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


20 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Test: Functions Of One,Two Or Three Real Variables - 5


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This mock test of Test: Functions Of One,Two Or Three Real Variables - 5 for Mathematics helps you for every Mathematics entrance exam. This contains 20 Multiple Choice Questions for Mathematics Test: Functions Of One,Two Or Three Real Variables - 5 (mcq) to study with solutions a complete question bank. The solved questions answers in this Test: Functions Of One,Two Or Three Real Variables - 5 quiz give you a good mix of easy questions and tough questions. Mathematics students definitely take this Test: Functions Of One,Two Or Three Real Variables - 5 exercise for a better result in the exam. You can find other Test: Functions Of One,Two Or Three Real Variables - 5 extra questions, long questions & short questions for Mathematics on EduRev as well by searching above.
QUESTION: 1

Let

then,

Solution:
QUESTION: 2

Let

then,

Solution:
QUESTION: 3

Let

then,

Solution:
QUESTION: 4

Let

then,

Solution:
QUESTION: 5

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

Solution:
QUESTION: 6

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

Solution:

g({0}) for the function g(x) is {x | 0 ≤ x ≤ 1}. Put g(x) = y and find the value of x in terms of y such that [x] = y.

QUESTION: 7

The function f(x) = has 

Solution:


irremovable discontinuity.

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?

Solution:

Given that

Clearly , the value of function is changing at x = l, therefore, we check limit at x = l

and 

 
 

QUESTION: 9

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

Solution:

Given that

Clearly, the rule of the function is changing of x = 1 and 2. So, we shall test the differentiability of f(x) only at the points x = 1, and 2
Clearly Rf'(1) = Lf'(1) and Rf'(2) ≠ Lf'(2) Hence ,f(x) is not differentiable at x = 2.

QUESTION: 10

If f(y) = then f(x) is

Solution:

Given that


Clearly f(x) is discontinuous for

QUESTION: 11

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

Solution:
QUESTION: 12

Let

then,

Solution:
QUESTION: 13

Let

then,

Solution:
QUESTION: 14

Let

then at (0, 0)

Solution:
QUESTION: 15

Let

then,

Solution:
QUESTION: 16

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

Solution:

Given that

It is clear that the funtion is twice differentiable at x = 0 and the other points the function is a polynomial.
Therfore, it is obviously differentiable.

QUESTION: 17

If f(x) = then

Solution:

Given that

Similarly, Lf'(0) = 0
Hence f(x) is differentiable at x = 0.

QUESTION: 18

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

Solution:
QUESTION: 19

​The derivative of a periodic function with period T is

Solution:
QUESTION: 20

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

Solution: