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Let N be the set of natural numbers and R be the relation in N defined as \(R = {(a, b) : a = b – 2, b > 6}\). Then \[ \begin{array} ((A)\: (2, 4) ∈ R \quad & (B)\: (3, 8) ∈ R \\ (C) \: (6, 8) ∈ R \quad & (D)\: (8, 7) ∈ R. \end{array} \]
cbse
class12
modelpaper
2012
sec-a
q1
math
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Dec 24, 2012
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thanvigandhi_1
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votes
0
answers
If R is the set of real numbers and f : R\( \rightarrow\)R be the function defined by \(f (x) = 1 (3 – x^3 )^{\frac{1}{3}}\) , then (fof) (x) is equal to \[ \begin{array} (A) \: x^{\frac{1}{3}} \quad & (B)\: x^3 \\ (C) \: x \quad & (D)\: (3 – x^3) \end{array} \]
asked
Dec 23, 2012
by
thanvigandhi_1
cbse
class12
modelpaper
2012
sec-a
q20
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0
votes
0
answers
Relation R is the set N of natural numbers defined as R = (x, y): y=x+5 and x < y}.
asked
Jan 10, 2013
by
thanvigandhi_1
cbse
class12
modelpaper
2012
sec-a
q1
math
0
votes
0
answers
Let N be the set of all natural numbers and R be the relation on N x N defined by (a, b) R (c, d) if ad = bc. Show that R is an equivalence relation.
asked
Dec 26, 2012
by
thanvigandhi_1
cbse
modelpaper
2012
sec-b
q11
0
votes
0
answers
Give an example to show that the relation R in the set of natural numbers, defined by \( R = ( (x,y), x, y \in\: N, x \leq \: y^2) \) is not transitive.
asked
Dec 26, 2012
by
thanvigandhi_1
cbse
modelpaper
2012
sec-a
q1
0
votes
0
answers
The rate of change of the area of a circle with respect to its radius r when r = 6 is \[ \begin{array} ((A) \: 10 π \quad & (B) \: 12 π \\ (C) \: 8 π \quad & (D)\: 11 π \end{array} \]
asked
Dec 24, 2012
by
thanvigandhi_1
cbse
class12
modelpaper
2012
sec-a
q8
math
0
votes
1
answer
A binary operation * on the set (0,1,2,3,4,5} is defined as : $ f(x) = \left\{ \begin{array}{l l}a+b, & \quad if { a+b < 6} \\ a+b-6, & \quad if { a+b \geq 6} \end{array} \right. $ Show that zero is the identity for this operation and each element 'a' of the set is invertible with 6-a, being the inverse of 'a'.
asked
Feb 5, 2013
by
thanvigandhi_1
cbse
class12
modelpaper
2012
sec-b
q11
medium
math
0
votes
0
answers
Let A be a square matrix of order 3 × 3, then \( | kA | \) is equal to \[ \begin{array} ((A) \: k | A | \quad & (B)\: k^2 | A | \\ (C) \: k^3 | A | \quad & (D) \: 3k | A | \end{array} \]
asked
Dec 24, 2012
by
thanvigandhi_1
cbse
class12
modelpaper
2012
sec-a
q5
math
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