PYQ Vault
Bank
Guides
Notes
NDA
Sign in
Filtered questions
4,860 questions match
Filters
1
Download
· 4860
Filtering by:
Exam: NDA
Clear all
Copy link
Q4526
#4526
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
Tap an option to check your answer.
Show solution
[Q26 · Apr · 2024]
Report
Q4527
#4527
Mathematics → Logarithms → Solving Logarithmic Equations and Applications
·
Moderate
What is the number of solutions of
log
4
(
x
−
1
)
=
log
2
(
x
−
3
)
\log_4(x-1)=\log_2(x-3)
lo
g
4
(
x
−
1
)
=
lo
g
2
(
x
−
3
)
?
Add
NDA Maths strategy
A
Zero
B
One
C
Two
D
Three
Tap an option to check your answer.
Show solution
[Q27 · Apr · 2024]
Report
Q4528
#4528
Mathematics → Logarithms → Solving Logarithmic Equations and Applications
·
Hard
For
x
≥
y
>
1
x\geq y>1
x
≥
y
>
1
, let
log
x
x
y
+
log
y
y
x
=
k
\log_x\!\dfrac{x}{y}+\log_y\!\dfrac{y}{x}=k
lo
g
x
y
x
+
lo
g
y
x
y
=
k
, then the value of
k
k
k
can never be equal to
Add
Lever: AM-GM / mean inequalities (incl. x + 1/x ≥ 2)
A
−
1
-1
−
1
B
−
1
2
-\dfrac{1}{2}
−
2
1
C
0
0
0
D
1
1
1
Tap an option to check your answer.
Show solution
[Q28 · Apr · 2024]
Report
Q4529
#4529
Mathematics → Matrices & Determinants → Special Matrices — Skew-Symmetric, Diagonal, Idempotent, Orthogonal, Rotation
·
Moderate
If
A
=
(
sin
2
θ
−
cos
2
θ
0
cos
2
θ
sin
2
θ
0
0
0
1
)
A=\begin{pmatrix}\sin2\theta & -\cos2\theta & 0\\\cos2\theta & \sin2\theta & 0\\0 & 0 & 1\end{pmatrix}
A
=
sin
2
θ
cos
2
θ
0
−
cos
2
θ
sin
2
θ
0
0
0
1
, then which of the following statements is/are correct? (A)
A
−
1
=
adj
A
A^{-1}=\text{adj }A
A
−
1
=
adj
A
(B)
A
A
A
is skew-symmetric matrix. (C)
A
−
1
=
A
T
A^{-1}=A^T
A
−
1
=
A
T
Select the correct answer using the code given below:
Add
NDA Maths strategy
Concept: Rotation matrices
A
A only
B
A and B only
C
A and C
D
B and C
Tap an option to check your answer.
Show solution
[Q29 · Apr · 2024]
Report
Q4530
#4530
Mathematics → Binomial Theorem → Coefficients and Specific Terms in Expansion
·
Hard
What is the coefficient of
x
10
x^{10}
x
10
in the expansion of
(
1
−
x
2
20
)
−
1
(
x
2
−
1
x
2
)
−
5
\left(1-\dfrac{x^2}{20}\right)^{-1}\left(x^2-\dfrac{1}{x^2}\right)^{-5}
(
1
−
20
x
2
)
−
1
(
x
2
−
x
2
1
)
−
5
?
Add
NDA Maths strategy
A
−
1
-1
−
1
B
1
1
1
C
10
10
10
D
Coefficient of
x
10
x^{10}
x
10
does not exist
Tap an option to check your answer.
Show solution
[Q30 · Apr · 2024]
Report
Q4531
#4531
Mathematics → Binomial Theorem → Coefficients and Specific Terms in Expansion
·
Moderate
If the 4th term in the expansion of
(
m
x
+
1
x
)
n
\left(mx+\dfrac{1}{x}\right)^n
(
m
x
+
x
1
)
n
is
5
2
\dfrac{5}{2}
2
5
, then what is the value of
m
n
mn
mn
?
Add
NDA Maths strategy
A
−
3
-3
−
3
B
3
3
3
C
6
6
6
D
12
12
12
Tap an option to check your answer.
Show solution
[Q31 · Apr · 2024]
Report
Q4532
#4532
Mathematics → Quadratic Equations → Nature of Roots and Boundary Conditions
·
Hard
If
a
,
b
a,b
a
,
b
and
c
(
a
>
0
,
c
>
0
)
c\;(a>0,\,c>0)
c
(
a
>
0
,
c
>
0
)
are in GP, then consider the following in respect of the equation
a
x
2
+
b
x
+
c
=
0
ax^2+bx+c=0
a
x
2
+
b
x
+
c
=
0
: (A) The equation has imaginary roots. (B) The ratio of the roots of the equation is
1
:
ω
1:\omega
1
:
ω
where
ω
\omega
ω
is a cube root of unity. (C) The product of roots of the equation is
b
2
a
2
\dfrac{b^2}{a^2}
a
2
b
2
. Which of the statements given above are correct?
Add
Lever: Cube roots of unity (1 + ω + ω² = 0, ω³ = 1)
A
(A) and (B) only
B
(B) and (C) only
C
(A) and (C) only
D
(A), (B) and (C)
Tap an option to check your answer.
Show solution
[Q32 · Apr · 2024]
Report
Q4533
#4533
Mathematics → Quadratic Equations → Vieta's Relations and Root-Coefficient Identities
·
Easy
If
x
2
+
m
x
+
n
x^2+mx+n
x
2
+
m
x
+
n
is an integer for all integral values of
x
x
x
, then which of the following is/are correct? (A)
m
m
m
must be an integer. (B)
n
n
n
must be an integer. Select the correct answer using the code given below:
Add
NDA Maths strategy
A
A only
B
B only
C
Both (A) and (B)
D
Neither (A) nor (B)
Tap an option to check your answer.
Show solution
[Q33 · Apr · 2024]
Report
Q4534
#4534
Mathematics → Binomial Theorem → Coefficients and Specific Terms in Expansion
·
Hard
In a binomial expansion of
(
x
+
y
)
2
n
+
1
(
x
−
y
)
2
n
+
1
(x+y)^{2n+1}(x-y)^{2n+1}
(
x
+
y
)
2
n
+
1
(
x
−
y
)
2
n
+
1
, the sum of middle terms is zero. What is the value of
x
2
y
2
\dfrac{x^2}{y^2}
y
2
x
2
?
Add
Lever: Pascal / binomial-coefficient identities
A
1
1
1
B
2
2
2
C
4
4
4
D
8
8
8
Tap an option to check your answer.
Show solution
[Q34 · Apr · 2024]
Report
Q4535
#4535
Mathematics → Functions → Function Definition and Classification — Injectivity, Surjectivity, Bijectivity
·
Easy
Let
A
=
{
1
,
2
,
3
,
4
,
5
}
A=\{1,2,3,4,5\}
A
=
{
1
,
2
,
3
,
4
,
5
}
and
B
=
{
6
,
7
}
B=\{6,7\}
B
=
{
6
,
7
}
. What is the number of onto functions from
A
A
A
to
B
B
B
?
Add
NDA Maths strategy
A
10
10
10
B
20
20
20
C
30
30
30
D
32
32
32
Tap an option to check your answer.
Show solution
[Q35 · Apr · 2024]
Report
Q4536
#4536
Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
What is
3
cos
10
°
−
sin
10
°
sin
25
°
cos
25
°
\dfrac{\sqrt{3}\cos10°-\sin10°}{\sin25°\cos25°}
sin
25°
cos
25°
3
cos
10°
−
sin
10°
equal to?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
1
1
1
B
3
3
3
C
2
2
2
D
4
4
4
Tap an option to check your answer.
Show solution
[Q36 · Apr · 2024]
Report
Q4537
#4537
Mathematics → Trigonometric Identities → Specific Values and Quadrants
·
Hard
What is
sin
9
°
−
cos
9
°
\sin9°-\cos9°
sin
9°
−
cos
9°
equal to?
Add
NDA Maths strategy
A
−
5
−
5
2
-\dfrac{\sqrt{5-\sqrt{5}}}{2}
−
2
5
−
5
B
−
5
−
3
2
-\dfrac{\sqrt{5-\sqrt{3}}}{2}
−
2
5
−
3
C
5
−
5
2
\dfrac{\sqrt{5-\sqrt{5}}}{2}
2
5
−
5
D
5
−
5
4
\dfrac{\sqrt{5-\sqrt{5}}}{4}
4
5
−
5
Tap an option to check your answer.
Show solution
[Q37 · Apr · 2024]
Report
Q4538
#4538
Mathematics → Matrices & Determinants → Special Determinants — Trig, Complex, Roots of Unity, Polynomial
·
Moderate
If in a triangle
A
B
C
ABC
A
B
C
,
sin
3
A
+
sin
3
B
+
sin
3
C
=
3
sin
A
sin
B
sin
C
\sin^3A+\sin^3B+\sin^3C=3\sin A\sin B\sin C
sin
3
A
+
sin
3
B
+
sin
3
C
=
3
sin
A
sin
B
sin
C
, then what is the value of the determinant
∣
a
b
c
b
c
a
c
a
b
∣
\begin{vmatrix}a&b&c\\b&c&a\\c&a&b\end{vmatrix}
a
b
c
b
c
a
c
a
b
?
Add
NDA Maths strategy
Concept: Trigonometric determinants
A
a
+
b
+
c
a+b+c
a
+
b
+
c
B
a
b
+
b
c
+
c
a
ab+bc+ca
ab
+
b
c
+
c
a
C
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
(a+b)(b+c)(c+a)
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
D
0
0
0
Tap an option to check your answer.
Show solution
[Q38 · Apr · 2024]
Report
Q4539
#4539
Mathematics → Inverse Trigonometry → Identities, Properties, and Sum-Difference Formulas
·
Easy
If
cos
−
1
x
=
sin
−
1
x
\cos^{-1}x=\sin^{-1}x
cos
−
1
x
=
sin
−
1
x
, then which one of the following is correct?
Add
NDA Maths strategy
A
x
=
1
x=1
x
=
1
B
x
=
1
2
x=\dfrac{1}{\sqrt{2}}
x
=
2
1
C
x
=
1
2
x=\dfrac{1}{2}
x
=
2
1
D
x
=
1
3
x=\dfrac{1}{\sqrt{3}}
x
=
3
1
Tap an option to check your answer.
Show solution
[Q39 · Apr · 2024]
Report
Q4540
#4540
Mathematics → Trigonometric Equations → General Solutions and Counting Solutions of Trigonometric Equations
·
Moderate
What is the number of solutions of
(
sin
θ
−
cos
θ
)
2
=
2
(\sin\theta-\cos\theta)^2=2
(
sin
θ
−
cos
θ
)
2
=
2
where
−
π
<
θ
<
π
-\pi<\theta<\pi
−
π
<
θ
<
π
?
Add
NDA Maths strategy
A
Only one
B
Only two
C
Four
D
No solution
Tap an option to check your answer.
Show solution
[Q40 · Apr · 2024]
Report
Q4541
#4541
Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Moderate
Triangle
A
B
C
ABC
A
B
C
such that
∠
C
=
60
°
\angle C=60°
∠
C
=
60°
, then what is
cos
A
+
cos
B
cos
(
A
−
B
2
)
\dfrac{\cos A+\cos B}{\cos\!\left(\dfrac{A-B}{2}\right)}
cos
(
2
A
−
B
)
cos
A
+
cos
B
equal to?
Add
Lever: Double / half-angle formulas
A
2
\sqrt{2}
2
B
2
2
2
C
1
1
1
D
1
2
\dfrac{1}{2}
2
1
Tap an option to check your answer.
Show solution
[Q41 · Apr · 2024]
Report
Q4542
#4542
Mathematics → Inverse Trigonometry → Evaluation of Composite Inverse Trigonometric Expressions
·
Hard
What is
1
5
+
cot
2
(
π
4
−
2
cot
−
1
3
)
\dfrac{1}{5+\cot^2\!\left(\dfrac{\pi}{4}-2\cot^{-1}3\right)}
5
+
cot
2
(
4
π
−
2
cot
−
1
3
)
1
equal to?
Add
NDA Maths strategy
A
1
1
1
B
7
7
7
C
8
8
8
D
16
16
16
Tap an option to check your answer.
Show solution
[Q42 · Apr · 2024]
Report
Q4543
#4543
Mathematics → Trigonometric Identities → Product-to-Sum and Sum-to-Product Identities
·
Hard
What is
sin
10
°
⋅
sin
50
°
+
sin
50
°
⋅
sin
250
°
+
sin
250
°
⋅
sin
10
°
\sin10°\cdot\sin50°+\sin50°\cdot\sin250°+\sin250°\cdot\sin10°
sin
10°
⋅
sin
50°
+
sin
50°
⋅
sin
250°
+
sin
250°
⋅
sin
10°
equal to?
Add
NDA Maths strategy
A
−
1
4
-\dfrac{1}{4}
−
4
1
B
−
3
4
-\dfrac{3}{4}
−
4
3
C
3
sin
10
°
4
\dfrac{3\sin10°}{4}
4
3
sin
10°
D
−
3
cos
10
°
4
-\dfrac{3\cos10°}{4}
−
4
3
cos
10°
Tap an option to check your answer.
Show solution
[Q43 · Apr · 2024]
Report
Q4544
#4544
Mathematics → Inverse Trigonometry → Identities, Properties, and Sum-Difference Formulas
·
Moderate
What is
tan
−
1
a
b
−
tan
−
1
a
−
b
a
+
b
\tan^{-1}\!\dfrac{a}{b}-\tan^{-1}\!\dfrac{a-b}{a+b}
tan
−
1
b
a
−
tan
−
1
a
+
b
a
−
b
equal to?
Add
NDA Maths strategy
A
−
π
4
-\dfrac{\pi}{4}
−
4
π
B
π
4
\dfrac{\pi}{4}
4
π
C
tan
−
1
a
2
−
b
2
a
2
+
b
2
\tan^{-1}\!\dfrac{a^2-b^2}{a^2+b^2}
tan
−
1
a
2
+
b
2
a
2
−
b
2
D
tan
−
1
2
a
b
a
2
+
b
2
\tan^{-1}\!\dfrac{2ab}{a^2+b^2}
tan
−
1
a
2
+
b
2
2
ab
Tap an option to check your answer.
Show solution
[Q44 · Apr · 2024]
Report
Q4545
#4545
Mathematics → Quadratic Equations → Nature of Roots and Boundary Conditions
·
Moderate
Under which one of the following conditions does the equation
(
cos
β
−
1
)
x
2
+
(
cos
β
)
x
+
sin
β
=
0
(\cos\beta-1)x^2+(\cos\beta)x+\sin\beta=0
(
cos
β
−
1
)
x
2
+
(
cos
β
)
x
+
sin
β
=
0
in
x
x
x
have a real root for
β
∈
[
0
,
π
]
\beta\in[0,\pi]
β
∈
[
0
,
π
]
?
Add
NDA Maths strategy
A
1
−
cos
β
<
0
1-\cos\beta<0
1
−
cos
β
<
0
B
1
−
cos
β
≤
0
1-\cos\beta\leq0
1
−
cos
β
≤
0
C
1
−
cos
β
>
0
1-\cos\beta>0
1
−
cos
β
>
0
D
1
−
cos
β
≥
0
1-\cos\beta\geq0
1
−
cos
β
≥
0
Tap an option to check your answer.
Show solution
[Q45 · Apr · 2024]
Report
Q4546
#4546
Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Moderate
In a triangle
A
B
C
ABC
A
B
C
,
A
B
=
16
AB=16
A
B
=
16
cm,
B
C
=
63
BC=63
B
C
=
63
cm and
A
C
=
65
AC=65
A
C
=
65
cm. What is the value of
cos
2
A
+
cos
2
B
+
cos
2
C
\cos2A+\cos2B+\cos2C
cos
2
A
+
cos
2
B
+
cos
2
C
?
Add
Lever: Double / half-angle formulas
A
−
1
-1
−
1
B
0
0
0
C
1
1
1
D
76
65
\dfrac{76}{65}
65
76
Tap an option to check your answer.
Show solution
[Q46 · Apr · 2024]
Report
Q4547
#4547
Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
f
(
θ
)
=
1
1
+
tan
θ
f(\theta)=\dfrac{1}{1+\tan\theta}
f
(
θ
)
=
1
+
tan
θ
1
and
α
+
β
=
5
π
4
\alpha+\beta=\dfrac{5\pi}{4}
α
+
β
=
4
5
π
, then what is the value of
f
(
α
)
⋅
f
(
β
)
f(\alpha)\cdot f(\beta)
f
(
α
)
⋅
f
(
β
)
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
−
1
2
-\dfrac{1}{2}
−
2
1
B
1
2
\dfrac{1}{2}
2
1
C
1
1
1
D
2
2
2
Tap an option to check your answer.
Show solution
[Q47 · Apr · 2024]
Report
Q4548
#4548
Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
If
tan
α
\tan\alpha
tan
α
and
tan
β
\tan\beta
tan
β
are the roots of the equation
x
2
−
6
x
+
8
=
0
x^2-6x+8=0
x
2
−
6
x
+
8
=
0
, then what is the value of
cos
(
2
α
+
2
β
)
\cos(2\alpha+2\beta)
cos
(
2
α
+
2
β
)
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
13
75
\dfrac{13}{75}
75
13
B
13
85
\dfrac{13}{85}
85
13
C
17
85
\dfrac{17}{85}
85
17
D
19
85
\dfrac{19}{85}
85
19
Tap an option to check your answer.
Show solution
[Q48 · Apr · 2024]
Report
Q4549
#4549
Mathematics → Trigonometric Identities → Compound Angle Formulas
·
Moderate
What is the value of
tan
65
°
+
2
tan
45
°
−
2
tan
40
°
−
tan
25
°
\tan65°+2\tan45°-2\tan40°-\tan25°
tan
65°
+
2
tan
45°
−
2
tan
40°
−
tan
25°
?
Add
Lever: Compound angle: sin/cos/tan(A ± B)
A
0
0
0
B
1
1
1
C
2
2
2
D
4
4
4
Tap an option to check your answer.
Show solution
[Q49 · Apr · 2024]
Report
Q4550
#4550
Mathematics → Properties of Triangle → Triangle Identities — A+B+C=π, Half-Angle, and Double-Angle
·
Moderate
Consider the following statements: A. In a triangle
A
B
C
ABC
A
B
C
, if
cot
A
⋅
cot
B
⋅
cot
C
>
0
\cot A\cdot\cot B\cdot\cot C>0
cot
A
⋅
cot
B
⋅
cot
C
>
0
, then the triangle is an acute angled triangle. B. In a triangle
A
B
C
ABC
A
B
C
, if
tan
A
⋅
tan
B
⋅
tan
C
>
0
\tan A\cdot\tan B\cdot\tan C>0
tan
A
⋅
tan
B
⋅
tan
C
>
0
, then the triangle is an obtuse angled triangle. Which of the statements given above is/are correct?
Add
NDA Maths strategy
A
A Only
B
B Only
C
Both A and B
D
Neither A nor B
Tap an option to check your answer.
Show solution
[Q50 · Apr · 2024]
Report
Prev
Page 182 of 195
Next
1
…
181
182
183
…
195
PYQ Vault
Bank
Guides
Notes
NDA
Sign in