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

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


Test Description

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

Test: Functions Of One,Two Or Three Real Variables - 5 for Mathematics 2024 is part of Mathematics preparation. The Test: Functions Of One,Two Or Three Real Variables - 5 questions and answers have been prepared according to the Mathematics exam syllabus.The Test: Functions Of One,Two Or Three Real Variables - 5 MCQs are made for Mathematics 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Functions Of One,Two Or Three Real Variables - 5 below.
Solutions of Test: Functions Of One,Two Or Three Real Variables - 5 questions in English are available as part of our course for Mathematics & Test: Functions Of One,Two Or Three Real Variables - 5 solutions in Hindi for Mathematics course. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free. Attempt Test: Functions Of One,Two Or Three Real Variables - 5 | 20 questions in 60 minutes | Mock test for Mathematics preparation | Free important questions MCQ to study for Mathematics Exam | Download free PDF with solutions
Test: Functions Of One,Two Or Three Real Variables - 5 - Question 1

Detailed Solution for Test: Functions Of One,Two Or Three Real Variables - 5 - Question 1


Test: Functions Of One,Two Or Three Real Variables - 5 - Question 2

Let

then,

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test: Functions Of One,Two Or Three Real Variables - 5 - 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

Detailed Solution for Test: Functions Of One,Two Or Three Real Variables - 5 - Question 3

Given,

f(x) = ax + b

And

f(-1) = -5

a(-1) + b = -5

-a + b = -5….(i)

Also, f(3) = 3

a(3) + b = 3

3a + b = 3….(ii)

From (i) and (ii),

a = 2, b = -3

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 4

Let

then,

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

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

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 6

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

Detailed Solution for Test: Functions Of One,Two Or Three Real Variables - 5 - Question 6

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.

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 7

The function f(x) = has 

Detailed Solution for Test: Functions Of One,Two Or Three Real Variables - 5 - Question 7


irremovable discontinuity.

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

Detailed Solution for Test: Functions Of One,Two Or Three Real Variables - 5 - Question 8

Given that

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

and 

 
 

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 9

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

Detailed Solution for Test: Functions Of One,Two Or Three Real Variables - 5 - Question 9

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.

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 10

If f(y) = then f(x) is

Detailed Solution for Test: Functions Of One,Two Or Three Real Variables - 5 - Question 10

Given that


Clearly f(x) is discontinuous for

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

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 12

Let

then,

Detailed Solution for Test: Functions Of One,Two Or Three Real Variables - 5 - Question 12

The function f(x,y) is given by:

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 13

Let

then,

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 14

Let
f(x) = 

then at (0, 0)

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 15

Let

then,

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 16

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

Detailed Solution for Test: Functions Of One,Two Or Three Real Variables - 5 - Question 16

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.

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 17

If f(x) = then

Detailed Solution for Test: Functions Of One,Two Or Three Real Variables - 5 - Question 17

Given that

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

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 18

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

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 19

​The derivative of a periodic function with period T is

Test: Functions Of One,Two Or Three Real Variables - 5 - Question 20

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

Information about Test: Functions Of One,Two Or Three Real Variables - 5 Page
In this test you can find the Exam questions for Test: Functions Of One,Two Or Three Real Variables - 5 solved & explained in the simplest way possible. Besides giving Questions and answers for Test: Functions Of One,Two Or Three Real Variables - 5, EduRev gives you an ample number of Online tests for practice
Download as PDF