Defence Exams Preparation Resources

Defence Exams

NDA

Q. If A = 5i + 5j and B = 5i - 5j, what is the value of A · B?

A. 0
B. 25
C. 50
D. 10

Solution

A · B = (5)(5) + (5)(-5) = 25 - 25 = 0.

Correct Answer: B — 25

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Q. If A = 5i - 2j + k and B = 3i + 4j - 2k, calculate A · B.

A. -1
B. 1
C. 0
D. 2

Solution

A · B = (5)(3) + (-2)(4) + (1)(-2) = 15 - 8 - 2 = 5.

Correct Answer: A — -1

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Q. If A = 5i - 2j and B = -3i + 4j, calculate A · B. (2023)

A. -23
B. -7
C. 7
D. 23

Solution

A · B = (5)(-3) + (-2)(4) = -15 - 8 = -23

Correct Answer: A — -23

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Q. If A = 5i - 2j and B = -3i + 4j, what is the value of A · B?

A. -23
B. -7
C. 7
D. 23

Solution

A · B = (5)(-3) + (-2)(4) = -15 - 8 = -23.

Correct Answer: A — -23

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Q. If A = 6i + 8j and B = 2i + 3j, calculate A · B.

A. 36
B. 42
C. 38
D. 30

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: A — 36

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Q. If A = 6i + 8j and B = 2i + 3j, find A · B.

A. 36
B. 42
C. 30
D. 24

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: A — 36

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Q. If A = 6i + 8j and B = 2i + 3j, find the scalar product A · B.

A. 42
B. 54
C. 48
D. 36

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: C — 48

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Q. If A = 6i + 8j and B = 2i + 3j, what is the scalar product A · B?

A. 42
B. 36
C. 30
D. 48

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: B — 36

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Q. If A = 6i + 8j and B = 2i + 3j, what is the value of A · B?

A. 54
B. 60
C. 48
D. 42

Solution

A · B = (6)(2) + (8)(3) = 12 + 24 = 36.

Correct Answer: A — 54

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Q. If A = 6i + 8j and B = 3i + 4j, what is the angle between A and B?

A. 0°
B. 30°
C. 45°
D. 90°

Solution

A · B = 6*3 + 8*4 = 18 + 32 = 50. |A| = 10, |B| = 5. cos(θ) = 50/(10*5) = 1. θ = 0°.

Correct Answer: D — 90°

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Q. If A = 6i + 8j and B = 3i + 4j, what is the value of A · B?

A. 50
B. 54
C. 48
D. 52

Solution

A · B = (6)(3) + (8)(4) = 18 + 32 = 50.

Correct Answer: C — 48

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Q. If A = 6i - 2j and B = -3i + 4j, find A · B.

A. -18
B. -24
C. -12
D. -6

Solution

A · B = (6)(-3) + (-2)(4) = -18 - 8 = -26.

Correct Answer: A — -18

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Q. If A = 7i + 1j and B = 1i + 7j, calculate A · B.

A. 56
B. 58
C. 60
D. 62

Solution

A · B = (7)(1) + (1)(7) = 7 + 7 = 14.

Correct Answer: A — 56

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Q. If A = 7i + 1j and B = 1i + 7j, find A · B.

A. 56
B. 14
C. 8
D. 50

Solution

A · B = (7)(1) + (1)(7) = 7 + 7 = 14.

Correct Answer: A — 56

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Q. If A = 7i + 1j and B = 2i + 3j, what is the scalar product A · B? (2022)

A. 23
B. 21
C. 19
D. 17

Solution

A · B = (7)(2) + (1)(3) = 14 + 3 = 17

Correct Answer: A — 23

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Q. If A = 7i - 2j and B = -3i + 4j, find A · B. (2021)

A. -26
B. -28
C. -30
D. -32

Solution

A · B = (7)(-3) + (-2)(4) = -21 - 8 = -29.

Correct Answer: A — -26

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Q. If A = 7i - 3j and B = -2i + 5j, what is the value of A · B?

A. -29
B. -31
C. -25
D. -27

Solution

A · B = (7)(-2) + (-3)(5) = -14 - 15 = -29.

Correct Answer: A — -29

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Q. If A = ai + bj and B = ci + dj, what is the expression for A · B?

A. ac + bd
B. ab + cd
C. ad + bc
D. a + b + c + d

Solution

A · B = (ai + bj) · (ci + dj) = ac + bd.

Correct Answer: A — ac + bd

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Q. If A = i + 2j + 3k and B = 4i + 5j + 6k, what is the value of A · B?

A. 32
B. 30
C. 28
D. 26

Solution

A · B = (1)(4) + (2)(5) + (3)(6) = 4 + 10 + 18 = 32.

Correct Answer: B — 30

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Q. If A = [[2, 3], [1, 4]], what is A^2? (2020)

A. [[7, 18], [18, 7]]
B. [[12, 21], [21, 12]]
C. [[12, 21], [21, 16]]
D. [[10, 21], [21, 10]]

Solution

A^2 = A * A = [[2*2 + 3*1, 2*3 + 3*4], [1*2 + 4*1, 1*3 + 4*4]] = [[10, 21], [21, 16]].

Correct Answer: C — [[12, 21], [21, 16]]

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Q. If A = [[2, 3], [1, 4]], what is the inverse of A?

A. [[4, -3], [-1, 2]]
B. [[4, 3], [-1, 2]]
C. [[2, -3], [-1, 2]]
D. [[3, -2], [-1, 2]]

Solution

The inverse of A is given by (1/det(A)) * adj(A). Det(A) = (2*4) - (3*1) = 5. The adjoint is [[4, -3], [-1, 2]]. Thus, A^(-1) = (1/5) * [[4, -3], [-1, 2]].

Correct Answer: A — [[4, -3], [-1, 2]]

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Q. If a basketball court is 28 meters long and 15 meters wide, what is the area of the court? (2022)

A. 420 m²
B. 300 m²
C. 450 m²
D. 350 m²

Solution

Area = Length * Width = 28 m * 15 m = 420 m².

Correct Answer: A — 420 m²

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Q. If a basketball hoop is 3.05 meters high and a player jumps 0.75 meters high, how far below the hoop is the player at the peak of their jump? (2023)

A. 2.3 m
B. 2.5 m
C. 2.75 m
D. 3.05 m

Solution

Height below the hoop = height of hoop - height of jump = 3.05 m - 0.75 m = 2.3 m.

Correct Answer: B — 2.5 m

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Q. If a basketball player makes 75% of his free throws and he attempts 40 free throws, how many successful free throws does he make? (2022)

A. 25
B. 30
C. 35
D. 40

Solution

Successful free throws = 75% of 40 = 0.75 * 40 = 30.

Correct Answer: B — 30

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Q. If a bill is introduced in the Lok Sabha and it takes 3 readings before being passed, how many readings are required if it is also to be passed in the Rajya Sabha, assuming the same process?

A. 6
B. 5
C. 4
D. 3

Solution

3 readings in Lok Sabha + 3 readings in Rajya Sabha = 6 readings total.

Correct Answer: A — 6

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Q. If a bill is introduced in the Lok Sabha and it takes 3 readings before being passed, how many total readings are required if it also needs to be passed in the Rajya Sabha, which requires 2 readings?

A. 5
B. 6
C. 7
D. 8

Solution

Total readings = 3 (Lok Sabha) + 2 (Rajya Sabha) = 5.

Correct Answer: B — 6

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Q. If a bill is introduced in the Lok Sabha and it takes 3 readings before being passed, how many readings are required in total for 5 bills?

A. 15
B. 12
C. 10
D. 8

Solution

Total readings = 5 bills * 3 readings = 15 readings.

Correct Answer: A — 15

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Q. If a bill is introduced in the Lok Sabha and it takes 3 readings before it can be passed, how many readings are required in total for 5 bills?

A. 10
B. 12
C. 15
D. 18

Solution

Total readings for 5 bills = 5 bills * 3 readings = 15 readings.

Correct Answer: A — 10

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Q. If a bill is introduced in the Lok Sabha and it takes 3 readings before it can be passed, how many total readings are required for 2 bills?

A. 6
B. 5
C. 4
D. 3

Solution

Total readings for 2 bills = 2 * 3 = 6

Correct Answer: A — 6

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Q. If a bill is introduced in the Lok Sabha and it takes 3 readings before it can be passed, how many total readings are required for 5 bills? (2023)

A. 10
B. 12
C. 15
D. 18

Solution

Each bill requires 3 readings. For 5 bills, total readings = 5 * 3 = 15.

Correct Answer: A — 10

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Defence Exams

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