NDA Reasoning & Aptitude — practice questions
120 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice NDA Reasoning & Aptitude in the app →Which of the following is a **well-defined set** (in the mathematical sense)?Write the set of all letters of the word **"SCHOOL"** in roster form.Express the set $\{x : x \text{ is a positive integer and } x^{2} < 40\}$ in roster form.The set $\{1, 4, 9, 16, 25, \ldots\}$ in set-builder form is:Write the solution set of the equation $x^{2} + x - 2 = 0$ in roster form.Match the set $\{1, 2, 3, 6, 9, 18\}$ (roster form) with the correct set-builder form.Which of the following is the **empty set** $\phi$?Which of the following is **NOT** an example of the empty set?Let $C = \{x : x \text{ is an even prime number greater than } 2\}$. Then $C$ is:Which set is **infinite**?Let $A = \{x : x \in \mathbb{N} \text{ and } 2x - 1 = 0\}$. Then $A$ is:How many elements are in the set $\{x : x \in \mathbb{Z}, -\dfrac{1}{2} < x < \dfrac{9}{2}\}$?Let $A = \{1, 2, 3, 4\}$ and $B = \{3, 1, 4, 2\}$. Which statement is true?Are $A = \{2, 3\}$ and $B = \{x : x \text{ is a solution of } x^{2} + 5x + 6 = 0\}$ equal?Let $X = $ letters in "FOLLOW" and $Y = $ letters in "WOLF". Are $X$ and $Y$ equal?Which of the following is **TRUE**?How many subsets does the set $\{a, b\}$ have?How many subsets does the set $\{1, 2, 3\}$ have?Let $A = \{1, 2, \{3, 4\}, 5\}$. Which statement is **TRUE**?Let $A = \{1, 3\}$, $B = \{1, 5, 9\}$, $C = \{1, 3, 5, 7, 9\}$. Which is **TRUE**?Express the set $\{x : x \in \mathbb{R}, -5 < x \le 7\}$ in interval notation.Write the interval $[-3, 5)$ in set-builder form.What is the **length** of the interval $[2, 11)$?Which interval describes the set of **non-negative real numbers**?Which of the following is **TRUE** about subsets of the real numbers?Which number does **NOT** belong to $\mathbb{Q}$ (the set of rational numbers)?If a set has $5$ elements, how many subsets does it have?The number of **proper subsets** of a set with $4$ elements is:Match $\{x : x \text{ is an integer and } x^{2} - 9 = 0\}$ with its roster form.If $A = \{\text{red}, \text{blue}\}$ and $B = \{b, c, s\}$, how many ordered pairs are in $A \times B$?If $n(A) = p$ and $n(B) = q$, then $n(A \times B)$ equals:If $(x + 1, y - 2) = (3, 1)$, what are the values of $x$ and $y$?If $P = \{a, b, c\}$ and $Q = \{r\}$, are the products $P \times Q$ and $Q \times P$ equal?If $P = \{1, 2\}$, how many elements does $P \times P \times P$ have?Let $A = \{1, 2, 3, 4, 5, 6\}$ and $R = \{(x, y) : y = x + 1, x, y \in A\}$. The relation $R$ in roster form iFor the relation $R = \{(1,2), (2,3), (3,4), (4,5), (5,6)\}$ on $\{1,2,3,4,5,6\}$, what is the **domain**?For the relation $R = \{(1,2), (2,3), (3,4), (4,5), (5,6)\}$ on $\{1,2,3,4,5,6\}$, what is the **range**?If $A = \{1, 2\}$ and $B = \{3, 4\}$, how many distinct **relations** can be defined from $A$ to $B$?If $A = \{x, y, z\}$ and $B = \{1, 2\}$, the number of relations from $A$ to $B$ is:A relation $f$ from $A$ to $B$ is a **function** if:Which of the following relations is a **function**?If $f: \mathbb{N} \to \mathbb{N}$ is defined by $f(x) = 2x + 1$, what is $f(5)$?Define $f: \mathbb{R} \to \mathbb{R}$ by $f(x) = x^{2}$. What is the **range** of $f$?What is the **domain** of $f(x) = \dfrac{1}{x}$?The function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = x$ is called the:For the constant function $f(x) = 3$ defined on $\mathbb{R}$, the **range** is:Which of the following is a **polynomial function**?For the modulus function $f(x) = |x|$, what is $f(-7)$?The function $f(x) = |x|$ can be expressed piecewise as:If $f(x) = x^{2}$ and $g(x) = x + 1$, what is $f(g(2))$?Let $f: \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = x^{3}$. What is $f(-3)$?The range of the function $f(x) = x^{2}$ for $x \in \{-4, -3, -2, -1, 0, 1, 2, 3, 4\}$ is:The function $f(x) = \dfrac{x^{2} - 1}{x - 1}$ is undefined at:If $f(x) = ax + b$ with $f(1) = 5$ and $f(3) = 11$, find $a$ and $b$.$\mathbb{R} \times \mathbb{R}$ represents:If $A = \{1, 2\}$, list the subsets of $A \times A$:If $A \times B = \{(p, q), (p, r), (m, q), (m, r)\}$, find $A$ and $B$.Let $R$ be the relation on $\mathbb{N}$ defined by $R = \{(x, y): y = 2x, x, y \in \mathbb{N}\}$. Is $R$ a funIf $A = \{1, 2, 3\}$, $B = \{3, 4\}$, $C = \{4, 5, 6\}$, then $A \times (B \cap C)$ equals:Convert $90^{\circ}$ to radian measure.Convert $180^{\circ}$ to radians.Convert $360^{\circ}$ to radians.Convert $45^{\circ}$ to radian measure.Convert $30^{\circ}$ to radian measure.Convert $\dfrac{5\pi}{3}$ radians to degree measure.Convert $\dfrac{7\pi}{6}$ radians to degree measure.Convert $240^{\circ}$ to radian measure.In a circle of radius $r$, an arc of length $l$ subtends an angle $\theta$ radian at the centre. The relation A central angle of $60^{\circ}$ intercepts an arc of length $37.4$ cm in a circle. Find the radius. (Use $\pi The minute hand of a clock is $1.5$ cm long. How far does its tip travel in $40$ minutes? (Use $\pi = 3.14$.)A wheel makes $360$ revolutions in one minute. Through how many radians does it turn in one **second**?Equal arcs in two circles subtend angles $65^{\circ}$ and $110^{\circ}$ at the centres. The ratio of the radiiWhat is the value of $ in 30^{\circ}$?What is the value of $\cos 60^{\circ}$?What is the value of $\tan 45^{\circ}$?What is $ in 90^{\circ}$?What is $\cos 0^{\circ}$?What is $\tan 60^{\circ}$?What is $\tan 90^{\circ}$?$ in^{2} 45^{\circ} + \cos^{2} 45^{\circ}$ equals:The value of $ in 0^{\circ} + \cos 0^{\circ} + \tan 45^{\circ}$ is:If $ in\theta = \dfrac{3}{5}$ and $\theta$ is in the first quadrant, what is $\cos\theta$?What is the **range** of the function $f(\theta) = in\theta$?What is the **range** of $f(\theta) = \cos\theta$?$\csc\theta$ (cosecant) is the reciprocal of:$ ec\theta \cdot \cos\theta$ equals (where defined):Express $40^{\circ} 20'$ in degrees as a fraction.$\dfrac{\pi}{6}$ radian = ?$\dfrac{3\pi}{2}$ radian = ?Which of the following is a **strict inequality**?Which rule must be applied when **dividing both sides of an inequality by a negative number**?Which of the following is a **double inequality**?Adding the **same number** to both sides of an inequality:The inequality $ax^{2} + bx + c > 0$ (with $a \neq 0$) is classified as:Which symbol is used for *strict* inequality "greater than"?Solve $30x < 200$ when $x$ is a natural number.Solve $5x - 3 < 3x + 1$ over the real numbers.Solve $4x + 3 < 6x + 7$ over the real numbers.Solve $\dfrac{5 - 2x}{3} \leq \dfrac{x}{6} - 5$.Solve $7x + 3 < 5x + 9$ over the real numbers.Solve $24x < 100$ when $x$ is a natural number.Solve $-12x > 30$ when $x$ is a natural number.Solve $5x - 3 < 7$ when $x$ is an integer.Solve $3x + 8 > 2$ when $x$ is a real number.Solve $3(x - 1) \leq 2(x - 3)$ for real $x$.Solve $3x - 7 > 5x - 1$ for real $x$.Solve $3(2 - x) \geq 2(1 - x)$ for real $x$.Solve $x + \dfrac{x}{2} + \dfrac{x}{3} < 11$ for real $x$.Solve $\dfrac{x}{3} > \dfrac{x}{2} + 1$ for real $x$.Solve $3x - 2 < 2x + 1$ for real $x$.Solve $5x - 3 \geq 3x - 5$ for real $x$.A student scored 62 and 48 in two terminal exams. What is the **minimum** mark she must obtain in the annual eRavi obtained 70 and 75 marks in his first two unit tests. What is the **minimum** he must score in the third Sunita has scored $87, 92, 94, 95$ in four exams (each out of $100$). To earn Grade A she needs an average of Find all pairs of consecutive **odd natural numbers** both greater than 10 such that their sum is less than 40Find all pairs of consecutive **odd positive integers** both smaller than 10 such that their sum is more than Find all pairs of consecutive **even positive integers** both greater than 5 such that their sum is less than The longest side of a triangle is three times the shortest side. The third side is $2$ cm shorter than the lonA man cuts three pieces from a $91$ cm board. The second is $3$ cm longer than the shortest; the third is twicWhat is the value of $i^{2}$ where $i = qrt{-1}$?