Test: Functions Of One,Two Or Three Real Variables - 5

Question 1

Accepted Answer

Answer

Answer

Answer

Question 2

Let <img src="https://cn.edurev.in/ApplicationImages/Temp/0817a914-f6bb-4d77-8c24-461dd454b1b4_lg.jpg" /> then,

Accepted Answer

one repeated limit exists but other does not exists

Answer

double limit exists

Answer

both the repeated limit exists

Answer

None of these

Question 3

If f(x) = ax + b, where a and b are integers, f(–1) = – 5 and f(3) = 3, then a and b are equal to

Accepted Answer

a = 2, b = – 3

Answer

a = – 3, b = –1

Answer

a = 0, b = 2

Answer

a = 2, b = 3

Question 4

Let <img src="https://cn.edurev.in/ApplicationImages/Temp/bb158c46-5674-441e-b4db-7ed766addece_lg.jpg" /> then,

Accepted Answer

<img src="https://cn.edurev.in/ApplicationImages/Temp/1a0c5c4b-f84b-4be3-8c22-e5832b0d091e_lg.jpg" />exists

Answer

<img src="https://cn.edurev.in/ApplicationImages/Temp/777bd109-2621-4aa5-9bc7-a2fe0b391bc1_lg.jpg" />exists

Answer

does not exists

Answer

does not exists

Question 5

For the function
f(x, y) = x³ + y³ - 3x — 12y + 20 has,

Accepted Answer

the saddle points are (-1, 2) and (1, -2)

Answer

maximum at (1, 2)

Answer

minimum at (-1, -2)

Answer

maximum at (1, 2) and minimum at (-1, -2)

Question 6

The g -1({0}) for the function g(x)= ⌊x⌋ is ___________

Accepted Answer

{x | 0 ≤ x ≤ 1}

Answer

{x | 0 ≤ x < 1}

Answer

{x | 0 < x ≤ 1}

Answer

{x | 0 < x < 1}

Question 7

The function f(x) = has

Accepted Answer

irremovable discontinuity at x = 0

Answer

continuity at x = 0

Answer

removable discontinuity at x = 0

Answer

none of the above

Question 8

If f(x) = then
(i)f(x) = 1
(ii) f(x) = 2
(iii) f (x) =2
Q. Which of these statement(s) is/are correct?

Accepted Answer

I and II are correct

Answer

I and III are correct

Answer

I, II and III are correct

Answer

II alone is correct

Question 9

If f(x) = (x² - 1) |x² - 3x + 2 | + cos (|x|), then set of point of non - differentiability is

Accepted Answer

{2}

Answer

{1 ,0 ,2}

Answer

{1, 2}

Answer

{0,2}

Question 10

If f(y) = then f(x) is

Accepted Answer

discontinuous,

Answer

discontinuous, ∈R

Answer

discotinuous, ∈ Q

Answer

discontinuous,

Question 11

Let us consider the pair of ordered pair of sequences
(a_n , b_n) and (c_n, d_n) such that
= (a,b) and (c_n, d_n) = (a,b), then does not exists, if

Accepted Answer

Answer

Answer

Answer

Question 12

Let <img src="https://cn.edurev.in/ApplicationImages/Temp/4e3c018e-9024-451c-a93a-b7e14604939d_lg.jpg" /> then,

Accepted Answer

Answer

fxy(0, 0) = - 1

Answer

fxy(0,0) =1

Answer

Question 13

Let
f(x,y)={x−yx3+y3,0,(x,y)=(0,0)(x,y)=(0,0)
then,

Accepted Answer

f is not continuous at origin

Answer

f_x(0, 0) does not exists

Answer

f_y{0, 0) does not exists

Answer

None of these

Question 14

Let
f(x) =

then at (0, 0)

Accepted Answer

f posses partial derivative

Answer

f is discontinuous

Answer

f is differentiable

Answer

None of these

Question 15

Let <img src="https://cn.edurev.in/ApplicationImages/Temp/ea96da88-ce2b-4bd0-8677-33b72701dffa_lg.jpg" /> then,

Accepted Answer

f is not differentiable at (0, 0)

Answer

f is differentiableat (0, 0)

Answer

f is continuous at (0, 0)

Answer

None of these

Question 16

Consider the function f(x) = |x³| where x is real, then the function f (x) at y = 0 is

Accepted Answer

twice differentiable but not thrice

Answer

continuous but not differentiable

Answer

once differentiable but not twice

Answer

thrice differentiable

Question 17

If f(x) = then

Accepted Answer

f is differentiable at x = 0

Answer

f is continuous but not differentiable at x = 0

Answer

f is continuous but not differentiable at x=1

Answer

f is differentiable at x = 1

Question 18

Let f : [0, 10] → [0 ,10] be continuous function then

Accepted Answer

f has atleast one fixed point

Answer

f need not to have any fixed point

Answer

f has atleast 10 fixed point

Answer

f has atleast 9 fixed points

Question 19

The derivative of a periodic function with period T is

Accepted Answer

None of the above

Answer

constant function

Answer

periodic function with period T

Answer

non-periodic function

Question 20

f(x) = x |x|, then choose the correct statement

Accepted Answer

f(x) is differentiable,

Answer

f(x) is strictly decreasing function

Answer

f(x) is not monotonic

Answer

f(x) is differentiable , except at x=0

Functions Of One,Two Or Three Real Variables - 5 - Free MCQ Practice Test

MCQ Practice Test & Solutions: Test: Functions Of One,Two Or Three Real Variables - 5 (20 Questions)

Let

then,

If f(x) = ax + b, where a and b are integers, f(–1) = – 5 and f(3) = 3, then a and b are equal to

Let

then,

For the function
f(x, y) = x³ + y³ - 3x — 12y + 20 has,

The g -1({0}) for the function g(x)= ⌊x⌋ is ___________

The function f(x) = has

If f(x) = then
(i)f(x) = 1
(ii) f(x) = 2
(iii) f (x) =2
Q. Which of these statement(s) is/are correct?

If f(x) = (x² - 1) |x² - 3x + 2 | + cos (|x|), then set of point of non - differentiability is

If f(y) = then f(x) is

Let us consider the pair of ordered pair of sequences
(a_n , b_n) and (c_n, d_n) such that
= (a,b) and (c_n, d_n) = (a,b), then does not exists, if

Let

then,

Let
f(x,y)={x−yx3+y3,0,(x,y)=(0,0)(x,y)=(0,0)
then,

Let
f(x) =

then at (0, 0)

Let

then,

Consider the function f(x) = |x³| where x is real, then the function f (x) at y = 0 is

If f(x) = then

Let f : [0, 10] → [0 ,10] be continuous function then

The derivative of a periodic function with period T is

f(x) = x |x|, then choose the correct statement

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Functions Of One,Two Or Three Real Variables - 5 - Free MCQ Practice Test

MCQ Practice Test & Solutions: Test: Functions Of One,Two Or Three Real Variables - 5 (20 Questions)

Let then,

If f(x) = ax + b, where a and b are integers, f(–1) = – 5 and f(3) = 3, then a and b are equal to

Let then,

For the function f(x, y) = x3 + y3 - 3x — 12y + 20 has,

The g -1({0}) for the function g(x)= ⌊x⌋ is ___________

The function f(x) = has

If f(x) = then (i)f(x) = 1 (ii) f(x) = 2 (iii) f (x) =2 Q. Which of these statement(s) is/are correct?

If f(x) = (x2 - 1) |x2 - 3x + 2 | + cos (|x|), then set of point of non - differentiability is

If f(y) = then f(x) is

Let us consider the pair of ordered pair of sequences (an , bn) and (cn, dn) such that = (a,b) and (cn, dn) = (a,b), then does not exists, if

Let then,

Let f(x,y)={x−yx3+y3​,0,​(x,y)=(0,0)(x,y)=(0,0)​ then,

Let f(x) = then at (0, 0)

Let then,

Consider the function f(x) = |x3| where x is real, then the function f (x) at y = 0 is

If f(x) = then

Let f : [0, 10] → [0 ,10] be continuous function then

​The derivative of a periodic function with period T is

f(x) = x |x|, then choose the correct statement

Topic-wise Tests & Solved Examples for Mathematics

Topic-wise Tests & Solved Examples for Mathematics

Top Courses for Mathematics

About this Mathematics Practice Test

Explore more Mathematics Study Resources

Let

then,

Let

then,

For the function
f(x, y) = x³ + y³ - 3x — 12y + 20 has,

If f(x) = then
(i)f(x) = 1
(ii) f(x) = 2
(iii) f (x) =2
Q. Which of these statement(s) is/are correct?

If f(x) = (x² - 1) |x² - 3x + 2 | + cos (|x|), then set of point of non - differentiability is

Let us consider the pair of ordered pair of sequences
(a_n , b_n) and (c_n, d_n) such that
= (a,b) and (c_n, d_n) = (a,b), then does not exists, if

Let

then,

Let
f(x,y)={x−yx3+y3,0,(x,y)=(0,0)(x,y)=(0,0)
then,

Let
f(x) =

then at (0, 0)

Let

then,

Consider the function f(x) = |x³| where x is real, then the function f (x) at y = 0 is

The derivative of a periodic function with period T is