Test: Functions Of One,Two Or Three Real Variables - 6 - Mathematics MCQ

positive number

negative number

zero

None of these

f(a, b) = a 

f(a, b) = a + b

f(a, b) = |b| 

f(a, b) = a – b

Both A and R are correct and R is correct reason of A

Both A and R are correct and R is not correct reason o f A

A is true but R is false

A is false but R is true

f(x)<0,∀ x∈R

f(x) can take any value in R.

f(x)>0,∀ x∈R  

f(x)=0,∀ x∈R

(– 1, ∞]

[ ∞, ∞)

(– ∞, ∞)

[– ∞, ∞]

f_x(a, 0) = 0, where a is constant 

f_y(e, 0) = 0

f_xy{ 1, 0) = 0

f_yx (1, 1 ) = 1

6

9

16

18

rt – s² = 0 and r>0

rt – s²>0 and r = 0

rt – s² < 0 and r = 0

rt – s² > 0 and r > 0

f(x ,y) is continuous at (0, 0)

f(x, y) is discontinuous at (0, 0)

f(x, y) is differentiable at (0, 0)

None of these

​​​​the directional derivative of f at (0,0) in the direction of  is 

the directional derivative of f at (0,0) in the direction of (0, 1 ) is 1

the directional derivative of f at (0,0) in the direction of (1, 0) is 0

f is NOT differentiable at (0,0)

constant function

identity function

sinx

x²

f need not to have any fixed point

f has atleast 10 fixed points

 f has atleast 9 fixed points

f has atleast on fixed point

f (x) is finite discontinuous at x = 2

f (x) is an infinite discontinuous at x = 2

f (x) is continuous at x = 2

None of these

 m > 0

 m > 1/2

m ≥ 1/2

∞

1

0

does not exists

Rolle’s Theorem

Mean value theorem

Intermediate value theorem

None of the above

y is strictly increasing

y is strictly decreasing

y is monotonic

y has finite countably infinite number is zero

2

1

0

None of these

x < y => f(x) ≤ f(y)

x < y => f (x ) ≥ f (y )

x < y => f(x) < f(y)

None of these

x²

Sin x

sin x²

None of these