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Mathematics Quiz - Class 9 Mathematics Medium Level 59 Quiz

Question 1/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (47) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (47) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (1128)

Step 1

Concept

\(S_{47}=\frac{47\times48}{2}=1128\). For odd (n), halve the next even factor.

Step 2

Why this answer is correct

The correct answer is B. (1128). \(S_{47}=\frac{47\times48}{2}=1128\). For odd (n), halve the next even factor.

Step 3

Exam Tip

\(S_{47}=\frac{47\times48}{2}=1128\) है। विषम (n) में अगले सम गुणक को आधा करें।

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Question 2/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि पहली (n) प्राकृतिक संख्याओं का योग (561) है तो (n) का मान क्या है?

If the sum of the first (n) natural numbers is (561), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (33)

Step 1

Concept

\(S_{33}=\frac{33\times34}{2}=561\), so (n=33). Checking options in the formula is fast.

Step 2

Why this answer is correct

The correct answer is C. (33). \(S_{33}=\frac{33\times34}{2}=561\), so (n=33). Checking options in the formula is fast.

Step 3

Exam Tip

\(S_{33}=\frac{33\times34}{2}=561\) इसलिए (n=33) है। विकल्पों को सूत्र में रखकर जांचना तेज होता है।

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Question 3/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

(12) से (29) तक की प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of natural numbers from (12) to (29).

Explanation opens after your attempt

Correct Answer

A. (369)

Step 1

Concept

The sum is \(S_{29}-S_{11}=435-66=369\). When the sequence does not start from (1), subtract the previous terms' sum.

Step 2

Why this answer is correct

The correct answer is A. (369). The sum is \(S_{29}-S_{11}=435-66=369\). When the sequence does not start from (1), subtract the previous terms' sum.

Step 3

Exam Tip

योग \(S_{29}-S_{11}=435-66=369\) होगा। जब क्रम (1) से शुरू न हो तो पहले वाले पदों का योग घटाएं।

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Question 4/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

एक अभ्यास में पहले दिन (1) प्रश्न और (38)वें दिन (38) प्रश्न हल किए गए। रोज प्रश्नों की संख्या (1) बढ़ी तो कुल प्रश्न कितने हुए?

In a practice, (1) question is solved on the first day and (38) questions on the (38)th day. If the number increases by (1) daily, how many questions are solved?

Explanation opens after your attempt

Correct Answer

C. (741)

Step 1

Concept

Total questions are \(S_{38}=\frac{38\times39}{2}=741\). A daily increase of (1) forms the sum of natural numbers.

Step 2

Why this answer is correct

The correct answer is C. (741). Total questions are \(S_{38}=\frac{38\times39}{2}=741\). A daily increase of (1) forms the sum of natural numbers.

Step 3

Exam Tip

कुल प्रश्न \(S_{38}=\frac{38\times39}{2}=741\) होंगे। रोज (1) की वृद्धि प्राकृतिक संख्याओं का योग बनाती है।

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Question 5/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{22}+S_{17}\) का मान क्या है?

What is the value of \(S_{22}+S_{17}\)?

Explanation opens after your attempt

Correct Answer

B. (406)

Step 1

Concept

\(S_{22}=253\) and \(S_{17}=153\), so the sum is (406). Find both sums separately first.

Step 2

Why this answer is correct

The correct answer is B. (406). \(S_{22}=253\) and \(S_{17}=153\), so the sum is (406). Find both sums separately first.

Step 3

Exam Tip

\(S_{22}=253\) और \(S_{17}=153\) इसलिए योग (406) है। पहले दोनों योग अलग-अलग निकालें।

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Question 6/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (41) प्राकृतिक संख्याओं के योग में से पहली (23) प्राकृतिक संख्याओं का योग घटाने पर क्या मिलेगा?

What is obtained by subtracting the sum of the first (23) natural numbers from the sum of the first (41) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (585)

Step 1

Concept

\(S_{41}-S_{23}=861-276=585\). This is the sum of terms from (24) to (41).

Step 2

Why this answer is correct

The correct answer is C. (585). \(S_{41}-S_{23}=861-276=585\). This is the sum of terms from (24) to (41).

Step 3

Exam Tip

\(S_{41}-S_{23}=861-276=585\) है। यह (24) से (41) तक के पदों का योग है।

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Question 7/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(1+2+3+\cdots+n=946\) है तो (n) का मान चुनिए।

If \(1+2+3+\cdots+n=946\), choose the value of (n).

Explanation opens after your attempt

Correct Answer

C. (43)

Step 1

Concept

\(S_{43}=\frac{43\times44}{2}=946\), so (n=43). Match \(2S_n\) with the product of two consecutive numbers.

Step 2

Why this answer is correct

The correct answer is C. (43). \(S_{43}=\frac{43\times44}{2}=946\), so (n=43). Match \(2S_n\) with the product of two consecutive numbers.

Step 3

Exam Tip

\(S_{43}=\frac{43\times44}{2}=946\) इसलिए (n=43) है। \(2S_n\) को दो क्रमागत संख्याओं के गुणनफल से मिलाएं।

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Question 8/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{35}-S_{19}\) का मान ज्ञात कीजिए।

Find the value of \(S_{35}-S_{19}\).

Explanation opens after your attempt

Correct Answer

B. (440)

Step 1

Concept

\(S_{35}=630\) and \(S_{19}=190\), so the difference is (440). It is also the sum from (20) to (35).

Step 2

Why this answer is correct

The correct answer is B. (440). \(S_{35}=630\) and \(S_{19}=190\), so the difference is (440). It is also the sum from (20) to (35).

Step 3

Exam Tip

\(S_{35}=630\) और \(S_{19}=190\) इसलिए अंतर (440) है। यह (20) से (35) तक का योग भी है।

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Question 9/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

एक हॉल में (1)वीं पंक्ति में (1) सीट और (26)वीं पंक्ति में (26) सीटें हैं। सभी पंक्तियों में कुल सीटें कितनी हैं?

In a hall, the (1)st row has (1) seat and the (26)th row has (26) seats. How many seats are there in all rows?

Explanation opens after your attempt

Correct Answer

C. (351)

Step 1

Concept

Total seats are \(S_{26}=\frac{26\times27}{2}=351\). If seats equal the row number, use \(S_n\).

Step 2

Why this answer is correct

The correct answer is C. (351). Total seats are \(S_{26}=\frac{26\times27}{2}=351\). If seats equal the row number, use \(S_n\).

Step 3

Exam Tip

कुल सीटें \(S_{26}=\frac{26\times27}{2}=351\) हैं। पंक्ति संख्या के बराबर सीटें हों तो \(S_n\) लगाएं।

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Question 10/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (54) प्राकृतिक संख्याओं के योग का दोगुना कितना होगा?

What is twice the sum of the first (54) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (2970)

Step 1

Concept

\(S_{54}=1485\), and \(2\times1485=2970\). First find the total sum and then multiply.

Step 2

Why this answer is correct

The correct answer is B. (2970). \(S_{54}=1485\), and \(2\times1485=2970\). First find the total sum and then multiply.

Step 3

Exam Tip

\(S_{54}=1485\) है और \(2\times1485=2970\) है। पहले पूरा योग निकालें फिर गुणा करें।

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Question 11/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(1+2+3+\cdots+40\) में अंतिम (6) पदों का योग कितना है?

What is the sum of the last (6) terms in \(1+2+3+\cdots+40\)?

Explanation opens after your attempt

Correct Answer

A. (225)

Step 1

Concept

The sum of the last (6) terms is (35+36+37+38+39+40=225). For last terms, finding full \(S_{40}\) is not necessary.

Step 2

Why this answer is correct

The correct answer is A. (225). The sum of the last (6) terms is (35+36+37+38+39+40=225). For last terms, finding full \(S_{40}\) is not necessary.

Step 3

Exam Tip

अंतिम (6) पदों का योग (35+36+37+38+39+40=225) है। अंतिम पदों के लिए पूरा \(S_{40}\) निकालना जरूरी नहीं है।

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Question 12/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि पहली (31) प्राकृतिक संख्याओं का योग (496) है तो पहली (34) प्राकृतिक संख्याओं का योग क्या होगा?

If the sum of the first (31) natural numbers is (496), what is the sum of the first (34) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (595)

Step 1

Concept

\(S_{34}=S_{31}+32+33+34=595\). While moving ahead, add all new terms in between.

Step 2

Why this answer is correct

The correct answer is C. (595). \(S_{34}=S_{31}+32+33+34=595\). While moving ahead, add all new terms in between.

Step 3

Exam Tip

\(S_{34}=S_{31}+32+33+34=595\) है। आगे बढ़ते समय बीच के सभी नए पद जोड़ें।

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Question 13/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (58) प्राकृतिक संख्याओं के योग और पहली (55) प्राकृतिक संख्याओं के योग का अंतर क्या है?

What is the difference between the sum of the first (58) natural numbers and the sum of the first (55) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (171)

Step 1

Concept

The difference is (56+57+58=171). The difference of nearby sums equals the sum of the terms in between.

Step 2

Why this answer is correct

The correct answer is B. (171). The difference is (56+57+58=171). The difference of nearby sums equals the sum of the terms in between.

Step 3

Exam Tip

अंतर (56+57+58=171) है। पास के दो योगों का अंतर बीच के पदों का योग होता है।

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Question 14/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

किस (n) के लिए \(S_n=1081\) होगा?

For which (n) will \(S_n=1081\)?

Explanation opens after your attempt

Correct Answer

C. (46)

Step 1

Concept

\(S_{46}=\frac{46\times47}{2}=1081\), so (n=46). Checking with options is useful for larger sums.

Step 2

Why this answer is correct

The correct answer is C. (46). \(S_{46}=\frac{46\times47}{2}=1081\), so (n=46). Checking with options is useful for larger sums.

Step 3

Exam Tip

\(S_{46}=\frac{46\times47}{2}=1081\) इसलिए (n=46) है। बड़े योग में विकल्पों से जांच करना उपयोगी है।

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Question 15/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

एक चित्र में (42) पंक्तियां हैं और (r)वीं पंक्ति में (r) बिंदु हैं। कुल बिंदु कितने होंगे?

A figure has (42) rows, and the (r)th row has (r) dots. How many dots will there be in total?

Explanation opens after your attempt

Correct Answer

C. (903)

Step 1

Concept

Total dots are \(S_{42}=\frac{42\times43}{2}=903\). Having (r) dots in the (r)th row is the sum of natural numbers.

Step 2

Why this answer is correct

The correct answer is C. (903). Total dots are \(S_{42}=\frac{42\times43}{2}=903\). Having (r) dots in the (r)th row is the sum of natural numbers.

Step 3

Exam Tip

कुल बिंदु \(S_{42}=\frac{42\times43}{2}=903\) हैं। (r)वीं पंक्ति में (r) बिंदु होना प्राकृतिक संख्याओं का योग है।

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Question 16/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{28}+28\) का मान क्या है?

What is the value of \(S_{28}+28\)?

Explanation opens after your attempt

Correct Answer

B. (434)

Step 1

Concept

\(S_{28}=406\), so \(S_{28}+28=434\). Do not mistake it for \(S_{29}\).

Step 2

Why this answer is correct

The correct answer is B. (434). \(S_{28}=406\), so \(S_{28}+28=434\). Do not mistake it for \(S_{29}\).

Step 3

Exam Tip

\(S_{28}=406\) है इसलिए \(S_{28}+28=434\)। इसे \(S_{29}\) समझने की गलती न करें।

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Question 17/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (65) प्राकृतिक संख्याओं के योग में से (1500) घटाने पर कितना बचेगा?

What remains after subtracting (1500) from the sum of the first (65) natural numbers?

Explanation opens after your attempt

Correct Answer

D. (645)

Step 1

Concept

\(S_{65}=2145\), and (2145-1500=645). First find the sum and then perform the given operation.

Step 2

Why this answer is correct

The correct answer is D. (645). \(S_{65}=2145\), and (2145-1500=645). First find the sum and then perform the given operation.

Step 3

Exam Tip

\(S_{65}=2145\) और (2145-1500=645) 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 59

यदि \(S_p=378\) और \(S_q=528\) है तो (q-p) का मान क्या है?

If \(S_p=378\) and \(S_q=528\), what is the value of (q-p)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

\(S_{27}=378\) and \(S_{32}=528\), so (q-p=5). Identifying both indices first is important.

Step 2

Why this answer is correct

The correct answer is B. (5). \(S_{27}=378\) and \(S_{32}=528\), so (q-p=5). Identifying both indices first is important.

Step 3

Exam Tip

\(S_{27}=378\) और \(S_{32}=528\) इसलिए (q-p=5)। पहले दोनों सूचकांक पहचानना जरूरी है।

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Question 19/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(18+19+20+\cdots+36\) का योग कितना है?

What is the sum of \(18+19+20+\cdots+36\)?

Explanation opens after your attempt

Correct Answer

A. (513)

Step 1

Concept

The sum is \(S_{36}-S_{17}=666-153=513\). Subtract the sum of the (17) terms before the start.

Step 2

Why this answer is correct

The correct answer is A. (513). The sum is \(S_{36}-S_{17}=666-153=513\). Subtract the sum of the (17) terms before the start.

Step 3

Exam Tip

योग \(S_{36}-S_{17}=666-153=513\) है। शुरू होने से पहले वाले (17) 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 59

पहली (57) प्राकृतिक संख्याओं का योग किसके बराबर है?

The sum of the first (57) natural numbers is equal to which value?

Explanation opens after your attempt

Correct Answer

C. (1653)

Step 1

Concept

\(S_{57}=\frac{57\times58}{2}=1653\). Change (58) to (29) and multiply.

Step 2

Why this answer is correct

The correct answer is C. (1653). \(S_{57}=\frac{57\times58}{2}=1653\). Change (58) to (29) and multiply.

Step 3

Exam Tip

\(S_{57}=\frac{57\times58}{2}=1653\) है। (58) को (29) बनाकर गुणा करें।

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Question 21/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_n=666\) है तो \(S_{n+2}\) का मान क्या होगा?

If \(S_n=666\), what will be the value of \(S_{n+2}\)?

Explanation opens after your attempt

Correct Answer

B. (741)

Step 1

Concept

\(S_{36}=666\), so \(S_{38}=666+37+38=741\). To move two steps ahead, add the next two terms.

Step 2

Why this answer is correct

The correct answer is B. (741). \(S_{36}=666\), so \(S_{38}=666+37+38=741\). To move two steps ahead, add the next two terms.

Step 3

Exam Tip

\(S_{36}=666\) इसलिए \(S_{38}=666+37+38=741\)। दो आगे जाने पर अगले दो पद जोड़ें।

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Question 22/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (72) प्राकृतिक संख्याओं का योग (2628) है। पहली (71) प्राकृतिक संख्याओं का योग क्या होगा?

The sum of the first (72) natural numbers is (2628). What is the sum of the first (71) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (2556)

Step 1

Concept

\(S_{71}=S_{72}-72=2628-72=2556\). For the previous sum, subtract the last term.

Step 2

Why this answer is correct

The correct answer is A. (2556). \(S_{71}=S_{72}-72=2628-72=2556\). For the previous sum, subtract the last term.

Step 3

Exam Tip

\(S_{71}=S_{72}-72=2628-72=2556\) है। पिछले योग के लिए अंतिम पद घटाएं।

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Question 23/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{24}+S_{26}\) का मान क्या होगा?

What will be the value of \(S_{24}+S_{26}\)?

Explanation opens after your attempt

Correct Answer

B. (651)

Step 1

Concept

\(S_{24}=300\) and \(S_{26}=351\), so the sum is (651). Read similar-looking indices carefully.

Step 2

Why this answer is correct

The correct answer is B. (651). \(S_{24}=300\) and \(S_{26}=351\), so the sum is (651). Read similar-looking indices carefully.

Step 3

Exam Tip

\(S_{24}=300\) और \(S_{26}=351\) इसलिए योग (651) है। समान दिखने वाले सूचकांकों को ध्यान से पढ़ें।

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Question 24/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(1+2+3+\cdots+n=1176\) है तो (n) का मान क्या है?

If \(1+2+3+\cdots+n=1176\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (48)

Step 1

Concept

\(S_{48}=\frac{48\times49}{2}=1176\), so (n=48). Verify the answer by substituting it back in the formula.

Step 2

Why this answer is correct

The correct answer is C. (48). \(S_{48}=\frac{48\times49}{2}=1176\), so (n=48). Verify the answer by substituting it back in the formula.

Step 3

Exam Tip

\(S_{48}=\frac{48\times49}{2}=1176\) इसलिए (n=48) है। उत्तर को सूत्र में वापस रखकर सत्यापित करें।

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Question 25/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

एक खेल में पहले (20) चरणों में क्रमशः (1) से (20) तक अंक मिले और बाद के (5) चरणों में (0) अंक मिले। कुल अंक कितने हैं?

In a game, marks from (1) to (20) are scored in the first (20) stages, and (0) marks in the next (5) stages. What is the total score?

Explanation opens after your attempt

Correct Answer

B. (210)

Step 1

Concept

The total score is \(S_{20}=210\). Stages with (0) marks do not change the sum.

Step 2

Why this answer is correct

The correct answer is B. (210). The total score is \(S_{20}=210\). Stages with (0) marks do not change the sum.

Step 3

Exam Tip

कुल अंक \(S_{20}=210\) होंगे। (0) अंक वाले चरण 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 59

पहली (63) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (63) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (2016)

Step 1

Concept

\(S_{63}=\frac{63\times64}{2}=2016\). Halve (64) and multiply by (32).

Step 2

Why this answer is correct

The correct answer is B. (2016). \(S_{63}=\frac{63\times64}{2}=2016\). Halve (64) and multiply by (32).

Step 3

Exam Tip

\(S_{63}=\frac{63\times64}{2}=2016\) है। (64) को आधा करके (32) से गुणा करें।

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Question 27/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{44}-S_{30}\) का मान क्या है?

What is the value of \(S_{44}-S_{30}\)?

Explanation opens after your attempt

Correct Answer

A. (525)

Step 1

Concept

\(S_{44}=990\) and \(S_{30}=465\), so the difference is (525). This is the sum from (31) to (44).

Step 2

Why this answer is correct

The correct answer is A. (525). \(S_{44}=990\) and \(S_{30}=465\), so the difference is (525). This is the sum from (31) to (44).

Step 3

Exam Tip

\(S_{44}=990\) और \(S_{30}=465\) इसलिए अंतर (525) है। यह (31) से (44) तक का योग है।

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Question 28/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि पहली (n) प्राकृतिक संख्याओं का योग (1540) है तो (n) क्या होगा?

If the sum of the first (n) natural numbers is (1540), what will (n) be?

Explanation opens after your attempt

Correct Answer

C. (55)

Step 1

Concept

\(S_{55}=\frac{55\times56}{2}=1540\), so (n=55). For a large sum, identify using \(2S_n\).

Step 2

Why this answer is correct

The correct answer is C. (55). \(S_{55}=\frac{55\times56}{2}=1540\), so (n=55). For a large sum, identify using \(2S_n\).

Step 3

Exam Tip

\(S_{55}=\frac{55\times56}{2}=1540\) इसलिए (n=55) है। बड़े योग में \(2S_n\) देखकर पहचानें।

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Question 29/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(1+2+3+\cdots+37\) में (38) और (39) जोड़ने पर कौन सा योग बनेगा?

Which sum is formed when (38) and (39) are added to \(1+2+3+\cdots+37\)?

Explanation opens after your attempt

Correct Answer

C. \(S_{39}\)

Step 1

Concept

\(1+2+\cdots+37+38+39=S_{39}\). When consecutive new terms are added, the last term becomes the new (n).

Step 2

Why this answer is correct

The correct answer is C. \(S_{39}\). \(1+2+\cdots+37+38+39=S_{39}\). When consecutive new terms are added, the last term becomes the new (n).

Step 3

Exam Tip

\(1+2+\cdots+37+38+39=S_{39}\) होता है। लगातार नए पद जोड़ने पर अंतिम पद नया (n) बनता है।

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Question 30/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

एक बचत योजना में (1)वें सप्ताह (1) रुपये और (49)वें सप्ताह (49) रुपये बचाए गए। राशि हर सप्ताह (1) रुपये बढ़ी तो कुल बचत कितनी है?

In a saving plan, (1) rupee is saved in the (1)st week and (49) rupees in the (49)th week. If the amount increases by (1) rupee each week, what is the total saving?

Explanation opens after your attempt

Correct Answer

B. (1225)

Step 1

Concept

Total saving is \(S_{49}=\frac{49\times50}{2}=1225\) rupees. A regular increase of (1) gives \(S_n\).

Step 2

Why this answer is correct

The correct answer is B. (1225). Total saving is \(S_{49}=\frac{49\times50}{2}=1225\) rupees. A regular increase of (1) gives \(S_n\).

Step 3

Exam Tip

कुल बचत \(S_{49}=\frac{49\times50}{2}=1225\) रुपये है। नियमित (1) की वृद्धि \(S_n\) देती है।

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Question 31/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (21) प्राकृतिक संख्याओं के योग का (4) गुना कितना होगा?

What is (4) times the sum of the first (21) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (924)

Step 1

Concept

\(S_{21}=231\), and \(4\times231=924\). First find the sum and then multiply.

Step 2

Why this answer is correct

The correct answer is C. (924). \(S_{21}=231\), and \(4\times231=924\). First find the sum and then multiply.

Step 3

Exam Tip

\(S_{21}=231\) है और \(4\times231=924\)। पहले योग निकालकर फिर गुणा करें।

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Question 32/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_n=1431\) है तो (n) का मान क्या होगा?

If \(S_n=1431\), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (53)

Step 1

Concept

\(S_{53}=\frac{53\times54}{2}=1431\), so (n=53). Match \(2S_n\) with a consecutive product.

Step 2

Why this answer is correct

The correct answer is C. (53). \(S_{53}=\frac{53\times54}{2}=1431\), so (n=53). Match \(2S_n\) with a consecutive product.

Step 3

Exam Tip

\(S_{53}=\frac{53\times54}{2}=1431\) इसलिए (n=53) है। \(2S_n\) को क्रमागत गुणनफल से मिलाएं।

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Question 33/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (39) प्राकृतिक संख्याओं के योग और (39) के बीच अंतर क्या है?

What is the difference between the sum of the first (39) natural numbers and (39)?

Explanation opens after your attempt

Correct Answer

C. (741)

Step 1

Concept

\(S_{39}=780\), and (780-39=741). Subtracting the last term gives \(S_{38}\).

Step 2

Why this answer is correct

The correct answer is C. (741). \(S_{39}=780\), and (780-39=741). Subtracting the last term gives \(S_{38}\).

Step 3

Exam Tip

\(S_{39}=780\) और (780-39=741) है। अंतिम पद घटाने पर \(S_{38}\) मिलता है।

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Question 34/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(23+24+25+\cdots+34\) का योग कितना है?

What is the sum of \(23+24+25+\cdots+34\)?

Explanation opens after your attempt

Correct Answer

A. (342)

Step 1

Concept

The sum is \(S_{34}-S_{22}=595-253=342\). Subtract the sum of terms before the start.

Step 2

Why this answer is correct

The correct answer is A. (342). The sum is \(S_{34}-S_{22}=595-253=342\). Subtract the sum of terms before the start.

Step 3

Exam Tip

योग \(S_{34}-S_{22}=595-253=342\) है। आरंभ से पहले वाले पदों का योग घटाएं।

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Question 35/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

किस (n) के लिए \(S_n-S_{n-1}=62\) होगा?

For which (n) will \(S_n-S_{n-1}=62\)?

Explanation opens after your attempt

Correct Answer

C. (62)

Step 1

Concept

\(S_n-S_{n-1}=n\), so (n=62). The difference of two consecutive sums is the new term.

Step 2

Why this answer is correct

The correct answer is C. (62). \(S_n-S_{n-1}=n\), so (n=62). The difference of two consecutive sums is the new term.

Step 3

Exam Tip

\(S_n-S_{n-1}=n\) होता है इसलिए (n=62)। दो लगातार योगों का अंतर नया पद होता है।

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Question 36/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (75) प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of the first (75) natural numbers.

Explanation opens after your attempt

Correct Answer

A. (2850)

Step 1

Concept

\(S_{75}=\frac{75\times76}{2}=2850\). Change (76) to (38) and multiply.

Step 2

Why this answer is correct

The correct answer is A. (2850). \(S_{75}=\frac{75\times76}{2}=2850\). Change (76) to (38) and multiply.

Step 3

Exam Tip

\(S_{75}=\frac{75\times76}{2}=2850\) है। (76) को (38) बनाकर गुणा करें।

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Question 37/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_{18}=171\) है तो \(S_{22}\) का मान क्या होगा?

If \(S_{18}=171\), what will be the value of \(S_{22}\)?

Explanation opens after your attempt

Correct Answer

B. (253)

Step 1

Concept

\(S_{22}=S_{18}+19+20+21+22=253\). Adding all new terms ahead is necessary.

Step 2

Why this answer is correct

The correct answer is B. (253). \(S_{22}=S_{18}+19+20+21+22=253\). Adding all new terms ahead is necessary.

Step 3

Exam Tip

\(S_{22}=S_{18}+19+20+21+22=253\) है। आगे के सभी नए पद जोड़ना जरूरी है।

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Question 38/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (45) प्राकृतिक संख्याओं के योग में (46), (47) और (48) जोड़ने पर क्या मिलेगा?

What is obtained by adding (46), (47), and (48) to the sum of the first (45) natural numbers?

Explanation opens after your attempt

Correct Answer

C. \(S_{48}\)

Step 1

Concept

\(S_{45}+46+47+48=S_{48}\). When consecutive terms are added, the new last term becomes the index.

Step 2

Why this answer is correct

The correct answer is C. \(S_{48}\). \(S_{45}+46+47+48=S_{48}\). When consecutive terms are added, the new last term becomes the index.

Step 3

Exam Tip

\(S_{45}+46+47+48=S_{48}\) होता है। लगातार पद जोड़ने पर नया अंतिम पद सूचकांक बनता है।

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Question 39/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{30}\) और \(S_{15}\) का अनुपात क्या है?

What is the ratio of \(S_{30}\) to \(S_{15}\)?

Explanation opens after your attempt

Correct Answer

A. (31:8)

Step 1

Concept

\(S_{30}:S_{15}=465:120=31:8\). Simplify the ratio by dividing by a common factor.

Step 2

Why this answer is correct

The correct answer is A. (31:8). \(S_{30}:S_{15}=465:120=31:8\). Simplify the ratio by dividing by a common factor.

Step 3

Exam Tip

\(S_{30}:S_{15}=465:120=31:8\) है। अनुपात को समान गुणक से भाग देकर सरल करें।

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Question 40/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

एक त्रिभुजाकार सजावट में (1) से (28) तक क्रमशः फूल रखे गए हैं। कुल फूल कितने हैं?

In a triangular decoration, flowers are arranged in rows from (1) to (28). How many flowers are there in total?

Explanation opens after your attempt

Correct Answer

B. (406)

Step 1

Concept

Total flowers are \(S_{28}=\frac{28\times29}{2}=406\). Triangular rows indicate \(S_n\).

Step 2

Why this answer is correct

The correct answer is B. (406). Total flowers are \(S_{28}=\frac{28\times29}{2}=406\). Triangular rows indicate \(S_n\).

Step 3

Exam Tip

कुल फूल \(S_{28}=\frac{28\times29}{2}=406\) हैं। त्रिभुजाकार पंक्तियां \(S_n\) का संकेत देती हैं।

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Question 41/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{64}-S_{63}\) का मान क्या है?

What is the value of \(S_{64}-S_{63}\)?

Explanation opens after your attempt

Correct Answer

C. (64)

Step 1

Concept

The difference of two consecutive sums is the new term, so \(S_{64}-S_{63}=64\). You can answer without finding full sums.

Step 2

Why this answer is correct

The correct answer is C. (64). The difference of two consecutive sums is the new term, so \(S_{64}-S_{63}=64\). You can answer without finding full sums.

Step 3

Exam Tip

दो लगातार योगों का अंतर नया पद होता है इसलिए \(S_{64}-S_{63}=64\)। पूरा योग निकाले बिना उत्तर मिल सकता है।

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Question 42/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि पहली (t) प्राकृतिक संख्याओं का योग (231) है तो (t+5) का मान क्या है?

If the sum of the first (t) natural numbers is (231), what is the value of (t+5)?

Explanation opens after your attempt

Correct Answer

B. (26)

Step 1

Concept

\(S_{21}=231\), so (t=21) and (t+5=26). First find the variable and then answer what is asked.

Step 2

Why this answer is correct

The correct answer is B. (26). \(S_{21}=231\), so (t=21) and (t+5=26). First find the variable and then answer what is asked.

Step 3

Exam Tip

\(S_{21}=231\) इसलिए (t=21) और (t+5=26)। पहले चर का मान निकालें फिर पूछा गया मान दें।

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Question 43/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (68) प्राकृतिक संख्याओं का योग कितना होगा?

What will be the sum of the first (68) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (2346)

Step 1

Concept

\(S_{68}=\frac{68\times69}{2}=2346\). Take half of (68) as (34) and calculate \(34\times69\).

Step 2

Why this answer is correct

The correct answer is A. (2346). \(S_{68}=\frac{68\times69}{2}=2346\). Take half of (68) as (34) and calculate \(34\times69\).

Step 3

Exam Tip

\(S_{68}=\frac{68\times69}{2}=2346\) है। (68) का आधा (34) लेकर \(34\times69\) करें।

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Question 44/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{13}+S_{16}+S_{20}\) का मान क्या है?

What is the value of \(S_{13}+S_{16}+S_{20}\)?

Explanation opens after your attempt

Correct Answer

B. (437)

Step 1

Concept

\(S_{13}=91\), \(S_{16}=136\), and \(S_{20}=210\), so the total is (437). Write the three sums separately and add.

Step 2

Why this answer is correct

The correct answer is B. (437). \(S_{13}=91\), \(S_{16}=136\), and \(S_{20}=210\), so the total is (437). Write the three sums separately and add.

Step 3

Exam Tip

\(S_{13}=91\), \(S_{16}=136\) और \(S_{20}=210\) इसलिए कुल (437) है। तीन योगों को अलग-अलग लिखकर जोड़ें।

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Question 45/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_a=820\) और \(S_b=1035\) है तो (b-a) कितना है?

If \(S_a=820\) and \(S_b=1035\), what is (b-a)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

\(S_{40}=820\) and \(S_{45}=1035\), so (b-a=5). First identify the indices of both sums.

Step 2

Why this answer is correct

The correct answer is C. (5). \(S_{40}=820\) and \(S_{45}=1035\), so (b-a=5). First identify the indices of both sums.

Step 3

Exam Tip

\(S_{40}=820\) और \(S_{45}=1035\) इसलिए (b-a=5)। पहले दोनों योगों के सूचकांक पहचानें।

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Question 46/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(1+2+\cdots+52\) में (53+54+55) जोड़ने पर प्राप्त योग क्या होगा?

What sum is obtained by adding (53+54+55) to \(1+2+\cdots+52\)?

Explanation opens after your attempt

Correct Answer

A. (1540)

Step 1

Concept

This becomes \(S_{55}\), and \(S_{55}=1540\). Adding consecutive next terms makes the new last term (n).

Step 2

Why this answer is correct

The correct answer is A. (1540). This becomes \(S_{55}\), and \(S_{55}=1540\). Adding consecutive next terms makes the new last term (n).

Step 3

Exam Tip

यह \(S_{55}\) बनेगा और \(S_{55}=1540\) है। लगातार अगले पद जोड़ने पर नया अंतिम पद (n) होता है।

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Question 47/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (80) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (80) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (3240)

Step 1

Concept

\(S_{80}=\frac{80\times81}{2}=3240\). For large (n), cancel by (2) first.

Step 2

Why this answer is correct

The correct answer is B. (3240). \(S_{80}=\frac{80\times81}{2}=3240\). For large (n), cancel by (2) first.

Step 3

Exam Tip

\(S_{80}=\frac{80\times81}{2}=3240\) है। बड़े (n) में पहले (2) से कटौती करें।

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Question 48/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

यदि \(S_n=1596\) है तो (n) का मान क्या होगा?

If \(S_n=1596\), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (56)

Step 1

Concept

\(S_{56}=\frac{56\times57}{2}=1596\), so (n=56). Check the answer by substituting it in the formula.

Step 2

Why this answer is correct

The correct answer is C. (56). \(S_{56}=\frac{56\times57}{2}=1596\), so (n=56). Check the answer by substituting it in the formula.

Step 3

Exam Tip

\(S_{56}=\frac{56\times57}{2}=1596\) इसलिए (n=56)। उत्तर को सूत्र में रखकर जांचें।

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Question 49/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

\(S_{25}+S_{27}\) का मान ज्ञात करें।

Find the value of \(S_{25}+S_{27}\).

Explanation opens after your attempt

Correct Answer

A. (703)

Step 1

Concept

\(S_{25}=325\) and \(S_{27}=378\), so the sum is (703). Do not make a mistake with nearby indices.

Step 2

Why this answer is correct

The correct answer is A. (703). \(S_{25}=325\) and \(S_{27}=378\), so the sum is (703). Do not make a mistake with nearby indices.

Step 3

Exam Tip

\(S_{25}=325\) और \(S_{27}=378\) इसलिए योग (703) है। पास-पास के सूचकांक देखकर गलती न करें।

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Question 50/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 59

पहली (67) प्राकृतिक संख्याओं के योग से पहली (62) प्राकृतिक संख्याओं का योग घटाने पर क्या मिलेगा?

What is obtained by subtracting the sum of the first (62) natural numbers from the sum of the first (67) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (325)

Step 1

Concept

The difference is (63+64+65+66+67=325). The difference of two sums gives the sum of the terms in between.

Step 2

Why this answer is correct

The correct answer is B. (325). The difference is (63+64+65+66+67=325). The difference of two sums gives the sum of the terms in between.

Step 3

Exam Tip

अंतर (63+64+65+66+67=325) है। दो योगों का अंतर बीच के पदों का योग देता है।

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Class 9 Mathematics Medium Quiz

पहली (47) प्राकृतिक संख्याओं का योग कितना है?

Concept

Why this answer is correct

Exam Tip

यदि पहली (n) प्राकृतिक संख्याओं का योग (561) है तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(12) से (29) तक की प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

Concept

Why this answer is correct

Exam Tip

\(S_{22}+S_{17}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

पहली (41) प्राकृतिक संख्याओं के योग में से पहली (23) प्राकृतिक संख्याओं का योग घटाने पर क्या मिलेगा?

Concept

Why this answer is correct

Exam Tip

यदि \(1+2+3+\cdots+n=946\) है तो (n) का मान चुनिए।

Concept

Why this answer is correct

Exam Tip

\(S_{35}-S_{19}\) का मान ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

एक हॉल में (1)वीं पंक्ति में (1) सीट और (26)वीं पंक्ति में (26) सीटें हैं। सभी पंक्तियों में कुल सीटें कितनी हैं?

Concept

Why this answer is correct

Exam Tip

पहली (54) प्राकृतिक संख्याओं के योग का दोगुना कितना होगा?

Concept

Why this answer is correct

Exam Tip

\(1+2+3+\cdots+40\) में अंतिम (6) पदों का योग कितना है?

Concept

Why this answer is correct

Exam Tip

यदि पहली (31) प्राकृतिक संख्याओं का योग (496) है तो पहली (34) प्राकृतिक संख्याओं का योग क्या होगा?

Concept

Why this answer is correct

Exam Tip

पहली (58) प्राकृतिक संख्याओं के योग और पहली (55) प्राकृतिक संख्याओं के योग का अंतर क्या है?

Concept

Why this answer is correct

Exam Tip

किस (n) के लिए \(S_n=1081\) होगा?

Concept

Why this answer is correct

Exam Tip

एक चित्र में (42) पंक्तियां हैं और (r)वीं पंक्ति में (r) बिंदु हैं। कुल बिंदु कितने होंगे?

Concept

Why this answer is correct

Exam Tip

\(S_{28}+28\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

पहली (65) प्राकृतिक संख्याओं के योग में से (1500) घटाने पर कितना बचेगा?

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यदि \(S_p=378\) और \(S_q=528\) है तो (q-p) का मान क्या है?

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\(18+19+20+\cdots+36\) का योग कितना है?

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पहली (57) प्राकृतिक संख्याओं का योग किसके बराबर है?

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