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______ is the trail of data we leave behind when we visit any website (or use any online application or portal) to fill in data or perform any transaction.
Concept: Digital Footprints
List any four benefits of e-waste management.
Concept: E-waste: Hazards and Management
Mention any four net etiquettes.
Concept: Digital Society and Netizen
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Nadar has recently shifted to a new city and school. She does not know many people in her new city and school. But all of a sudden, someone is posting negative, demeaning comments on her social networking profile, etc. She is also getting repeated mails from unknown people. Every time she goes online, she finds someone chasing her online. |
- What is this happening to Nadar?
- What immediate action should she take to handle it?
- Is there any law in India to handle such issues? Discuss briefly.
Concept: Cyber Crimes
What do you understand by plagiarism?
Concept: Data Protection
Why is plagiarism a punishable offence?
Concept: Data Protection
Show that the function f in `A=R-{2/3} ` defined as `f(x)=(4x+3)/(6x-4)` is one-one and onto hence find f-1
Concept: Types of Functions
Show that the function f : R → {x ∈ R : −1 < x < 1} defined by f(x) = `x/(1 + |x|)`, x ∈ R is one-one and onto function.
Concept: Types of Functions
Let R = {(a, a3) : a is a prime number less than 5} be a relation. Find the range of R.
Concept: Types of Relations
If f, g : R → R be two functions defined as f(x) = |x| + x and g(x) = |x|- x, ∀x∈R" .Then find fog and gof. Hence find fog(–3), fog(5) and gof (–2).
Concept: Types of Functions
Let \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.
Concept: Types of Functions
Let A = ℝ − {3}, B = ℝ − {1}. Let f : A → B be defined by \[f\left( x \right) = \frac{x - 2}{x - 3}, \forall x \in A\] Show that f is bijective. Also, find
(i) x, if f−1(x) = 4
(ii) f−1(7)
Concept: Types of Functions
Let f : N → ℝ be a function defined as f(x) = 4x2 + 12x + 15. Show that f : N → S, where S is the range of f, is invertible. Also find the inverse of f.
Concept: Inverse of a Function
Show that the relation R on the set Z of integers, given by R = {(a,b):2divides (a - b)} is an equivalence relation.
Concept: Types of Relations
Show that the relation R on the set Z of all integers, given by R = {(a,b) : 2 divides (a-b)} is an equivalence relation.
Concept: Types of Relations
Show that the relation R defined by (a, b)R(c,d) ⇒ a + d = b + c on the A x A , where A = {1, 2,3,...,10} is an equivalence relation. Hence write the equivalence class [(3, 4)]; a, b, c,d ∈ A.
Concept: Types of Relations
Find: `int (x + 1)/((x^2 + 1)x) dx`
Concept: Types of Relations
Prove that the function f is surjective, where f: N → N such that `f(n) = {{:((n + 1)/2",", if "n is odd"),(n/2",", if "n is even"):}` Is the function injective? Justify your answer.
Concept: Types of Functions
Define the relation R in the set N × N as follows:
For (a, b), (c, d) ∈ N × N, (a, b) R (c, d) if ad = bc. Prove that R is an equivalence relation in N × N.
Concept: Types of Relations
Given a non-empty set X, define the relation R in P(X) as follows:
For A, B ∈ P(X), (4, B) ∈ R iff A ⊂ B. Prove that R is reflexive, transitive and not symmetric.
Concept: Types of Relations
