List of top Mathematics Questions on Relations and functions

The modulus function $ f : \mathbb{R} \to \mathbb{R}^+ $ given by $ f(x) = |x| $ is

A relation $ R = \{(a, b) : a = b - 1, b \geq 3\ $ is defined on set $ N $, then}

Let $R$ be a relation defined on the set $\{1,2,3,4\times\{1,2,3,4\}$ by \[ R=\{((a,b),(c,d)) : 2a+3b=3c+4d\} \] Then the number of elements in $R$ is

Consider a set $ S = \{a, b, c, d\} $. Then the number of reflexive as well as symmetric relations from $ S \to S $ is:

Let $ A = \{-2,-1,0,1,2,3,4\} $ and $ R $ be a relation such that \[ R=\{(x,y): 2x+y \le -2,\ x\in A,\ y\in A\}. \] Let
$ l $ = number of elements in $ R $,
$ m $ = minimum number of elements to be added to $ R $ to make it reflexive,
$ n $ = minimum number of elements to be added to $ R $ to make it symmetric. Then $ (l+m+n) $ is:

Let $M = \{1, 2, 3, ....., 16\}$, if a relation R defined on set M such that R = $(x, y) : 4y = 5x – 3, x, y (\in) M$. How many elements should be added to R to make it symmetric.

Let f: R $\rightarrow$ R be defined as f(x) = 10x. Then (Where R is the set of real numbers)

Let A = \{1, 2, 3\}. Then, the number of relations containing (1, 2) and (1, 3), which are reflexive and symmetric but not transitive, is

If set $A$ has 3 elements and set $B$ has 4 elements, then the number of injective mappings from $A$ to $B$ is

Let A = \{1, 2, 3\}. Then, the number of relations containing (1, 2) and (1, 3), which are reflexive and symmetric but not transitive, is

Let f: R $\rightarrow$ R be defined as f(x) = 10x. Then (Where R is the set of real numbers)

Let \[ L_1 : \frac{x-1}{1} = \frac{y-2}{-1} = \frac{z-1}{-1} \quad {and} \quad L_2 : \frac{x+1}{1} = \frac{y-2}{2} = \frac{z-2}{2} \] be two lines. Let $ L_3 $ be a line passing through the point $ (\alpha, \beta, \gamma) $ and be perpendicular to both $ L_1 $ and $ L_2 $. If $ L_3 $ intersects $ L_1 $ where $ 5x - 11y - 8z = 1 $, then $ 5x - 11y - 8z $ equals:

Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:

Let $ A $ be the set of all functions $ f: \mathbb{Z} \to \mathbb{Z} $ and $ R $ be a relation on $ A $ such that $$ R = \{ (f, g) : f(0) = g(1) \text{ and } f(1) = g(0) \} $$ Then $ R $ is:

If the domain of the function $ f(x) = \log_7(1 - \log_4(x^2 - 9x + 18)) $ is $ (\alpha, \beta) \cup (\gamma, \delta) $, then $ \alpha + \beta + \gamma + \delta $ is equal to

Let $ f $ be a function such that $ f(x) + 3f\left(\frac{24}{x}\right) = 4x $, $ x \neq 0 $. Then $ f(3) + f(8) $ is equal to

Let $ A = \{-2, -1, 0, 1, 2, 3\} $. Let $ R $ be a relation on $ A $ defined by $ (x, y) \in R $ if and only if $ |x| \le |y| $. Let $ m $ be the number of reflexive elements in $ R $ and $ n $ be the minimum number of elements required to be added in $ R $ to make it reflexive and symmetric relations, respectively. Then $ l + m + n $ is equal to

Let A = $\{-3,-2,-1,0,1,2,3\}$. Let R be a relation on A defined by xRy if and only if $ 0 \le x^2 + 2y \le 4 $. Let $ l $ be the number of elements in R and m be the minimum number of elements required to be added in R to make it a reflexive relation. then $ l + m $ is equal to

Let $ A = \{0, 1, 2, 3, 4, 5\} $. Let $ R $ be a relation on $ A $ defined by $(x, y) \in R$ if and only if $\max\{x, y\} \in \{3, 4\}$. Then among the statements $ (S_1) : $ The number of elements in $ R $ is 18, and $ (S_2) : $ The relation $ R $ is symmetric but neither reflexive nor transitive Options 1. only $ (S_1) $ is true
2. both are true
3. only $ (S_2) $ is true
4. both are false

Let $ A = \{0, 1, 2, 3, 4, 5, 6\} $ and $ R_1 = \{(x, y): \max(x, y) \in \{3, 4 \}$. Consider the two statements:
Statement 1: Total number of elements in $ R_1 $ is 18.
Statement 2: $ R $ is symmetric but not reflexive and transitive.

Let the position vectors of three vertices of a triangle be $ \overrightarrow{p} = 4\hat{i} + \hat{j} - 3\hat{k} $, $ \overrightarrow{q} = -5\hat{i} + 2\hat{j} + 3\hat{k} $, and $ \overrightarrow{r} = -5\hat{i} + 3\hat{j} + 2\hat{k} $. Then $ \alpha + 2\beta + 5\gamma $ is equal to:

The relation $ R = \{(x, y) : x, y \in \mathbb{Z} \text{ and } x + y \text{ is even} \} $ is:

Let the range of the function \[ f(x) = 6 + 16 \cos x \cdot \cos\left(\frac{\pi}{3} - x\right) \cdot \cos\left(\frac{\pi}{3} + x\right) \cdot \sin 3x \cdot \cos 6x, \quad x \in R \text{ be } [\alpha, \beta]. \] Then the distance of the point $(\alpha, \beta)$ from the line $3x + 4y + 12 = 0$ is:

Let the position vectors of three vertices of a triangle be $ \overrightarrow{p} = 4\hat{i} + \hat{j} - 3\hat{k} $, $ \overrightarrow{q} = -5\hat{i} + 2\hat{j} + 3\hat{k} $, and $ \overrightarrow{r} = -5\hat{i} + 3\hat{j} + 2\hat{k} $. Then $ \alpha + 2\beta + 5\gamma $ is equal to:

The relation $ R = \{(x, y) : x, y \in \mathbb{Z} \text{ and } x + y \text{ is even} \} $ is: