Relations & Functions · Class 12
20 PYQs · answers only
1
Let \(R\) on \(\mathbb{N}\) defined by \(nRm\) if \(n\) divides \(m\). Then \(R\) is:
✅ Correct Answer: D
2
\(f:\mathbb{R}\to\mathbb{R}\), \(f(x)=3x-4\). Then \(f\) is:
✅ Correct Answer: C
3
\(A=\{1,2,3\}\). Number of equivalence relations containing \((1,2)\) is:
✅ Correct Answer: B
4
\(f(x) = (3 - x^3)^{1/3}\), then \(f(f(x)) =\)
✅ Correct Answer: C
5
\(R = \{(a,b): a = b - 2, b > 6\}\) on \(\mathbb{N}\). Which is correct?
✅ Correct Answer: C
6
\(f(x)=x^2,\; f:\mathbb{R}\to\mathbb{R}\) is:
✅ Correct Answer: D
7
\(A=\{1,2,3\} \), \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}.\)Then \(R\) is:
✅ Correct Answer: A
8
Total equivalence relations on \(\{1,2,3\}\) is:
✅ Correct Answer: B
9
\(f(x)=[x]\) (greatest integer). Then \(f\) is:
✅ Correct Answer: D
10
\(f(x)=\frac{x-1}{x+1}\;(x\neq-1)\). Then \(f(f(x)) =\)
✅ Correct Answer: C
11
\(R=\{(a,b):2\mid(a-b)\}\) on \(\mathbb{Z}\). Then \(R\) is:
✅ Correct Answer: D
12
If \(f:A\to B\) bijective, then \(f^{-1}\) is:
✅ Correct Answer: C
13
\(f(x)=|x|,\; f:\mathbb{R}\to\mathbb{R}\). Then:
✅ Correct Answer: D
14
One-one functions from 3-element set to 4-element set =
✅ Correct Answer: B
15
\(f(x)=2x,\;g(x)=x^2+1\). Then \((f\circ g)(x)=\)
✅ Correct Answer: C
16
\(R=\{(1,2),(2,1)\}\) on \(\{1,2,3\}\) is:
✅ Correct Answer: B
17
\(f(x)=e^x,\;f:\mathbb{R}\to\mathbb{R}\). Then \(f\) is:
✅ Correct Answer: A
18
Total relations on set with 3 elements =
✅ Correct Answer: C
19
\(f(x)=\sin x,\;g(x)=x^2\). Then \((g\circ f)(x)=\)
✅ Correct Answer: B
20
Lines in a plane, \(l_1 R l_2\) if \(l_1\perp l_2\). Then \(R\) is:
✅ Correct Answer: B
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