Available Questions 30 found Page 1 of 2
Standalone Questions
#1473
Mathematics
Relations and Functions
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Let R be a relation defined on a set N of natural numbers such that $R=\{(x,y): xy \text{ is a square of a natural number, } x, y\in N\}$. Determine if the relation R is an equivalence relation.
Key:
Sol:
Sol:
#1472
Mathematics
Relations and Functions
SA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Show that the function $f:R\rightarrow R$ defined by $f(x)=4x^{3}-5$, $\forall x\in R$ is one-one and onto.
Key:
Sol:
Sol:
#1465
Mathematics
Relations and Functions
VSA
UNDERSTAND
2025
AISSCE(Board Exam)
KNOWLEDGE
2 Marks
Let $f:A\rightarrow B$ be defined by $f(x)=\frac{x-2}{x-3}$ where $A=R-\{3\}$ and $B=R-\{1\}$. Discuss the bijectivity of the function.
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#1454
Mathematics
Relations and Functions
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Show that the function $f:N\rightarrow N$, where N is a set of natural numbers, given by $f(n) = n-1$, if n is even, $n+1$, if n is odd, is a bijection.
Key:
Sol:
Sol:
#1453
Mathematics
Relations and Functions
SA
UNDERSTAND
2025
AISSCE(Board Exam)
Competency
3 Marks
A student wants to pair up natural numbers in such a way that they satisfy the equation $2x+y=41$, $x, y\in N$. Find the domain and range of the relation. Check if the relation thus formed is reflexive, symmetric and transitive. Hence, state whether it is an equivalence relation or not.
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Sol:
Sol:
#1407
Mathematics
Relations and Functions
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Let $A=\{1,2,3\}$ and $B=\{4,5,6\}$. A relation R from A to B is defined as $R=\{(x,y):x+y=6, x\in A, y\in B\}$. (i) Write all elements of R. (ii) Is R a function? Justify. (iii) Determine domain and range of R.
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#1406
Mathematics
Relations and Functions
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
If $f:R^{+}\rightarrow R$ is defined as $f(x) = \log_{a} x$ ($a > 0$ and $a\ne1$), prove that f is a bijection. ($R^{+}$ is a set of all positive real numbers.)
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Sol:
Sol:
#1386
Mathematics
Relations and Functions
SA
REMEMBER
2025
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
Let R be a relation defined over N, where N is set of natural numbers, defined as "mRn if and only if m is a multiple of n, m, $n\in N$." Find whether R is reflexive, symmetric and transitive or not.
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Sol:
Sol:
#1329
Mathematics
Relations and Functions
LA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Check whether the relation S in the set of real numbers R defined by $S=\{(a,b)$: where $a-b+\sqrt{2}$ is an irrational number is reflexive, symmetric or transitive.
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Sol:
Sol:
#1328
Mathematics
Relations and Functions
LA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Let $A=R-\{5\}$ and $B=R-\{1\}$. Consider the function $f:A\rightarrow B$, defined by $f(x)=\frac{x-3}{x-5}$ Show that f is one-one and onto.
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Sol:
Sol:
#1296
Mathematics
Relations and Functions
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
A function f is defined from $R\rightarrow R$ as $f(x)=ax+b$, such that $f(1)=1$ and $f(2)=3$ Find function $f(x)$. Hence, check whether function $f(x)$ is one-one and onto or not.
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Sol:
Sol:
#1295
Mathematics
Relations and Functions
SA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
3 Marks
A relation R on set $A=\{1,2,3,4,5\}$ is defined as $R=\{(x,y):|x^{2}-y^{2}|<8\}$. Check whether the relation R is reflexive, symmetric and transitive.
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Sol:
Sol:
#1283
Mathematics
Relations and Functions
LA
UNDERSTAND
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
A relation R is defined on $N\times N$ (where N is the set of natural numbers) as: $(a, b)~R~(c,d)\Leftrightarrow a-c=b-d$ Show that R is an equivalence relation.
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Sol:
Sol:
#1282
Mathematics
Relations and Functions
LA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
Show that a function $f:R\rightarrow R$ defined by $f(x)=\frac{2x}{1+x^{2}}$ is neither one-one nor onto. Further, find set A so that the given function $f:R\rightarrow A$ becomes an onto function.
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Sol:
Sol:
#1260
Mathematics
Relations and Functions
LA
REMEMBER
2024
AISSCE(Board Exam)
KNOWLEDGE
5 Marks
A relation R on set $A=\{-4,-3,-2,-1,0,1,2,3,4\}$ be defined as $R=\{(x,y):x+y$ is an integer divisible by 2). Show that R is an equivalence relation. Also, write the equivalence class [2].
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Sol:
#977
Mathematics
Relations and Functions
ASSERTION_REASON
APPLY
2025
AISSCE(Board Exam)
Competency
1 Marks
Assertion (A): Let $f(x) = e^{x}$ and $g(x) = \log x$. Then $(f + g)x = e^{x} + \log x$ where domain of $(f + g)$ is $\mathbb{R}$.
Reason (R): $\text{Dom}(f + g) = \text{Dom}(f) \cap \text{Dom}(g)$.
Key: D
Sol:
Sol:
#959
Mathematics
Relations and Functions
MCQ_SINGLE
APPLY
2025
JEE Main 2025
Competency
0 Marks
Let A = { (α, β) ∈ R x R : |α - 1| ≤ 4 and |β - 5| ≤ 6} and B = { (α, β) ∈ R × R: 16(α-2)²+9(β-6)² ≤ 144}. Then
(A) A ⊂ B
(B) B ⊂ A
(C) neither A ⊂ B nor B ⊂ A
(D) A ∪ B = {(x, y) : -4 ≤ x ≤ 4, -1 ≤ y ≤ 11}
Key: B
Sol:
Sol:
#923
Mathematics
Relations and Functions
LA
APPLY
2023
Competency
5 Marks
Show that a function $f:\mathbb{R}\rightarrow\mathbb{R}$ defined as $f(x)=\frac{5x-3}{4}$ is both one-one and onto.
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Sol:
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#922
Mathematics
Relations and Functions
LA
APPLY
2023
Competency
5 Marks
Let $f : \mathbb{R} - \left\{ \frac{4}{3} \right\} \to \mathbb{R}$ be a function defined as:$$f(x) = \frac{4x}{3x+4}$$Show that $f$ is a one-one function. Also, check whether $f$ is an onto function or not.
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#921
Mathematics
Relations and Functions
LA
APPLY
2023
Competency
5 Marks
34. (a) If N denotes the set of all natural numbers and R is the relation on $N \times N$ defined by $(a, b) R (c, d)$, if $ad(b+c)=bc(a+d)$. Show that R is an equivalence relation.
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Case-Based Questions
CASE ID: #108
Cl: CBSE Class 12
Mathematics
A bank offers loan to its customers on different types of interest namely, fixed rate, floating rate and variable rate. From the past data with the bank, it is known that a customer avails loan on fixed rate, floating rate or variable rate with probabilities 10%, 20% and 70% respectively. A customer after availing loan can pay the loan or default on loan repayment. The bank data suggests that the probability that a person defaults on loan after availing it at fixed rate, floating rate and variable rate is 5%, 3% and 1% respectively.
VSA
APPLY
2025
AISSCE(Board Exam)
Competency
2 Marks
What is the probability that a customer after availing the loan will default on the loan repayment?
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VSA
APPLY
2025
AISSCE(Board Exam)
Competency
2 Marks
A customer after availing the loan, defaults on loan repayment. What is the probability that he availed the loan at a variable rate of interest?
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