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CUET Mathematics 2022 PYQs7 Aug Shift 2. Free, no login required.

Algebra

past year questions, CUET Mathematics 2022 7 Aug Shift 2

Relations & Functions

past year questions, Algebra, CUET Mathematics 2022 7 Aug Shift 2

Easy

Let L be the set of all lines in a plane and R be the relation in L defined as R={(l1,l2):l1 is perpendicular to l2, where l1,l2∈L}R = \{(l_1, l_2) : l_1 \text{ is perpendicular to } l_2, \text{ where } l_1, l_2 \in L\}. Choose the correct answer :

Solution

✅ Correct Option: 2

Reflexive: a line is not perpendicular to itself, so not reflexive.

Symmetric: if l1⊥l2l_1 \perp l_2 then l2⊥l1l_2 \perp l_1, so symmetric.

Transitive: if l1⊥l2l_1 \perp l_2 and l2⊥l3l_2 \perp l_3, then l1∥l3l_1 \parallel l_3, not perpendicular. Not transitive.

Hence R is only symmetric.

Related questions:

2025: 13 May Shift 2

Let L be the set of all lines in a plane and R be the relation on set L defined by R={(L1,L2):L1⊥L2}R = \{(L_1, L_2): L_1 \perp L_2\} Then R is

(A) an equivalence Relation

(B) a symmetric Relation

(C) not a transitive Relation

(D) a reflexive Relation

Choose the correct answer from the options given below:

2026: 19 May Shift 2

Match the LIST-I with LIST-II

[Where R and Z denotes set of real numbers and set of integers respectively]

LIST-I
Function		LIST-II
Nature
A.f:R→R,f(x)=sin⁡2x+cos⁡2xf: R \to R, f(x) = \sin^2 x + \cos^2 xI.Bijective
B.f:Z→Z,f(x)=x3f: Z \to Z, f(x) = x^3II.Surjective but not injective
C.f:R→R,f(x)=x3−xf: R \to R, f(x) = x^3 - xIII.Injective but not surjective
D.f:R→R,f(x)=3−4xf: R \to R, f(x) = 3 - 4xIV.Neither injective nor surjective

Choose the correct answer from the options given below:

2025: 13 May Shift 2

Match List-I with List-II

Let f:A→Bf: A \rightarrow B be a function given by f(x)=x2f(x) = x^2

List-IList-II
Domain and Co-domainKind
(A) A=RA = \mathbb{R} and B=RB = \mathbb{R}(I) ff is both one-one and onto
(B) A=RA = \mathbb{R} and B=[0,∞]B = [0, \infty](II) ff is one-one but not onto
(C) A=B=[0,∞]A = B = [0, \infty](III) ff is not one-one but onto
(D) A=[0,∞]A = [0, \infty] and B=RB = \mathbb{R}(IV) ff is neither one-one nor onto

Choose the correct answer from the options given below:

2026: 30 May Shift 2

The greatest integer function f:R→Rf: R\to R defined by f(x)=[x]f(x) = [x], then which of the following are true?

(A) f(x)f(x) is one - one and onto.

(B) Domain of f(x)=Rf(x) = R (the set of real numbers).

(C) f(x)f(x) is neither one-one nor onto.

(D) Range of f(x)=Zf(x) = Z (The set of integers).

Choose the correct answer from the options given below:

2023: 15 June Shift 2

The inverse of the function f:R→Rf : R \to R given by f(x)=2x+7f(x) = 2x + 7 is :

2026: 29 May Shift 2

Match the LIST-I with LIST-II (Consider N and R as set of natural numbers and set of real numbers respectively)

LIST-I
Function		LIST-II
A.f:N→N,f(x)=x2f: N \to N, f(x) = x^2 isI.Neither one-one nor onto
B.f:R→R,f(x)=3−2xf: R \to R, f(x) = 3 - 2x isII.one-one but not onto
C.f:R→R,f(x)=x2f: R \to R, f(x) = x^2 isIII.onto but not one-one
D.f:{−1,1}→{1},f(x)=∣x∣f: \{-1,1\} \to \{1\}, f(x) = \vert x \vert isIV.one-one and onto

Choose the correct answer from the options given below:

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