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complement cardinality MCQ Questions for Class 11

complement cardinality se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

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3 questions tagged with complement cardinality.

Question 1/3 Medium Mathematics Sets Complement of a Set and its properties Class 11 Level 21

\(यदि (U={x:x \in \mathbb{N},\ 1\le x\le 30}) और (A={x:x \in U,\ x\) 2 और 3 दोनों से विभाज्य है\(}), तो (n(A^{c})) क्या है\)?

\(If (U={x:x \in \mathbb{N},\ 1\le x\le 30}) and (A={x:x \in U,\ x\) is divisible by both 2 and \(3}), what is (n(A^{c}))\)?

Explanation opens after your attempt
Correct Answer

B. (25)

Step 1

Concept

Numbers divisible by both (2) and (3) are multiples of (6), giving (5) numbers. Thus (n\(A^{c}\)=30-5=25).

Step 2

Why this answer is correct

The correct answer is B. (25). Numbers divisible by both (2) and (3) are multiples of (6), giving (5) numbers. Thus (n\(A^{c}\)=30-5=25).

Step 3

Exam Tip

(2) और (3) दोनों से विभाज्य संख्याएं (6) के गुणज हैं, यानी (5) संख्याएं। इसलिए (n\(A^{c}\)=30-5=25)।

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Question 2/3 Hard Mathematics Sets Power Set and Universal Set Class 11 Level 11

\(यदि (U={x:x\in \mathbb{N}, x\le 50}) और (A={x:x\in U, x\) 10 का गुणज है\(}), तो (|\mathcal{P}(A')|) क्या है\)?

\(If (U={x:x\in \mathbb{N}, x\le 50}) and (A={x:x\in U, x\) is a multiple of \(10}), what is (|\mathcal{P}(A')|)\)?

Explanation opens after your attempt
Correct Answer

B. \(2^{45}\)

Step 1

Concept

The multiples of (10) are (10,20,30,40,50), so (|A|=5). (A') has (45) elements, hence (|\mathcal{P}(A')|=2^{45}).

Step 2

Why this answer is correct

The correct answer is B. \(2^{45}\). The multiples of (10) are (10,20,30,40,50), so (|A|=5). (A') has (45) elements, hence (|\mathcal{P}(A')|=2^{45}).

Step 3

Exam Tip

(10) के गुणज (10,20,30,40,50) हैं, इसलिए (|A|=5)। (A') में (45) तत्व हैं, अतः (|\mathcal{P}(A')|=2^{45})।

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Question 3/3 Medium Mathematics Sets Power Set and Universal Set Class 11 Level 11

यदि \(A\subseteq U\), (n(U)=60), (n(A)=28), और (n(A')=x) है, तो (x) का मान क्या है?

If \(A\subseteq U\), (n(U)=60), (n(A)=28), and (n(A')=x), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (32)

Step 1

Concept

Elements of the complement are in (U) but not in (A). Therefore (x=60-28=32).

Step 2

Why this answer is correct

The correct answer is B. (32). Elements of the complement are in (U) but not in (A). Therefore (x=60-28=32).

Step 3

Exam Tip

पूरक के तत्व (U) में होते हैं पर (A) में नहीं होते। इसलिए (x=60-28=32) है।

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