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

one repeated limit exists but other does not exists 

double limit exists

both the repeated limit exists

None of these 

a = – 3, b = –1

a = 2, b = – 3

a = 0, b = 2

a = 2, b = 3

exists

does not exists

does not exists

exists

maximum at (1, 2)

minimum at (-1, -2)

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

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

{x | 0 ≤ x < 1} 

{x | 0 ≤ x ≤ 1}

{x | 0 < x ≤ 1} 

{x | 0 < x < 1} 

continuity at x = 0

removable discontinuity at x = 0

irremovable discontinuity at x = 0

none of the above

I and III are correct

I, II and III are correct

I and II are correct

 II alone is correct

{1 ,0 ,2}

{1, 2}

{2}

{0,2}

discontinuous, ∈R

discotinuous, ∈ Q

discontinuous,

discontinuous,

fxy(0, 0) = - 1 

fxy(0,0) =1

f is continuous at origin

f_x(0, 0) does not exists 

f_y{0, 0) does not exists

None of these

f is discontinuous

f posses partial derivative

f is differentiable

None of these

f is differentiableat (0, 0)

f  is not differentiable at (0, 0)

f is continuous at (0, 0)

None of these

continuous but not differentiable

once differentiable but not twice

twice differentiable but not thrice

thrice differentiable

 f is continuous but not differentiable at x = 0

 f is differentiable at x = 0

f is continuous but not differentiable at x=1

f is differentiable at x = 1

f need not to have any fixed point

f has atleast 10 fixed point

f has atleast 9 fixed points

f has atleast one fixed point

constant function

periodic function with period T

non-periodic function

None of the above

f(x) is strictly decreasing function

f(x) is not monotonic

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

f(x) is differentiable,