यदि \(A=\{1,2,3,4,5,6,7\}\) और \(B=\{0,1\}\) हों, तो (A) से (B) में ऐसे कितने फलन हैं जिनमें ठीक (4) इनपुटों की छवि (1) हो?
If \(A=\{1,2,3,4,5,6,7\}\) and \(B=\{0,1\}\), how many functions from (A) to (B) have exactly (4) inputs with image (1)?
Explanation opens after your attempt
Step 1
Concept
Exactly four of the seven inputs must be mapped to (1). The number is \(\binom{7}{4}=35\).
Step 2
Why this answer is correct
The correct answer is C. (35). Exactly four of the seven inputs must be mapped to (1). The number is \(\binom{7}{4}=35\).
Step 3
Exam Tip
सात इनपुटों में से ठीक चार को (1) पर भेजना है। संख्या \(\binom{7}{4}=35\) है।
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यदि \(A=\{1,2,3,4,5,6\}\) और \(B=\{0,1\}\) हों, तो (A) से (B) में ऐसे कितने फलन हैं जिनमें ठीक (3) इनपुटों की छवि (1) हो?
If \(A=\{1,2,3,4,5,6\}\) and \(B=\{0,1\}\), how many functions from (A) to (B) have exactly (3) inputs with image (1)?
Explanation opens after your attempt
Step 1
Concept
Exactly three of the six inputs must be mapped to (1). The number is \(\binom{6}{3}=20\).
Step 2
Why this answer is correct
The correct answer is C. (20). Exactly three of the six inputs must be mapped to (1). The number is \(\binom{6}{3}=20\).
Step 3
Exam Tip
छह इनपुटों में से ठीक तीन को (1) पर भेजना है। संख्या \(\binom{6}{3}=20\) है।
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यदि \(A=\{1,2,3,4,5\}\) और \(B=\{0,1\}\) हों तो (A) से (B) में ऐसे कितने फलन हैं जिनमें (f(1)+f(2)+f(3)+f(4)+f(5)=2) हो?
If \(A=\{1,2,3,4,5\}\) and \(B=\{0,1\}\), how many functions from (A) to (B) satisfy (f(1)+f(2)+f(3)+f(4)+f(5)=2)?
Explanation opens after your attempt
Step 1
Concept
Exactly two of the five positions must have value (1). The count is \(\binom{5}{2}=10\).
Step 2
Why this answer is correct
The correct answer is B. (10). Exactly two of the five positions must have value (1). The count is \(\binom{5}{2}=10\).
Step 3
Exam Tip
पांच स्थानों में ठीक दो स्थानों पर मान (1) होना चाहिए। संख्या \(\binom{5}{2}=10\) है।
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