Class 9 Mathematics - Sequences and Progressions - Sum of first n natural numbers Hard Quiz

Mathematics Sequences and Progressions Sum of first n natural numbers Hard Class 9 Level 61

Level 61 • 50/50 questions • 30 seconds per question.

Level readiness 50/50 Questions
Time Left 25:00 30 sec/question
RewardsCoins + XP
ModeClassic Quiz
Previous Next Level
Share
Question 1 / 50 0 score
Answered 0/50 Correct 0 Time 25:00
Question 1/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहली (64) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (64) natural numbers?

Explanation opens after your attempt
Correct Answer

B. (2080)

Step 1

Concept

\(S_{64}=\frac{64\times65}{2}=2080\). For large (n), divide by (2) first.

Step 2

Why this answer is correct

The correct answer is B. (2080). \(S_{64}=\frac{64\times65}{2}=2080\). For large (n), divide by (2) first.

Step 3

Exam Tip

\(S_{64}=\frac{64\times65}{2}=2080\) है। बड़े (n) में पहले (2) से भाग देकर गणना करें।

Open Question Page
Ask Friends
Question 2/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि पहली (n) प्राकृतिक संख्याओं का योग (2016) है तो (n) का मान क्या है?

If the sum of the first (n) natural numbers is (2016), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (63)

Step 1

Concept

\(S_{63}=\frac{63\times64}{2}=2016\), so (n=63). Match \(2S_n\) with the product of two consecutive numbers.

Step 2

Why this answer is correct

The correct answer is C. (63). \(S_{63}=\frac{63\times64}{2}=2016\), so (n=63). Match \(2S_n\) with the product of two consecutive numbers.

Step 3

Exam Tip

\(S_{63}=\frac{63\times64}{2}=2016\) इसलिए (n=63) है। \(2S_n\) को दो क्रमागत संख्याओं के गुणनफल से मिलाएं।

Open Question Page
Ask Friends
Question 3/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(31) से (72) तक की प्राकृतिक संख्याओं का योग कितना है?

What is the sum of natural numbers from (31) to (72)?

Explanation opens after your attempt
Correct Answer

C. (2163)

Step 1

Concept

The sum is \(S_{72}-S_{30}=2628-465=2163\). To find a middle range sum, subtract the previous terms.

Step 2

Why this answer is correct

The correct answer is C. (2163). The sum is \(S_{72}-S_{30}=2628-465=2163\). To find a middle range sum, subtract the previous terms.

Step 3

Exam Tip

योग \(S_{72}-S_{30}=2628-465=2163\) है। बीच की संख्याओं का योग निकालने के लिए पहले वाले पद घटाएं।

Open Question Page
Ask Friends
Question 4/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{85}-S_{80}\) का मान क्या होगा?

What will be the value of \(S_{85}-S_{80}\)?

Explanation opens after your attempt
Correct Answer

C. (415)

Step 1

Concept

\(S_{85}-S_{80}=81+82+83+84+85=415\). The difference of nearby sums equals the sum of terms in between.

Step 2

Why this answer is correct

The correct answer is C. (415). \(S_{85}-S_{80}=81+82+83+84+85=415\). The difference of nearby sums equals the sum of terms in between.

Step 3

Exam Tip

\(S_{85}-S_{80}=81+82+83+84+85=415\) है। पास के योगों का अंतर बीच के पदों का योग होता है।

Open Question Page
Ask Friends
Question 5/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=465\) है तो \(S_{n+5}\) का मान क्या होगा?

If \(S_n=465\), what will be the value of \(S_{n+5}\)?

Explanation opens after your attempt
Correct Answer

A. (630)

Step 1

Concept

\(S_{30}=465\), so \(S_{35}=630\). Identify (n) first and then use the new index.

Step 2

Why this answer is correct

The correct answer is A. (630). \(S_{30}=465\), so \(S_{35}=630\). Identify (n) first and then use the new index.

Step 3

Exam Tip

\(S_{30}=465\) इसलिए \(S_{35}=630\) होगा। पहले (n) पहचानें फिर नया सूचकांक लगाएं।

Open Question Page
Ask Friends
Question 6/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{49}+S_{51}-2S_{50}\) का मान क्या है?

What is the value of \(S_{49}+S_{51}-2S_{50}\)?

Explanation opens after your attempt
Correct Answer

B. (1)

Step 1

Concept

\(S_{51}=S_{50}+51\) and \(S_{49}=S_{50}-50\), so the value is (1). Use differences of consecutive sums.

Step 2

Why this answer is correct

The correct answer is B. (1). \(S_{51}=S_{50}+51\) and \(S_{49}=S_{50}-50\), so the value is (1). Use differences of consecutive sums.

Step 3

Exam Tip

\(S_{51}=S_{50}+51\) और \(S_{49}=S_{50}-50\), इसलिए मान (1) है। लगातार योगों के अंतर का उपयोग करें।

Open Question Page
Ask Friends
Question 7/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहली (40) प्राकृतिक संख्याओं का योग पहली (20) प्राकृतिक संख्याओं के योग से कितना अधिक है?

How much greater is the sum of the first (40) natural numbers than the sum of the first (20) natural numbers?

Explanation opens after your attempt
Correct Answer

C. (610)

Step 1

Concept

The difference is \(S_{40}-S_{20}=820-210=610\). In comparison questions, find both sums separately.

Step 2

Why this answer is correct

The correct answer is C. (610). The difference is \(S_{40}-S_{20}=820-210=610\). In comparison questions, find both sums separately.

Step 3

Exam Tip

अंतर \(S_{40}-S_{20}=820-210=610\) है। तुलना में दोनों योगों को अलग-अलग निकालें।

Open Question Page
Ask Friends
Question 8/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(1+2+3+\cdots+n=2556\) है तो (n) कौन सा होगा?

If \(1+2+3+\cdots+n=2556\), which is (n)?

Explanation opens after your attempt
Correct Answer

C. (71)

Step 1

Concept

\(S_{71}=\frac{71\times72}{2}=2556\), so (n=71). Substitute options in the formula for a quick check.

Step 2

Why this answer is correct

The correct answer is C. (71). \(S_{71}=\frac{71\times72}{2}=2556\), so (n=71). Substitute options in the formula for a quick check.

Step 3

Exam Tip

\(S_{71}=\frac{71\times72}{2}=2556\) इसलिए (n=71) है। विकल्पों को सूत्र में रखकर तेज जांच करें।

Open Question Page
Ask Friends
Question 9/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{60}\) और \(S_{30}\) का अनुपात क्या है?

What is the ratio of \(S_{60}\) to \(S_{30}\)?

Explanation opens after your attempt
Correct Answer

A. (122:31)

Step 1

Concept

\(S_{60}:S_{30}=1830:465=122:31\). Simplify the ratio by the greatest common factor.

Step 2

Why this answer is correct

The correct answer is A. (122:31). \(S_{60}:S_{30}=1830:465=122:31\). Simplify the ratio by the greatest common factor.

Step 3

Exam Tip

\(S_{60}:S_{30}=1830:465=122:31\) है। अनुपात को सबसे बड़े समान गुणक से सरल करें।

Open Question Page
Ask Friends
Question 10/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

किस (n) के लिए \(S_n-S_{n-3}=144\) होगा?

For which (n) will \(S_n-S_{n-3}=144\)?

Explanation opens after your attempt
Correct Answer

D. (49)

Step 1

Concept

(S_n-S_{n-3}=(n-2)+(n-1)+n=3n-3), so (3n-3=144) gives (n=49). Write the difference as the last three terms.

Step 2

Why this answer is correct

The correct answer is D. (49). (S_n-S_{n-3}=(n-2)+(n-1)+n=3n-3), so (3n-3=144) gives (n=49). Write the difference as the last three terms.

Step 3

Exam Tip

(S_n-S_{n-3}=(n-2)+(n-1)+n=3n-3) है, इसलिए (3n-3=144) से (n=49)। अंतर को अंतिम तीन पदों के रूप में लिखें।

Open Question Page
Ask Friends
Question 11/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

एक सीढ़ीनुमा आकृति में कुल (1275) ब्लॉक हैं और (r)वीं पंक्ति में (r) ब्लॉक हैं। पंक्तियों की संख्या क्या है?

A staircase figure has (1275) blocks, and the (r)th row has (r) blocks. What is the number of rows?

Explanation opens after your attempt
Correct Answer

C. (50)

Step 1

Concept

Total blocks are \(S_r=1275\), and \(S_{50}=1275\), so there are (50) rows. In such figures, the total objects form a triangular number.

Step 2

Why this answer is correct

The correct answer is C. (50). Total blocks are \(S_r=1275\), and \(S_{50}=1275\), so there are (50) rows. In such figures, the total objects form a triangular number.

Step 3

Exam Tip

कुल ब्लॉक \(S_r=1275\) हैं और \(S_{50}=1275\), इसलिए पंक्तियां (50) हैं। ऐसी आकृति में कुल वस्तुएं त्रिभुज संख्या होती हैं।

Open Question Page
Ask Friends
Question 12/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_a=1540\) और \(S_b=2080\) है तो (b-a) का मान क्या होगा?

If \(S_a=1540\) and \(S_b=2080\), what will be the value of (b-a)?

Explanation opens after your attempt
Correct Answer

C. (9)

Step 1

Concept

\(S_{55}=1540\) and \(S_{64}=2080\), so (b-a=9). Identifying both indices first is necessary.

Step 2

Why this answer is correct

The correct answer is C. (9). \(S_{55}=1540\) and \(S_{64}=2080\), so (b-a=9). Identifying both indices first is necessary.

Step 3

Exam Tip

\(S_{55}=1540\) और \(S_{64}=2080\), इसलिए (b-a=9)। पहले दोनों सूचकांक पहचानना जरूरी है।

Open Question Page
Ask Friends
Question 13/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(46+47+48+\cdots+90\) का योग कितना है?

What is the sum of \(46+47+48+\cdots+90\)?

Explanation opens after your attempt
Correct Answer

A. (3060)

Step 1

Concept

The sum is \(S_{90}-S_{45}=4095-1035=3060\). When starting from (46), subtract the sum up to (45).

Step 2

Why this answer is correct

The correct answer is A. (3060). The sum is \(S_{90}-S_{45}=4095-1035=3060\). When starting from (46), subtract the sum up to (45).

Step 3

Exam Tip

योग \(S_{90}-S_{45}=4095-1035=3060\) है। (46) से शुरू होने पर (45) तक का योग घटाएं।

Open Question Page
Ask Friends
Question 14/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_{m+1}-S_m=76\) है तो (m) का मान क्या है?

If \(S_{m+1}-S_m=76\), what is the value of (m)?

Explanation opens after your attempt
Correct Answer

B. (75)

Step 1

Concept

\(S_{m+1}-S_m=m+1\), so (m+1=76) and (m=75). The difference of consecutive sums is the next term.

Step 2

Why this answer is correct

The correct answer is B. (75). \(S_{m+1}-S_m=m+1\), so (m+1=76) and (m=75). The difference of consecutive sums is the next term.

Step 3

Exam Tip

\(S_{m+1}-S_m=m+1\) होता है, इसलिए (m+1=76) और (m=75)। लगातार योगों का अंतर अगला पद होता है।

Open Question Page
Ask Friends
Question 15/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहली (100) प्राकृतिक संख्याओं के योग में से पहली (75) प्राकृतिक संख्याओं का योग घटाएं।

Subtract the sum of the first (75) natural numbers from the sum of the first (100) natural numbers.

Explanation opens after your attempt
Correct Answer

B. (2200)

Step 1

Concept

The difference is \(S_{100}-S_{75}=5050-2850=2200\). It is the sum of terms from (76) to (100).

Step 2

Why this answer is correct

The correct answer is B. (2200). The difference is \(S_{100}-S_{75}=5050-2850=2200\). It is the sum of terms from (76) to (100).

Step 3

Exam Tip

अंतर \(S_{100}-S_{75}=5050-2850=2200\) है। यह (76) से (100) तक के पदों का योग है।

Open Question Page
Ask Friends
Question 16/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

किस (n) के लिए पहली (n) प्राकृतिक संख्याओं का योग (3000) से अधिक पहली बार होगा?

For which (n) will the sum of the first (n) natural numbers exceed (3000) for the first time?

Explanation opens after your attempt
Correct Answer

B. (77)

Step 1

Concept

\(S_{76}=2926\) and \(S_{77}=3003\), so the sum first exceeds (3000) at (n=77). In boundary questions, check the two nearby sums.

Step 2

Why this answer is correct

The correct answer is B. (77). \(S_{76}=2926\) and \(S_{77}=3003\), so the sum first exceeds (3000) at (n=77). In boundary questions, check the two nearby sums.

Step 3

Exam Tip

\(S_{76}=2926\) और \(S_{77}=3003\), इसलिए पहली बार (n=77) पर योग (3000) से अधिक होता है। सीमा वाले प्रश्नों में आसपास के दो योग जांचें।

Open Question Page
Ask Friends
Question 17/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{25}+S_{35}+S_{45}\) का मान क्या है?

What is the value of \(S_{25}+S_{35}+S_{45}\)?

Explanation opens after your attempt
Correct Answer

B. (1990)

Step 1

Concept

\(S_{25}=325\), \(S_{35}=630\), and \(S_{45}=1035\), so the total is (1990). Write all three sums separately and add.

Step 2

Why this answer is correct

The correct answer is B. (1990). \(S_{25}=325\), \(S_{35}=630\), and \(S_{45}=1035\), so the total is (1990). Write all three sums separately and add.

Step 3

Exam Tip

\(S_{25}=325\), \(S_{35}=630\) और \(S_{45}=1035\) इसलिए कुल (1990) है। तीनों योग अलग-अलग लिखकर जोड़ें।

Open Question Page
Ask Friends
Question 18/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=3240\) है तो \(S_{n-4}\) का मान क्या होगा?

If \(S_n=3240\), what will be the value of \(S_{n-4}\)?

Explanation opens after your attempt
Correct Answer

A. (2850)

Step 1

Concept

\(S_{80}=3240\), so \(S_{76}=3240-77-78-79-80=2926\). Subtract the last four terms carefully.

Step 2

Why this answer is correct

The correct answer is A. (2850). \(S_{80}=3240\), so \(S_{76}=3240-77-78-79-80=2926\). Subtract the last four terms carefully.

Step 3

Exam Tip

\(S_{80}=3240\) है, इसलिए \(S_{76}=3240-77-78-79-80=2926\) नहीं बल्कि (2926) होगा।

Open Question Page
Ask Friends
Question 19/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहली (96) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (96) natural numbers?

Explanation opens after your attempt
Correct Answer

A. (4656)

Step 1

Concept

\(S_{96}=\frac{96\times97}{2}=4656\). Halve (96) and calculate \(48\times97\).

Step 2

Why this answer is correct

The correct answer is A. (4656). \(S_{96}=\frac{96\times97}{2}=4656\). Halve (96) and calculate \(48\times97\).

Step 3

Exam Tip

\(S_{96}=\frac{96\times97}{2}=4656\) है। (96) को आधा करके \(48\times97\) करें।

Open Question Page
Ask Friends
Question 20/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{40}+S_{60}-S_{50}\) का मान ज्ञात कीजिए।

Find the value of \(S_{40}+S_{60}-S_{50}\).

Explanation opens after your attempt
Correct Answer

A. (1375)

Step 1

Concept

(820+1830-1275=1375). In mixed sums, write the value of each \(S_n\) first.

Step 2

Why this answer is correct

The correct answer is A. (1375). (820+1830-1275=1375). In mixed sums, write the value of each \(S_n\) first.

Step 3

Exam Tip

(820+1830-1275=1375) है। मिश्रित योगों में प्रत्येक \(S_n\) का मान पहले लिखें।

Open Question Page
Ask Friends
Question 21/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_{2p}=820\) है तो (p) का मान क्या है?

If \(S_{2p}=820\), what is the value of (p)?

Explanation opens after your attempt
Correct Answer

C. (20)

Step 1

Concept

\(S_{40}=820\), so (2p=40) and (p=20). First identify the value of the index (2p).

Step 2

Why this answer is correct

The correct answer is C. (20). \(S_{40}=820\), so (2p=40) and (p=20). First identify the value of the index (2p).

Step 3

Exam Tip

\(S_{40}=820\) इसलिए (2p=40) और (p=20)। पहले सूचकांक (2p) का मान पहचानें।

Open Question Page
Ask Friends
Question 22/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{70}-2S_{35}\) का मान क्या होगा?

What will be the value of \(S_{70}-2S_{35}\)?

Explanation opens after your attempt
Correct Answer

B. (1225)

Step 1

Concept

\(S_{70}=2485\) and \(2S_{35}=1260\), so the value is (1225). Keep the order of multiplication and subtraction clear.

Step 2

Why this answer is correct

The correct answer is B. (1225). \(S_{70}=2485\) and \(2S_{35}=1260\), so the value is (1225). Keep the order of multiplication and subtraction clear.

Step 3

Exam Tip

\(S_{70}=2485\) और \(2S_{35}=1260\), इसलिए मान (1225) है। गुणा और घटाव का क्रम ध्यान से रखें।

Open Question Page
Ask Friends
Question 23/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

एक मंच पर (1)वीं पंक्ति में (3) दीपक, (2)वीं में (6) दीपक और (30)वीं में (90) दीपक हैं। यदि पंक्ति (r) में (3r) दीपक हैं तो कुल दीपक कितने हैं?

On a stage, the (1)st row has (3) lamps, the (2)nd has (6) lamps, and the (30)th has (90) lamps. If row (r) has (3r) lamps, how many lamps are there in total?

Explanation opens after your attempt
Correct Answer

A. (1395)

Step 1

Concept

Total lamps are \(3S_{30}=3\times465=1395\). If there is a common multiplier, it can be placed outside the sum.

Step 2

Why this answer is correct

The correct answer is A. (1395). Total lamps are \(3S_{30}=3\times465=1395\). If there is a common multiplier, it can be placed outside the sum.

Step 3

Exam Tip

कुल दीपक \(3S_{30}=3\times465=1395\) हैं। समान गुणक हो तो उसे योग के बाहर रखा जा सकता है।

Open Question Page
Ask Friends
Question 24/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=4095\) है तो (n) का मान क्या होगा?

If \(S_n=4095\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (90)

Step 1

Concept

\(S_{90}=\frac{90\times91}{2}=4095\), so (n=90). Matching \(2S_n\) with a consecutive product is useful.

Step 2

Why this answer is correct

The correct answer is C. (90). \(S_{90}=\frac{90\times91}{2}=4095\), so (n=90). Matching \(2S_n\) with a consecutive product is useful.

Step 3

Exam Tip

\(S_{90}=\frac{90\times91}{2}=4095\) इसलिए (n=90) है। \(2S_n\) को क्रमागत गुणनफल से मिलाना उपयोगी है।

Open Question Page
Ask Friends
Question 25/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_n-S_{n-1}+S_{n-2}-S_{n-3}\) का मान (99) है। (n) कितना है?

The value of \(S_n-S_{n-1}+S_{n-2}-S_{n-3}\) is (99). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (50)

Step 1

Concept

The expression is (n+(n-2)=2n-2), so (2n-2=99) gives no natural (n). Check parity before choosing an option.

Step 2

Why this answer is correct

The correct answer is B. (50). The expression is (n+(n-2)=2n-2), so (2n-2=99) gives no natural (n). Check parity before choosing an option.

Step 3

Exam Tip

व्यंजक (n+(n-2)=2n-2) है, इसलिए (2n-2=99) प्राकृतिक (n) नहीं देता; सही मान कोई नहीं है।

Open Question Page
Ask Friends
Question 26/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{44}\) में कौन सी संख्या जोड़ने पर \(S_{50}\) प्राप्त होगा?

Which number should be added to \(S_{44}\) to get \(S_{50}\)?

Explanation opens after your attempt
Correct Answer

A. (279)

Step 1

Concept

The needed number is (45+46+47+48+49+50=285). First find the sum of the terms in between.

Step 2

Why this answer is correct

The correct answer is A. (279). The needed number is (45+46+47+48+49+50=285). First find the sum of the terms in between.

Step 3

Exam Tip

जरूरी संख्या (45+46+47+48+49+50=285) है। विकल्पों से पहले बीच के पदों का योग निकालें।

Open Question Page
Ask Friends
Question 27/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_{u}=1225\) और \(S_{v}=2628\) है तो (u+v) का मान क्या है?

If \(S_u=1225\) and \(S_v=2628\), what is the value of (u+v)?

Explanation opens after your attempt
Correct Answer

C. (121)

Step 1

Concept

\(S_{49}=1225\) and \(S_{72}=2628\), so (u+v=121). First identify the indices of both triangular numbers.

Step 2

Why this answer is correct

The correct answer is C. (121). \(S_{49}=1225\) and \(S_{72}=2628\), so (u+v=121). First identify the indices of both triangular numbers.

Step 3

Exam Tip

\(S_{49}=1225\) और \(S_{72}=2628\), इसलिए (u+v=121)। पहले दोनों त्रिभुज संख्याओं के सूचकांक पहचानें।

Open Question Page
Ask Friends
Question 28/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहली (88) प्राकृतिक संख्याओं के योग का (25%) कितना है?

What is (25%) of the sum of the first (88) natural numbers?

Explanation opens after your attempt
Correct Answer

A. (979)

Step 1

Concept

\(S_{88}=3916\), and (25%), or \(\frac{1}{4}\), of it is (979). Converting percent to a fraction makes it easier.

Step 2

Why this answer is correct

The correct answer is A. (979). \(S_{88}=3916\), and (25%), or \(\frac{1}{4}\), of it is (979). Converting percent to a fraction makes it easier.

Step 3

Exam Tip

\(S_{88}=3916\) है और उसका (25%) यानी \(\frac{1}{4}\) भाग (979) है। प्रतिशत को भिन्न में बदलना आसान रहता है।

Open Question Page
Ask Friends
Question 29/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{58}+S_{59}-S_{57}\) का मान क्या है?

What is the value of \(S_{58}+S_{59}-S_{57}\)?

Explanation opens after your attempt
Correct Answer

C. (1887)

Step 1

Concept

\(S_{58}=1711\), \(S_{59}=1770\), and \(S_{57}=1653\), so the value is (1887). Subtract carefully with nearby indices.

Step 2

Why this answer is correct

The correct answer is C. (1887). \(S_{58}=1711\), \(S_{59}=1770\), and \(S_{57}=1653\), so the value is (1887). Subtract carefully with nearby indices.

Step 3

Exam Tip

\(S_{58}=1711\), \(S_{59}=1770\) और \(S_{57}=1653\), इसलिए मान (1887) है। निकट सूचकांकों में सावधानी से घटाएं।

Open Question Page
Ask Friends
Question 30/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n-S_{n-5}=390\) है तो (n) का मान क्या होगा?

If \(S_n-S_{n-5}=390\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (78)

Step 1

Concept

The difference is ((n-4)+(n-3)+(n-2)+(n-1)+n=5n-10), so (5n-10=390) gives (n=80). Form the sum of the last five terms.

Step 2

Why this answer is correct

The correct answer is C. (78). The difference is ((n-4)+(n-3)+(n-2)+(n-1)+n=5n-10), so (5n-10=390) gives (n=80). Form the sum of the last five terms.

Step 3

Exam Tip

अंतर ((n-4)+(n-3)+(n-2)+(n-1)+n=5n-10) है, इसलिए (5n-10=390) से (n=80)। अंतिम पांच पदों का योग बनाएं।

Open Question Page
Ask Friends
Question 31/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहली (150) प्राकृतिक संख्याओं का योग कितना है?

What is the sum of the first (150) natural numbers?

Explanation opens after your attempt
Correct Answer

B. (11325)

Step 1

Concept

\(S_{150}=\frac{150\times151}{2}=11325\). For large (n), first change (150) to (75).

Step 2

Why this answer is correct

The correct answer is B. (11325). \(S_{150}=\frac{150\times151}{2}=11325\). For large (n), first change (150) to (75).

Step 3

Exam Tip

\(S_{150}=\frac{150\times151}{2}=11325\) है। बड़े (n) में पहले (150) को (75) बनाएं।

Open Question Page
Ask Friends
Question 32/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{100}-S_{90}+S_{10}\) का मान ज्ञात कीजिए।

Find the value of \(S_{100}-S_{90}+S_{10}\).

Explanation opens after your attempt
Correct Answer

A. (1010)

Step 1

Concept

(5050-4095+55=1010). First subtract and then add the smaller sum.

Step 2

Why this answer is correct

The correct answer is A. (1010). (5050-4095+55=1010). First subtract and then add the smaller sum.

Step 3

Exam Tip

(5050-4095+55=1010) है। पहले घटाव करें फिर छोटे योग को जोड़ें।

Open Question Page
Ask Friends
Question 33/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_{3k}=1176\) है तो (k) का मान क्या होगा?

If \(S_{3k}=1176\), what will be the value of (k)?

Explanation opens after your attempt
Correct Answer

C. (16)

Step 1

Concept

\(S_{48}=1176\), so (3k=48) and (k=16). First identify the index of (S).

Step 2

Why this answer is correct

The correct answer is C. (16). \(S_{48}=1176\), so (3k=48) and (k=16). First identify the index of (S).

Step 3

Exam Tip

\(S_{48}=1176\) इसलिए (3k=48) और (k=16)। पहले (S) के सूचकांक को पहचानें।

Open Question Page
Ask Friends
Question 34/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(71+72+73+\cdots+100\) का योग कितना है?

What is the sum of \(71+72+73+\cdots+100\)?

Explanation opens after your attempt
Correct Answer

B. (2565)

Step 1

Concept

The sum is \(S_{100}-S_{70}=5050-2485=2565\). When starting from (71), subtract the sum up to (70).

Step 2

Why this answer is correct

The correct answer is B. (2565). The sum is \(S_{100}-S_{70}=5050-2485=2565\). When starting from (71), subtract the sum up to (70).

Step 3

Exam Tip

योग \(S_{100}-S_{70}=5050-2485=2565\) है। (71) से शुरू होने पर (70) तक का योग घटाएं।

Open Question Page
Ask Friends
Question 35/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=1830\) है तो \(S_{n+10}-S_n\) का मान क्या है?

If \(S_n=1830\), what is the value of \(S_{n+10}-S_n\)?

Explanation opens after your attempt
Correct Answer

B. (655)

Step 1

Concept

\(S_{60}=1830\), so the difference is \(61+62+\cdots+70=655\). Find the sum of the next (10) terms separately.

Step 2

Why this answer is correct

The correct answer is B. (655). \(S_{60}=1830\), so the difference is \(61+62+\cdots+70=655\). Find the sum of the next (10) terms separately.

Step 3

Exam Tip

\(S_{60}=1830\) इसलिए अंतर \(61+62+\cdots+70=655\) है। आगे के (10) पदों का योग अलग से निकालें।

Open Question Page
Ask Friends
Question 36/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

किस (n) पर \(S_n\) पहली बार (5000) से अधिक होगा?

At which (n) will \(S_n\) first become greater than (5000)?

Explanation opens after your attempt
Correct Answer

C. (100)

Step 1

Concept

\(S_{99}=4950\) and \(S_{100}=5050\), so it first exceeds (5000) at (n=100). In boundary questions, check nearby values.

Step 2

Why this answer is correct

The correct answer is C. (100). \(S_{99}=4950\) and \(S_{100}=5050\), so it first exceeds (5000) at (n=100). In boundary questions, check nearby values.

Step 3

Exam Tip

\(S_{99}=4950\) और \(S_{100}=5050\), इसलिए पहली बार (n=100) पर (5000) से अधिक है। सीमा प्रश्न में आसपास के मान जांचें।

Open Question Page
Ask Friends
Question 37/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

एक त्रिभुजाकार पार्किंग में (1)वीं पंक्ति में (2) वाहन, (2)वीं में (4) वाहन और (40)वीं में (80) वाहन हैं। कुल वाहन कितने होंगे?

In a triangular parking arrangement, the (1)st row has (2) vehicles, the (2)nd has (4) vehicles, and the (40)th has (80) vehicles. How many vehicles are there in total?

Explanation opens after your attempt
Correct Answer

B. (1640)

Step 1

Concept

Total vehicles are \(2S_{40}=2\times820=1640\). For a pattern like (2r), take (2) outside.

Step 2

Why this answer is correct

The correct answer is B. (1640). Total vehicles are \(2S_{40}=2\times820=1640\). For a pattern like (2r), take (2) outside.

Step 3

Exam Tip

कुल वाहन \(2S_{40}=2\times820=1640\) हैं। (2r) जैसा पैटर्न हो तो (2) को बाहर लें।

Open Question Page
Ask Friends
Question 38/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_x=2278\) है तो (x) का मान क्या है?

If \(S_x=2278\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (67)

Step 1

Concept

\(S_{67}=\frac{67\times68}{2}=2278\), so (x=67). Use \(2S_x\) to find the consecutive product.

Step 2

Why this answer is correct

The correct answer is B. (67). \(S_{67}=\frac{67\times68}{2}=2278\), so (x=67). Use \(2S_x\) to find the consecutive product.

Step 3

Exam Tip

\(S_{67}=\frac{67\times68}{2}=2278\) इसलिए (x=67) है। \(2S_x\) करके क्रमागत गुणनफल ढूंढें।

Open Question Page
Ask Friends
Question 39/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{33}+S_{66}-S_{22}\) का मान क्या है?

What is the value of \(S_{33}+S_{66}-S_{22}\)?

Explanation opens after your attempt
Correct Answer

B. (2496)

Step 1

Concept

(561+2211-253=2519). Writing each sum correctly is the most important step.

Step 2

Why this answer is correct

The correct answer is B. (2496). (561+2211-253=2519). Writing each sum correctly is the most important step.

Step 3

Exam Tip

(561+2211-253=2519) है। प्रत्येक योग को सही लिखना सबसे जरूरी है।

Open Question Page
Ask Friends
Question 40/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहली (120) प्राकृतिक संख्याओं के योग और पहली (80) प्राकृतिक संख्याओं के योग का अंतर क्या है?

What is the difference between the sum of the first (120) natural numbers and the sum of the first (80) natural numbers?

Explanation opens after your attempt
Correct Answer

D. (4060)

Step 1

Concept

The difference is \(S_{120}-S_{80}=7260-3240=4020\). It is the sum from (81) to (120).

Step 2

Why this answer is correct

The correct answer is D. (4060). The difference is \(S_{120}-S_{80}=7260-3240=4020\). It is the sum from (81) to (120).

Step 3

Exam Tip

अंतर \(S_{120}-S_{80}=7260-3240=4020\) है। यह (81) से (120) तक का योग है।

Open Question Page
Ask Friends
Question 41/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n-S_{n-1}=84\) और \(S_m=990\) है तो (n-m) कितना है?

If \(S_n-S_{n-1}=84\) and \(S_m=990\), what is (n-m)?

Explanation opens after your attempt
Correct Answer

C. (40)

Step 1

Concept

First (n=84), and \(S_m=990\) gives (m=44), so (n-m=40). The difference of consecutive sums gives the index.

Step 2

Why this answer is correct

The correct answer is C. (40). First (n=84), and \(S_m=990\) gives (m=44), so (n-m=40). The difference of consecutive sums gives the index.

Step 3

Exam Tip

पहले (n=84) और \(S_m=990\) से (m=44), इसलिए (n-m=40)। लगातार योगों का अंतर सूचकांक देता है।

Open Question Page
Ask Friends
Question 42/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{75}\) में (76+77+78+79+80) जोड़ने पर कौन सा योग प्राप्त होगा?

Which sum is obtained by adding (76+77+78+79+80) to \(S_{75}\)?

Explanation opens after your attempt
Correct Answer

C. \(S_{80}\)

Step 1

Concept

\(S_{75}+76+77+78+79+80=S_{80}\). When consecutive new terms are added, the last term becomes the new index.

Step 2

Why this answer is correct

The correct answer is C. \(S_{80}\). \(S_{75}+76+77+78+79+80=S_{80}\). When consecutive new terms are added, the last term becomes the new index.

Step 3

Exam Tip

\(S_{75}+76+77+78+79+80=S_{80}\) है। लगातार नए पद जुड़ने पर अंतिम पद नया सूचकांक बनता है।

Open Question Page
Ask Friends
Question 43/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=2926\) है तो (n) का मान क्या है?

If \(S_n=2926\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (76)

Step 1

Concept

\(S_{76}=\frac{76\times77}{2}=2926\), so (n=76). For large values, using \(2S_n\) makes identification easier.

Step 2

Why this answer is correct

The correct answer is C. (76). \(S_{76}=\frac{76\times77}{2}=2926\), so (n=76). For large values, using \(2S_n\) makes identification easier.

Step 3

Exam Tip

\(S_{76}=\frac{76\times77}{2}=2926\) इसलिए (n=76) है। बड़े मानों में \(2S_n\) से पहचान आसान होती है।

Open Question Page
Ask Friends
Question 44/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{19}+S_{39}+S_{59}\) का मान ज्ञात करें।

Find the value of \(S_{19}+S_{39}+S_{59}\).

Explanation opens after your attempt
Correct Answer

A. (2740)

Step 1

Concept

\(S_{19}=190\), \(S_{39}=780\), and \(S_{59}=1770\), so the total is (2740). Add the three different indices carefully.

Step 2

Why this answer is correct

The correct answer is A. (2740). \(S_{19}=190\), \(S_{39}=780\), and \(S_{59}=1770\), so the total is (2740). Add the three different indices carefully.

Step 3

Exam Tip

\(S_{19}=190\), \(S_{39}=780\) और \(S_{59}=1770\), इसलिए कुल (2740) है। तीन अलग सूचकांकों को ध्यान से जोड़ें।

Open Question Page
Ask Friends
Question 45/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहली (n) प्राकृतिक संख्याओं का योग (4656) है। (n-10) का मान क्या होगा?

The sum of the first (n) natural numbers is (4656). What is the value of (n-10)?

Explanation opens after your attempt
Correct Answer

B. (86)

Step 1

Concept

\(S_{96}=4656\), so (n=96) and (n-10=86). Find (n) first and then answer what is asked.

Step 2

Why this answer is correct

The correct answer is B. (86). \(S_{96}=4656\), so (n=96) and (n-10=86). Find (n) first and then answer what is asked.

Step 3

Exam Tip

\(S_{96}=4656\) इसलिए (n=96) और (n-10=86)। पहले (n) निकालें फिर पूछा गया मान दें।

Open Question Page
Ask Friends
Question 46/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_{n+1}-S_{n-1}=151\) है तो (n) का मान क्या होगा?

If \(S_{n+1}-S_{n-1}=151\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (75)

Step 1

Concept

The difference is (n+(n+1)=2n+1), so (2n+1=151) gives (n=75). Write the two-term difference directly.

Step 2

Why this answer is correct

The correct answer is B. (75). The difference is (n+(n+1)=2n+1), so (2n+1=151) gives (n=75). Write the two-term difference directly.

Step 3

Exam Tip

अंतर (n+(n+1)=2n+1) है, इसलिए (2n+1=151) से (n=75)। दो पदों के अंतर को सीधे लिखें।

Open Question Page
Ask Friends
Question 47/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{200}-S_{190}\) का मान क्या है?

What is the value of \(S_{200}-S_{190}\)?

Explanation opens after your attempt
Correct Answer

A. (1955)

Step 1

Concept

The difference is \(191+192+\cdots+200=1955\). Even with large indices, only the terms in between need to be added.

Step 2

Why this answer is correct

The correct answer is A. (1955). The difference is \(191+192+\cdots+200=1955\). Even with large indices, only the terms in between need to be added.

Step 3

Exam Tip

अंतर \(191+192+\cdots+200=1955\) है। बड़े सूचकांक में भी केवल बीच के पद जोड़ने होते हैं।

Open Question Page
Ask Friends
Question 48/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=6216\) है तो (n) का मान क्या है?

If \(S_n=6216\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (111)

Step 1

Concept

\(S_{111}=\frac{111\times112}{2}=6216\), so (n=111). Use \(2S_n\) to identify consecutive numbers.

Step 2

Why this answer is correct

The correct answer is B. (111). \(S_{111}=\frac{111\times112}{2}=6216\), so (n=111). Use \(2S_n\) to identify consecutive numbers.

Step 3

Exam Tip

\(S_{111}=\frac{111\times112}{2}=6216\) इसलिए (n=111) है। \(2S_n\) से क्रमागत संख्याओं की पहचान करें।

Open Question Page
Ask Friends
Question 49/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(S_{48}\) और \(S_{24}\) के अंतर का (3) गुना कितना है?

What is (3) times the difference between \(S_{48}\) and \(S_{24}\)?

Explanation opens after your attempt
Correct Answer

B. (2628)

Step 1

Concept

\(S_{48}-S_{24}=1176-300=876\), and \(3\times876=2628\). First find the difference and then multiply.

Step 2

Why this answer is correct

The correct answer is B. (2628). \(S_{48}-S_{24}=1176-300=876\), and \(3\times876=2628\). First find the difference and then multiply.

Step 3

Exam Tip

\(S_{48}-S_{24}=1176-300=876\) और \(3\times876=2628\) है। पहले अंतर निकालें फिर गुणा करें।

Open Question Page
Ask Friends
Question 50/50 Hard Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_y=4950\) है तो \(S_{y+1}\) का मान क्या होगा?

If \(S_y=4950\), what will be the value of \(S_{y+1}\)?

Explanation opens after your attempt
Correct Answer

C. (5050)

Step 1

Concept

\(S_{99}=4950\), so \(S_{100}=4950+100=5050\). For the next sum, add the next term.

Step 2

Why this answer is correct

The correct answer is C. (5050). \(S_{99}=4950\), so \(S_{100}=4950+100=5050\). For the next sum, add the next term.

Step 3

Exam Tip

\(S_{99}=4950\) है इसलिए \(S_{100}=4950+100=5050\)। अगले योग के लिए अगला पद जोड़ें।

Open Question Page
Ask Friends

Mathematics Quiz Navigation

Mathematics Subject

All difficulty level maps

Sum of first n natural numbers Topic

Topic question list

Sequences and Progressions Chapter

Chapter question list

Search Mathematics

Find related MCQs

All Subjects

Choose another subject
FAQs

Class 9 Mathematics Quiz FAQs

How many questions are in this quiz?

This level is designed for 50 active questions. Currently 50 questions are available for the selected class and difficulty.

Is there a timer in this quiz?

Yes, the timer uses 30 seconds per question for Hard difficulty and shows the total remaining time on the page.

Can I open each question separately?

Yes, every question has its own SEO-friendly page with answer, explanation and related practice links.