Sets Test

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Sets Test - 38

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Weekly Quiz Competition

Question 1
1 / -0

In a selection process, a hundred candidate participate in Group Discussion sessions (GD) and Personal Interview (PI). The possibilities of a candidate's good performance in GD and in PI are independent of each other. It was found that $$20$$ candidates were good in GD and $$30$$ were good in PI. The number of candidates good in both GD and PI is expected to be about:

A
$$6$$

B
$$10$$

C
$$20$$

D
$$30$$

Solution

$$P(GD and PI)\\=P(GD)\times P(PI)\\=(\frac{20}{100})\times(\frac{30}{100})\\=(\frac{6}{100})\\\therefore no. of candidates expected\\=P(GD and PI)\times100\\=6$$
So, the correct option is '6'.
Question 2
1 / -0

Let $$A\subset B$$ then $$A'\cap B'=$$

A
$$A'$$

B
$$B'$$

C
$$B$$

D
none of these

Solution

Now, given $$A\subset B$$.
This gives $$A\cup B=B$$......(1).
Now,
$$A'\cap B'$$
$$=(A\cup B)'$$ [ Using De Morgan's law]
$$=B'$$. [ Using (1)]
Question 3
1 / -0

$$s = \{ x \in N:2 + {\log _2}\sqrt {x + 1} > 1 - {\log _{1/2}}\sqrt {4 - {x^2}} \} $$ , then

A
$$S={ 1 }$$

B
$$S=Z$$

C
$$S=N$$

D
none of these

Solution
Question 4
1 / -0

Range of the function f(x) = cos (K sinx) is [-1, 1], then the positive integral value of K can be?

A
1

B
2

C
5

D
4

Solution
Question 5
1 / -0

If n(U) = 50, n(A) = 20, $$n((A \cup B)')$$ = 18 then n(B - A) is

A
$$14$$

B
$$12$$

C
$$16$$

D
$$20$$

Solution

$$n(U)=50, n(A)=20$$
$$n(A\cup B)=18$$ $$n(B-A)=?$$
So, $$n(A\cup B)=n(0)-n(A\cup B)$$
So. $$n(A\cup B)=32$$
$$n(B-A)=n(A\cup B)-n(A)$$
$$=32-20$$
$$n(B-A)=12$$
Question 6
1 / -0

Let $$N$$ be the set of non-negative integers, $$I$$ the set of integers,$$N_p$$ the set of non-positive integers, $$E$$ the set of even integers and $$P$$ the set of prime numbers. Then

A
$$I-N=N_p$$

B
$$N \cap {N_p} = \phi $$

C
$$E \cap P = \phi $$

D
$$N\Delta {N_p} = 1 - \{ 0\} $$

Solution

By option verification,

$$I-N=N_p$$

$$I$$ is the set of integers,$$ \implies N\cup N_p$$

$$N$$ is set of non-negative integers,

$$N_p$$ is non-positive integers.

So $$I-N=N\cup N_p-N=N_p$$
Question 7
1 / -0

The number of elements in the set $$\left\{ \left( a,b \right) /2{ a }^{ 2 }+3{ b }^{ 2 }=35,a,b\in z \right\} $$ when $$z$$ is the set of all integers is

A
$$2$$

B
$$4$$

C
$$8$$

D
$$12$$

Solution

Let $$2x+3y=35,\quad x, y > 0$$
Integral solution $$\Rightarrow \quad (a^2=x, y^2=b^2)$$
$$\therefore \ (a^2 , b^2)=(4, a)$$ and $$(16, 1)$$
$$\therefore \ (a, b)\cong (2, 3), (-2, -3), (2, -3), (-2, 3), (4, 1), (-4, -1), (-4, 1), (4, -1)$$
$$\therefore \ 8$$ elements $$\Rightarrow (C)$$
Question 8
1 / -0

If $$A=\{4^n-3n-1:n\in N\}$$ and $$B=\{9(n-1): n\in N\}$$, then?

A
$$B\subset A$$

B
$$A\cup B = N$$

C
$$A\subset B$$

D
None of these

Solution

$$ { 4^{ n } }-3n-1,n\in N \\ { \left( { 3+1 } \right) ^{ n } }-3n-1 \\ by\, u\sin g\, binomal\, ension \\ \Rightarrow \left[ { 1+3n{ +^{ n } }{ C_{ 2 } }\cdot { 3^{ 2 } }{ +^{ n } }{ C_{ 3 } }\cdot { 3^{ 3 } }+{ { ...... }^{ n } }{ C_{ n } }\cdot { 3^{ n } } } \right] -3n-1 \\ \Rightarrow 1+3n+{ 9^{ n } }{ C_{ 2 } }+{ 27^{ n } }{ C_{ 3 } }+{ ....3^{ n } }-3n-1 \\ \Rightarrow 9\left( { ^{ n }{ C_{ 2 } }+{ 3^{ n } }{ C_{ 3 } }+{ { ..... }^{ n } }{ C_{ n } }{ 3^{ \left( { n-2 } \right) } } } \right) \\ Which\, is\, divisible\, by\, \left( q \right) , \\ All\, element\, of\left( B \right) is\, including\, in\, \left( A \right) \\ B\subset A \\ $$
Question 9
1 / -0

$$A \cup B= A \cap B$$ if :

A
$$A\supset B$$

B
$$A=B$$

C
$$A\subset B$$

D
$$A \subseteq B$$

Solution

$$\Rightarrow A\cup B=A\cap B$$
$$\Rightarrow A=B$$
Question 10
1 / -0

The set $$ \left( A\cup B\cup C \right) \cap \left( A\cap B'\cap C' \right) '\cap C'$$ is equal to

A
$$ B\cap C'$$

B
$$ A\cap C'$$

C
$$ B\cap C$$

D
$$A\cap B\cap C'$$

Solution

$$ (A\cup B\cup C)\bigcap (A\bigcap {B}'\cap {C}'),'\cap {C}'$$
$$ (A\cup B\cup C)\cap ({A}'\cup B\cup C)\cap {C}' $$
$$ \left [ (A\cap {A}')\phi \cup (A\cap B)\cup (A\cap C)\cup(B\cap {A}' )\phi\cup (B\cap B)\phi \cup (B\cap C)\cap {C}' \right ]$$
$$ \left [ (A\cap B) \cup (A\cap C)\cup (B\cap C) \right ] \cap {C}'$$
$$ (A\cap B\cap {C}') \cup (A\cap \dfrac{C\cap {C}'}{\phi })\cup (B\cap \dfrac{C\cap {C}'}{\phi })$$
$$ (A\cap B\cap {C}') \cup (A\cap \phi ) \cup (B\cap \phi )$$
$$ (A\cap B\cap {C}') \cup \phi \cup \phi $$
$$ = A\cap B\cap {C}'$$

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Re-Attempt Weekly Quiz Competition

Sets Test - 38

Result

Sets Test - 38

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Rank

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SHARING IS CARING

Question 1

$$6$$

$$10$$

$$20$$

$$30$$

Solution

Question 2

$$A'$$

$$B'$$

$$B$$

none of these

Solution

Question 3

$$S={ 1 }$$

$$S=Z$$

$$S=N$$

none of these

Solution

Question 4

1

2

5

4

Solution

Question 5

$$14$$

$$12$$

$$16$$

$$20$$

Solution

Question 6

$$I-N=N_p$$

$$N \cap {N_p} = \phi $$

$$E \cap P = \phi $$

$$N\Delta {N_p} = 1 - \{ 0\} $$

Solution

Question 7

$$2$$

$$4$$

$$8$$

$$12$$

Solution

Question 8

$$B\subset A$$

$$A\cup B = N$$

$$A\subset B$$

None of these

Solution

Question 9

$$A\supset B$$

$$A=B$$

$$A\subset B$$

$$A \subseteq B$$

Solution

Question 10

$$ B\cap C'$$

$$ A\cap C'$$

$$ B\cap C$$

$$A\cap B\cap C'$$

Solution

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