Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced
Test Description
25 Questions MCQ Test Maths 35 Years JEE Main & Advanced Past year Papers | Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced
Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced for JEE 2022 is part of Maths 35 Years JEE Main & Advanced Past year Papers preparation. The Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced questions and answers have been
prepared according to the JEE exam syllabus.The Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced MCQs are made for JEE 2022 Exam. Find important
definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced below.
Solutions of Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced questions in English are available as part of our Maths 35 Years JEE Main & Advanced Past year Papers for JEE & Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced solutions in
Hindi for Maths 35 Years JEE Main & Advanced Past year Papers course. Download more important topics, notes, lectures and mock
test series for JEE Exam by signing up for free. Attempt Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced | 25 questions in 50 minutes | Mock test for JEE preparation | Free important questions MCQ to study Maths 35 Years JEE Main & Advanced Past year Papers for JEE Exam | Download free PDF with solutions
1 Crore+ students have signed up on EduRev. Have you?
*Multiple options can be correct
Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 1
Detailed Solution for Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 3
The graph of f (x) = 1 + | sin x | is as shown in the fig.
From graph it is clear that function is continuous every where but not differentiable at integral multiples of π (∴ at these points curve has sharp turnings)
*Multiple options can be correct
Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 4
Let [x] denote the greatest integer less than or equal to x. If f(x) = [x sin π x], then f(x) is
Detailed Solution for Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 4
We have, for – 1 < x < 1 ⇒ 0 < x sin π x < 1/2
∴ f (x) = [x sin π x] = 0
Also x sin p x becomes negative and numerically less than 1 when x is slightly greater than 1 and so by definition of [x],
f (x) = [x sin π x] = – 1 when 1 < x < 1 + h
Thus f (x) is constant and equal to 0 in the closed interval [– 1, 1] and so f (x) is continuous and differentiable in the open interval (– 1, 1).
At x = 1, f (x) is clearly discontinuous, since f (1– 0) = 0 and f (1 + 0) = – 1 and f (x) is non-differentiable at x = 1
*Multiple options can be correct
Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 5
Detailed Solution for Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 6
∴ f is differentiable at x = 1 and hence continuous at x = 1.
Again, Lf ' (3) = – 1 and Rf ' (3) = 1
⇒ Lf ' (3) ≠ Rf ' (3)
⇒ f is not differentiable at x = 3
*Multiple options can be correct
Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 7
Detailed Solution for Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 18
Also at x = 0
Lf '(0) = sin 0 = 0; Rf '(0) = 1 – 0 = 1
∴ Lf '(0) ≠ Rf '(0)
⇒ f is not differentiable at x = 0
At x = 1
Lf '(1) = R'f (1) ⇒ f is differentiable at x = 1.
which is differentiable.
∴ All four options are correct.
*Multiple options can be correct
Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 19
For every pair of continuous functions f, g : [0, 1] → R such that max {f ( x) :x ∈[ 0,1]} = max {g (x) :x ∈[ 0,1]} , the correct statement(s) is (are):
Detailed Solution for Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 22
Let f and g be maximum at c_{1} and c_{2} respectively,
which shows that (a) and (d) are correct.
*Multiple options can be correct
Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 23
Let g : R → R be a differentiable function with g(0) = 0, g'(0) = 0 and g'(1) ≠ 0. Let and Let (foh)(x) denote f(h(x)) and (hof)(x) denote h(f(x)). Then which of the following is (are) true?
Detailed Solution for Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 23
∴ hof is differentiable at x = 0.
*Multiple options can be correct
Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 24
Let be defined by f (x) = a cos (|x^{3} –x|) + b |x| sin (|x^{3} +x|).
Then f is
Detailed Solution for Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 24
f(x) = a cos^{3}(|x^{3 }–x|) + b |x| sin (|x^{3} + x|)
(a) If a = 0, b = 1
⇒ f(x) = |x| sin |x^{3} + x|
= x sin (x^{3} + x), x ∈ R
∴ f is differentiable every where.
(b), (c) If a = 1, b = 0 ⇒ f(x) = cos^{3} (|x^{3} – x|)
= cos^{3}(x^{3} – x)
which is differentiable every where.
(d) when a = 1, b = 1, f(x) = cos(x^{3} – x) + x sin (x^{3} + x) which is differentiable at x = 1
∴ Only a and b are the correct options.
*Multiple options can be correct
Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 25
be fun ctions defined by f (x) = [x^{2}–3] and g(x) = |x| f (x) + |4x–7 | f (x), where [y] denotes the greatest integer less than or equal to y for y ∈ R. Then
Detailed Solution for Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced - Question 25
f(x) = [x^{2} – 3] is discontinuous at all integral points in
∴ f is discontinuous exactly at four points in
Also g (x) = (|x| + |4x- 7|)f (x)
Here f is not differentiable at
and |x| + |4x – 7| is not differentiable at 0 and 7/4
∴ g(x) becomes differentiable at x = 7/4
Hence g(x) is non-differentiable at four points i.e.
Information about Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced Page
In this test you can find the Exam questions for Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced solved & explained in the simplest way possible.
Besides giving Questions and answers for Test: MCQs (One or More Correct Option): Limits, Continuity and Differentiability | JEE Advanced, EduRev gives you an ample number of Online tests for practice