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NDA Mock Test - 2 - Defence MCQ

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30 Questions MCQ Test - NDA Mock Test - 2

NDA Mock Test - 2 for Defence 2024 is part of Defence preparation. The NDA Mock Test - 2 questions and answers have been prepared according to the Defence exam syllabus.The NDA Mock Test - 2 MCQs are made for Defence 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for NDA Mock Test - 2 below.

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NDA Mock Test - 2 - Question 1

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What is the modulus of

A.
B.
C.
D.
None of these

NDA Mock Test - 2 - Question 2

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If α is a complex number such that α² + α + 1 = 0, then what is α³¹ equal to?

A.
α
B.
α²
C.
0
D.
1

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NDA Mock Test - 2 - Question 3

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If ω is the cube root of unity, then what is the conjugate of 2ω² + 3i?

A.
2ω – 3i
B.
3ω + 2i
C.
2ω + 3i
D.
3ω – 2i

NDA Mock Test - 2 - Question 4

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If one root of 5x²+13x+k=0 is reciprocal of the other, then k is equal to

A.
5
B.
6
C.
1/6
D.
2

Detailed Solution for NDA Mock Test - 2 - Question 4

let the two roots be a and 1/a

so product of roots

a x 1/a = k/5

k = 5

NDA Mock Test - 2 - Question 5

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The quadratic equation x² + bx + 4 = 0 will have real roots, if

A.
Only b ≤ –4
B.
Only b ≥ 4
C.
–4 < b < 4
D.
b ≤ –4, b ≥ 4

NDA Mock Test - 2 - Question 6

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The roots of the equation x² – 8x + 16 = 0

A.
are imaginary
B.
are distinct and real
C.
are equal and real
D.
Cannot be determined

NDA Mock Test - 2 - Question 7

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If the roots of a quadratic equation ax² + bx + c = 0 are α and β, then the quadratic equation having roots α² and β² is

A.
x² – (b² – 2ac) x + c = 0
B.
a²x² – (b² – 2ac) x + c = 0
C.
ax² – (b² – 2ac) x + c² = 0
D.
a²x² – (b² – 2ac) x + c² = 0

NDA Mock Test - 2 - Question 8

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Consider the following statements

I. The matrix is singular.
II. The matrix is non-singular.

Which of the above statement is/are correct?

A.
Only I
B.
Only II
C.
Both I and II
D.
Either I nor II

NDA Mock Test - 2 - Question 9

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Consider the following statements

I. Every zero matrix is a square matrix.
II. A matrix has a numerical value.
III. A unit matrix is a diagonal matrix.

Which of the above statement is/are correct?

A.
Only II
B.
Only III
C.
Both II and III
D.
Both I and III

NDA Mock Test - 2 - Question 10

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What is the order of the product

A.
3 x 1
B.
1 x 1
C.
1 x 3
D.
3 x 3

NDA Mock Test - 2 - Question 11

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For what value of x does hold?

A.
–1
B.
1
C.
9/8
D.
–9/8

NDA Mock Test - 2 - Question 12

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The value of the determinant

A.
is a perfect cube
B.
is a perfect square
C.
has linear factor
D.
is zero

NDA Mock Test - 2 - Question 13

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If a–1 + b–1 + c–1 = 0 such that λ, then what is λ equal to?

A.
–abc
B.
abc
C.
0
D.
1

NDA Mock Test - 2 - Question 14

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then what is the value of the determinant

A.
10
B.
20
C.
40
D.
60

NDA Mock Test - 2 - Question 15

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then what is the value of ?

A.
12
B.
–12
C.
7
D.
–7

NDA Mock Test - 2 - Question 16

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What is the value of sin

NDA Mock Test - 2 - Question 17

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NDA Mock Test - 2 - Question 18

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If A + B + C = π/2, then what is the value of tan A tan B + tan B tan C + tan C tan A?

A.
0
B.
1
C.
–1
D.
tan A tan B tan C

NDA Mock Test - 2 - Question 19

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where m is a non-square natural number m, then sec 2θ is

A.
a negative number
B.
a transcendental number
C.
an irrational number
D.
a rational number

NDA Mock Test - 2 - Question 20

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If A then what is the value of

A.
-1
B.
1
C.
1/3
D.
3

NDA Mock Test - 2 - Question 21

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If (sin x + cosec x)² + (cos x + sec x)² = k + tan²xcot²x, then what is the value of k?

A.
8
B.
7
C.
4
D.
3

Detailed Solution for NDA Mock Test - 2 - Question 21

NDA Mock Test - 2 - Question 22

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is equal to

A.
sin γ
B.
C.
D.
cos γ

NDA Mock Test - 2 - Question 23

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If 4 (sin²α + sin²β + sin²γ) = a², then a is equal to

NDA Mock Test - 2 - Question 24

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A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point P on the plane, the angle of elevation of the bottom of the flag staff α and that of the top is β. What is the height of the tower?

Detailed Solution for NDA Mock Test - 2 - Question 24

NDA Mock Test - 2 - Question 25

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Looking from the top of a 20 m high building, the angle of elevation of the top of a tower is 60^o and the angle of depression of its bottom is 30^o. What is the height of the tower?

A.
50 m
B.
60 m
C.
70 m
D.
80 m

Detailed Solution for NDA Mock Test - 2 - Question 25

NDA Mock Test - 2 - Question 26

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If the angles of a triangle are 30^o and 45^o and the included side is cm, then what is the area of the triangle?

NDA Mock Test - 2 - Question 27

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If, in general, the value of sin A is known but the value of A is not known, then how many values of tan can be calculated?

A.
1
B.
2
C.
3
D.
4

NDA Mock Test - 2 - Question 28

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If in a ΔABC, cos B = (sin A)/(2 sin C), then the triangle is

A.
isosceles triangle
B.
equilateral triangle
C.
right angled triangle
D.
scalene triangle

NDA Mock Test - 2 - Question 29

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The equation to the locus of a point which is always equidistant from the points (1, 0) and (0, –2) is

A.
2x + 4y + 3 = 0
B.
4x + 2y + 3 = 0
C.
2x + 4y – 3 = 0
D.
4x + 2y – 3 = 0

NDA Mock Test - 2 - Question 30

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The points (5, 1), (1, –1) and (11, 4) are

A.
collinear
B.
vertices of right angled triangle
C.
vertices of equilateral triangle
D.
vertices of an isosceles triangle

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