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Q4676
#4676
Mathematics → Lines → Triangles, Quadrilaterals, and Polygons
·
Easy
The diagonals of a quadrilateral
A
B
C
D
ABCD
A
B
C
D
are along the lines
x
−
2
y
=
1
x-2y=1
x
−
2
y
=
1
and
4
x
+
2
y
=
3
4x+2y=3
4
x
+
2
y
=
3
. The quadrilateral
A
B
C
D
ABCD
A
B
C
D
may be a
Add
NDA Maths strategy
A
rectangle
B
cyclic quadrilateral
C
parallelogram
D
rhombus
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[Q56 · Sep · 2024]
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Q4677
#4677
Mathematics → Conics → Ellipse — Foci, Eccentricity, and Focal Distances
·
Easy
The foci of the ellipse
4
x
2
+
9
y
2
=
1
4x^2+9y^2=1
4
x
2
+
9
y
2
=
1
are at
Q
Q
Q
and
R
R
R
. If
P
(
x
,
y
)
P(x,y)
P
(
x
,
y
)
is any point on the ellipse, then what is
P
Q
+
P
R
PQ+PR
P
Q
+
P
R
equal to?
Add
NDA Maths strategy
A
2
2
2
B
1
1
1
C
2
3
\dfrac{2}{3}
3
2
D
1
3
\dfrac{1}{3}
3
1
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[Q57 · Sep · 2024]
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Q4678
#4678
Mathematics → Lines → Triangles, Quadrilaterals, and Polygons
·
Easy
If
P
(
2
,
4
)
P(2,4)
P
(
2
,
4
)
,
Q
(
8
,
12
)
Q(8,12)
Q
(
8
,
12
)
,
R
(
10
,
14
)
R(10,14)
R
(
10
,
14
)
and
S
(
x
,
y
)
S(x,y)
S
(
x
,
y
)
are vertices of a parallelogram, then what is
(
x
+
y
)
(x+y)
(
x
+
y
)
equal to?
Add
NDA Maths strategy
A
8
8
8
B
10
10
10
C
12
12
12
D
14
14
14
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[Q58 · Sep · 2024]
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Q4679
#4679
Mathematics → Circles → Circle Equation — Centre, Radius, Diameter, and Properties
·
Moderate
The equation of a circle is
(
x
2
−
4
x
+
3
)
+
(
y
2
−
6
y
+
8
)
=
0
(x^2-4x+3)+(y^2-6y+8)=0
(
x
2
−
4
x
+
3
)
+
(
y
2
−
6
y
+
8
)
=
0
. Which of the following statements are correct? A. The end points of a diameter of the circle are at
(
1
,
2
)
(1,2)
(
1
,
2
)
and
(
3
,
4
)
(3,4)
(
3
,
4
)
. B. The end points of a diameter of the circle are at
(
1
,
4
)
(1,4)
(
1
,
4
)
and
(
3
,
2
)
(3,2)
(
3
,
2
)
. C. The end points of a diameter of the circle are at
(
2
,
4
)
(2,4)
(
2
,
4
)
and
(
4
,
2
)
(4,2)
(
4
,
2
)
. Select the answer using the code given below.
Add
NDA Maths strategy
A
A and B only
B
B and C only
C
A and C only
D
A, B and C
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[Q59 · Sep · 2024]
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Q4680
#4680
Mathematics → Conics → Parabola — Equation, Properties, and Latus Rectum
·
Easy
Consider the points
P
(
4
k
,
4
k
)
P(4k,4k)
P
(
4
k
,
4
k
)
and
Q
(
4
k
,
−
4
k
)
Q(4k,-4k)
Q
(
4
k
,
−
4
k
)
lying on the parabola
y
2
=
4
k
x
y^2=4kx
y
2
=
4
k
x
. If the vertex is
A
A
A
, then what is
∠
P
A
Q
\angle PAQ
∠
P
A
Q
equal to?
Add
NDA Maths strategy
A
60
°
60°
60°
B
90
°
90°
90°
C
120
°
120°
120°
D
135
°
135°
135°
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[Q60 · Sep · 2024]
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Set · 2 questions
A triangle
A
B
C
ABC
A
B
C
is inscribed in the circle
x
2
+
y
2
=
100
x^2+y^2=100
x
2
+
y
2
=
100
.
B
B
B
and
C
C
C
have coordinates
(
6
,
8
)
(6,8)
(
6
,
8
)
and
(
−
8
,
6
)
(-8,6)
(
−
8
,
6
)
respectively.
Q4681
#4681
Mathematics → Circles → Inscribed Geometry, Tangents, and Segments
·
Hard
What is
∠
B
A
C
\angle BAC
∠
B
A
C
equal to?
Add
NDA Maths strategy
A
π
2
\dfrac{\pi}{2}
2
π
B
π
3
\dfrac{\pi}{3}
3
π
or
2
π
3
\dfrac{2\pi}{3}
3
2
π
C
π
4
\dfrac{\pi}{4}
4
π
or
3
π
4
\dfrac{3\pi}{4}
4
3
π
D
π
6
\dfrac{\pi}{6}
6
π
or
5
π
6
\dfrac{5\pi}{6}
6
5
π
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[Q61 · Sep · 2024]
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Q4682
#4682
Mathematics → Circles → Inscribed Geometry, Tangents, and Segments
·
Hard
What are the coordinates of
A
A
A
?
Add
NDA Maths strategy
A
(
−
6
,
8
)
(-6,8)
(
−
6
,
8
)
B
(
−
6
,
−
8
)
(-6,-8)
(
−
6
,
−
8
)
C
(
5
2
,
5
2
)
\left(\frac{5}{\sqrt{2}},\frac{5}{\sqrt{2}}\right)
(
2
5
,
2
5
)
D
Cannot be determined due to insufficient data
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[Q62 · Sep · 2024]
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Set · 2 questions
ABCD is an isosceles trapezium and AB is parallel to DC. Let
A
(
2
,
3
)
A(2,3)
A
(
2
,
3
)
,
B
(
4
,
3
)
B(4,3)
B
(
4
,
3
)
,
C
(
5
,
1
)
C(5,1)
C
(
5
,
1
)
be the vertices.
Q4683
#4683
Mathematics → Lines → Triangles, Quadrilaterals, and Polygons
·
Moderate
What are the coordinates of vertex
D
D
D
?
Add
NDA Maths strategy
A
(
2
,
1
)
(2,1)
(
2
,
1
)
B
(
1
,
2
)
(1,2)
(
1
,
2
)
C
(
1
,
1
)
(1,1)
(
1
,
1
)
D
(
3
,
1
)
(3,1)
(
3
,
1
)
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[Q63 · Sep · 2024]
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Q4684
#4684
Mathematics → Lines → Triangles, Quadrilaterals, and Polygons
·
Moderate
What is the point of intersection of the diagonals of the trapezium?
Add
NDA Maths strategy
A
(
3
,
7
2
)
\left(3,\dfrac{7}{2}\right)
(
3
,
2
7
)
B
(
3
,
7
3
)
\left(3,\dfrac{7}{3}\right)
(
3
,
3
7
)
C
(
7
2
,
2
)
\left(\dfrac{7}{2},2\right)
(
2
7
,
2
)
D
(
5
2
,
2
)
\left(\dfrac{5}{2},2\right)
(
2
5
,
2
)
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[Q64 · Sep · 2024]
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Set · 2 questions
Let
2
x
2
+
2
y
2
+
2
z
2
+
3
x
+
3
y
+
3
z
−
6
=
0
2x^2+2y^2+2z^2+3x+3y+3z-6=0
2
x
2
+
2
y
2
+
2
z
2
+
3
x
+
3
y
+
3
z
−
6
=
0
be a sphere.
Q4685
#4685
Mathematics → 3D Geometry → Sphere
·
Moderate
What is the diameter of the sphere?
Add
NDA Maths strategy
Concept: General equation, centre, and radius
A
5
3
4
\dfrac{5\sqrt{3}}{4}
4
5
3
B
5
3
2
\dfrac{5\sqrt{3}}{2}
2
5
3
C
3
5
4
\dfrac{3\sqrt{5}}{4}
4
3
5
D
3
5
2
\dfrac{3\sqrt{5}}{2}
2
3
5
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[Q65 · Sep · 2024]
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Q4686
#4686
Mathematics → 3D Geometry → Sphere
·
Moderate
The centre of the sphere lies on the plane
Add
NDA Maths strategy
Concept: General equation, centre, and radius
A
2
x
+
2
y
+
2
z
−
3
=
0
2x+2y+2z-3=0
2
x
+
2
y
+
2
z
−
3
=
0
B
4
x
+
4
y
+
4
z
−
3
=
0
4x+4y+4z-3=0
4
x
+
4
y
+
4
z
−
3
=
0
C
4
x
+
8
y
+
8
z
−
15
=
0
4x+8y+8z-15=0
4
x
+
8
y
+
8
z
−
15
=
0
D
4
x
+
8
y
+
8
z
+
15
=
0
4x+8y+8z+15=0
4
x
+
8
y
+
8
z
+
15
=
0
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[Q66 · Sep · 2024]
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Set · 2 questions
Let
S
S
S
be the line of intersection of two planes
x
+
y
+
z
=
1
x+y+z=1
x
+
y
+
z
=
1
and
2
x
+
3
y
−
4
z
=
8
2x+3y-4z=8
2
x
+
3
y
−
4
z
=
8
with direction ratios
⟨
−
7
,
6
,
1
⟩
\langle -7,6,1\rangle
⟨
−
7
,
6
,
1
⟩
. If
(
l
,
m
,
n
)
(l,m,n)
(
l
,
m
,
n
)
are direction cosines of
S
S
S
, then what is the value of
43
l
2
−
m
2
−
n
2
43l^2-m^2-n^2
43
l
2
−
m
2
−
n
2
?
Q4687
#4687
Mathematics → 3D Geometry → Direction Cosines and Ratios
·
Moderate
Which of the following are the direction ratios of
S
S
S
?
Add
NDA Maths strategy
Concept: Reading direction ratios off a line
A
⟨
−
7
,
−
6
,
1
⟩
\langle -7,-6,1\rangle
⟨
−
7
,
−
6
,
1
⟩
B
⟨
−
7
,
6
,
1
⟩
\langle -7,6,1\rangle
⟨
−
7
,
6
,
1
⟩
C
⟨
−
6
,
5
,
1
⟩
\langle -6,5,1\rangle
⟨
−
6
,
5
,
1
⟩
D
⟨
6
,
5
,
1
⟩
\langle 6,5,1\rangle
⟨
6
,
5
,
1
⟩
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[Q67 · Sep · 2024]
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Q4688
#4688
Mathematics → 3D Geometry → Direction Cosines and Ratios
·
Hard
6
6
6
Add
NDA Maths strategy
Concept: Reading direction ratios off a line
A
5
5
5
B
4
4
4
C
1
1
1
D
4
4
4
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[Q68 · Sep · 2024]
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Set · 2 questions
Let
L
:
x
+
y
+
z
+
4
=
0
=
2
x
−
y
−
z
+
8
L:x+y+z+4=0=2x-y-z+8
L
:
x
+
y
+
z
+
4
=
0
=
2
x
−
y
−
z
+
8
be a line and
P
:
x
+
2
y
+
3
z
+
1
=
0
P: x+2y+3z+1=0
P
:
x
+
2
y
+
3
z
+
1
=
0
be a plane.
Q4689
#4689
Mathematics → 3D Geometry → The Straight Line in 3D
·
Moderate
What are the direction ratios of the line?
Add
NDA Maths strategy
Concept: Intersection of a line and a plane
A
⟨
2
,
1
,
−
1
⟩
\langle 2,1,-1\rangle
⟨
2
,
1
,
−
1
⟩
B
⟨
0
,
−
1
,
2
⟩
\langle 0,-1,2\rangle
⟨
0
,
−
1
,
2
⟩
C
⟨
0
,
1
,
−
1
⟩
\langle 0,1,-1\rangle
⟨
0
,
1
,
−
1
⟩
D
⟨
2
,
3
,
−
3
⟩
\langle 2,3,-3\rangle
⟨
2
,
3
,
−
3
⟩
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[Q69 · Sep · 2024]
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Q4690
#4690
Mathematics → 3D Geometry → The Straight Line in 3D
·
Moderate
What is the point of intersection of
L
L
L
and
P
P
P
?
Add
NDA Maths strategy
Concept: Intersection of a line and a plane
A
(
4
,
3
,
−
3
)
(4,3,-3)
(
4
,
3
,
−
3
)
B
(
4
,
−
3
,
3
)
(4,-3,3)
(
4
,
−
3
,
3
)
C
(
−
4
,
−
3
,
−
3
)
(-4,-3,-3)
(
−
4
,
−
3
,
−
3
)
D
(
−
4
,
−
3
,
3
)
(-4,-3,3)
(
−
4
,
−
3
,
3
)
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[Q70 · Sep · 2024]
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Q4691
#4691
Mathematics → Functions → Greatest Integer Function
·
Moderate
Let
z
=
[
y
]
z=[y]
z
=
[
y
]
and
y
=
[
x
]
−
x
y=[x]-x
y
=
[
x
]
−
x
, where
[
⋅
]
[\cdot]
[
⋅
]
is the greatest integer function. If
x
x
x
is not an integer but positive, then what is the value of
z
z
z
?
Add
Lever: Modulus / absolute value behaviour
A
−
1
-1
−
1
B
0
0
0
C
1
1
1
D
2
2
2
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[Q71 · Sep · 2024]
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Q4692
#4692
Mathematics → Functions → Composition and Inverse of Functions
·
Easy
If
f
(
x
)
=
4
x
+
1
f(x)=4x+1
f
(
x
)
=
4
x
+
1
and
g
(
x
)
=
k
x
+
2
g(x)=kx+2
g
(
x
)
=
k
x
+
2
such that
f
∘
g
(
x
)
=
g
∘
f
(
x
)
f\circ g(x)=g\circ f(x)
f
∘
g
(
x
)
=
g
∘
f
(
x
)
, then what is the value of
k
k
k
?
Add
NDA Maths strategy
A
7
7
7
B
5
5
5
C
4
4
4
D
3
3
3
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[Q72 · Sep · 2024]
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Q4693
#4693
Mathematics → Functions → Domain, Range, and Function Properties
·
Easy
What is the minimum value of the function
f
(
x
)
=
log
10
(
x
2
+
2
x
+
11
)
f(x)=\log_{10}(x^2+2x+11)
f
(
x
)
=
lo
g
10
(
x
2
+
2
x
+
11
)
?
Add
NDA Maths strategy
A
0
0
0
B
1
1
1
C
2
2
2
D
10
10
10
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[Q73 · Sep · 2024]
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Q4694
#4694
Mathematics → Limits & Continuity → One-Sided Limits, Greatest Integer, and Absolute Value Limits
·
Easy
Which one of the following is correct regarding
lim
x
→
3
∣
x
−
3
∣
x
−
3
\displaystyle\lim_{x\to3}\dfrac{|x-3|}{x-3}
x
→
3
lim
x
−
3
∣
x
−
3∣
?
Add
Lever: Modulus / absolute value behaviour
A
Limit exists and is equal to 1
B
Limit exists and is equal to 0
C
Limit exists and is equal to -1
D
Limit does not exist
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[Q74 · Sep · 2024]
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Q4695
#4695
Mathematics → Application of Derivatives → Monotonicity, Extrema, and Critical Points
·
Easy
What is the maximum value of
a
cos
x
+
b
sin
x
+
c
a\cos x+b\sin x+c
a
cos
x
+
b
sin
x
+
c
?
Add
NDA Maths strategy
A
a
2
+
b
2
+
c
\sqrt{a^2+b^2}+c
a
2
+
b
2
+
c
B
a
2
+
b
2
+
c
\sqrt{a^2+b^2+c}
a
2
+
b
2
+
c
C
a
2
+
b
2
−
c
\sqrt{a^2+b^2-c}
a
2
+
b
2
−
c
D
a
2
+
b
2
\sqrt{a^2+b^2}
a
2
+
b
2
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[Q75 · Sep · 2024]
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Q4696
#4696
Mathematics → Functions → Functional Equations
·
Moderate
If
f
(
2
x
)
=
4
x
2
+
1
f(2x)=4x^2+1
f
(
2
x
)
=
4
x
2
+
1
, then for how many real values of
x
x
x
will
f
(
2
x
)
f(2x)
f
(
2
x
)
be the GM of
f
(
x
)
f(x)
f
(
x
)
and
f
(
4
x
)
f(4x)
f
(
4
x
)
?
Add
NDA Maths strategy
A
Four
B
Two
C
One
D
None
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[Q76 · Sep · 2024]
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Q4697
#4697
Mathematics → Functions → Greatest Integer Function
·
Moderate
If
f
(
x
)
=
[
x
]
2
−
30
[
x
]
+
221
=
0
f(x)=[x]^2-30[x]+221=0
f
(
x
)
=
[
x
]
2
−
30
[
x
]
+
221
=
0
, where
[
x
]
[x]
[
x
]
is the greatest integer function, then what is the sum of all integer solutions?
Add
Lever: Modulus / absolute value behaviour
A
13
13
13
B
17
17
17
C
27
27
27
D
30
30
30
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[Q77 · Sep · 2024]
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Q4698
#4698
Mathematics → Functions → Functional Equations
·
Moderate
If
f
(
x
)
=
9
x
−
8
x
f(x)=9^x-8^x
f
(
x
)
=
9
x
−
8
x
such that
g
(
x
)
=
f
(
x
)
−
1
g(x)=f(x)-1
g
(
x
)
=
f
(
x
)
−
1
, then which one of the following is correct?
Add
NDA Maths strategy
A
g
(
x
)
=
0
g(x)=0
g
(
x
)
=
0
has no real roots
B
g
(
x
)
=
0
g(x)=0
g
(
x
)
=
0
has only one real root which is an integer
C
g
(
x
)
=
0
g(x)=0
g
(
x
)
=
0
has two real roots which are integers
D
g
(
x
)
=
0
g(x)=0
g
(
x
)
=
0
has only one real root which is not an integer
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[Q78 · Sep · 2024]
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Q4699
#4699
Mathematics → Limits & Continuity → Limit Evaluation Techniques — L'Hôpital, Rationalization, Standard Forms
·
Easy
What is
lim
θ
→
π
/
2
(
sec
θ
−
tan
θ
)
\displaystyle\lim_{\theta\to\pi/2}(\sec\theta-\tan\theta)
θ
→
π
/2
lim
(
sec
θ
−
tan
θ
)
equal to?
Add
NDA Maths strategy
A
−
1
-1
−
1
B
0
0
0
C
1
2
\dfrac{1}{2}
2
1
D
1
1
1
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[Q79 · Sep · 2024]
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Q4700
#4700
Mathematics → Functions → Functional Equations
·
Easy
Let
f
(
x
)
f
(
y
)
=
f
(
x
y
)
f(x)f(y)=f(xy)
f
(
x
)
f
(
y
)
=
f
(
x
y
)
for all real
x
,
y
x,y
x
,
y
. If
f
(
2
)
=
4
f(2)=4
f
(
2
)
=
4
, then what is the value of
f
(
1
2
)
f\!\left(\dfrac{1}{2}\right)
f
(
2
1
)
?
Add
NDA Maths strategy
A
1
4
\dfrac{1}{4}
4
1
B
1
2
\dfrac{1}{2}
2
1
C
1
1
1
D
4
4
4
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[Q80 · Sep · 2024]
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