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Principle: AP three-term: 2b = a + c
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Set · 1 question
For the next two (02) items that follow: Let X(a,p), Y(b,q) and Z(c,r) be the points such that a, b and c are in AP.
Q26
#26
NDA → Mathematics → Lines → Equation, Slope, and Family of Lines
·
Moderate
If p, q and r are not in AP and
b
=
c
b=c
b
=
c
, then the line joining the points X, Y and Z is parallel to
Add
Lever: AP three-term: 2b = a + c
A
y-axis
B
x-axis
C
y
=
x
y=x
y
=
x
D
y
=
−
x
y=-x
y
=
−
x
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[Q58 · Apr · 2026]
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Q27
#27
NDA → Mathematics → Sequence & Series → Interrelating AP, GP and HP
·
Hard
If
p
x
=
q
y
=
r
z
p^x = q^y = r^z
p
x
=
q
y
=
r
z
, where
x
x
x
,
y
y
y
and
z
z
z
are in GP, then consider the following statements: I.
p
p
p
,
q
q
q
and
r
r
r
are in AP. II.
ln
p
\ln p
ln
p
,
ln
q
\ln q
ln
q
and
ln
r
\ln r
ln
r
are in GP. Which of the statements given above is/are correct?
Add
Lever: AP three-term: 2b = a + c
Concept: The log bridge: a GP becomes an AP
A
I only
B
II only
C
Both I and II
D
Neither I nor II
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[Q1 · Sep · 2025]
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Set · 1 question
For the following two (02) items: Let
α
\alpha
α
and
β
\beta
β
be the roots of the quadratic equation
x
2
+
(
log
0.5
(
a
2
)
)
x
+
(
log
0.5
(
a
2
)
)
4
=
0
x^2 + (\log_{0.5}(a^2))x + (\log_{0.5}(a^2))^4 = 0
x
2
+
(
lo
g
0.5
(
a
2
))
x
+
(
lo
g
0.5
(
a
2
)
)
4
=
0
where
a
2
≠
1
a^2 \neq 1
a
2
=
1
and
log
0.5
(
a
2
)
>
0
\log_{0.5}(a^2) > 0
lo
g
0.5
(
a
2
)
>
0
. Further,
β
2
=
α
(
log
a
2
(
0.5
)
)
\beta^2 = \alpha(\log_{a^2}(0.5))
β
2
=
α
(
lo
g
a
2
(
0.5
))
.
Q28
#28
NDA → Mathematics → Sequence & Series → Interrelating AP, GP and HP
·
Moderate
If
(
10
+
log
10
x
)
(10 + \log_{10} x)
(
10
+
lo
g
10
x
)
,
(
10
+
log
10
y
)
(10 + \log_{10} y)
(
10
+
lo
g
10
y
)
and
(
10
+
log
10
z
)
(10 + \log_{10} z)
(
10
+
lo
g
10
z
)
are in AP, then consider the following statements: I. The GM of
x
x
x
and
z
z
z
is
y
2
y^2
y
2
. II. The AM of
log
10
x
\log_{10} x
lo
g
10
x
and
log
10
z
\log_{10} z
lo
g
10
z
is
log
10
y
\log_{10} y
lo
g
10
y
. Which of the statements given above is/are correct?
Add
Lever: AM-GM / mean inequalities (incl. x + 1/x ≥ 2)
Concept: The log bridge: a GP becomes an AP
A
I only
B
II only
C
Both I and II
D
Neither I nor II
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[Q5 · Sep · 2025]
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Q29
#29
NDA → Mathematics → Sequence & Series → Interrelating AP, GP and HP
·
Hard
If
a
,
b
,
c
a,b,c
a
,
b
,
c
are in AP;
b
,
c
,
d
b,c,d
b
,
c
,
d
are in GP;
c
,
d
,
e
c,d,e
c
,
d
,
e
are in HP, then which of the following is/are correct? (A)
a
,
c
a,c
a
,
c
and
e
e
e
are in GP. (B)
1
a
,
1
c
,
1
e
\dfrac{1}{a},\dfrac{1}{c},\dfrac{1}{e}
a
1
,
c
1
,
e
1
are in GP. Select the correct answer using the code given below:
Add
Lever: AP three-term: 2b = a + c
Concept: Mixed and chained progression problems
A
A only
B
B only
C
Both A and B
D
Neither A nor B
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[Q26 · Apr · 2024]
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Q30
#30
NDA → Mathematics → Logarithms → Logarithm Identities, Change of Base, and Sums
·
Moderate
Let
p
=
ln
x
p=\ln x
p
=
ln
x
,
q
=
ln
x
3
q=\ln x^3
q
=
ln
x
3
and
r
=
ln
x
5
r=\ln x^5
r
=
ln
x
5
, where
x
>
1
x>1
x
>
1
. Which of the following statements is/are correct? A.
p
,
q
p,q
p
,
q
and
r
r
r
are in AP. B.
p
,
q
p,q
p
,
q
and
r
r
r
can never be in GP. Select the answer using the code given below.
Add
Lever: AP three-term: 2b = a + c
A
A only
B
B only
C
Both A and B
D
Neither A nor B
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[Q8 · Sep · 2024]
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Q31
#31
NDA → Mathematics → Sequence & Series → Interrelating AP, GP and HP
·
Moderate
If
p
,
1
,
q
p, 1, q
p
,
1
,
q
are in AP and
p
,
2
,
q
p, 2, q
p
,
2
,
q
are in GP, then which of the following statements is/are correct? I.
p
,
4
,
q
p, 4, q
p
,
4
,
q
are in HP. II.
1
p
,
1
4
,
1
q
\frac{1}{p}, \frac{1}{4}, \frac{1}{q}
p
1
,
4
1
,
q
1
are in AP. Select the answer using the code given below.
Add
Lever: AM-GM / mean inequalities (incl. x + 1/x ≥ 2)
Concept: Mixed and chained progression problems
A
I only
B
II only
C
Both I and II
D
Neither I nor II
Tap an option to check your answer.
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[Q6 · Apr · 2025]
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Set · 1 question
In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3:1.
Q32
#32
NDA → Mathematics → Properties of Triangle → Sine and Cosine Rules — Solving Triangles
·
Hard
Consider the following statements: (I). The triangle is right-angled. (II). One of the sides of the triangle is
3
\sqrt{3}
3
times the other. (III). The angles A, C and B of the triangle are in AP. Which of the statements given above is/are correct?
Add
Lever: AP three-term: 2b = a + c
A
I only
B
II and III only
C
I and III only
D
I, II and III
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[Q47 · Apr · 2025]
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