एक सभागार में (24) पंक्तियों में कुल (2520) सीटें हैं। यदि हर अगली पंक्ति में (5) सीटें अधिक हैं तो पहली पंक्ति में कितनी सीटें थीं?
An auditorium has (2520) seats in (24) rows. If each next row has (5) more seats, how many seats were in the first row?
Explanation opens after your attempt
Step 1
Concept
Using \(S_{24}=2520\) and (d=5) gives (a=47). Exam tip: find the first term from total and difference.
Step 2
Why this answer is correct
The correct answer is B. (47). Using \(S_{24}=2520\) and (d=5) gives (a=47). Exam tip: find the first term from total and difference.
Step 3
Exam Tip
\(S_{24}=2520\) और (d=5) रखने पर (a=47) मिलता है। परीक्षा में कुल और अंतर से प्रथम पद निकालें।
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एक सभागार की पहली पंक्ति में (34) सीटें हैं और हर अगली पंक्ति में (7) सीटें अधिक हैं। (21) पंक्तियों में कुल कितनी सीटें होंगी?
The first row of an auditorium has (34) seats and each next row has (7) more seats. How many seats are there in (21) rows?
Explanation opens after your attempt
Step 1
Concept
The seats form an AP and \(S_{21}=2184\). Exam tip: use the sum formula for total seats.
Step 2
Why this answer is correct
The correct answer is C. (2184). The seats form an AP and \(S_{21}=2184\). Exam tip: use the sum formula for total seats.
Step 3
Exam Tip
सीटें समान्तर श्रेणी बनाती हैं और \(S_{21}=2184\)। परीक्षा में कुल सीटों के लिए योग सूत्र लगाएं।
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एक सभागार में पहली पंक्ति में (22) सीटें हैं और हर अगली पंक्ति में (3) सीटें अधिक हैं। यदि (25) पंक्तियाँ हैं तो कुल सीटें कितनी होंगी?
In an auditorium the first row has (22) seats and each next row has (3) more seats. If there are (25) rows, how many seats are there in total?
Explanation opens after your attempt
Step 1
Concept
Total seats are (S_{25}=\frac{25}{2}[44+24(3)]=1450). Exam tip: convert real-life situations into an AP.
Step 2
Why this answer is correct
The correct answer is A. (1450). Total seats are (S_{25}=\frac{25}{2}[44+24(3)]=1450). Exam tip: convert real-life situations into an AP.
Step 3
Exam Tip
कुल सीटें (S_{25}=\frac{25}{2}[44+24(3)]=1450) हैं। परीक्षा में वास्तविक जीवन प्रश्नों को समान्तर श्रेणी में बदलें।
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एक सभागार में पंक्तियों की सीटें \(40,48,56,\ldots\) हैं। (30)वीं पंक्ति से (75)वीं पंक्ति तक कुल सीटें कितनी होंगी?
In an auditorium, the seats in rows are \(40,48,56,\ldots\). How many seats are there from the (30)th row to the (75)th row?
Explanation opens after your attempt
Correct Answer
C. (20792)
Step 1
Concept
The total seats are \(S_{75}-S_{29}=20792\). To exclude earlier rows, subtract their sum.
Step 2
Why this answer is correct
The correct answer is C. (20792). The total seats are \(S_{75}-S_{29}=20792\). To exclude earlier rows, subtract their sum.
Step 3
Exam Tip
कुल सीटें \(S_{75}-S_{29}=20792\) हैं। शुरुआती पंक्तियों को हटाने के लिए उनका योग घटाएँ।
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एक सभागार में पंक्तियों की सीटें \(30,36,42,\ldots\) हैं। (25)वीं पंक्ति से (50)वीं पंक्ति तक कुल सीटें कितनी होंगी?
In an auditorium, the seats in rows are \(30,36,42,\ldots\). How many seats are there from the (25)th row to the (50)th row?
Explanation opens after your attempt
Step 1
Concept
The total seats are \(S_{50}-S_{24}=6474\). To exclude earlier rows, subtract their sum.
Step 2
Why this answer is correct
The correct answer is D. (6474). The total seats are \(S_{50}-S_{24}=6474\). To exclude earlier rows, subtract their sum.
Step 3
Exam Tip
कुल सीटें \(S_{50}-S_{24}=6474\) हैं। शुरुआती पंक्तियों को हटाने के लिए उनका योग घटाएँ।
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एक सभागार में पंक्तियों की सीटें \(25,30,35,\ldots\) हैं। (18)वीं पंक्ति से (42)वीं पंक्ति तक कुल सीटें कितनी होंगी?
In an auditorium, the seats in rows are \(25,30,35,\ldots\). How many seats are there from the (18)th row to the (42)nd row?
Explanation opens after your attempt
Step 1
Concept
The total seats are \(S_{42}-S_{17}=4250\). To exclude earlier rows, subtract their sum.
Step 2
Why this answer is correct
The correct answer is B. (4250). The total seats are \(S_{42}-S_{17}=4250\). To exclude earlier rows, subtract their sum.
Step 3
Exam Tip
कुल सीटें \(S_{42}-S_{17}=4250\) हैं। शुरुआती पंक्तियों को हटाने के लिए उनका योग घटाएँ।
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एक सभागार में पंक्तियों की सीटें \(20,24,28,\ldots\) हैं। (15)वीं पंक्ति से (35)वीं पंक्ति तक कुल सीटें कितनी होंगी?
In an auditorium, the seats in rows are \(20,24,28,\ldots\). How many seats are there from the (15)th row to the (35)th row?
Explanation opens after your attempt
Step 1
Concept
The total seats are \(S_{35}-S_{14}=2436\). To exclude earlier rows, subtract their sum.
Step 2
Why this answer is correct
The correct answer is B. (2436). The total seats are \(S_{35}-S_{14}=2436\). To exclude earlier rows, subtract their sum.
Step 3
Exam Tip
कुल सीटें \(S_{35}-S_{14}=2436\) हैं। शुरुआती कुछ पंक्तियों को हटाने के लिए उनके योग को घटाएँ।
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