BITSAT SERIES Mathematics
Continuity And Differentiability
29 previous year questions.
Volume: 29 Ques
Yield: High
High-Yield Trend
7
2023 2
2021 2
2020 2
2019 2
2018 1
2017 3
2016 2
2015 1
2014 2
2012 2
2011 3
2010 Chapter Questions 29 MCQs
01
PYQ 2010
medium
mathematics ID: bitsat-2
Let f(x)=(eˣ-1)²(xa)(1+x4) for x≠0, and f(0)=12.
If f(x) is continuous at x=0, then the value of a is
1
1
2
-1
3
2
4
3
02
PYQ 2010
medium
mathematics ID: bitsat-2
Which of the following functions is differentiable at x=0?
1
(|x|)+|x|
2
(|x|)-|x|
3
(|x|)+|x|
4
(|x|)-|x|
03
PYQ 2010
medium
mathematics ID: bitsat-2
Let f(x)=cases
ax²+1, & x>1
x+a, & x\le1 cases Then f(x) is derivable at x=1, if
x+a, & x\le1 cases Then f(x) is derivable at x=1, if
1
a=2
2
a=1
3
a=0
4
a=\frac12
04
PYQ 2011
medium
mathematics ID: bitsat-2
If y=xˣ^², then dydx is equal to:
1
2ln x
2
2ln x+1
3
(ln x+1)xˣ^²
4
None of these
05
PYQ 2011
medium
mathematics ID: bitsat-2
The function f(x)=(x-1)√|x| is at x=1:
1
discontinuous
2
continuous but not differentiable
3
differentiable with f'(1)=0
4
differentiable with f'(1)≠0
06
PYQ 2012
medium
mathematics ID: bitsat-2
If and , then is:
1
2
3
4
07
PYQ 2012
medium
mathematics ID: bitsat-2
Let for all , where . If and , then is equal to:
1
6
2
3
3
1
4
None of these
08
PYQ 2014
medium
mathematics ID: bitsat-2
Let
Then which one of the following is true?
1
is differentiable at and
2
is differentiable at but not at
3
is differentiable at but not at
4
is neither differentiable at nor at
09
PYQ 2015
medium
mathematics ID: bitsat-2
Let be a function such that
for all .
If is differentiable at , then which one of the following is incorrect?
1
is continuous,
2
is constant,
3
is differentiable,
4
is differentiable only on a finite interval containing zero
10
PYQ 2015
medium
mathematics ID: bitsat-2
If , then is
1
2
3
4
11
PYQ 2016
medium
mathematics ID: bitsat-2
If
f(x)=
begincases
(xlog(cos x))/(log(1+x²)), & x\ne0
0, & x=0 endcases then f(x) is
0, & x=0 endcases then f(x) is
1
continuous as well as differentiable at x=0
2
continuous but not differentiable at x=0
3
differentiable but not continuous at x=0
4
neither continuous nor differentiable at x=0
12
PYQ 2016
medium
mathematics ID: bitsat-2
The number of points at which the function
f(x)=(1)/(log|x|)
is discontinuous is
1
1
2
2
3
3
4
4
13
PYQ 2016
medium
mathematics ID: bitsat-2
For any differentiable function of ,
1
2
3
4
x
14
PYQ 2017
medium
mathematics ID: bitsat-2
If
then is
then is
1
continuous as well as differentiable at x=0
2
continuous but not differentiable at x=0
3
differentiable but not continuous at x=0
4
neither continuous nor differentiable at x=0
15
PYQ 2018
medium
mathematics ID: bitsat-2
If
then:
then:
1
is continuous at
2
is continuous at
3
is continuous at
4
f(x) is discontinuous at x=(3π)/(4)
16
PYQ 2018
medium
mathematics ID: bitsat-2
If
f(x)=
begincases
sin x, & when x is rational
cos x, & when x is irrational endcases then the function is:
cos x, & when x is irrational endcases then the function is:
1
discontinuous at x=nπ+π/4
2
continuous at x=nπ+π/4
3
discontinuous at all x
4
none of these
17
PYQ 2019
medium
mathematics ID: bitsat-2
Let f:RtoR be a function such that f(x+y)=f(x)+f(y).
If f(x) is differentiable at x=0, then which one of the following is incorrect?
1
is continuous,
2
is constant,
3
is differentiable,
4
f(x) is differentiable only in a finite interval containing zero
18
PYQ 2019
medium
mathematics ID: bitsat-2
If
then at , is:
then at , is:
1
has no limit
2
is not continuous
3
is continuous but not differentiable
4
is differentiable
19
PYQ 2020
medium
mathematics ID: bitsat-2
If
f(x)=
begincases
(xlog(cos x))/(log(1+x²)), & x≠0
0, & x=0 endcases then f(x) is
0, & x=0 endcases then f(x) is
1
continuous as well as differentiable at x=0
2
continuous but not differentiable at x=0
3
differentiable but not continuous at x=0
4
neither continuous nor differentiable at x=0
20
PYQ 2020
medium
mathematics ID: bitsat-2
The number of points at which the function
f(x)=(1)/(log|x|)
is discontinuous is
1
2
3
4
4
21
PYQ 2021
medium
mathematics ID: bitsat-2
If
f(x)=
begincases
(xlog(cos x))/(log(1+x²)), & x≠ 0
0, & x=0 endcases then f(x) is
0, & x=0 endcases then f(x) is
1
continuous as well as differentiable at x=0
2
continuous but not differentiable at x=0
3
differentiable but not continuous at x=0
4
neither continuous nor differentiable at x=0
22
PYQ 2021
medium
mathematics ID: bitsat-2
The function f(x)=x-|x-x²|,-1≤ x\le1 is
1
[-1,1]
2
(-1,1)
3
[-1,1] but not differentiable at 0
4
(-1,1)setminus0
23
PYQ 2023
medium
mathematics ID: bitsat-2
The equation of a common tangent to the parabolas and is:
1
2
3
4
24
PYQ 2023
medium
mathematics ID: bitsat-2
The function is an increasing function in:
1
2
3
4
25
PYQ 2023
medium
mathematics ID: bitsat-2
The curve given by has a tangent parallel to the Y-axis at the point:
1
2
3
4
None of these
26
PYQ 2023
medium
mathematics ID: bitsat-2
Find:
1
1
2
-1
3
Does not exist
4
None of these
27
PYQ 2023
medium
mathematics ID: bitsat-2
If , then at is:
1
-2
2
2
3
4
None of these
28
PYQ 2023
medium
mathematics ID: bitsat-2
The lines
and
are coplanar if:
1
or
2
or
3
or
4
or
29
PYQ 2023
medium
mathematics ID: bitsat-2
The maximum value of subject to the constraints:
1
10
2
26
3
35
4
70