Week 6 Mathematics 1 Questions | Prasnya
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Question type
20
Difficulty
20
Years
20
Q1
Find the number of solutions of the equation
e
2
x
−
9
e
x
=
−
18
e^{2x}-9e^x=-18
.
Integer answer
AUGUST 03, 2025
AUGUST 03, 2025
Q2
Find the value of
x
x
that satisfies
log
2
(
x
+
1
)
−
log
4
(
x
−
3
)
=
2
\log_2(x+1)-\log_4(x-3)=2
.
Integer answer
AUGUST 03, 2025
AUGUST 03, 2025
Q3
Choose the correct option for the domain of
f
(
x
)
=
log
3
∣
x
+
1
∣
f(x)=\log_3|x+1|
.
Comprehension
AUGUST 03, 2025
AUGUST 03, 2025
Q4
Suppose
m
,
n
m,n
are two solutions of
f
(
x
)
=
3
f(x)=3
such that
m
<
n
m<n
. Find the value of
n
−
m
n-m
.
Comprehension
AUGUST 03, 2025
AUGUST 03, 2025
Q5
If
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
, then the possible value(s) of
x
x
is(are)
Single correct
MARCH 16, 2025
MARCH 16, 2025
Q6
Choose the set of correct options.
Multiple correct
MARCH 16, 2025
MARCH 16, 2025
Q7
Consider the function
f
(
x
)
=
∣
log
(
x
+
1
)
∣
f(x)=|\log(x+1)|
. Choose the correct option(s) from the following.
Multiple correct
DECEMBER 01, 2024
DECEMBER 01, 2024
Q8
If
m
log
3
2
+
2
log
3
m
=
8
m^{\log_3 2}+2^{\log_3 m}=8
, then what is the value of
m
m
?
Integer answer
DECEMBER 01, 2024
DECEMBER 01, 2024
Q9
Choose the set of correct options.
Multiple correct
AUGUST 04, 2024
AUGUST 04, 2024
Q10
If
m
log
3
2
+
2
log
3
m
=
8
m^{\log_3 2}+2^{\log_3 m}=8
, then what is the value of
m
m
?
Integer answer
AUGUST 04, 2024
AUGUST 04, 2024
Q11
Find the number of solution(s) of the equation
9
x
+
3
x
−
6
=
0
9^x+3^x-6=0
.
Comprehension
MARCH 24, 2024
MARCH 24, 2024
Q12
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)
.
Comprehension
MARCH 24, 2024
MARCH 24, 2024
Q13
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
.
Comprehension
DECEMBER 03, 2023
DECEMBER 03, 2023
Q14
Find the value of
x
x
that satisfies the equation
9
x
−
2
⋅
3
x
+
1
−
27
=
0
9^x-2\cdot3^{x+1}-27=0
.
Comprehension
DECEMBER 03, 2023
DECEMBER 03, 2023
Q15
If
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
, then find the value of
4
n
4n
.
Integer answer
AUGUST 06, 2023
AUGUST 06, 2023
Q16
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
. Find the value of
x
(
x
2
+
1
)
+
7
x(x^2+1)+7
.
Integer answer
AUGUST 06, 2023
AUGUST 06, 2023
Q17
Which of the following options is/are true?
Multiple correct
APRIL 02, 2023
APRIL 02, 2023
Q18
Find the number of solutions of the equation
2
x
=
2
x
2^x=2x
.
Integer answer
APRIL 02, 2023
APRIL 02, 2023
Q19
Find the number of solutions of the equation
e
2
x
−
2
e
x
=
15
e^{2x}-2e^x=15
.
Comprehension
NOVEMBER 20, 2022
NOVEMBER 20, 2022
Q20
Find the value of
x
x
that satisfies the equation
log
4
(
x
−
1
)
−
log
2
(
x
−
3
)
=
0
\log_4(x-1)-\log_2(x-3)=0
.
Comprehension
NOVEMBER 20, 2022
NOVEMBER 20, 2022
Showing 20 questions.