sets relations and functions jee mains questions | JEE Main Mathematics Sets Relations And Functions

Q 21 :

Let $S_{1} = {x \in R - {1, 2} : \frac{(x + 2) (x^{2} + 3 x + 5)}{- 2 + 3 x - x^{2}} \geq 0}$ and $S_{2} = {x \in R : 3^{2 x} - 3^{x + 1} - 3^{x + 2} + 27 \leq 0}$ . Then, $S_{1} \cup S_{2}$ is equal to

$(- \infty, - 2] \cup (1, 2)$
$(- \infty, - 2] \cup [1, 2]$
$(- 2, 1] \cup (2, \infty)$
$(- \infty, 2]$

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2

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4

(2)

$For S_{1} we have$ $\Rightarrow \frac{(x + 1) (x^{2} + 3 x + 5)}{x^{2} - 3 x + 2} \leq 0$

$\Rightarrow x \in (- \infty, - 2) \cup (1, 2)$

$For S_{2} we have$

$3^{x} (3^{x} - 3) - 3^{2} (3^{x} - 3) \leq 0$

$For S_{2}, x \in [1, 2]$

$\Rightarrow (- \infty, - 2) \cup [1, 2]$

Q 22 :

Let $\cup_{i = 1}^{50} X_{i} = \cup_{i = 1}^{n} Y_{i} = T$ , where each $X_{i}$ contains 10 elements and each $Y_{i}$ contains 5 elements. If each element of the set T is an element of exactly 20 of sets $X_{i}$ 's and exactly 6 of sets $Y_{i}$ 's, then $n$ is equal to

15
50
45
30

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(4)

$\cup_{i = 1}^{50} X_{i} = \cup_{i = 1}^{50} Y_{i} = T$

$∵$ $n (X_{i}) = 10, n (Y_{i}) = 5$

$So, ∪_{i = 1}^{50} X_{i} = 500,$ $\cup_{i = 1}^{50} Y_{i} = 5 n$

$\Rightarrow \frac{500}{20} = \frac{5 n}{6}$

$\Rightarrow n = 30$

Q 23 :

Let set $A = {x \in I^{+} : f (x) = x^{3} - 8 x^{2} + 20 x - 13$ is a prime number $}$ . Consider the statements:

Statement – I: Number of elements in set A is 3

Statement – II: Sum of all elements in set A is 9, then

Both Statement – I and Statement – II are true
Statement – I is true and Statement – II is false
Statement – I is false and Statement – II is true
Both Statement – I and Statement – II are false

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4

(1)

$A = {2, 3, 4}$

Q 24 :

Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economic, 14 Mathematics and Economics and 2 study all the three subjects. Then the number of students who study English and Mathematics but not Economics is

7
5
10
4

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(2)

$n (A \cup B \cup C) = 16 + 22 + 6 - 5 - 14 - K + 2 \Rightarrow 40 = 47 - K \Rightarrow K = 7$

$\Rightarrow Number of students who study English and Mathematics but not economics = 5$

Topic Question Set

Q 21 :

Let $S_{1} = {x \in R - {1, 2} : \frac{(x + 2) (x^{2} + 3 x + 5)}{- 2 + 3 x - x^{2}} \geq 0}$ and $S_{2} = {x \in R : 3^{2 x} - 3^{x + 1} - 3^{x + 2} + 27 \leq 0}$ . Then, $S_{1} \cup S_{2}$ is equal to

Q 22 :

Let $\cup_{i = 1}^{50} X_{i} = \cup_{i = 1}^{n} Y_{i} = T$ , where each $X_{i}$ contains 10 elements and each $Y_{i}$ contains 5 elements. If each element of the set T is an element of exactly 20 of sets $X_{i}$ 's and exactly 6 of sets $Y_{i}$ 's, then $n$ is equal to

Q 23 :

Let set $A = {x \in I^{+} : f (x) = x^{3} - 8 x^{2} + 20 x - 13$ is a prime number $}$ . Consider the statements:

Statement – I: Number of elements in set A is 3

Statement – II: Sum of all elements in set A is 9, then

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Topic Question Set

Q 21 : Let S1={x∈R-{1,2}:(x+2)(x2+3x+5)-2+3x-x2≥0} and S2={x∈R:32x-3x+1-3x+2+27≤0}. Then, S1∪S2 is equal to

Q 22 : Let ∪i=150Xi=∪i=1nYi=T, where each Xi contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets Xi's and exactly 6 of sets Yi's, then n is equal to

Q 23 : Let set A={x∈I+:f(x)=x3-8x2+20x-13 is a prime number}. Consider the statements: Statement – I: Number of elements in set A is 3 Statement – II: Sum of all elements in set A is 9, then

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Q 21 :

Let $S_{1} = {x \in R - {1, 2} : \frac{(x + 2) (x^{2} + 3 x + 5)}{- 2 + 3 x - x^{2}} \geq 0}$ and $S_{2} = {x \in R : 3^{2 x} - 3^{x + 1} - 3^{x + 2} + 27 \leq 0}$ . Then, $S_{1} \cup S_{2}$ is equal to

Q 22 :

Let $\cup_{i = 1}^{50} X_{i} = \cup_{i = 1}^{n} Y_{i} = T$ , where each $X_{i}$ contains 10 elements and each $Y_{i}$ contains 5 elements. If each element of the set T is an element of exactly 20 of sets $X_{i}$ 's and exactly 6 of sets $Y_{i}$ 's, then $n$ is equal to

Q 23 :

Let set $A = {x \in I^{+} : f (x) = x^{3} - 8 x^{2} + 20 x - 13$ is a prime number $}$ . Consider the statements:

Statement – I: Number of elements in set A is 3

Statement – II: Sum of all elements in set A is 9, then