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IITM BS Week 5 Mathematics 1 Questions | Prasnya
Mathematics 1 > Week 5
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6Q
01
Consider the real-valued functions
f
f
f
and
g
g
g
defined (on appropriate domains) by
f
(
x
)
=
e
x
f(x) = e^x
f
(
x
)
=
e
x
,
g
(
x
)
=
1
−
x
g(x) = \sqrt{1 - x}
g
(
x
)
=
1
−
x
. Which of the following is a valid domain for the composite real-valued function
g
∘
f
g \circ f
g
∘
f
?
Single correct
MEDIUM
3 marks
10 May 2026
02
Consider the functions
f
(
x
)
=
x
+
4
f(x) = \sqrt{x + 4}
f
(
x
)
=
x
+
4
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
21 December 2025
03
What is the value of
f
(
0
)
f(0)
f
(
0
)
?
Comprehension
MEDIUM
2 marks
22 December 2024
04
Consider the functions
f
(
x
)
=
x
+
4
f(x) = \sqrt{x + 4}
f
(
x
)
=
x
+
4
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?
Single correct
MEDIUM
4 marks
01 September 2024
05
What is the value of
f
(
0
)
f(0)
f
(
0
)
?
Comprehension
EASY
2 marks
28 April 2024
06
Two types of bacteria (type A and type B) are present in a glass of water. Suppose
f
A
(
t
)
=
2
(
2
t
+
1
)
2
−
81
f_A(t) = 2^{(2t+1)^2 - 81}
f
A
(
t
)
=
2
(
2
t
+
1
)
2
−
81
and
f
B
(
t
)
=
5
t
2
+
t
−
20
f_B(t) = 5^{t^2 + t - 20}
f
B
(
t
)
=
5
t
2
+
t
−
20
, where
f
A
(
t
)
f_A(t)
f
A
(
t
)
and
f
B
(
t
)
f_B(t)
f
B
(
t
)
represent the number of bacteria of type A and type B at some time
t
t
t
respectively. At what time is the number of type A bacteria equal to the number of type B bacteria?
Numerical
MEDIUM
3 marks
11 December 2022
Showing 6 questions.
Complete question index for this section:
Question 1 (single):
Question 2 (multiple):
Question 3 (comprehension):
Question 4 (single):
Question 5 (comprehension):
Question 6 (integer):
