(C) Given $D_{30} = \{1, 2, 3, 5, 6, 10, 15, 30\}$.We need to calculate $f(2, 5, 15) = (2+5) \cdot (5^{\prime} + 15)$.First,calculate $2+5 = \operator

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(C) Given $D_{30} = \{1, 2, 3, 5, 6, 10, 15, 30\}$.We need to calculate $f(2, 5, 15) = (2+5) \cdot (5^{\prime} + 15)$.First,calculate $2+5 = \operatorname{LCM}(2, 5) = 10$.Next,calculate $5^{\prime} = \frac{30}{5} = 6$.Then,$5^{\prime} + 15 = 6 + 15 = \operatorname{LCM}(6, 15) = 30$.Finally,$f(2, 5, 15) = 10 \cdot 30 = \operatorname{GCD}(10, 30) = 10$.

Class 11 Mathematics Sets Basic of Set theory

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If $D_{30}$ is the set of all divisors of $30$,$x, y \in D_{30}$,we define $x+y=\operatorname{LCM}(x, y)$,$x \cdot y=\operatorname{GCD}(x, y)$,$x^{\prime}=\frac{30}{x}$ and $f(x, y, z)=(x+y) \cdot (y^{\prime}+z)$,then $f(2, 5, 15)$ is equal to

MHT CET 2009 All MHT CET

A
$2$
B
$5$
C
$10$
D
$15$

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Sets

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Basic of Set theory

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MHT CET 2009 Paper All MHT CET years →

Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank space:
$8 \dots A$

Easy

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Match each of the set on the left in the roster form with the same set on the right described in set-builder form:

$(i)$ $\{1, 2, 3, 6\}$ $(a)$ $\{x : x \text{ is a prime number and a divisor of } 6\}$

$(ii)$ $\{2, 3\}$ $(b)$ $\{x : x \text{ is an odd natural number less than } 10\}$

$(iii)$ $\{M, A, T, H, E, I, C, S\}$ $(c)$ $\{x : x \text{ is a natural number and divisor of } 6\}$

$(iv)$ $\{1, 3, 5, 7, 9\}$ $(d)$ $\{x : x \text{ is a letter of the word } MATHEMATICS\}$

Medium

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If $A = \{2, 3, 4, 5, 6\}$,then which of the following statements has a truth value of 'false'?

EasyMHT CET 2020

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Given the sets $A = \{1, 3, 5\}$,$B = \{2, 4, 6\}$,and $C = \{0, 2, 4, 6, 8\}$,which of the following sets can be considered as a universal set for all the three sets $A$,$B$,and $C$?
$X = \{0, 1, 2, 3, 4, 5, 6\}$

Easy

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Show that $A \cap B = A \cap C$ does not necessarily imply $B = C$.

Easy

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$(i)$ $\{1, 2, 3, 6\}$	$(a)$ $\{x : x \text{ is a prime number and a divisor of } 6\}$
$(ii)$ $\{2, 3\}$	$(b)$ $\{x : x \text{ is an odd natural number less than } 10\}$
$(iii)$ $\{M, A, T, H, E, I, C, S\}$	$(c)$ $\{x : x \text{ is a natural number and divisor of } 6\}$
$(iv)$ $\{1, 3, 5, 7, 9\}$	$(d)$ $\{x : x \text{ is a letter of the word } MATHEMATICS\}$

If $D_{30}$ is the set of all divisors of $30$,$x, y \in D_{30}$,we define $x+y=\operatorname{LCM}(x, y)$,$x \cdot y=\operatorname{GCD}(x, y)$,$x^{\prime}=\frac{30}{x}$ and $f(x, y, z)=(x+y) \cdot (y^{\prime}+z)$,then $f(2, 5, 15)$ is equal to

Similar Questions

Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank space:$8 \dots A$

If $A = \{2, 3, 4, 5, 6\}$,then which of the following statements has a truth value of 'false'?

Given the sets $A = \{1, 3, 5\}$,$B = \{2, 4, 6\}$,and $C = \{0, 2, 4, 6, 8\}$,which of the following sets can be considered as a universal set for all the three sets $A$,$B$,and $C$?$X = \{0, 1, 2, 3, 4, 5, 6\}$

Show that $A \cap B = A \cap C$ does not necessarily imply $B = C$.

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Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank space:
$8 \dots A$

Given the sets $A = \{1, 3, 5\}$,$B = \{2, 4, 6\}$,and $C = \{0, 2, 4, 6, 8\}$,which of the following sets can be considered as a universal set for all the three sets $A$,$B$,and $C$?
$X = \{0, 1, 2, 3, 4, 5, 6\}$