Algebra
Sets, Relations and Functions
MCQ (Single Correct Answer)
Quadratic Equations and Inequalities
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Sequence And Series
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Permutations and Combinations
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Three Dimensional Geometry
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Trigonometry
Trigonometric Angles and Equations
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Inverse Trigonometric Function
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Height and Distance
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Properties of Triangles
MCQ (Single Correct Answer)
Calculus
Limit, Continuity and Differentiability
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Application of Derivatives
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Indefinite Integration
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Definite Integration
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Area Under The Curves
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Differential Equations
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1
NDA Mathematics 14 November 2021
MCQ (Single Correct Answer)
+2.5
-0.83

Consider the following statements:

1. A-line in space can have infinitely many direction ratios.

2. It is possible for certain lines that the sum of the squares of direction cosines can be equal to the sum of its direction cosines.

Which of the above statements is/are correct?

A
1 only
B
2 only
C
Both 1 and 2
D
Neither 1 nor 2
2
NDA Mathematics 14 November 2021
MCQ (Single Correct Answer)
+2.5
-0.83
The xy-plane divides the line segment joining the points (-1, 3, 4) and (2, -5, 6)
A
internally in the ratio 2 ∶ 3 
B
internally in the ratio 3 ∶ 2 
C
externally in the ratio 2 ∶ 3 
D
internally in the ratio 2 ∶ 1 
3
NDA Mathematics 14 November 2021
MCQ (Single Correct Answer)
+2.5
-0.83
The number of spheres of radius r touching the coordinate axes is
A
4
B
6
C
8
D
infinite
4
NDA Mathematics 14 November 2021
MCQ (Single Correct Answer)
+2.5
-0.83
ABCDEFGH is a cuboid with base ABCD. Let A(0, 0, 0), B(12, 0, 0), C(12, 6, 0) and G(12, 6, 4) be the vertices. If α is the angle between AB and AG; β is the angle between AC and AG, then what is the value of cos 2α + cos 2β? 
A
$\frac{40}{49}$
B
$\frac{64}{49}$
C
$\frac{120}{49}$
D
$\frac{160}{49}$