Algebra

Relations & Functions

Medium

common

For the function $f(x) = |x-1| + |x-2| + |x-3|$

Match the LIST-I with LIST-II

LIST-I
Function $f(x) =$ LIST-II
For Interval
A. $-3x + 6$ I. $x \geq 3$
B. $-x + 4$ II. $x < 1$
C. $x$ III. $1 \leq x < 2$
D. $3x - 6$ IV. $2 \leq x < 3$

Choose the correct answer from the options given below:

	LIST-I Function $f(x) =$		LIST-II For Interval
A.	$-3x + 6$	I.	$x \geq 3$
B.	$-x + 4$	II.	$x < 1$
C.	$x$	III.	$1 \leq x < 2$
D.	$3x - 6$	IV.	$2 \leq x < 3$

A - II, B - III, C - IV, D - I

A - I, B - IV, C - III, D - II

A - I, B - II, C - III, D - IV

A - IV, B - III, C - II, D - I

✅ Correct Option: 1

Split at the critical points 1, 2, 3. For $x<1$ all three moduli flip: $f=6-3x$ (A-II). For $1\le x<2$ : $(x-1)+(2-x)+(3-x)=4-x$ (B-III). For $2\le x<3$ : $(x-1)+(x-2)+(3-x)=x$ (C-IV). For $x\ge3$ : $3x-6$ (D-I).

2026: 18 May Shift 2

For the relation R defined below, where $\mathbb{R}$ and N denotes set of real numbers and set of natural numbers respectively, Match the LIST-I with LIST-II

LIST-I Relation	LIST-II Properties of relation hold by R
A. $R=\{(a,b): a,b\in \mathbb{R}; a^2+b^2=4\}$	I. Neither reflexive, nor symmetric, nor transitive
B. $R=\{(a,b): a,b\in \mathbb{R}; 1+ab>0\}$	II. Equivalence relation
C. $R=\{(a,b): a,b\in N; a+2b=8\}$	III. Symmetric but neither reflexive nor transitive
D. On N×N, relation R defined by $(a,b)R(c,d) \Leftrightarrow a+d=b+c$	IV. Reflexive and symmetric, but not transitive

Choose the correct answer from the options given below:

2025: 15 May Shift 2

If $A = \{1, 2, 3, 4, ..., n\}$ and $B = \{x, y\}$ , then the number of surjections from A to B is

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A function $f: \mathbb{R} \rightarrow \{x \in \mathbb{R}: -1 < x < 1\}$ is defined as $f(x) = \frac{x}{1+|x|}$ , then $f$ is:

2025: 3 June Shift 2

The function $f: [-1, 1] \rightarrow R$ is given by $f(x) = \frac{x}{x + 2}$

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Let $R = \{(L_1, L_2): L_1 \perp L_2\$ where $L_1, L_2 \in L$ (set of straight line in a plane)}, then

2026: 21 May Shift 1

If $A = R - \{2\}$ and $B = R - \{1\}$ and function $f: A \rightarrow B$ defined by $f(x) = \frac{x-1}{x-2}$ , then $f$ is

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