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the number of integer solutions of equation 2 x x2
Question:
The number of integer solutions of equation
2
∣
x
∣
(
x
2
+
1
)
=
5
x
2
2|x|(x^2+1)=5x^2
2∣
x
∣
(
x
2
+
1
)
=
5
x
2
is
CAT - 2023
CAT
Updated On:
Aug 12, 2024
0
3
5
-1
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The Correct Option is
B
Solution and Explanation
The correct answer is 3.
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3
Top Questions on Number of integer solutions
The number of integer solutions of equation
2
∣
x
∣
(
x
2
+
1
)
=
5
x
2
2|x|(x^2+1)=5x^2
2∣
x
∣
(
x
2
+
1
)
=
5
x
2
is
CAT - 2023
Quantitative Aptitude
Number of integer solutions
View Solution
The sum of all possible values of
x
x
x
satisfying the equation
2
4
x
2
−
2
2
x
2
+
x
+
16
+
2
2
x
+
30
=
0
2^{4x^2} - 2^{2x^2+x+16} + 2^{2x+30} = 0
2
4
x
2
−
2
2
x
2
+
x
+
16
+
2
2
x
+
30
=
0
, is
CAT - 2023
Quantitative Aptitude
Number of integer solutions
View Solution
The number of integer solutions of the equation (x2−10)(x2−3x−10)=1 is
CAT - 2022
Quantitative Aptitude
Number of integer solutions
View Solution
Let
0
≤
a
≤
x
≤
100
0≤a≤x≤100
0
≤
a
≤
x
≤
100
and f(x)=
∣
x
−
a
∣
+
∣
x
−
100
∣
+
∣
x
−
a
−
50
∣
|x−a|+|x−100|+|x−a−50|
∣
x
−
a
∣
+
∣
x
−
100∣
+
∣
x
−
a
−
50∣
.Then the maximum value of f(x) becomes 100 when a is equal to
CAT - 2022
Quantitative Aptitude
Number of integer solutions
View Solution
Let
A
A
A
be the largest positive integer that divides all the numbers of form
3
k
+
4
k
+
5
k
3^k+4^k+5^k
3
k
+
4
k
+
5
k
, and
B
B
B
be the largest positive integer that divides all the numbers of the form
4
k
+
3
(
4
k
)
+
4
k
+
2
4^k+3(4^k)+4^{k+2}
4
k
+
3
(
4
k
)
+
4
k
+
2
, where k is any positive integer. Then
(
A
+
B
)
(A+B)
(
A
+
B
)
equals
CAT - 2022
Quantitative Aptitude
Number of integer solutions
View Solution
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x
and
y
satisfy the equations |
x
| +
x
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y
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x
+ |
y
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y
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x
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n
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n
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n
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k
k
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1
8
)
k
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1
32768
)
4
3
=
1
8
×
(
1
32768
)
k
3
(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}
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8
1
)
k
×
(
32768
1
)
3
4
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8
1
×
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32768
1
)
3
k
is
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1
0
100
10^{100}
1
0
100
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