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Test: Continuity And Differentiability - JEE MCQ


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25 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Continuity And Differentiability

Test: Continuity And Differentiability for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Continuity And Differentiability questions and answers have been prepared according to the JEE exam syllabus.The Test: Continuity And Differentiability MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Continuity And Differentiability below.
Solutions of Test: Continuity And Differentiability questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & Test: Continuity And Differentiability solutions in Hindi for Mathematics (Maths) Class 12 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Continuity And Differentiability | 25 questions in 25 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
Test: Continuity And Differentiability - Question 1
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Test: Continuity And Differentiability - Question 3
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Let f(x) = x – [x], then f ‘ (x) = 1 for

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f(x) = x -[x] is derivable at all x ∈ R – I , and f ‘(x) = 1 for all x ∈ R – I .

Test: Continuity And Differentiability - Question 4
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f (x) = max {x, x3},then the number of points where f (x) is not differentiable, are
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f(x)=m{x,x3}
= x;x<−1 and
= x3;−1≤x≤0
⇒ f(x)=x;0≤x≤1 and
= x3;x≥1
∴ f(x)=1;x<−1
∴ f′(x)=3x2;− 1≤x≤0 and =1
 0<x<1
Hence answer is 3

Test: Continuity And Differentiability - Question 5
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If f(x) = tan-1x and g(x) = , then
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Test: Continuity And Differentiability - Question 6
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Test: Continuity And Differentiability - Question 7
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The function f (x) = 1 + | sin x l is
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f(x) = 1+|sinx| is not derivable at those x for which sinx = 0, however, 1+|sinx| is continuous everywhere (being the sum of two continuous functions)

Test: Continuity And Differentiability - Question 8
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Let f (x + y) = f(x) + f(y) ∀ x, y ∈ R. Suppose that f (6) = 5 and f ‘ (0) = 1, then f ‘ (6) is equal to
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Test: Continuity And Differentiability - Question 9
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Test: Continuity And Differentiability - Question 10
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Derivative of log | x | w.r.t. | x | is
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d/dx(log|x|)
= 1/|x|

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Test: Continuity And Differentiability - Question 12
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The function, f (x) = (x – a) sin   for x ≠ a and f (a) = 0 is
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Test: Continuity And Differentiability - Question 13
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If x sin (a + y) = sin y, then  is equal to
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x sin(a+y) = sin y
⇒ 

 

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Test: Continuity And Differentiability - Question 15
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now put x=a ,and you will get (b) 1/2a

Test: Continuity And Differentiability - Question 16
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If [x] stands for the integral part of x, then
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If c is an integer , then  Does not exist.

Test: Continuity And Differentiability - Question 17
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Let f (x) = [x], then f (x) is
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f(x) = [x] is derivable at all x except at integral points i.e. on R – I .

Test: Continuity And Differentiability - Question 18
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Test: Continuity And Differentiability - Question 19
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Test: Continuity And Differentiability - Question 20
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Test: Continuity And Differentiability - Question 21
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Test: Continuity And Differentiability - Question 22
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The function f (x) = [x] is
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The function f (x) = [x] isdiscontinuous only for all integral values of x.

Test: Continuity And Differentiability - Question 23
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Let f be a function satisfying f(x + y) = f(x) + f(y) for all x, y ∈ R, then f ‘ (x) =
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Test: Continuity And Differentiability - Question 24
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Test: Continuity And Differentiability - Question 25
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If x = at2, y = 2at, then  is equal to 
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