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Mathematics Quiz - Class 9 Mathematics Medium Level 60 Quiz

Question 1/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (48) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (48) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (1176)

Step 1

Concept

\(S_{48}=\frac{48\times49}{2}=1176\). Divide the even number by (2) first to make calculation easier.

Step 2

Why this answer is correct

The correct answer is A. (1176). \(S_{48}=\frac{48\times49}{2}=1176\). Divide the even number by (2) first to make calculation easier.

Step 3

Exam Tip

\(S_{48}=\frac{48\times49}{2}=1176\) है। सम संख्या को पहले (2) से भाग देने पर गणना आसान होती है।

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Question 2/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि पहली (n) प्राकृतिक संख्याओं का योग (406) है तो (n) का मान क्या है?

If the sum of the first (n) natural numbers is (406), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (28)

Step 1

Concept

\(S_{28}=\frac{28\times29}{2}=406\), so (n=28). You can quickly check by substituting the options in the formula.

Step 2

Why this answer is correct

The correct answer is C. (28). \(S_{28}=\frac{28\times29}{2}=406\), so (n=28). You can quickly check by substituting the options in the formula.

Step 3

Exam Tip

\(S_{28}=\frac{28\times29}{2}=406\) इसलिए (n=28) है। विकल्पों को सूत्र में रखकर जल्दी जांच सकते हैं।

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Question 3/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

(21) से (35) तक की प्राकृतिक संख्याओं का योग कितना है?

What is the sum of natural numbers from (21) to (35)?

Explanation opens after your attempt

Correct Answer

D. (420)

Step 1

Concept

The sum is \(S_{35}-S_{20}=630-210=420\). When the sequence does not start from (1), take the difference of two sums.

Step 2

Why this answer is correct

The correct answer is D. (420). The sum is \(S_{35}-S_{20}=630-210=420\). When the sequence does not start from (1), take the difference of two sums.

Step 3

Exam Tip

योग \(S_{35}-S_{20}=630-210=420\) होगा। जब क्रम (1) से शुरू न हो तो दो योगों का अंतर लें।

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Question 4/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

एक विद्यार्थी (24) दिनों तक रोज पिछले दिन से (1) अधिक प्रश्न हल करता है और पहले दिन (1) प्रश्न हल करता है। कुल प्रश्न कितने होंगे?

A student solves (1) question on the first day and (1) more question each next day for (24) days. How many questions are solved in total?

Explanation opens after your attempt

Correct Answer

C. (300)

Step 1

Concept

Total questions are \(1+2+\cdots+24=300\). In such daily increasing patterns, identify \(S_n\).

Step 2

Why this answer is correct

The correct answer is C. (300). Total questions are \(1+2+\cdots+24=300\). In such daily increasing patterns, identify \(S_n\).

Step 3

Exam Tip

कुल प्रश्न \(1+2+\cdots+24=300\) होंगे। ऐसे दैनिक बढ़ते पैटर्न में \(S_n\) पहचानें।

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Question 5/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(S_{18}+S_{12}\) का मान क्या है जहां \(S_n\) पहली (n) प्राकृतिक संख्याओं का योग है?

What is the value of \(S_{18}+S_{12}\), where \(S_n\) is the sum of the first (n) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (249)

Step 1

Concept

\(S_{18}=171\) and \(S_{12}=78\), so the total is (249). Find each sum separately and then add.

Step 2

Why this answer is correct

The correct answer is A. (249). \(S_{18}=171\) and \(S_{12}=78\), so the total is (249). Find each sum separately and then add.

Step 3

Exam Tip

\(S_{18}=171\) और \(S_{12}=78\) इसलिए कुल (249) है। पहले अलग-अलग योग निकालें फिर जोड़ें।

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Question 6/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (25) प्राकृतिक संख्याओं के योग में से पहली (10) प्राकृतिक संख्याओं का योग घटाने पर क्या मिलेगा?

What is obtained by subtracting the sum of the first (10) natural numbers from the sum of the first (25) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (270)

Step 1

Concept

\(S_{25}-S_{10}=325-55=270\). This equals the sum from (11) to (25).

Step 2

Why this answer is correct

The correct answer is C. (270). \(S_{25}-S_{10}=325-55=270\). This equals the sum from (11) to (25).

Step 3

Exam Tip

\(S_{25}-S_{10}=325-55=270\) है। यह (11) से (25) तक के योग के बराबर है।

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Question 7/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(1+2+3+\cdots+n=595\) है तो (n) क्या होगा?

If \(1+2+3+\cdots+n=595\), what is (n)?

Explanation opens after your attempt

Correct Answer

C. (34)

Step 1

Concept

\(S_{34}=\frac{34\times35}{2}=595\), so (n=34). Match the given sum with nearby triangular numbers.

Step 2

Why this answer is correct

The correct answer is C. (34). \(S_{34}=\frac{34\times35}{2}=595\), so (n=34). Match the given sum with nearby triangular numbers.

Step 3

Exam Tip

\(S_{34}=\frac{34\times35}{2}=595\) इसलिए (n=34) है। दिए गए योग को पास के त्रिभुज संख्याओं से मिलाएं।

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Question 8/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(S_{30}-S_{18}\) का मान ज्ञात कीजिए।

Find the value of \(S_{30}-S_{18}\).

Explanation opens after your attempt

Correct Answer

B. (294)

Step 1

Concept

\(S_{30}=465\) and \(S_{18}=171\), so the difference is (294). Write both sums correctly before subtracting.

Step 2

Why this answer is correct

The correct answer is B. (294). \(S_{30}=465\) and \(S_{18}=171\), so the difference is (294). Write both sums correctly before subtracting.

Step 3

Exam Tip

\(S_{30}=465\) और \(S_{18}=171\) इसलिए अंतर (294) है। अंतर निकालते समय दोनों योग सही लिखें।

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Question 9/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

एक सभा में (1)वीं पंक्ति में (1) कुर्सी और (32)वीं पंक्ति में (32) कुर्सियाँ हैं। सभी पंक्तियों में कुल कुर्सियाँ कितनी हैं?

In a hall, the (1)st row has (1) chair and the (32)nd row has (32) chairs. How many chairs are there in all rows?

Explanation opens after your attempt

Correct Answer

C. (528)

Step 1

Concept

Total chairs are \(S_{32}=\frac{32\times33}{2}=528\). A pattern increasing by row number forms \(S_n\).

Step 2

Why this answer is correct

The correct answer is C. (528). Total chairs are \(S_{32}=\frac{32\times33}{2}=528\). A pattern increasing by row number forms \(S_n\).

Step 3

Exam Tip

कुल कुर्सियाँ \(S_{32}=\frac{32\times33}{2}=528\) हैं। पंक्ति संख्या के अनुसार बढ़ता पैटर्न \(S_n\) बनाता है।

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Question 10/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (40) प्राकृतिक संख्याओं के योग का आधा कितना होगा?

What is half of the sum of the first (40) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (410)

Step 1

Concept

\(S_{40}=820\), and half of it is (410). First find the total sum and then apply the condition.

Step 2

Why this answer is correct

The correct answer is B. (410). \(S_{40}=820\), and half of it is (410). First find the total sum and then apply the condition.

Step 3

Exam Tip

\(S_{40}=820\) है और उसका आधा (410) है। पहले पूरा योग निकालें फिर शर्त लागू करें।

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Question 11/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(1+2+3+\cdots+45\) में अंतिम (5) पदों का योग कितना है?

What is the sum of the last (5) terms in \(1+2+3+\cdots+45\)?

Explanation opens after your attempt

Correct Answer

A. (215)

Step 1

Concept

The last (5) terms are (41+42+43+44+45=215). If last terms are asked, finding the total sum is not necessary.

Step 2

Why this answer is correct

The correct answer is A. (215). The last (5) terms are (41+42+43+44+45=215). If last terms are asked, finding the total sum is not necessary.

Step 3

Exam Tip

अंतिम (5) पद (41+42+43+44+45=215) हैं। अंतिम पद पूछे जाएं तो पूरा योग निकालना जरूरी नहीं होता।

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Question 12/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि पहली (20) प्राकृतिक संख्याओं का योग (210) है तो पहली (21) प्राकृतिक संख्याओं का योग क्या होगा?

If the sum of the first (20) natural numbers is (210), what is the sum of the first (21) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (231)

Step 1

Concept

\(S_{21}=S_{20}+21=210+21=231\). For the next sum, add the next term.

Step 2

Why this answer is correct

The correct answer is B. (231). \(S_{21}=S_{20}+21=210+21=231\). For the next sum, add the next term.

Step 3

Exam Tip

\(S_{21}=S_{20}+21=210+21=231\) है। अगले योग के लिए अगला पद जोड़ दें।

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Question 13/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (36) प्राकृतिक संख्याओं के योग और पहली (30) प्राकृतिक संख्याओं के योग का अंतर क्या है?

What is the difference between the sum of the first (36) natural numbers and the sum of the first (30) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (201)

Step 1

Concept

The difference is \(S_{36}-S_{30}=666-465=201\). It equals the sum from (31) to (36).

Step 2

Why this answer is correct

The correct answer is C. (201). The difference is \(S_{36}-S_{30}=666-465=201\). It equals the sum from (31) to (36).

Step 3

Exam Tip

अंतर \(S_{36}-S_{30}=666-465=201\) है। यह (31) से (36) तक के योग के बराबर होता है।

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Question 14/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

किस (n) के लिए \(S_n=780\) होगा?

For which (n) will \(S_n=780\)?

Explanation opens after your attempt

Correct Answer

B. (39)

Step 1

Concept

\(S_{39}=\frac{39\times40}{2}=780\), so (n=39). In such questions, match (n(n+1)) with \(2S_n\).

Step 2

Why this answer is correct

The correct answer is B. (39). \(S_{39}=\frac{39\times40}{2}=780\), so (n=39). In such questions, match (n(n+1)) with \(2S_n\).

Step 3

Exam Tip

\(S_{39}=\frac{39\times40}{2}=780\) इसलिए (n=39) है। ऐसे प्रश्नों में (n(n+1)) को \(2S_n\) से मिलाएं।

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Question 15/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

एक चित्र में बिंदुओं की (27) पंक्तियाँ हैं और (k)वीं पंक्ति में (k) बिंदु हैं। कुल बिंदु कितने हैं?

A figure has (27) rows of dots, and the (k)th row has (k) dots. How many dots are there in total?

Explanation opens after your attempt

Correct Answer

A. (378)

Step 1

Concept

Total dots are \(S_{27}=\frac{27\times28}{2}=378\). Having (k) dots in the (k)th row shows the sum of natural numbers.

Step 2

Why this answer is correct

The correct answer is A. (378). Total dots are \(S_{27}=\frac{27\times28}{2}=378\). Having (k) dots in the (k)th row shows the sum of natural numbers.

Step 3

Exam Tip

कुल बिंदु \(S_{27}=\frac{27\times28}{2}=378\) होंगे। (k)वीं पंक्ति में (k) बिंदु होना प्राकृतिक संख्याओं का योग दिखाता है।

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Question 16/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(S_{16}+16\) का मान क्या है?

What is the value of \(S_{16}+16\)?

Explanation opens after your attempt

Correct Answer

B. (152)

Step 1

Concept

\(S_{16}=136\), so \(S_{16}+16=152\). Do not mistake \(S_{16}+16\) for \(S_{17}\).

Step 2

Why this answer is correct

The correct answer is B. (152). \(S_{16}=136\), so \(S_{16}+16=152\). Do not mistake \(S_{16}+16\) for \(S_{17}\).

Step 3

Exam Tip

\(S_{16}=136\) है इसलिए \(S_{16}+16=152\)। गणना में \(S_{16}\) को दोबारा \(S_{17}\) न समझें।

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Question 17/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (50) प्राकृतिक संख्याओं के योग में से (1000) घटाने पर कितना बचेगा?

What remains after subtracting (1000) from the sum of the first (50) natural numbers?

Explanation opens after your attempt

Correct Answer

D. (275)

Step 1

Concept

\(S_{50}=1275\), and (1275-1000=275). First find the sum and then perform the given operation.

Step 2

Why this answer is correct

The correct answer is D. (275). \(S_{50}=1275\), and (1275-1000=275). First find the sum and then perform the given operation.

Step 3

Exam Tip

\(S_{50}=1275\) और (1275-1000=275) है। पहले योग निकालें फिर दी गई क्रिया करें।

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Question 18/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_m=210\) और \(S_n=325\) है तो (n-m) का मान क्या है?

If \(S_m=210\) and \(S_n=325\), what is the value of (n-m)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

\(S_{20}=210\) and \(S_{25}=325\), so (n-m=5). Identify both indices first.

Step 2

Why this answer is correct

The correct answer is C. (5). \(S_{20}=210\) and \(S_{25}=325\), so (n-m=5). Identify both indices first.

Step 3

Exam Tip

\(S_{20}=210\) और \(S_{25}=325\) इसलिए (n-m=5)। पहले दोनों सूचकांक पहचानें।

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Question 19/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(11+12+13+\cdots+30\) का योग कितना है?

What is the sum of \(11+12+13+\cdots+30\)?

Explanation opens after your attempt

Correct Answer

D. (410)

Step 1

Concept

The sum is \(S_{30}-S_{10}=465-55=410\). When it starts from (11), subtract the sum of the first (10) terms.

Step 2

Why this answer is correct

The correct answer is D. (410). The sum is \(S_{30}-S_{10}=465-55=410\). When it starts from (11), subtract the sum of the first (10) terms.

Step 3

Exam Tip

योग \(S_{30}-S_{10}=465-55=410\) है। (11) से शुरू होने पर पहले (10) पदों का योग घटाएं।

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Question 20/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (44) प्राकृतिक संख्याओं का योग किसके बराबर है?

The sum of the first (44) natural numbers is equal to which value?

Explanation opens after your attempt

Correct Answer

A. (990)

Step 1

Concept

\(S_{44}=\frac{44\times45}{2}=990\). Take half of (44) as (22) and calculate \(22\times45\).

Step 2

Why this answer is correct

The correct answer is A. (990). \(S_{44}=\frac{44\times45}{2}=990\). Take half of (44) as (22) and calculate \(22\times45\).

Step 3

Exam Tip

\(S_{44}=\frac{44\times45}{2}=990\) है। (44) का आधा (22) लेकर \(22\times45\) करें।

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Question 21/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_n=496\) है तो \(S_{n+1}\) का मान क्या होगा?

If \(S_n=496\), what will be the value of \(S_{n+1}\)?

Explanation opens after your attempt

Correct Answer

B. (528)

Step 1

Concept

\(S_{31}=496\), so \(S_{32}=496+32=528\). For \(S_{n+1}\), add the next term (n+1).

Step 2

Why this answer is correct

The correct answer is B. (528). \(S_{31}=496\), so \(S_{32}=496+32=528\). For \(S_{n+1}\), add the next term (n+1).

Step 3

Exam Tip

\(S_{31}=496\) इसलिए \(S_{32}=496+32=528\)। \(S_{n+1}\) के लिए अगला पद (n+1) जोड़ें।

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Question 22/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (60) प्राकृतिक संख्याओं का योग (1830) है। पहली (59) प्राकृतिक संख्याओं का योग क्या होगा?

The sum of the first (60) natural numbers is (1830). What is the sum of the first (59) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (1770)

Step 1

Concept

\(S_{59}=S_{60}-60=1830-60=1770\). For the previous sum, subtract the last term.

Step 2

Why this answer is correct

The correct answer is B. (1770). \(S_{59}=S_{60}-60=1830-60=1770\). For the previous sum, subtract the last term.

Step 3

Exam Tip

\(S_{59}=S_{60}-60=1830-60=1770\)। पिछले योग के लिए अंतिम पद घटा दें।

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Question 23/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(S_{14}+S_{15}\) का मान क्या होगा?

What will be the value of \(S_{14}+S_{15}\)?

Explanation opens after your attempt

Correct Answer

C. (225)

Step 1

Concept

\(S_{14}=105\) and \(S_{15}=120\), so the sum is (225). Find the two similar-looking sums separately.

Step 2

Why this answer is correct

The correct answer is C. (225). \(S_{14}=105\) and \(S_{15}=120\), so the sum is (225). Find the two similar-looking sums separately.

Step 3

Exam Tip

\(S_{14}=105\) और \(S_{15}=120\) इसलिए योग (225) है। समान दिखने वाले दो योगों को अलग-अलग निकालें।

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Question 24/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(1+2+3+\cdots+n=903\) है तो (n) का मान चुनिए।

If \(1+2+3+\cdots+n=903\), choose the value of (n).

Explanation opens after your attempt

Correct Answer

C. (42)

Step 1

Concept

\(S_{42}=\frac{42\times43}{2}=903\), so (n=42). Use \(2S_n\) to see the product of two consecutive numbers.

Step 2

Why this answer is correct

The correct answer is C. (42). \(S_{42}=\frac{42\times43}{2}=903\), so (n=42). Use \(2S_n\) to see the product of two consecutive numbers.

Step 3

Exam Tip

\(S_{42}=\frac{42\times43}{2}=903\) इसलिए (n=42)। \(2S_n\) करके दो क्रमागत संख्याओं का गुणनफल देखें।

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Question 25/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

एक अभ्यास में पहले (15) चरणों में क्रमशः (1) से (15) तक अंक मिले और अगले (10) चरणों में कोई अंक नहीं मिला। कुल अंक कितने हैं?

In a practice session, marks from (1) to (15) are scored in the first (15) steps, and no marks are scored in the next (10) steps. What is the total score?

Explanation opens after your attempt

Correct Answer

C. (120)

Step 1

Concept

The total score is only \(S_{15}=120\). Extra zero marks do not change the sum.

Step 2

Why this answer is correct

The correct answer is C. (120). The total score is only \(S_{15}=120\). Extra zero marks do not change the sum.

Step 3

Exam Tip

कुल अंक केवल \(S_{15}=120\) होंगे। अतिरिक्त शून्य अंक योग को नहीं बदलते।

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Question 26/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (52) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (52) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (1378)

Step 1

Concept

\(S_{52}=\frac{52\times53}{2}=1378\). Halve (52) and calculate \(26\times53\).

Step 2

Why this answer is correct

The correct answer is B. (1378). \(S_{52}=\frac{52\times53}{2}=1378\). Halve (52) and calculate \(26\times53\).

Step 3

Exam Tip

\(S_{52}=\frac{52\times53}{2}=1378\) है। (52) को आधा करके \(26\times53\) करें।

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Question 27/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(S_{33}-S_{22}\) का मान क्या है?

What is the value of \(S_{33}-S_{22}\)?

Explanation opens after your attempt

Correct Answer

B. (308)

Step 1

Concept

\(S_{33}=561\) and \(S_{22}=253\), so the difference is (308). It is also the sum from (23) to (33).

Step 2

Why this answer is correct

The correct answer is B. (308). \(S_{33}=561\) and \(S_{22}=253\), so the difference is (308). It is also the sum from (23) to (33).

Step 3

Exam Tip

\(S_{33}=561\) और \(S_{22}=253\) इसलिए अंतर (308) है। यह (23) से (33) तक का योग भी है।

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Question 28/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि पहली (n) प्राकृतिक संख्याओं का योग (1035) है तो (n) क्या है?

If the sum of the first (n) natural numbers is (1035), what is (n)?

Explanation opens after your attempt

Correct Answer

C. (45)

Step 1

Concept

\(S_{45}=\frac{45\times46}{2}=1035\), so (n=45). Checking options saves time in larger sums.

Step 2

Why this answer is correct

The correct answer is C. (45). \(S_{45}=\frac{45\times46}{2}=1035\), so (n=45). Checking options saves time in larger sums.

Step 3

Exam Tip

\(S_{45}=\frac{45\times46}{2}=1035\) इसलिए (n=45)। बड़े योग में विकल्प जांचना समय बचाता है।

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Question 29/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(1+2+3+\cdots+19\) में (20) जोड़ने पर कौन सा योग बनेगा?

Which sum is formed when (20) is added to \(1+2+3+\cdots+19\)?

Explanation opens after your attempt

Correct Answer

C. \(S_{20}\)

Step 1

Concept

\(1+2+\cdots+19+20=S_{20}\). Adding the next term gives the next partial sum.

Step 2

Why this answer is correct

The correct answer is C. \(S_{20}\). \(1+2+\cdots+19+20=S_{20}\). Adding the next term gives the next partial sum.

Step 3

Exam Tip

\(1+2+\cdots+19+20=S_{20}\) होता है। अगला पद जोड़ने पर अगला आंशिक योग मिलता है।

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Question 30/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

एक बचत योजना में बच्चा पहले दिन (1) रुपये और (31)वें दिन (31) रुपये बचाता है। यदि राशि रोज (1) रुपये बढ़ती है तो कुल बचत कितनी है?

In a saving plan, a child saves (1) rupee on the first day and (31) rupees on the (31)st day. If the amount increases by (1) rupee daily, what is the total saving?

Explanation opens after your attempt

Correct Answer

B. (496)

Step 1

Concept

Total saving is \(S_{31}=\frac{31\times32}{2}=496\) rupees. A daily increase of (1) forms the sum of natural numbers.

Step 2

Why this answer is correct

The correct answer is B. (496). Total saving is \(S_{31}=\frac{31\times32}{2}=496\) rupees. A daily increase of (1) forms the sum of natural numbers.

Step 3

Exam Tip

कुल बचत \(S_{31}=\frac{31\times32}{2}=496\) रुपये है। दैनिक वृद्धि (1) हो तो प्राकृतिक संख्याओं का योग बनता है।

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Question 31/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (18) प्राकृतिक संख्याओं के योग का तीन गुना कितना होगा?

What is three times the sum of the first (18) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (513)

Step 1

Concept

\(S_{18}=171\), and \(3\times171=513\). Find the sum first and then multiply.

Step 2

Why this answer is correct

The correct answer is C. (513). \(S_{18}=171\), and \(3\times171=513\). Find the sum first and then multiply.

Step 3

Exam Tip

\(S_{18}=171\) है और \(3\times171=513\)। पहले योग निकालकर गुणा करें।

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Question 32/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (26) प्राकृतिक संख्याओं के योग और (26) के बीच अंतर क्या है?

What is the difference between the sum of the first (26) natural numbers and (26)?

Explanation opens after your attempt

Correct Answer

B. (325)

Step 1

Concept

\(S_{26}=351\), and (351-26=325). Subtracting the last term gives \(S_{25}\).

Step 2

Why this answer is correct

The correct answer is B. (325). \(S_{26}=351\), and (351-26=325). Subtracting the last term gives \(S_{25}\).

Step 3

Exam Tip

\(S_{26}=351\) और (351-26=325) है। अंतिम पद घटाने पर \(S_{25}\) मिल जाता है।

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Question 33/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(16+17+18+\cdots+25\) का योग कितना है?

What is the sum of \(16+17+18+\cdots+25\)?

Explanation opens after your attempt

Correct Answer

B. (205)

Step 1

Concept

The sum is \(S_{25}-S_{15}=325-120=205\). Subtract the sum of the terms before the starting point.

Step 2

Why this answer is correct

The correct answer is B. (205). The sum is \(S_{25}-S_{15}=325-120=205\). Subtract the sum of the terms before the starting point.

Step 3

Exam Tip

योग \(S_{25}-S_{15}=325-120=205\) है। शुरू होने से पहले वाले पदों का योग घटाएं।

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Question 34/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

किस (n) के लिए \(S_n-S_{n-1}=37\) होगा?

For which (n) will \(S_n-S_{n-1}=37\)?

Explanation opens after your attempt

Correct Answer

C. (37)

Step 1

Concept

\(S_n-S_{n-1}=n\), so (n=37). The difference of two consecutive sums is the new term.

Step 2

Why this answer is correct

The correct answer is C. (37). \(S_n-S_{n-1}=n\), so (n=37). The difference of two consecutive sums is the new term.

Step 3

Exam Tip

\(S_n-S_{n-1}=n\) होता है इसलिए (n=37)। दो लगातार योगों का अंतर नया पद होता है।

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Question 35/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (55) प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of the first (55) natural numbers.

Explanation opens after your attempt

Correct Answer

A. (1540)

Step 1

Concept

\(S_{55}=\frac{55\times56}{2}=1540\). For odd (n), halving the next even factor is easier.

Step 2

Why this answer is correct

The correct answer is A. (1540). \(S_{55}=\frac{55\times56}{2}=1540\). For odd (n), halving the next even factor is easier.

Step 3

Exam Tip

\(S_{55}=\frac{55\times56}{2}=1540\) है। विषम (n) में अगले सम गुणक को आधा करना आसान है।

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Question 36/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_{23}=276\) है तो \(S_{25}\) का मान क्या होगा?

If \(S_{23}=276\), what will be the value of \(S_{25}\)?

Explanation opens after your attempt

Correct Answer

B. (325)

Step 1

Concept

\(S_{25}=S_{23}+24+25=276+49=325\). Do not forget to add the new terms in between.

Step 2

Why this answer is correct

The correct answer is B. (325). \(S_{25}=S_{23}+24+25=276+49=325\). Do not forget to add the new terms in between.

Step 3

Exam Tip

\(S_{25}=S_{23}+24+25=276+49=325\)। बीच के नए पद जोड़ना न भूलें।

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Question 37/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (29) प्राकृतिक संख्याओं के योग में (30) और (31) जोड़ने पर क्या मिलेगा?

What is obtained by adding (30) and (31) to the sum of the first (29) natural numbers?

Explanation opens after your attempt

Correct Answer

C. \(S_{31}\)

Step 1

Concept

\(S_{29}+30+31=S_{31}\). Adding consecutive next terms gives the new partial sum.

Step 2

Why this answer is correct

The correct answer is C. \(S_{31}\). \(S_{29}+30+31=S_{31}\). Adding consecutive next terms gives the new partial sum.

Step 3

Exam Tip

\(S_{29}+30+31=S_{31}\) होता है। लगातार अगले पद जोड़ने से नया आंशिक योग बनता है।

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Question 38/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(S_{20}\) और \(S_{10}\) का अनुपात क्या है?

What is the ratio of \(S_{20}\) to \(S_{10}\)?

Explanation opens after your attempt

Correct Answer

B. (42:11)

Step 1

Concept

\(S_{20}:S_{10}=210:55=42:11\). Simplify a ratio by dividing both numbers by a common factor.

Step 2

Why this answer is correct

The correct answer is B. (42:11). \(S_{20}:S_{10}=210:55=42:11\). Simplify a ratio by dividing both numbers by a common factor.

Step 3

Exam Tip

\(S_{20}:S_{10}=210:55=42:11\) है। अनुपात में दोनों संख्याओं को समान गुणक से सरल करें।

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Question 39/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

एक त्रिभुजाकार सजावट में (1) से (19) तक क्रमशः मोती रखे गए हैं। कुल मोती कितने हैं?

In a triangular decoration, beads are placed in rows from (1) to (19). How many beads are there in total?

Explanation opens after your attempt

Correct Answer

C. (190)

Step 1

Concept

Total beads are \(S_{19}=\frac{19\times20}{2}=190\). Triangular rows often give the sum of natural numbers.

Step 2

Why this answer is correct

The correct answer is C. (190). Total beads are \(S_{19}=\frac{19\times20}{2}=190\). Triangular rows often give the sum of natural numbers.

Step 3

Exam Tip

कुल मोती \(S_{19}=\frac{19\times20}{2}=190\) हैं। त्रिभुजाकार पंक्तियां अक्सर प्राकृतिक संख्याओं का योग देती हैं।

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Question 40/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(S_{41}-S_{40}\) का मान क्या है?

What is the value of \(S_{41}-S_{40}\)?

Explanation opens after your attempt

Correct Answer

C. (41)

Step 1

Concept

The difference of two consecutive sums is the new term, so \(S_{41}-S_{40}=41\). You can answer without finding the full sums.

Step 2

Why this answer is correct

The correct answer is C. (41). The difference of two consecutive sums is the new term, so \(S_{41}-S_{40}=41\). You can answer without finding the full sums.

Step 3

Exam Tip

दो लगातार योगों का अंतर नया पद होता है इसलिए \(S_{41}-S_{40}=41\)। पूरा योग निकाले बिना भी उत्तर मिल सकता है।

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Question 41/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि पहली (r) प्राकृतिक संख्याओं का योग (153) है तो (r+2) का मान क्या है?

If the sum of the first (r) natural numbers is (153), what is the value of (r+2)?

Explanation opens after your attempt

Correct Answer

C. (19)

Step 1

Concept

\(S_{17}=153\), so (r=17) and (r+2=19). First find the variable and then answer what is asked.

Step 2

Why this answer is correct

The correct answer is C. (19). \(S_{17}=153\), so (r=17) and (r+2=19). First find the variable and then answer what is asked.

Step 3

Exam Tip

\(S_{17}=153\) इसलिए (r=17) और (r+2=19)। पहले चर का मान निकालें फिर पूछा गया मान दें।

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Question 42/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (46) प्राकृतिक संख्याओं का योग कितना होगा?

What will be the sum of the first (46) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (1081)

Step 1

Concept

\(S_{46}=\frac{46\times47}{2}=1081\). Take half of (46) as (23) and calculate \(23\times47\).

Step 2

Why this answer is correct

The correct answer is A. (1081). \(S_{46}=\frac{46\times47}{2}=1081\). Take half of (46) as (23) and calculate \(23\times47\).

Step 3

Exam Tip

\(S_{46}=\frac{46\times47}{2}=1081\) है। (46) का आधा (23) लेकर \(23\times47\) करें।

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Question 43/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(S_{12}+S_{13}+S_{14}\) का मान क्या है?

What is the value of \(S_{12}+S_{13}+S_{14}\)?

Explanation opens after your attempt

Correct Answer

B. (306)

Step 1

Concept

\(S_{12}=78\), \(S_{13}=91\), and \(S_{14}=105\), so the total is (274). Add carefully to avoid option traps.

Step 2

Why this answer is correct

The correct answer is B. (306). \(S_{12}=78\), \(S_{13}=91\), and \(S_{14}=105\), so the total is (274). Add carefully to avoid option traps.

Step 3

Exam Tip

\(S_{12}=78\), \(S_{13}=91\) और \(S_{14}=105\) इसलिए कुल (274) नहीं बल्कि (274) है।

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Question 44/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_a=351\) और \(S_b=465\) है तो (b-a) कितना है?

If \(S_a=351\) and \(S_b=465\), what is (b-a)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

\(S_{26}=351\) and \(S_{30}=465\), so (b-a=4). Identify the indices of both sums first.

Step 2

Why this answer is correct

The correct answer is C. (4). \(S_{26}=351\) and \(S_{30}=465\), so (b-a=4). Identify the indices of both sums first.

Step 3

Exam Tip

\(S_{26}=351\) और \(S_{30}=465\) इसलिए (b-a=4)। पहले दोनों योगों के सूचकांक पहचानें।

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Question 45/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(1+2+\cdots+28\) में (29+30+31) जोड़ने पर प्राप्त योग क्या होगा?

What sum is obtained by adding (29+30+31) to \(1+2+\cdots+28\)?

Explanation opens after your attempt

Correct Answer

A. (496)

Step 1

Concept

This becomes \(S_{31}\), and \(S_{31}=496\). When consecutive terms are added, the last term becomes the new (n).

Step 2

Why this answer is correct

The correct answer is A. (496). This becomes \(S_{31}\), and \(S_{31}=496\). When consecutive terms are added, the last term becomes the new (n).

Step 3

Exam Tip

यह \(S_{31}\) बनेगा और \(S_{31}=496\) है। लगातार पद जुड़ने पर अंतिम पद नया (n) बन जाता है।

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Question 46/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (70) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (70) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (2485)

Step 1

Concept

\(S_{70}=\frac{70\times71}{2}=2485\). For large (n), cancel by (2) first.

Step 2

Why this answer is correct

The correct answer is B. (2485). \(S_{70}=\frac{70\times71}{2}=2485\). For large (n), cancel by (2) first.

Step 3

Exam Tip

\(S_{70}=\frac{70\times71}{2}=2485\) है। बड़े (n) में पहले (2) से कटौती करें।

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Question 47/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_n=300\) है तो (n) का मान क्या होगा?

If \(S_n=300\), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (24)

Step 1

Concept

\(S_{24}=\frac{24\times25}{2}=300\), so (n=24). After finding the answer, verify it in the formula.

Step 2

Why this answer is correct

The correct answer is B. (24). \(S_{24}=\frac{24\times25}{2}=300\), so (n=24). After finding the answer, verify it in the formula.

Step 3

Exam Tip

\(S_{24}=\frac{24\times25}{2}=300\) इसलिए (n=24)। उत्तर मिलते ही सूत्र में वापस जांच करें।

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Question 48/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

\(S_{37}+S_{38}\) का मान ज्ञात करें।

Find the value of \(S_{37}+S_{38}\).

Explanation opens after your attempt

Correct Answer

A. (1444)

Step 1

Concept

\(S_{37}=703\) and \(S_{38}=741\), so the sum is (1444). Notice the one-term difference in nearby sums.

Step 2

Why this answer is correct

The correct answer is A. (1444). \(S_{37}=703\) and \(S_{38}=741\), so the sum is (1444). Notice the one-term difference in nearby sums.

Step 3

Exam Tip

\(S_{37}=703\) और \(S_{38}=741\) इसलिए योग (1444) है। पास-पास के योगों में एक पद का अंतर ध्यान रखें।

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Question 49/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

पहली (64) प्राकृतिक संख्याओं के योग से पहली (60) प्राकृतिक संख्याओं का योग घटाने पर क्या मिलेगा?

What is obtained by subtracting the sum of the first (60) natural numbers from the sum of the first (64) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (250)

Step 1

Concept

The difference is (61+62+63+64=250). The difference of two nearby sums equals the sum of the terms in between.

Step 2

Why this answer is correct

The correct answer is C. (250). The difference is (61+62+63+64=250). The difference of two nearby sums equals the sum of the terms in between.

Step 3

Exam Tip

अंतर (61+62+63+64=250) है। पास के दो योगों का अंतर बीच के पदों का योग होता है।

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Question 50/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 60

यदि \(S_{52}=1378\) है तो \(S_{54}\) का मान क्या होगा?

If \(S_{52}=1378\), what will be the value of \(S_{54}\)?

Explanation opens after your attempt

Correct Answer

A. (1485)

Step 1

Concept

\(S_{54}=S_{52}+53+54=1378+107=1485\). To move two sums ahead, add both new terms.

Step 2

Why this answer is correct

The correct answer is A. (1485). \(S_{54}=S_{52}+53+54=1378+107=1485\). To move two sums ahead, add both new terms.

Step 3

Exam Tip

\(S_{54}=S_{52}+53+54=1378+107=1485\) है। दो आगे के योग के लिए बीच के दोनों नए पद जोड़ें।

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Class 9 Mathematics Medium Quiz

पहली (48) प्राकृतिक संख्याओं का योग कितना है?

Concept

Why this answer is correct

Exam Tip

यदि पहली (n) प्राकृतिक संख्याओं का योग (406) है तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(21) से (35) तक की प्राकृतिक संख्याओं का योग कितना है?

Concept

Why this answer is correct

Exam Tip

Concept

Why this answer is correct

Exam Tip

\(S_{18}+S_{12}\) का मान क्या है जहां \(S_n\) पहली (n) प्राकृतिक संख्याओं का योग है?

Concept

Why this answer is correct

Exam Tip

पहली (25) प्राकृतिक संख्याओं के योग में से पहली (10) प्राकृतिक संख्याओं का योग घटाने पर क्या मिलेगा?

Concept

Why this answer is correct

Exam Tip

यदि \(1+2+3+\cdots+n=595\) है तो (n) क्या होगा?

Concept

Why this answer is correct

Exam Tip

\(S_{30}-S_{18}\) का मान ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

Concept

Why this answer is correct

Exam Tip

पहली (40) प्राकृतिक संख्याओं के योग का आधा कितना होगा?

Concept

Why this answer is correct

Exam Tip

\(1+2+3+\cdots+45\) में अंतिम (5) पदों का योग कितना है?

Concept

Why this answer is correct

Exam Tip

यदि पहली (20) प्राकृतिक संख्याओं का योग (210) है तो पहली (21) प्राकृतिक संख्याओं का योग क्या होगा?

Concept

Why this answer is correct

Exam Tip

पहली (36) प्राकृतिक संख्याओं के योग और पहली (30) प्राकृतिक संख्याओं के योग का अंतर क्या है?

Concept

Why this answer is correct

Exam Tip

किस (n) के लिए \(S_n=780\) होगा?

Concept

Why this answer is correct

Exam Tip

एक चित्र में बिंदुओं की (27) पंक्तियाँ हैं और (k)वीं पंक्ति में (k) बिंदु हैं। कुल बिंदु कितने हैं?

Concept

Why this answer is correct

Exam Tip

\(S_{16}+16\) का मान क्या है?

Concept

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Exam Tip

पहली (50) प्राकृतिक संख्याओं के योग में से (1000) घटाने पर कितना बचेगा?

Concept

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Exam Tip

यदि \(S_m=210\) और \(S_n=325\) है तो (n-m) का मान क्या है?

Concept

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Exam Tip

\(11+12+13+\cdots+30\) का योग कितना है?

Concept

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Exam Tip

पहली (44) प्राकृतिक संख्याओं का योग किसके बराबर है?

Concept

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Exam Tip

यदि \(S_n=496\) है तो \(S_{n+1}\) का मान क्या होगा?