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Week 5 Mathematics 1 Questions | Prasnya
Mathematics 1 > Week 5
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Type:
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Difficulty:
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Year:
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35Q
01
Which of the following functions are one-one?
Multiple correct
EASY
4 marks
03 August 2025
02
Find the domain of
g
∘
f
g\circ f
g
∘
f
.
Comprehension
EASY
3 marks
03 August 2025
03
Find the value of
(
g
∘
f
∘
g
∘
f
)
(
2
)
(g\circ f\circ g\circ f)(2)
(
g
∘
f
∘
g
∘
f
)
(
2
)
.
Comprehension
EASY
3 marks
03 August 2025
04
Let functions
f
(
x
)
=
log
(
x
2
)
f(x)=\log(x^2)
f
(
x
)
=
lo
g
(
x
2
)
,
g
(
x
)
=
2
log
x
g(x)=2\log x
g
(
x
)
=
2
lo
g
x
, and
h
(
x
)
=
(
log
x
)
2
h(x)=(\log x)^2
h
(
x
)
=
(
lo
g
x
)
2
respectively. Choose the set of correct options.
Single correct
MEDIUM
4 marks
16 March 2025
05
Choose the set of correct options.
Single correct
EASY
3 marks
16 March 2025
06
Let
f
f
f
be a function whose domain is
[
−
5
,
7
]
[-5,7]
[
−
5
,
7
]
. If
g
(
x
)
=
∣
2
x
+
5
∣
g(x)=|2x+5|
g
(
x
)
=
∣2
x
+
5∣
and
[
a
,
b
]
[a,b]
[
a
,
b
]
denotes the largest interval which can be a domain for the composition function
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
, then find the value of
a
+
b
a+b
a
+
b
.
Numerical
MEDIUM
4 marks
16 March 2025
07
If
4
m
−
n
=
0
4m-n=0
4
m
−
n
=
0
, then find the value of
16
m
2
n
+
27
n
9
6
m
\displaystyle \frac{16^m}{2^n}+\frac{27^n}{9^{6m}}
2
n
1
6
m
+
9
6
m
2
7
n
.
Comprehension
EASY
2 marks
16 March 2025
08
Consider a function
f
(
x
)
=
2
x
+
4
3
x
f(x)=\frac{2x+4}{3x}
f
(
x
)
=
3
x
2
x
+
4
. If
g
(
x
)
g(x)
g
(
x
)
is the inverse function of
f
(
x
)
f(x)
f
(
x
)
, then which of the following option(s) is(are) true?
Multiple correct
MEDIUM
2 marks
16 March 2025
09
For item (i) in the given composition table, choose the correct matching option.
Comprehension
EASY
2 marks
01 December 2024
10
For item (ii) in the given composition table, choose the correct matching option.
Comprehension
EASY
2 marks
01 December 2024
11
For item (iii) in the given composition table, choose the correct matching option.
Comprehension
EASY
2 marks
01 December 2024
12
For item (iv) in the given composition table, choose the correct matching option.
Comprehension
EASY
2 marks
01 December 2024
13
If
f
(
x
)
=
x
2
f(x)=x^2
f
(
x
)
=
x
2
and
h
(
x
)
=
x
−
1
h(x)=x-1
h
(
x
)
=
x
−
1
, then which of the following option is/are correct?
Single correct
MEDIUM
3 marks
01 December 2024
14
Find the domain of the inverse function of
y
=
x
3
−
1
y=x^3-1
y
=
x
3
−
1
.
Single correct
EASY
2 marks
04 August 2024
15
Choose the correct option(s) from the following.
Multiple correct
MEDIUM
4 marks
24 March 2024
16
Find the smallest value of
a
a
a
such that the function
f
f
f
is defined for all real numbers.
Comprehension
MEDIUM
3 marks
24 March 2024
17
Find the largest value of
a
a
a
such that the function
f
f
f
is defined for all real numbers and satisfies the horizontal line test.
Comprehension
HARD
3 marks
24 March 2024
18
For item (i) in the given composition table, choose the correct matching option.
Comprehension
MEDIUM
2 marks
24 March 2024
19
For item (ii) in the given composition table, choose the correct matching option.
Comprehension
MEDIUM
2 marks
24 March 2024
20
For item (iii) in the given composition table, choose the correct matching option.
Comprehension
MEDIUM
2 marks
24 March 2024
21
For item (iv) in the given composition table, choose the correct matching option.
Comprehension
MEDIUM
2 marks
24 March 2024
22
Find the maximum value of
h
(
x
)
h(x)
h
(
x
)
.
Comprehension
MEDIUM
3 marks
03 December 2023
23
Consider the functions
f
(
x
)
=
x
+
2
f(x)=\sqrt{x+2}
f
(
x
)
=
x
+
2
and
g
(
x
)
=
log
(
1
+
x
2
)
g(x)=\log(1+x^2)
g
(
x
)
=
lo
g
(
1
+
x
2
)
. Which of the following options is/are true?
Multiple correct
MEDIUM
4 marks
03 December 2023
24
Which of the following options is/are true?
Comprehension
MEDIUM
3 marks
06 August 2023
25
Define a function
f
(
x
)
=
{
x
2
+
1
,
x
<
1
,
x
3
,
x
≥
1.
f(x)=\begin{cases}x^2+1, & x<1,\\ x^3, & x\ge1.\end{cases}
f
(
x
)
=
{
x
2
+
1
,
x
3
,
x
<
1
,
x
≥
1.
Which of the following options is/are true?
Multiple correct
MEDIUM
4 marks
06 August 2023
26
Consider the functions
f
(
x
)
=
log
x
2
f(x)=\log x^2
f
(
x
)
=
lo
g
x
2
and
g
(
x
)
=
2
x
+
1
g(x)=2x+1
g
(
x
)
=
2
x
+
1
. Which of the following options is/are true?
Multiple correct
MEDIUM
5 marks
06 August 2023
27
Which of the following options is/are true?
Comprehension
MEDIUM
4 marks
02 April 2023
28
For what value of
x
x
x
does the function
h
(
x
)
h(x)
h
(
x
)
have value
64
64
64
?
Comprehension
EASY
3 marks
02 April 2023
29
Which of the following options is/are true?
Comprehension
EASY
4 marks
02 April 2023
30
Which of the following is the graph of the function
f
(
x
)
=
e
∣
x
∣
f(x)=e^{|x|}
f
(
x
)
=
e
∣
x
∣
?
Comprehension
EASY
2 marks
02 April 2023
31
Consider the graph of a function
f
(
x
)
f(x)
f
(
x
)
in the interval
[
−
2
,
6
]
[-2,6]
[
−
2
,
6
]
, where a bullet point represents a point included in the line segment and a circle represents a point not included in the line segment. Which of the following options is/are true?
Multiple correct
MEDIUM
4 marks
02 April 2023
32
Choose the set of correct options.
Multiple correct
MEDIUM
5 marks
20 November 2022
33
Let
f
f
f
be a function whose domain is
[
−
5
,
7
]
[-5,7]
[
−
5
,
7
]
. If
g
(
x
)
=
∣
2
x
+
5
∣
g(x)=|2x+5|
g
(
x
)
=
∣2
x
+
5∣
and
[
a
,
b
]
⊂
R
[a,b]\subset\mathbb{R}
[
a
,
b
]
⊂
R
denotes the largest interval which can be a domain for the composition function
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
, then find the value of
a
+
b
a+b
a
+
b
.
Numerical
MEDIUM
5 marks
20 November 2022
34
Find the maximum value of
g
(
x
)
g(x)
g
(
x
)
.
Comprehension
EASY
2 marks
20 November 2022
35
Find the maximum value of
h
(
x
)
h(x)
h
(
x
)
.
Comprehension
MEDIUM
3 marks
20 November 2022
Showing 35 questions.
Mathematics 1 > Week 5
All PYQs
Topic-Wise PYQs
Start Weekly Test
Mock tests
Week mock
Topic mock
Subject mock
Type:
All
Difficulty:
All
Year:
All
35Q
01
Which of the following functions are one-one?
Multiple correct
EASY
4 marks
03 August 2025
02
Find the domain of
g
∘
f
g\circ f
g
∘
f
.
Comprehension
EASY
3 marks
03 August 2025
03
Find the value of
(
g
∘
f
∘
g
∘
f
)
(
2
)
(g\circ f\circ g\circ f)(2)
(
g
∘
f
∘
g
∘
f
)
(
2
)
.
Comprehension
EASY
3 marks
03 August 2025
04
Let functions
f
(
x
)
=
log
(
x
2
)
f(x)=\log(x^2)
f
(
x
)
=
lo
g
(
x
2
)
,
g
(
x
)
=
2
log
x
g(x)=2\log x
g
(
x
)
=
2
lo
g
x
, and
h
(
x
)
=
(
log
x
)
2
h(x)=(\log x)^2
h
(
x
)
=
(
lo
g
x
)
2
respectively. Choose the set of correct options.
Single correct
MEDIUM
4 marks
16 March 2025
05
Choose the set of correct options.
Single correct
EASY
3 marks
16 March 2025
06
Let
f
f
f
be a function whose domain is
[
−
5
,
7
]
[-5,7]
[
−
5
,
7
]
. If
g
(
x
)
=
∣
2
x
+
5
∣
g(x)=|2x+5|
g
(
x
)
=
∣2
x
+
5∣
and
[
a
,
b
]
[a,b]
[
a
,
b
]
denotes the largest interval which can be a domain for the composition function
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
, then find the value of
a
+
b
a+b
a
+
b
.
Numerical
MEDIUM
4 marks
16 March 2025
07
If
4
m
−
n
=
0
4m-n=0
4
m
−
n
=
0
, then find the value of
16
m
2
n
+
27
n
9
6
m
\displaystyle \frac{16^m}{2^n}+\frac{27^n}{9^{6m}}
2
n
1
6
m
+
9
6
m
2
7
n
.
Comprehension
EASY
2 marks
16 March 2025
08
Consider a function
f
(
x
)
=
2
x
+
4
3
x
f(x)=\frac{2x+4}{3x}
f
(
x
)
=
3
x
2
x
+
4
. If
g
(
x
)
g(x)
g
(
x
)
is the inverse function of
f
(
x
)
f(x)
f
(
x
)
, then which of the following option(s) is(are) true?
Multiple correct
MEDIUM
2 marks
16 March 2025
09
For item (i) in the given composition table, choose the correct matching option.
Comprehension
EASY
2 marks
01 December 2024
10
For item (ii) in the given composition table, choose the correct matching option.
Comprehension
EASY
2 marks
01 December 2024
11
For item (iii) in the given composition table, choose the correct matching option.
Comprehension
EASY
2 marks
01 December 2024
12
For item (iv) in the given composition table, choose the correct matching option.
Comprehension
EASY
2 marks
01 December 2024
13
If
f
(
x
)
=
x
2
f(x)=x^2
f
(
x
)
=
x
2
and
h
(
x
)
=
x
−
1
h(x)=x-1
h
(
x
)
=
x
−
1
, then which of the following option is/are correct?
Single correct
MEDIUM
3 marks
01 December 2024
14
Find the domain of the inverse function of
y
=
x
3
−
1
y=x^3-1
y
=
x
3
−
1
.
Single correct
EASY
2 marks
04 August 2024
15
Choose the correct option(s) from the following.
Multiple correct
MEDIUM
4 marks
24 March 2024
16
Find the smallest value of
a
a
a
such that the function
f
f
f
is defined for all real numbers.
Comprehension
MEDIUM
3 marks
24 March 2024
17
Find the largest value of
a
a
a
such that the function
f
f
f
is defined for all real numbers and satisfies the horizontal line test.
Comprehension
HARD
3 marks
24 March 2024
18
For item (i) in the given composition table, choose the correct matching option.
Comprehension
MEDIUM
2 marks
24 March 2024
19
For item (ii) in the given composition table, choose the correct matching option.
Comprehension
MEDIUM
2 marks
24 March 2024
20
For item (iii) in the given composition table, choose the correct matching option.
Comprehension
MEDIUM
2 marks
24 March 2024
21
For item (iv) in the given composition table, choose the correct matching option.
Comprehension
MEDIUM
2 marks
24 March 2024
22
Find the maximum value of
h
(
x
)
h(x)
h
(
x
)
.
Comprehension
MEDIUM
3 marks
03 December 2023
23
Consider the functions
f
(
x
)
=
x
+
2
f(x)=\sqrt{x+2}
f
(
x
)
=
x
+
2
and
g
(
x
)
=
log
(
1
+
x
2
)
g(x)=\log(1+x^2)
g
(
x
)
=
lo
g
(
1
+
x
2
)
. Which of the following options is/are true?
Multiple correct
MEDIUM
4 marks
03 December 2023
24
Which of the following options is/are true?
Comprehension
MEDIUM
3 marks
06 August 2023
25
Define a function
f
(
x
)
=
{
x
2
+
1
,
x
<
1
,
x
3
,
x
≥
1.
f(x)=\begin{cases}x^2+1, & x<1,\\ x^3, & x\ge1.\end{cases}
f
(
x
)
=
{
x
2
+
1
,
x
3
,
x
<
1
,
x
≥
1.
Which of the following options is/are true?
Multiple correct
MEDIUM
4 marks
06 August 2023
26
Consider the functions
f
(
x
)
=
log
x
2
f(x)=\log x^2
f
(
x
)
=
lo
g
x
2
and
g
(
x
)
=
2
x
+
1
g(x)=2x+1
g
(
x
)
=
2
x
+
1
. Which of the following options is/are true?
Multiple correct
MEDIUM
5 marks
06 August 2023
27
Which of the following options is/are true?
Comprehension
MEDIUM
4 marks
02 April 2023
28
For what value of
x
x
x
does the function
h
(
x
)
h(x)
h
(
x
)
have value
64
64
64
?
Comprehension
EASY
3 marks
02 April 2023
29
Which of the following options is/are true?
Comprehension
EASY
4 marks
02 April 2023
30
Which of the following is the graph of the function
f
(
x
)
=
e
∣
x
∣
f(x)=e^{|x|}
f
(
x
)
=
e
∣
x
∣
?
Comprehension
EASY
2 marks
02 April 2023
31
Consider the graph of a function
f
(
x
)
f(x)
f
(
x
)
in the interval
[
−
2
,
6
]
[-2,6]
[
−
2
,
6
]
, where a bullet point represents a point included in the line segment and a circle represents a point not included in the line segment. Which of the following options is/are true?
Multiple correct
MEDIUM
4 marks
02 April 2023
32
Choose the set of correct options.
Multiple correct
MEDIUM
5 marks
20 November 2022
33
Let
f
f
f
be a function whose domain is
[
−
5
,
7
]
[-5,7]
[
−
5
,
7
]
. If
g
(
x
)
=
∣
2
x
+
5
∣
g(x)=|2x+5|
g
(
x
)
=
∣2
x
+
5∣
and
[
a
,
b
]
⊂
R
[a,b]\subset\mathbb{R}
[
a
,
b
]
⊂
R
denotes the largest interval which can be a domain for the composition function
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
, then find the value of
a
+
b
a+b
a
+
b
.
Numerical
MEDIUM
5 marks
20 November 2022
34
Find the maximum value of
g
(
x
)
g(x)
g
(
x
)
.
Comprehension
EASY
2 marks
20 November 2022
35
Find the maximum value of
h
(
x
)
h(x)
h
(
x
)
.
Comprehension
MEDIUM
3 marks
20 November 2022
Showing 35 questions.
