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Week 6 Mathematics 1 Questions | Prasnya
Mathematics 1 > Week 6
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Year:
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20Q
01
Find the number of solutions of the equation
e
2
x
−
9
e
x
=
−
18
e^{2x}-9e^x=-18
e
2
x
−
9
e
x
=
−
18
.
Numerical
EASY
3 marks
03 August 2025
02
Find the value of
x
x
x
that satisfies
log
2
(
x
+
1
)
−
log
4
(
x
−
3
)
=
2
\log_2(x+1)-\log_4(x-3)=2
lo
g
2
(
x
+
1
)
−
lo
g
4
(
x
−
3
)
=
2
.
Numerical
MEDIUM
4 marks
03 August 2025
03
Choose the correct option for the domain of
f
(
x
)
=
log
3
∣
x
+
1
∣
f(x)=\log_3|x+1|
f
(
x
)
=
lo
g
3
∣
x
+
1∣
.
Comprehension
EASY
3 marks
03 August 2025
04
Suppose
m
,
n
m,n
m
,
n
are two solutions of
f
(
x
)
=
3
f(x)=3
f
(
x
)
=
3
such that
m
<
n
m<n
m
<
n
. Find the value of
n
−
m
n-m
n
−
m
.
Comprehension
MEDIUM
3 marks
03 August 2025
05
If
b
>
0
b>0
b
>
0
and
4
log
x
b
+
9
log
x
x
b
=
1
4\log_x b+9\log_{x\sqrt{x}} b=1
4
lo
g
x
b
+
9
lo
g
x
x
b
=
1
, then the possible value(s) of
x
x
x
is(are)
Single correct
MEDIUM
4 marks
16 March 2025
06
Choose the set of correct options.
Multiple correct
MEDIUM
4 marks
16 March 2025
07
Consider the function
f
(
x
)
=
∣
log
(
x
+
1
)
∣
f(x)=|\log(x+1)|
f
(
x
)
=
∣
lo
g
(
x
+
1
)
∣
. Choose the correct option(s) from the following.
Multiple correct
MEDIUM
4 marks
01 December 2024
08
If
m
log
3
2
+
2
log
3
m
=
8
m^{\log_3 2}+2^{\log_3 m}=8
m
l
o
g
3
2
+
2
l
o
g
3
m
=
8
, then what is the value of
m
m
m
?
Numerical
EASY
4 marks
01 December 2024
09
Choose the set of correct options.
Multiple correct
MEDIUM
3 marks
04 August 2024
10
If
m
log
3
2
+
2
log
3
m
=
8
m^{\log_3 2}+2^{\log_3 m}=8
m
l
o
g
3
2
+
2
l
o
g
3
m
=
8
, then what is the value of
m
m
m
?
Numerical
MEDIUM
2 marks
04 August 2024
11
Find the number of solution(s) of the equation
9
x
+
3
x
−
6
=
0
9^x+3^x-6=0
9
x
+
3
x
−
6
=
0
.
Comprehension
MEDIUM
3 marks
24 March 2024
12
Find the number of solution(s) of the equation
ln
(
7
)
+
ln
(
2
−
4
x
2
)
=
ln
(
14
)
\ln(7)+\ln(2-4x^2)=\ln(14)
ln
(
7
)
+
ln
(
2
−
4
x
2
)
=
ln
(
14
)
.
Comprehension
MEDIUM
3 marks
24 March 2024
13
Find the number of solutions of the equation
e
4
x
−
4
e
2
x
+
3
e
x
=
0
e^{4x}-4e^{2x}+3e^x=0
e
4
x
−
4
e
2
x
+
3
e
x
=
0
.
Comprehension
MEDIUM
4 marks
03 December 2023
14
Find the value of
x
x
x
that satisfies the equation
9
x
−
2
⋅
3
x
+
1
−
27
=
0
9^x-2\cdot3^{x+1}-27=0
9
x
−
2
⋅
3
x
+
1
−
27
=
0
.
Comprehension
MEDIUM
3 marks
03 December 2023
15
If
n
n
n
is the number of solutions of the equation
2
2
x
−
5
−
6
⋅
2
x
+
1
=
0
2^{2x-5}-6\cdot2^x+1=0
2
2
x
−
5
−
6
⋅
2
x
+
1
=
0
, then find the value of
4
n
4n
4
n
.
Numerical
MEDIUM
5 marks
06 August 2023
16
Consider the equation
log
x
(
log
5
(
(
x
2
+
1
)
2
)
−
log
x
(
32
x
)
)
=
0
\log_x\left(\log_5((x^2+1)^2)-\log_x(32^x)\right)=0
lo
g
x
(
lo
g
5
((
x
2
+
1
)
2
)
−
lo
g
x
(
3
2
x
)
)
=
0
. Find the value of
x
(
x
2
+
1
)
+
7
x(x^2+1)+7
x
(
x
2
+
1
)
+
7
.
Numerical
HARD
5 marks
06 August 2023
17
Which of the following options is/are true?
Multiple correct
MEDIUM
5 marks
02 April 2023
18
Find the number of solutions of the equation
2
x
=
2
x
2^x=2x
2
x
=
2
x
.
Numerical
MEDIUM
3 marks
02 April 2023
19
Find the number of solutions of the equation
e
2
x
−
2
e
x
=
15
e^{2x}-2e^x=15
e
2
x
−
2
e
x
=
15
.
Comprehension
EASY
3 marks
20 November 2022
20
Find the value of
x
x
x
that satisfies the equation
log
4
(
x
−
1
)
−
log
2
(
x
−
3
)
=
0
\log_4(x-1)-\log_2(x-3)=0
lo
g
4
(
x
−
1
)
−
lo
g
2
(
x
−
3
)
=
0
.
Comprehension
MEDIUM
3 marks
20 November 2022
Showing 20 questions.
Mathematics 1 > Week 6
All PYQs
Topic-Wise PYQs
Start Weekly Test
Mock tests
Week mock
Topic mock
Subject mock
Type:
All
Difficulty:
All
Year:
All
20Q
01
Find the number of solutions of the equation
e
2
x
−
9
e
x
=
−
18
e^{2x}-9e^x=-18
e
2
x
−
9
e
x
=
−
18
.
Numerical
EASY
3 marks
03 August 2025
02
Find the value of
x
x
x
that satisfies
log
2
(
x
+
1
)
−
log
4
(
x
−
3
)
=
2
\log_2(x+1)-\log_4(x-3)=2
lo
g
2
(
x
+
1
)
−
lo
g
4
(
x
−
3
)
=
2
.
Numerical
MEDIUM
4 marks
03 August 2025
03
Choose the correct option for the domain of
f
(
x
)
=
log
3
∣
x
+
1
∣
f(x)=\log_3|x+1|
f
(
x
)
=
lo
g
3
∣
x
+
1∣
.
Comprehension
EASY
3 marks
03 August 2025
04
Suppose
m
,
n
m,n
m
,
n
are two solutions of
f
(
x
)
=
3
f(x)=3
f
(
x
)
=
3
such that
m
<
n
m<n
m
<
n
. Find the value of
n
−
m
n-m
n
−
m
.
Comprehension
MEDIUM
3 marks
03 August 2025
05
If
b
>
0
b>0
b
>
0
and
4
log
x
b
+
9
log
x
x
b
=
1
4\log_x b+9\log_{x\sqrt{x}} b=1
4
lo
g
x
b
+
9
lo
g
x
x
b
=
1
, then the possible value(s) of
x
x
x
is(are)
Single correct
MEDIUM
4 marks
16 March 2025
06
Choose the set of correct options.
Multiple correct
MEDIUM
4 marks
16 March 2025
07
Consider the function
f
(
x
)
=
∣
log
(
x
+
1
)
∣
f(x)=|\log(x+1)|
f
(
x
)
=
∣
lo
g
(
x
+
1
)
∣
. Choose the correct option(s) from the following.
Multiple correct
MEDIUM
4 marks
01 December 2024
08
If
m
log
3
2
+
2
log
3
m
=
8
m^{\log_3 2}+2^{\log_3 m}=8
m
l
o
g
3
2
+
2
l
o
g
3
m
=
8
, then what is the value of
m
m
m
?
Numerical
EASY
4 marks
01 December 2024
09
Choose the set of correct options.
Multiple correct
MEDIUM
3 marks
04 August 2024
10
If
m
log
3
2
+
2
log
3
m
=
8
m^{\log_3 2}+2^{\log_3 m}=8
m
l
o
g
3
2
+
2
l
o
g
3
m
=
8
, then what is the value of
m
m
m
?
Numerical
MEDIUM
2 marks
04 August 2024
11
Find the number of solution(s) of the equation
9
x
+
3
x
−
6
=
0
9^x+3^x-6=0
9
x
+
3
x
−
6
=
0
.
Comprehension
MEDIUM
3 marks
24 March 2024
12
Find the number of solution(s) of the equation
ln
(
7
)
+
ln
(
2
−
4
x
2
)
=
ln
(
14
)
\ln(7)+\ln(2-4x^2)=\ln(14)
ln
(
7
)
+
ln
(
2
−
4
x
2
)
=
ln
(
14
)
.
Comprehension
MEDIUM
3 marks
24 March 2024
13
Find the number of solutions of the equation
e
4
x
−
4
e
2
x
+
3
e
x
=
0
e^{4x}-4e^{2x}+3e^x=0
e
4
x
−
4
e
2
x
+
3
e
x
=
0
.
Comprehension
MEDIUM
4 marks
03 December 2023
14
Find the value of
x
x
x
that satisfies the equation
9
x
−
2
⋅
3
x
+
1
−
27
=
0
9^x-2\cdot3^{x+1}-27=0
9
x
−
2
⋅
3
x
+
1
−
27
=
0
.
Comprehension
MEDIUM
3 marks
03 December 2023
15
If
n
n
n
is the number of solutions of the equation
2
2
x
−
5
−
6
⋅
2
x
+
1
=
0
2^{2x-5}-6\cdot2^x+1=0
2
2
x
−
5
−
6
⋅
2
x
+
1
=
0
, then find the value of
4
n
4n
4
n
.
Numerical
MEDIUM
5 marks
06 August 2023
16
Consider the equation
log
x
(
log
5
(
(
x
2
+
1
)
2
)
−
log
x
(
32
x
)
)
=
0
\log_x\left(\log_5((x^2+1)^2)-\log_x(32^x)\right)=0
lo
g
x
(
lo
g
5
((
x
2
+
1
)
2
)
−
lo
g
x
(
3
2
x
)
)
=
0
. Find the value of
x
(
x
2
+
1
)
+
7
x(x^2+1)+7
x
(
x
2
+
1
)
+
7
.
Numerical
HARD
5 marks
06 August 2023
17
Which of the following options is/are true?
Multiple correct
MEDIUM
5 marks
02 April 2023
18
Find the number of solutions of the equation
2
x
=
2
x
2^x=2x
2
x
=
2
x
.
Numerical
MEDIUM
3 marks
02 April 2023
19
Find the number of solutions of the equation
e
2
x
−
2
e
x
=
15
e^{2x}-2e^x=15
e
2
x
−
2
e
x
=
15
.
Comprehension
EASY
3 marks
20 November 2022
20
Find the value of
x
x
x
that satisfies the equation
log
4
(
x
−
1
)
−
log
2
(
x
−
3
)
=
0
\log_4(x-1)-\log_2(x-3)=0
lo
g
4
(
x
−
1
)
−
lo
g
2
(
x
−
3
)
=
0
.
Comprehension
MEDIUM
3 marks
20 November 2022
Showing 20 questions.
