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Q4126
#4126
Mathematics → Matrices & Determinants → Determinant Properties, Operations, and Sums
·
Moderate
The value of the determinant
∣
a
b
c
l
m
n
p
q
r
∣
\begin{vmatrix}a&b&c\\l&m&n\\p&q&r\end{vmatrix}
a
l
p
b
m
q
c
n
r
is equal to
Add
NDA Maths strategy
Concept: Evaluating 2×2 and 3×3 determinants
A
∣
a
b
c
p
q
r
l
m
n
∣
\begin{vmatrix}a&b&c\\p&q&r\\l&m&n\end{vmatrix}
a
p
l
b
q
m
c
r
n
B
∣
l
m
n
a
b
c
p
q
r
∣
\begin{vmatrix}l&m&n\\a&b&c\\p&q&r\end{vmatrix}
l
a
p
m
b
q
n
c
r
C
∣
p
q
r
a
b
c
l
m
n
∣
\begin{vmatrix}p&q&r\\a&b&c\\l&m&n\end{vmatrix}
p
a
l
q
b
m
r
c
n
D
∣
a
p
l
b
q
m
c
r
n
∣
\begin{vmatrix}a&p&l\\b&q&m\\c&r&n\end{vmatrix}
a
b
c
p
q
r
l
m
n
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[Q16 · Sep · 2025]
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Q4127
#4127
Mathematics → Complex Numbers → Cube Roots of Unity
·
Hard
Let
1
,
ω
,
ω
2
1,\omega,\omega^2
1
,
ω
,
ω
2
be three cube roots of unity. If
x
=
a
+
b
x=a+b
x
=
a
+
b
,
y
=
a
ω
+
b
ω
2
y=a\omega+b\omega^2
y
=
aω
+
b
ω
2
,
z
=
a
ω
2
+
b
ω
z=a\omega^2+b\omega
z
=
a
ω
2
+
bω
, then what is
x
2
+
y
2
+
z
2
x^2+y^2+z^2
x
2
+
y
2
+
z
2
equal to?
Add
Lever: Cube roots of unity (1 + ω + ω² = 0, ω³ = 1)
A
6
a
b
6ab
6
ab
B
3
a
b
3ab
3
ab
C
a
2
+
b
2
a^2+b^2
a
2
+
b
2
D
1
1
1
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[Q17 · Sep · 2025]
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Q4128
#4128
Mathematics → Permutation & Combination → Forming Numbers from Digits
·
Moderate
How many 4-digit numbers that are divisible by 4 can be formed using the digits 1, 2, 3 and 4 (repetition of digits is not allowed)?
Add
NDA Maths strategy
A
3
B
6
C
9
D
12
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[Q18 · Sep · 2025]
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Q4129
#4129
Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
·
Hard
If
a
a
a
,
b
b
b
,
c
c
c
are the sides of a triangle
A
B
C
ABC
A
B
C
and
p
p
p
is the perimeter of the triangle, then what is
∣
p
+
c
a
b
c
p
+
a
b
c
a
p
+
b
∣
\begin{vmatrix}p+c & a & b\\c & p+a & b\\c & a & p+b\end{vmatrix}
p
+
c
c
c
a
p
+
a
a
b
b
p
+
b
equal to?
Add
NDA Maths strategy
Concept: Trigonometric determinants
A
p
3
p^3
p
3
B
2
p
3
2p^3
2
p
3
C
3
p
3
3p^3
3
p
3
D
4
p
3
4p^3
4
p
3
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[Q19 · Sep · 2025]
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Q4130
#4130
Mathematics → Binomial Theorem → Coefficients and Specific Terms in Expansion
·
Easy
Which one of the following is the greatest coefficient in the expansion of
(
1
+
x
)
100
(1+x)^{100}
(
1
+
x
)
100
?
Add
Lever: Pascal / binomial-coefficient identities
A
The coefficient of
x
100
x^{100}
x
100
B
The coefficient of
x
99
x^{99}
x
99
C
The coefficient of
x
51
x^{51}
x
51
D
The coefficient of
x
50
x^{50}
x
50
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[Q20 · Sep · 2025]
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Set · 2 questions
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
))
.
Q4131
#4131
Mathematics → Quadratic Equations → Special Quadratics — Parametric, Logarithmic, Constructed
·
Hard
What is
β
\beta
β
equal to?
Add
NDA Maths strategy
A
log
a
2
(
0.5
)
\log_{a^2}(0.5)
lo
g
a
2
(
0.5
)
B
log
0.5
(
a
2
)
\log_{0.5}(a^2)
lo
g
0.5
(
a
2
)
C
2
(
log
a
2
(
0.5
)
)
2(\log_{a^2}(0.5))
2
(
lo
g
a
2
(
0.5
))
D
2
log
0.5
(
a
2
)
2\log_{0.5}(a^2)
2
lo
g
0.5
(
a
2
)
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[Q21 · Sep · 2025]
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Q4132
#4132
Mathematics → Quadratic Equations → Special Quadratics — Parametric, Logarithmic, Constructed
·
Hard
What is the relation between
α
\alpha
α
and
β
\beta
β
?
Add
NDA Maths strategy
A
α
=
2
β
\alpha=2\beta
α
=
2
β
B
2
α
=
β
2\alpha=\beta
2
α
=
β
C
α
=
−
2
β
\alpha=-2\beta
α
=
−
2
β
D
2
α
=
−
β
2\alpha=-\beta
2
α
=
−
β
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[Q22 · Sep · 2025]
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Set · 2 questions
For the following two (02) items: Let
p
=
∑
j
=
1
n
log
10
2
j
p=\sum_{j=1}^{n}\log_{10}2^j
p
=
∑
j
=
1
n
lo
g
10
2
j
and
q
=
∑
j
=
1
n
log
10
5
j
q=\sum_{j=1}^{n}\log_{10}5^j
q
=
∑
j
=
1
n
lo
g
10
5
j
.
Q4133
#4133
Mathematics → Logarithms → Logarithm Identities, Change of Base, and Sums
·
Moderate
If
p
+
q
=
66
p+q=66
p
+
q
=
66
, then which one of the following is correct?
Add
NDA Maths strategy
A
n
<
7
n<7
n
<
7
B
7
<
n
<
9
7<n<9
7
<
n
<
9
C
9
<
n
<
12
9<n<12
9
<
n
<
12
D
n
>
12
n>12
n
>
12
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[Q23 · Sep · 2025]
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Q4134
#4134
Mathematics → Logarithms → Logarithm Identities, Change of Base, and Sums
·
Moderate
If
p
+
q
=
15
p+q=15
p
+
q
=
15
, then what is
q
−
p
q-p
q
−
p
equal to?
Add
NDA Maths strategy
A
log
10
2.5
\log_{10}2.5
lo
g
10
2.5
B
5
log
10
2.5
5\log_{10}2.5
5
lo
g
10
2.5
C
10
log
10
2.5
10\log_{10}2.5
10
lo
g
10
2.5
D
15
log
10
2.5
15\log_{10}2.5
15
lo
g
10
2.5
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[Q24 · Sep · 2025]
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Set · 2 questions
For the following two (02) items: Let
sin
A
+
sin
B
=
p
\sin A + \sin B = p
sin
A
+
sin
B
=
p
and
cos
A
+
cos
B
=
q
\cos A + \cos B = q
cos
A
+
cos
B
=
q
.
Q4135
#4135
Mathematics → Trigonometric Identities → Product-to-Sum and Sum-to-Product Identities
·
Easy
What is
p
q
\dfrac{p}{q}
q
p
equal to?
Add
NDA Maths strategy
A
tan
(
A
−
B
2
)
\tan\!\left(\dfrac{A-B}{2}\right)
tan
(
2
A
−
B
)
B
cot
(
A
−
B
2
)
\cot\!\left(\dfrac{A-B}{2}\right)
cot
(
2
A
−
B
)
C
tan
(
A
+
B
2
)
\tan\!\left(\dfrac{A+B}{2}\right)
tan
(
2
A
+
B
)
D
cot
(
A
+
B
2
)
\cot\!\left(\dfrac{A+B}{2}\right)
cot
(
2
A
+
B
)
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[Q25 · Sep · 2025]
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Q4136
#4136
Mathematics → Trigonometric Identities → Product-to-Sum and Sum-to-Product Identities
·
Moderate
What is
p
2
−
q
2
p
2
+
q
2
\dfrac{p^2-q^2}{p^2+q^2}
p
2
+
q
2
p
2
−
q
2
equal to?
Add
NDA Maths strategy
A
cos
(
A
+
B
)
\cos(A+B)
cos
(
A
+
B
)
B
cos
(
A
−
B
)
\cos(A-B)
cos
(
A
−
B
)
C
cos
(
π
2
−
A
−
B
)
\cos\!\left(\dfrac{\pi}{2}-A-B\right)
cos
(
2
π
−
A
−
B
)
D
cos
(
π
−
A
−
B
)
\cos(\pi-A-B)
cos
(
π
−
A
−
B
)
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[Q26 · Sep · 2025]
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Set · 2 questions
For the following two (02) items: Let
p
=
csc
20
°
p = \csc 20°
p
=
csc
20°
and
q
=
csc
70
°
q = \csc 70°
q
=
csc
70°
.
Q4137
#4137
Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Hard
What is
(
3
p
4
−
q
4
)
\left(\dfrac{\sqrt{3}p}{4}-\dfrac{q}{4}\right)
(
4
3
p
−
4
q
)
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
-1
B
0
C
1
D
2
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[Q27 · Sep · 2025]
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Q4138
#4138
Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Easy
What is
p
2
+
q
2
p
2
q
2
\dfrac{p^2+q^2}{p^2 q^2}
p
2
q
2
p
2
+
q
2
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
1
2
\dfrac{1}{2}
2
1
B
1
C
3
2
\dfrac{3}{2}
2
3
D
2
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[Q28 · Sep · 2025]
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Set · 2 questions
For the following two (02) items: Let
cos
(
2
x
+
3
y
)
=
1
2
\cos(2x+3y)=\frac{1}{2}
cos
(
2
x
+
3
y
)
=
2
1
and
cos
(
3
x
+
2
y
)
=
3
2
\cos(3x+2y)=\frac{\sqrt{3}}{2}
cos
(
3
x
+
2
y
)
=
2
3
, where
−
π
<
(
2
x
+
3
y
)
<
π
-\pi<(2x+3y)<\pi
−
π
<
(
2
x
+
3
y
)
<
π
and
−
π
<
(
3
x
+
2
y
)
<
π
-\pi<(3x+2y)<\pi
−
π
<
(
3
x
+
2
y
)
<
π
.
Q4139
#4139
Mathematics → Trigonometric Equations → General Solutions and Counting Solutions of Trigonometric Equations
·
Hard
How many values does
(
x
+
y
)
(x+y)
(
x
+
y
)
have?
Add
NDA Maths strategy
A
Two
B
Three
C
Four
D
More than four
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[Q29 · Sep · 2025]
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Q4140
#4140
Mathematics → Trigonometric Equations → General Solutions and Counting Solutions of Trigonometric Equations
·
Hard
How many values does
(
y
−
x
)
(y-x)
(
y
−
x
)
have?
Add
NDA Maths strategy
A
Two
B
Three
C
Four
D
More than four
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[Q30 · Sep · 2025]
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Set · 2 questions
For the following two (02) items: Consider the equation
a
b
x
2
+
b
c
x
+
c
a
=
c
a
x
2
+
a
b
x
+
b
c
abx^2+bcx+ca = cax^2+abx+bc
ab
x
2
+
b
c
x
+
c
a
=
c
a
x
2
+
ab
x
+
b
c
.
Q4141
#4141
Mathematics → Quadratic Equations → Nature of Roots and Boundary Conditions
·
Hard
If the roots of the equation are equal, then which one of the following is correct?
Add
NDA Maths strategy
A
a
c
=
b
2
ac=b^2
a
c
=
b
2
B
a
+
c
=
2
b
a+c=2b
a
+
c
=
2
b
C
1
a
+
1
c
=
1
2
b
\frac{1}{a}+\frac{1}{c}=\frac{1}{2b}
a
1
+
c
1
=
2
b
1
D
1
a
+
1
c
=
2
b
\frac{1}{a}+\frac{1}{c}=\frac{2}{b}
a
1
+
c
1
=
b
2
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[Q31 · Sep · 2025]
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Q4142
#4142
Mathematics → Quadratic Equations → Nature of Roots and Boundary Conditions
·
Moderate
If the roots of the equation are equal, then
a
a
a
,
b
b
b
,
c
c
c
are in
Add
Lever: Vieta — sum and product of roots
A
AP
B
GP
C
HP
D
None of the above
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[Q32 · Sep · 2025]
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Set · 2 questions
For the following two (02) items: Let
(
6
+
10
+
14
+
…
(6+10+14+\ldots
(
6
+
10
+
14
+
…
up to
m
m
m
terms
)
=
(
1
+
3
+
5
+
7
+
…
) = (1+3+5+7+\ldots
)
=
(
1
+
3
+
5
+
7
+
…
up to
n
n
n
terms
)
)
)
where
m
<
25
m<25
m
<
25
and
n
<
25
n<25
n
<
25
.
Q4143
#4143
Mathematics → Sequence & Series → Arithmetic Progressions
·
Moderate
What is the relation between
m
m
m
and
n
n
n
?
Add
NDA Maths strategy
Concept: The clever AP identities
A
n
2
=
m
(
m
+
1
)
n^2=m(m+1)
n
2
=
m
(
m
+
1
)
B
n
2
=
m
(
m
+
2
)
n^2=m(m+2)
n
2
=
m
(
m
+
2
)
C
n
2
=
2
m
(
m
+
1
)
n^2=2m(m+1)
n
2
=
2
m
(
m
+
1
)
D
n
2
=
2
m
(
m
+
2
)
n^2=2m(m+2)
n
2
=
2
m
(
m
+
2
)
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[Q33 · Sep · 2025]
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Q4144
#4144
Mathematics → Sequence & Series → Arithmetic Progressions
·
Hard
How many values of
m
m
m
are possible?
Add
NDA Maths strategy
Concept: The clever AP identities
A
None
B
One
C
Two
D
More than two
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[Q34 · Sep · 2025]
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Set · 2 questions
For the following two (02) items: There are 8 points on a plane out of which 4 points are collinear.
Q4145
#4145
Mathematics → Permutation & Combination → Geometric Counting
·
Moderate
How many triangles can be formed by joining these points?
Add
NDA Maths strategy
A
56
B
54
C
53
D
52
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[Q35 · Sep · 2025]
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Q4146
#4146
Mathematics → Permutation & Combination → Geometric Counting
·
Moderate
How many quadrilaterals can be formed by joining these points?
Add
NDA Maths strategy
A
70
B
69
C
53
D
None of the above
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[Q36 · Sep · 2025]
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Set · 2 questions
For the following two (02) items: Let
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x)=ax^2+bx+c
f
(
x
)
=
a
x
2
+
b
x
+
c
be a quadratic polynomial such that
f
(
1
)
=
f
(
4
)
=
2
f(1)=f(4)=2
f
(
1
)
=
f
(
4
)
=
2
. Further, 2 is a root of
f
(
x
)
=
0
f(x)=0
f
(
x
)
=
0
.
Q4147
#4147
Mathematics → Quadratic Equations → Nature of Roots and Boundary Conditions
·
Moderate
What is the other root of
f
(
x
)
=
0
f(x)=0
f
(
x
)
=
0
?
Add
NDA Maths strategy
A
1
B
2
C
3
D
Cannot be determined
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[Q37 · Sep · 2025]
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Q4148
#4148
Mathematics → Quadratic Equations → Nature of Roots and Boundary Conditions
·
Easy
What is
(
a
+
b
+
c
)
(a+b+c)
(
a
+
b
+
c
)
equal to?
Add
NDA Maths strategy
A
0
B
1
C
2
D
Cannot be determined
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[Q38 · Sep · 2025]
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Set · 2 questions
For the following two (02) items: Let
A
=
(
cos
θ
sin
θ
−
sin
θ
cos
θ
)
A=\begin{pmatrix}\cos\theta & \sin\theta\\-\sin\theta & \cos\theta\end{pmatrix}
A
=
(
cos
θ
−
sin
θ
sin
θ
cos
θ
)
.
Q4149
#4149
Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
·
Easy
What is the value of the determinant of the matrix
A
4
A^4
A
4
?
Add
NDA Maths strategy
Concept: Orthogonal matrices
A
0
B
1
C
cos
4
θ
−
sin
4
θ
\cos4\theta-\sin4\theta
cos
4
θ
−
sin
4
θ
D
cos
2
4
θ
−
sin
2
4
θ
\cos^24\theta-\sin^24\theta
cos
2
4
θ
−
sin
2
4
θ
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[Q39 · Sep · 2025]
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Q4150
#4150
Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
·
Moderate
What is
[
adj
A
]
−
1
[\text{adj}\,A]^{-1}
[
adj
A
]
−
1
equal to?
Add
NDA Maths strategy
Concept: Orthogonal matrices
A
−
A
-A
−
A
B
−
A
T
-A^T
−
A
T
C
A
A
A
D
A
T
A^T
A
T
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Show solution
[Q40 · Sep · 2025]
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