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NDA Mock Test - 4 - NDA MCQ

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30 Questions MCQ Test NDA (National Defence Academy) Mock Test Series 2024 - NDA Mock Test - 4

NDA Mock Test - 4 for NDA 2024 is part of NDA (National Defence Academy) Mock Test Series 2024 preparation. The NDA Mock Test - 4 questions and answers have been prepared according to the NDA exam syllabus.The NDA Mock Test - 4 MCQs are made for NDA 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for NDA Mock Test - 4 below.

Solutions of NDA Mock Test - 4 questions in English are available as part of our NDA (National Defence Academy) Mock Test Series 2024 for NDA & NDA Mock Test - 4 solutions in Hindi for NDA (National Defence Academy) Mock Test Series 2024 course. Download more important topics, notes, lectures and mock test series for NDA Exam by signing up for free. Attempt NDA Mock Test - 4 | 150 questions in 150 minutes | Mock test for NDA preparation | Free important questions MCQ to study NDA (National Defence Academy) Mock Test Series 2024 for NDA Exam | Download free PDF with solutions

NDA Mock Test - 4 - Question 1

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Directions : The students of a class are offered three languages (Hindi, English and French). 15 students learn all the three languages whereas 28 students do not learn any language. The number of students learning Hindi and English but not French is twice the number of students learning Hindi and French but not English. The number of students learning English and French but not Hindi is thrice the number of students learning Hindi and French but not English. 23 students learn only Hindi and 17 students learn only English. The total number of students learning French is 46 and the total number of students learning only French is 11.

Q.

How many students learn precisely two languages

A.
55
B.
40
C.
30
D.
13

NDA Mock Test - 4 - Question 2

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The students of a class are offered three languages (Hindi, English and French). 15 students learn all the three languages whereas 28 students do not learn any language. The number of students learning Hindi and English but not French is twice the number of students learning Hindi and French but not English. The number of students learning English and French but not Hindi is thrice the number of students learning Hindi and French but not English. 23 students learn only Hindi and 17 students learn only English. The total number of students learning French is 46 and the total number of students learning only French is 11.

Q.

How many students learn at least two languages

A.
15
B.
30
C.
45
D.
55

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NDA Mock Test - 4 - Question 3

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The students of a class are offered three languages (Hindi, English and French). 15 students learn all the three languages whereas 28 students do not learn any language. The number of students learning Hindi and English but not French is twice the number of students learning Hindi and French but not English. The number of students learning English and French but not Hindi is thrice the number of students learning Hindi and French but not English. 23 students learn only Hindi and 17 students learn only English. The total number of students learning French is 46 and the total number of students learning only French is 11.

Q.

How many students learn English and French

A.
30
B.
43
C.
45
D.
73

NDA Mock Test - 4 - Question 4

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Let A = {x| x ≤ 9, x ∈ N}. Let B = {a, b, c} be the subset of A where (a + b + c) is a multiple of 3. What is the largest possible number of subsets like B?

A.
12
B.
21
C.
27
D.
30

NDA Mock Test - 4 - Question 5

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A mapping f : R → R which is defined as f (x) = cos x; x ∈ R is

A.
only one-one
B.
only onto
C.
one-one onto
D.
Neither one-one nor onto

NDA Mock Test - 4 - Question 6

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If ω is a complex cube root of unity, then what is ω¹⁰ + ω^–10 equal to

A.
2
B.
–1
C.
–2
D.
1

NDA Mock Test - 4 - Question 7

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What is the value of

A.
–1
B.
0
C.
1
D.
2

NDA Mock Test - 4 - Question 8

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What is the modulus of

A.
5
B.
4
C.
3
D.
1

NDA Mock Test - 4 - Question 9

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100101 + 101 + 1101 + 100 is equal to

A.
1101001
B.
100000
C.
111011
D.
None of these

NDA Mock Test - 4 - Question 10

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The decimal number (57.375)₁₀ when converted to binary number takes the form

A.
(111001.011)₂
B.
(100111.110)₂
C.
(110011.101)₂
D.
(111011.011)₂

NDA Mock Test - 4 - Question 11

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The number 292 in decimal system is expressed in binary system by

A.
100001010
B.
100010001
C.
100100100
D.
10101000

NDA Mock Test - 4 - Question 12

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In a GP of positive terms, any term is equal to one-third of the sum of next two terms. What is the common ratio of the GP?

NDA Mock Test - 4 - Question 13

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If the AM and GM between two numbers are in the ratio m : n, then what is the ratio between the two numbers?

NDA Mock Test - 4 - Question 14

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If the roots of the equation 3ax² + 2bx + c = 0 are in the ratio 2 : 3, then which one of the following is correct?

A.
8ac = 25b
B.
8ac = 9b²
C.
8b² = 9ac
D.
8b² = 25ac

NDA Mock Test - 4 - Question 15

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If the roots of a quadratic equation are m + n and m – n, then the quadratic equation will be

A.
x² + 2mx + m² – mn + n² = 0
B.
x² + 2mx + (m – n)² = 0
C.
x² – 2mx + m² – n² = 0
D.
x² + 2mx + m² – n² = 0

NDA Mock Test - 4 - Question 16

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What is the sum of the squares of the roots of the equation x² + 2x – 143 = 0

A.
170
B.
180
C.
190
D.
290

NDA Mock Test - 4 - Question 17

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How many diagonals will be there in an n-sided regular polygon

A.
B.
C.
n² – n
D.

NDA Mock Test - 4 - Question 18

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There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. What is the number of ways in which the votes can be given

A.
1048
B.
1072
C.
1024
D.
625

NDA Mock Test - 4 - Question 19

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What is the number of three digit odd numbers formed by using the digits 1, 2, 3, 4, 5, 6 if repetition of digits is allowed

A.
60
B.
108
C.
120
D.
216

NDA Mock Test - 4 - Question 20

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What is the ratio of coefficient of x¹⁵ to the term independent of x in

A.
1/64
B.
1/32
C.
1/16
D.
1/4

NDA Mock Test - 4 - Question 21

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What is the coefficient of x¹⁷ in the expansion of

A.
189/8
B.
567/2
C.
21/16
D.
None of these

NDA Mock Test - 4 - Question 22

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What is the term independent of x in the expansion of (1 + x + 2x³)

A.
1/3
B.
19/54
C.
1/4
D.
No such term exists in the expansion

NDA Mock Test - 4 - Question 23

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A.
0
B.
1
C.
17/8
D.
23/17

NDA Mock Test - 4 - Question 24

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A.
0
B.
1
C.
2
D.
None of these

NDA Mock Test - 4 - Question 25

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Directions : If A and B are two matrices of same order, then

(AB)ⁿ = AⁿBⁿ is

A.
always true
B.
never true
C.
true only when AB = BA
D.
None of these

NDA Mock Test - 4 - Question 26

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If A and B are two matrices of same order, then

If A and B are symmetric matrices, then (ABA)^T is

A.
symmetric matrix
B.
skew-symmetric matrix
C.
diagonal matrix
D.
None of these

NDA Mock Test - 4 - Question 27

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If A and B are two matrices of same order, then

If AB = BA, then (A + B)² is equal to

A.
A² + 2AB + B²
B.
A² + B²
C.
A² + 2BA – B²
D.
None of these

NDA Mock Test - 4 - Question 28

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If the sum of the matrices is the matrix then what is the value of y?

A.
–5
B.
0
C.
5
D.
10

NDA Mock Test - 4 - Question 29

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If where a, b are natural numbers, then which one of the following is correct?

A.
There exist more than one but finite number of B's such that AB = BA
B.
There exist exactly one B such that AB = BA
C.
There exist infinitely many B's such that AB = BA
D.
There cannot exist any B such that AB = BA

NDA Mock Test - 4 - Question 30

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What is the value of the determinant

A.
x + 2
B.
x² + 2
C.
2
D.
–2

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