 0 ≤ x 1/2, f(x) = 1 for x = 1-x for 1/2<x<1 then at x =1/2 the function is

A.
Discontinuous
B.
Continuous
C.
Left-hand limit coincides with f(1/2)
D.
Right-hand limit coicides with left-hand limit.

Solution:

QUESTION: 6

e^-1/x[1+e^1/x]^-1 is

A.
Discontinuous at x = 0
B.
Continuous at x = 0
C.
Maxima at x = 0
D.
Minima at x = 0

Solution:

QUESTION: 7

If f(x)=9x÷(x+2) for x<1, f(1)=3, f(x)=(x+3)x-1 for x>1, then in the interval (-3,3) the function is

A.
Continuous at x = -2
B.
Continuous at x = 1
C.
Discontinuous for values of x other than -2 1 in the interval
D.
None

Solution:

QUESTION: 8

A.
-3
B.
0
C.
2
D.
4

Solution:

QUESTION: 9

Function f(x) = K.x-1 for x < 2
= x-k for x ≥ 2
is continuous at x = 2
The value of 'k' is __________.

A.
2
B.
1
C.
-1
D.
-2

Solution:

QUESTION: 10

A.
5
B.
6
C.
8
D.
None of the above.

Solution:

QUESTION: 11

Evaluate

A.
1/3
B.
2/3
C.
4/3
D.
1

Solution:

QUESTION: 12

Evaluate

A.
1
B.
2
C.
∞
D.
0

Solution:

QUESTION: 13

The points of discontinuity of the function, F(x) = are

A.
x = 0, x = 1
B.
x = 1, x = 2
C.
x = 0, x = 2
D.
None of these

Solution:

QUESTION: 14

A.
1/8
B.
+ ∞
C.
- ∞
D.
None of these

Solution:

QUESTION: 15

A.
+ ∞
B.
- ∞
C.
0
D.
Does not exist

Solution:

QUESTION: 16

Find limn→∞(2n-1)2ⁿ(2n+1)^-1 2^1-n

A.
2
B.
1/2
C.
1
D.
None

Solution:

QUESTION: 17

Find lim_n→∞[4n² + 6n +2] ÷ 4n²

A.
1/2
B.
3/2
C.
1
D.
-1

Solution:

QUESTION: 18

Find lim_n→∞[xⁿ.(n+1)] ÷ [nx ⁿ⁺¹ ]

A.
x^-1
B.
x
C.
1
D.
None

Solution:

QUESTION: 19

Find lim_n→∞[n(n+2)] ÷ (n+1)²

A.
2
B.
1/2
C.
1
D.
None

Solution:

QUESTION: 20

Find lim_n→∞(n³ +a )[(n+1)³a]^-1 (2ⁿ⁺¹ +a ) (2ⁿ +a)^-1

A.
0
B.
1
C.
-1
D.
2

Solution:

QUESTION: 21

Find lim_n→∞(n² +1)[(n+1)² +1]^-1 5ⁿ⁺¹ 5^-n

A.
5
B.
e^-1
C.
0
D.
None

Solution:

QUESTION: 22

Find lim_n→∞nⁿ(n+1)^-n-1 ÷ n^-1

A.
e^-1
B.
e
C.
1
D.
-1

Solution:

QUESTION: 23

Find lim_n→∞2^n-1 (10 +n) (9+n)^-1 2^-n

A.
2
B.
1/2
C.
1
D.
None

Solution:

QUESTION: 24

Find lim_n→∞(1+n^-1)[1+2n)^-1]^-1

A.
1/2
B.
3/2
C.
1
D.
-1

Solution:

QUESTION: 25

Find lim_n→∞[nⁿ. (n+1)!] ÷ [n! (n+1)ⁿ⁺¹]

A.
5
B.
e^-1
C.
0
D.
None

Solution:

QUESTION: 26

Find lim_n→∞[(n+1)^ⁿ⁺¹. n^-n-1 -(n+1).n^-1]^-n

A.
(e-1)^-1
B.
(e+1)^-1
C.
e-1
D.
e+1

Solution:

QUESTION: 27

3x²+2x-1 is continuous

A.
At x = 2
B.
For every value of x
C.
Both (a) and (b)
D.
None

Solution:

QUESTION: 28

Find lim_n→∞nⁿ (1+n)^-n

A.
e^-1
B.
e
C.
-1
D.
1

Solution:

QUESTION: 29

Find lim_n→∞[n!3ⁿ⁺¹] ÷[3ⁿ(n+1)!]

A.
0
B.
1
C.
-1
D.
2

Solution:

QUESTION: 30

The value of the limit when x tends to zero of the expression (1+n)^1/n is

A.
e
B.
0
C.
1
D.
-1

Solution:

QUESTION: 31

The value of the limit when x tends to zero of the expression (1+n)^1/n is

A.
e
B.
0
C.
1
D.
-1

Solution:

QUESTION: 32

The value of the limit when x tends to zero of the expression [(1+x)ⁿ-1] ]

A.
n
B.
n+1
C.
n-1
D.
n(n-1)

Solution:

QUESTION: 33

The value of the limit when x tends to 2 of the expression (x-2)^-1-(x²-3x+2)^-1 is

A.
1
B.
0
C.
-1
D.
None

Solution:

QUESTION: 34

The value of the limit when x tends to zero of the expression (e^x-1)/x is

A.
1
B.
0
C.
-1
D.
indeterminate

Solution:

QUESTION: 35

The value of the limit when n tends to infinity of the expression 2^-n(n²+5n+6)[(n+4)(n+5)]^-1 is

A.
0
B.
1
C.
-1
D.
None

Solution:

QUESTION: 36

The value of the limit when x tends to zero of the expression (1+n)^1/n is

A.
e
B.
0
C.
1
D.
-1

Solution:

QUESTION: 37

Find lim_n→∞[n^1/2 + (n+1)^1/2]^-1 ÷ n^-1/2

A.
1/2
B.
0
C.
1
D.
None

Solution:

QUESTION: 38

The value of the limit when x tends to zero of the expression [(a+x²)^1/2

A.
a^-1/2
B.
a^1/2
C.
a
D.
a^-1

Solution:

QUESTION: 39

Find lim_n→∞ (2ⁿ-2)(2ⁿ+1)^-1

A.
1/4
B.
1/2
C.
1
D.
None

Solution:

QUESTION: 40

Find lim_n→∞ [(n³ +1)^1/2- n ^{3/2] ÷ n^3/2}

A.
1/4
B.
0
C.
1
D.
None

Solution:

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Test: Limits And Continuity : Intuitive Approach - 3

40 Questions MCQ Test Quantitative Aptitude for CA CPT | Test: Limits And Continuity : Intuitive Approach - 3