Sets, Relations & Functions · NDA previous year questions

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2018 29 questions

Q12018 · 9 Sept 2018
If A, B and C are subsets of a Universal set, then which one of the following is not correct?
1. A. $A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$
2. B. $A^{'} \cup (A \cup B) = (B^{'} \cap A)^{'} \cup A$
3. C. $A^{'} \cup (B \cup C) = (C^{'} \cap B)^{'} \cap A^{'}$
4. D. $(A \cap B) \cup C = (A \cup C) \cap (B \cup C)$
Show answer
Answer: C
Q22018 · 9 Sept 2018
Passage
Consider the information given below and answer the two (02) items that follow: A survey was conducted among 300 students. It was found that 125 students like to play cricket, 145 students like to play football and 90 students like to play tennis. 32 students like to play exactly two games out of the three games.
How many students like to play all the three games?
1. A.14
2. B.21
3. C.28
4. D.35
Show answer
Answer: A
Q32018 · 9 Sept 2018
Passage
Consider the information given below and answer the two (02) items that follow: A survey was conducted among 300 students. It was found that 125 students like to play cricket, 145 students like to play football and 90 students like to play tennis. 32 students like to play exactly two games out of the three games.
How many students like to play exactly only one game?
1. A.196
2. B.228
3. C.254
4. D.268
Show answer
Answer: C
Q42018 · 9 Sept 2018
Let $A = {x \in R : - 1 \leq x \leq 1}$ , $B = {y \in R : - 1 \leq y \leq 1}$ and S be the subset of $A \times B$ , defined by $S = {(x, y) \in A \times B : x^{2} + y^{2} = 1}$ . Which one of the following is correct?
1. A.S is a one-one function from A into B
2. B.S is a many-one function from A into B
3. C.S is a bijective mapping from A into B
4. D.S is not a function
Show answer
Answer: D
Q52018 · 9 Sept 2018
What is the value of $(\frac{- 1 + i 3}{2})^{3 n} + (\frac{- 1 - i 3}{2})^{3 n}$ , where $i = - 1$ ?
1. A.3
2. B.2
3. C.1
4. D.0
Show answer
Answer: B
Q582018 · 9 Sept 2018
If $f (x) = \frac{x - 1}{x - 4}$ defines a function on $R$ , then what is its domain?
1. A. $(- \infty, 4) \cup (4, \infty)$
2. B. $[4, \infty)$
3. C. $(1, 4) \cup (4, \infty)$
4. D. $[1, 4) \cup (4, \infty)$
Show answer
Answer: D
Q782018 · 9 Sept 2018
What is $\int_{a}^{b} [x] d x + \int_{a}^{b} [- x] d x$ equal to, where $[.]$ is the greatest integer function?
1. A. $b - a$
2. B. $a - b$
3. C. $0$
4. D. $2 (b - a)$
Show answer
Answer: B
Q792018 · 9 Sept 2018
What is $\int_{- 1}^{1} {\frac{d}{d x} (tan^{- 1} \frac{1}{x})} d x$ equal to?
1. A. $0$
2. B. $- \frac{π}{4}$
3. C. $- \frac{π}{2}$
4. D. $\frac{π}{2}$
Show answer
Answer: C
Q1162018 · 9 Sept 2018
A function $f : A \to R$ is defined by the equation $f (x) = x^{2} - 4 x + 5$ where $A = (1, 4)$ . What is the range of the function?
1. A. $(2, 5)$
2. B. $(1, 5)$
3. C. $[1, 5)$
4. D. $[1, 5]$
Show answer
Answer: C
Q1172018 · 9 Sept 2018
What is $\int_{2}^{8} ∣ x - 5∣ d x$ equal to?
1. A. $2$
2. B. $3$
3. C. $4$
4. D. $9$
Show answer
Answer: D
Q12018 · 22 Apr 2018
Let A and B be subsets of X and $C = (A \cap B^{'}) \cup (A^{'} \cap B)$ , where $A^{'}$ and $B^{'}$ are complements of A and B respectively in X. What is C equal to ?
1. A. $(A \cup B^{'}) - (A \cap B^{'})$
2. B. $(A^{'} \cup B) - (A^{'} \cap B)$
3. C. $(A \cup B) - (A \cap B)$
4. D. $(A^{'} \cup B^{'}) - (A^{'} \cap B^{'})$
Show answer
Answer: C
Q22018 · 22 Apr 2018
Passage
Consider the information given below and answer the two items (02) that follow : In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.
What is the number of students who are good in either Hindi or Mathematics but not in English ?
1. A.99
2. B.107
3. C.125
4. D.130
Show answer
Answer: C
Q32018 · 22 Apr 2018
Passage
Consider the information given below and answer the two items (02) that follow : In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all three subjects.
What is the number of students who are good in Hindi and Mathematics but not in English ?
1. A.18
2. B.12
3. C.10
4. D.8
Show answer
Answer: D
Q42018 · 22 Apr 2018
A survey of 850 students in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance ?
1. A.40
2. B.45
3. C.50
4. D.55
Show answer
Answer: B
Q182018 · 22 Apr 2018
Let $[x]$ denote the greatest integer function. What is the number of solutions of the equation $x^{2} - 4 x + [x] = 0$ in the interval $[0, 2]$ ?
1. A.Zero (No solution)
2. B.One
3. C.Two
4. D.Three
Show answer
Answer: B
Q192018 · 22 Apr 2018
How many numbers between 100 and 1000 can be formed with the digits 5, 6, 7, 8, 9, if the repetition of digits is not allowed ?
1. A. $3^{5}$
2. B. $5^{3}$
3. C.120
4. D.60
Show answer
Answer: D
Q202018 · 22 Apr 2018
How many four-digit numbers divisible by 10 can be formed using 1, 5, 0, 6, 7 without repetition of digits ?
1. A.24
2. B.36
3. C.44
4. D.64
Show answer
Answer: A
Q502018 · 22 Apr 2018
What is the equation of the line passing through the point of intersection of the lines $x + 2 y - 3 = 0$ and $2 x - y + 5 = 0$ and parallel to the line $y - x + 10 = 0$ ?
1. A. $7 x - 7 y + 18 = 0$
2. B. $5 x - 7 y + 18 = 0$
3. C. $5 x - 5 y + 18 = 0$
4. D. $x - y + 5 = 0$
Show answer
Answer: C
Q612018 · 22 Apr 2018
Which one of the following is correct in respect of the function $f : R \to R^{+}$ defined as $f (x) = ∣ x + 1∣$ ?
1. A. $f (x^{2}) = [f (x)]^{2}$
2. B. $f (∣ x ∣) = ∣ f (x) ∣$
3. C. $f (x + y) = f (x) + f (y)$
4. D.None of the above
Show answer
Answer: D
Q622018 · 22 Apr 2018
Suppose $f : R \to R$ is defined by $f (x) = \frac{x ^{2}}{1 + x ^{2}}$ . What is the range of the function?
1. A. $[0, 1)$
2. B. $[0, 1]$
3. C. $(0, 1]$
4. D. $(0, 1)$
Show answer
Answer: A
Q632018 · 22 Apr 2018
For f to be a function, what is the domain of f, if $f (x) = \frac{1}{∣ x ∣ - x}$ ?
1. A. $(- \infty, 0)$
2. B. $(0, \infty)$
3. C. $(- \infty, \infty)$
4. D. $(- \infty, 0]$
Show answer
Answer: A
Q642018 · 22 Apr 2018
What is the period of the function $f (x) = sin x$ ?
1. A. $π /4$
2. B. $π /2$
3. C. $π$
4. D. $2 π$
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Answer: D
Q652018 · 22 Apr 2018
If $f (x)$ is an even function, where $f (x) \neq = 0$ , then which one of the following is correct?
1. A. $f^{'} (x)$ is an even function
2. B. $f^{'} (x)$ is an odd function
3. C. $f^{'} (x)$ may be an even or odd function depending on the type of function
4. D. $f^{'} (x)$ is a constant function
Show answer
Answer: B
Q662018 · 22 Apr 2018
If $f : R \to S$ defined by $f (x) = 4 sin x - 3 cos x + 1$ is onto, then what is S equal to?
1. A. $[- 5, 5]$
2. B. $(- 5, 5)$
3. C. $(- 4, 6)$
4. D. $[- 4, 6]$
Show answer
Answer: D
Q672018 · 22 Apr 2018
Consider the function $f (x) = {x^{2} ln ∣ x ∣ 0 x \neq = 0 x = 0$ What is $f^{'} (0)$ equal to?
1. A. $0$
2. B. $1$
3. C. $- 1$
4. D.It does not exist
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Answer: A