Sets, Relations & Functions · NDA previous year questions

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2024 29 questions

Q22024 · 1 Sept 2024
Consider the following statements: I. The set of all irrational numbers between $12$ and $15$ is an infinite set. II. The set of all odd integers less than 1000 is a finite set. Which of the statements given above are correct?
1. A.I only
2. B.II only
3. C.Both I and II
4. D.Neither I nor II
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Answer: A
Q32024 · 1 Sept 2024
How many 4-digit numbers are there having all digits as odd?
1. A.625
2. B.400
3. C.196
4. D.120
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Answer: A
Q342024 · 1 Sept 2024
Let P and Q be two non-void relations on a set A. Which of the following statements are correct? I. P and Q are reflexive ⇒ P ∩ Q is reflexive. II. P and Q are symmetric ⇒ P ∪ Q is symmetric. III. P and Q are transitive ⇒ P ∩ Q is transitive. Select the answer using the code given below.
1. A.I and II only
2. B.II and III only
3. C.I and III only
4. D.I, II and III
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Answer: D
Q352024 · 1 Sept 2024
If A and B are two non-empty sets having 10 elements in common, then how many elements do A x B and B x A have in common?
1. A.10
2. B.20
3. C.40
4. D.100
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Answer: D
Q362024 · 1 Sept 2024
What is the remainder when $7^{n} - 6 n$ is divided by 36 for $n = 100$ ?
1. A.0
2. B.1
3. C.2
4. D.6
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Answer: B
Q642024 · 1 Sept 2024
What is the point of intersection of the diagonals of the trapezium?
1. A.(3, 7/2)
2. B.(3, 7/3)
3. C.(7/2, 2)
4. D.(5/2, 2)
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Answer: C
Q702024 · 1 Sept 2024
What is the point of intersection of L and P?
1. A.(4, 3, -3)
2. B.(4, -3, 3)
3. C.(-4, -3, -3)
4. D.(-4, -3, 3)
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Answer: D
Q712024 · 1 Sept 2024
Let z = [y] and y = [x] - x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z?
1. A.-1
2. B.0
3. C.1
4. D.2
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Answer: A
Q722024 · 1 Sept 2024
If f(x) = 4x + 1 and g(x) = kx + 2 such that f o g(x) = g o f(x), then what is the value of k?
1. A.7
2. B.5
3. C.4
4. D.3
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Answer: A
Q772024 · 1 Sept 2024
If $f (x) = [x]^{2} - 30 [x] + 221 = 0$ , where [x] is the greatest integer function, then what is the sum of all integer solutions?
1. A.13
2. B.17
3. C.27
4. D.30
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Answer: D
Q782024 · 1 Sept 2024
If f(x) = 9x - 8√x such that g(x) = f(x) - 1, then which one of the following is correct?
1. A.g(x) = 0 has no real roots
2. B.g(x) = 0 has only one real root which is an integer
3. C.g(x) = 0 has two real roots which are integers
4. D.g(x) = 0 has only one real root which is not an integer
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Answer: B
Q792024 · 1 Sept 2024
What is $lim_{θ \to \frac{π}{2}} (sec θ - tan θ)$ equal to?
1. A.-1
2. B.0
3. C.1/2
4. D.1
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Answer: B
Q802024 · 1 Sept 2024
Let f(x) f(y) = f(xy) for all real x, y. If f(2) = 4, then what is the value of f(1/2)?
1. A.1/4
2. B.1/2
3. C.1
4. D.4
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Answer: A
Q222024 · 21 Apr 2024
Let $A = {x \in R : - 1 < x < 1}$ . Which of the following is/are bijective functions from A to itself? 1. $f (x) = x ∣ x ∣$ 2. $g (x) = cos (π x)$ Select the correct answer using the code given below:
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: A
Q232024 · 21 Apr 2024
Let $R$ be a relation on the open interval $(- 1, 1)$ and is given by $R = {(x, y) : ∣ x + y ∣ < 2}$ . Then which one of the following is correct?
1. A. $R$ is reflexive but neither symmetric nor transitive
2. B. $R$ is reflexive and symmetric but not transitive
3. C. $R$ is reflexive and transitive but not symmetric
4. D. $R$ is an equivalence relation
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Answer: D
Q242024 · 21 Apr 2024
For any three non-empty sets $A, B, C$ , what is $(A \cup B - {(A - B) \cup (B - A) \cup (A \cap B)})$ equal to?
1. A.Null set
2. B. $A$
3. C. $B$
4. D. $(A \cup B) - (A \cap B)$
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Answer: A
Q252024 · 21 Apr 2024
If $a, b, c$ are the sides of a triangle $A B C$ , then what is $b sin A c sin A 1 cos A cos A 1$ equal to?
1. A.Zero
2. B.Area of triangle
3. C.Perimeter of triangle
4. D. $a^{2} + b^{2} + c^{2}$
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Answer: A
Q352024 · 21 Apr 2024
Let $A = {1, 2, 3, 4, 5}$ and $B = {6, 7}$ . What is the number of onto functions from $A$ to $B$ ?
1. A.10
2. B.20
3. C.30
4. D.32
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Answer: C
Q362024 · 21 Apr 2024
What is $\frac{3 c o s 1 0 ^{\circ} - s i n 1 0 ^{\circ}}{s i n 2 5 ^{\circ} c o s 2 5 ^{\circ}}$ equal to ?
1. A.1
2. B. $3$
3. C.2
4. D.4
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Answer: D
Q372024 · 21 Apr 2024
What is $sin 9^{\circ} - cos 9^{\circ}$ equal to?
1. A. $- \frac{5 - 5}{2}$
2. B. $- \frac{5 - 3}{2}$
3. C. $\frac{5 - 5}{2}$
4. D. $\frac{5 - 5}{4}$
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Answer: A
Q802024 · 21 Apr 2024
Which one of the following is correct in respect of $f (x) = \frac{1}{∣ x ∣ - x}$ and $g (x) = \frac{1}{x - ∣ x ∣}$ ?
1. A. $f (x)$ has some domain and $g (x)$ has no domain
2. B. $f (x)$ has no domain and $g (x)$ has some domain
3. C. $f (x)$ and $g (x)$ have the same domain
4. D. $f (x)$ and $g (x)$ do not have any domain
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Answer: A
Q812024 · 21 Apr 2024
Consider the following for the next two (02) items that follow: Given that $\int \frac{3 c o s x + 4 s i n x}{2 c o s x + 5 s i n x} d x = \frac{α x}{29} + \frac{β}{29} ln ∣2 cos x + 5 sin x ∣ + c$ What is the value of $α$ ?
1. A.7
2. B.13
3. C.17
4. D.26
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Answer: D
Q822024 · 21 Apr 2024
Consider the following for the next two (02) items that follow: Given that $\int \frac{3 c o s x + 4 s i n x}{2 c o s x + 5 s i n x} d x = \frac{α x}{29} + \frac{β}{29} ln ∣2 cos x + 5 sin x ∣ + c$ What is the value of $β$ ?
1. A.7
2. B.13
3. C.17
4. D.26
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Answer: A
Q852024 · 21 Apr 2024
Consider the following for the next two (02) items that follow: Let $f (x)$ and $g (x)$ be two functions such that $g (x) = x - \frac{1}{x}$ and $f \circ g (x) = x^{3} - \frac{1}{x ^{3}}$ . What is $g [f (x) - 3 x]$ equal to?
1. A. $x^{3} - \frac{1}{x ^{3}}$
2. B. $x^{3} + \frac{1}{x ^{3}}$
3. C. $x^{2} - \frac{1}{x ^{2}}$
4. D. $x^{2} + \frac{1}{x ^{2}}$
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Answer: A
Q862024 · 21 Apr 2024
Consider the following for the next two (02) items that follow: Let $f (x)$ and $g (x)$ be two functions such that $g (x) = x - \frac{1}{x}$ and $f \circ g (x) = x^{3} - \frac{1}{x ^{3}}$ . What is $f^{''} (x)$ equal to?
1. A. $\frac{- 2}{x ^{3}}$
2. B. $2 x + \frac{2}{x ^{3}}$
3. C. $6 x + 3$
4. D. $6 x$
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Answer: D