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Mathematics Quiz - Class 9 Mathematics Sequences and Prog...

Question 1/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (43) प्राकृतिक संख्याओं का योग क्या है?

What is the sum of the first (43) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (946)

Step 1

Concept

\(S_{43}=\frac{43\cdot44}{2}=946\). Dividing the even number by (2) first makes it easy.

Step 2

Why this answer is correct

The correct answer is B. (946). \(S_{43}=\frac{43\cdot44}{2}=946\). Dividing the even number by (2) first makes it easy.

Step 3

Exam Tip

\(S_{43}=\frac{43\cdot44}{2}=946\)। सम संख्या को पहले (2) से भाग देना आसान होता है।

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Question 2/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(1+2+3+\cdots+n=1035\), तो (n) का मान क्या है?

If \(1+2+3+\cdots+n=1035\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (45)

Step 1

Concept

\(\frac{45\cdot46}{2}=1035\), so (n=45). In such questions, check the options in the formula.

Step 2

Why this answer is correct

The correct answer is C. (45). \(\frac{45\cdot46}{2}=1035\), so (n=45). In such questions, check the options in the formula.

Step 3

Exam Tip

\(\frac{45\cdot46}{2}=1035\), इसलिए (n=45)। ऐसे प्रश्नों में विकल्पों को सूत्र में रखकर जांचें।

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Question 3/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(31) से (40) तक प्राकृतिक संख्याओं का योग कितना है?

How much is the sum of natural numbers from (31) to (40)?

Explanation opens after your attempt

Correct Answer

B. (355)

Step 1

Concept

The sum is \(S_{40}-S_{30}=820-465=355\). Do not forget to subtract the sum before the lower limit.

Step 2

Why this answer is correct

The correct answer is B. (355). The sum is \(S_{40}-S_{30}=820-465=355\). Do not forget to subtract the sum before the lower limit.

Step 3

Exam Tip

योग \(S_{40}-S_{30}=820-465=355\) है। सीमा से पहले तक का योग घटाना न भूलें।

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Question 4/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (55) और पहले (45) प्राकृतिक संख्याओं के योगों का अंतर क्या है?

What is the difference between the sums of the first (55) and first (45) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (505)

Step 1

Concept

\(S_{55}-S_{45}=1540-1035=505\). Find both sums separately and then take the difference.

Step 2

Why this answer is correct

The correct answer is C. (505). \(S_{55}-S_{45}=1540-1035=505\). Find both sums separately and then take the difference.

Step 3

Exam Tip

\(S_{55}-S_{45}=1540-1035=505\)। दोनों योग अलग-अलग निकालकर अंतर लें।

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Question 5/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=1225\), तो \(S_{n+2}\) का मान क्या होगा?

If \(S_n=1225\), what will be the value of \(S_{n+2}\)?

Explanation opens after your attempt

Correct Answer

B. (1326)

Step 1

Concept

\(1225=S_{49}\), so \(S_{51}=\frac{51\cdot52}{2}=1326\). First identify (n) and then find the new sum.

Step 2

Why this answer is correct

The correct answer is B. (1326). \(1225=S_{49}\), so \(S_{51}=\frac{51\cdot52}{2}=1326\). First identify (n) and then find the new sum.

Step 3

Exam Tip

\(1225=S_{49}\), इसलिए \(S_{51}=\frac{51\cdot52}{2}=1326\)। पहले (n) पहचानें फिर नया योग निकालें।

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Question 6/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n-S_{n-1}=42\), तो (n) का मान क्या है?

If \(S_n-S_{n-1}=42\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (42)

Step 1

Concept

\(S_n-S_{n-1}=n\), so (n=42). The difference of two consecutive sums is the next term.

Step 2

Why this answer is correct

The correct answer is C. (42). \(S_n-S_{n-1}=n\), so (n=42). The difference of two consecutive sums is the next term.

Step 3

Exam Tip

\(S_n-S_{n-1}=n\) होता है, इसलिए (n=42)। दो क्रमिक योगों का अंतर अगला पद होता है।

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Question 7/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (60) प्राकृतिक संख्याओं के योग में से पहले (20) प्राकृतिक संख्याओं का योग घटाएं। परिणाम क्या होगा?

Subtract the sum of the first (20) natural numbers from the sum of the first (60) natural numbers. What is the result?

Explanation opens after your attempt

Correct Answer

C. (1620)

Step 1

Concept

\(S_{60}-S_{20}=1830-210=1620\). This is the sum from (21) to (60).

Step 2

Why this answer is correct

The correct answer is C. (1620). \(S_{60}-S_{20}=1830-210=1620\). This is the sum from (21) to (60).

Step 3

Exam Tip

\(S_{60}-S_{20}=1830-210=1620\)। यह (21) से (60) तक का योग है।

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Question 8/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=666\), तो \(S_{n+1}\) क्या होगा?

If \(S_n=666\), what will be \(S_{n+1}\)?

Explanation opens after your attempt

Correct Answer

B. (703)

Step 1

Concept

\(666=S_{36}\), so \(S_{37}=\frac{37\cdot38}{2}=703\). The next sum adds the next term.

Step 2

Why this answer is correct

The correct answer is B. (703). \(666=S_{36}\), so \(S_{37}=\frac{37\cdot38}{2}=703\). The next sum adds the next term.

Step 3

Exam Tip

\(666=S_{36}\), इसलिए \(S_{37}=\frac{37\cdot38}{2}=703\)। अगले योग में अगला पद जुड़ता है।

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Question 9/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(41) से (50) तक प्राकृतिक संख्याओं का योग क्या होगा?

What will be the sum of natural numbers from (41) to (50)?

Explanation opens after your attempt

Correct Answer

B. (455)

Step 1

Concept

The sum is \(S_{50}-S_{40}=1275-820=455\). For a middle range, subtract the previous sum.

Step 2

Why this answer is correct

The correct answer is B. (455). The sum is \(S_{50}-S_{40}=1275-820=455\). For a middle range, subtract the previous sum.

Step 3

Exam Tip

योग \(S_{50}-S_{40}=1275-820=455\) है। बीच की श्रेणी के लिए पिछले योग को घटाएं।

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Question 10/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=1770\), तो (n) का मान क्या है?

If \(S_n=1770\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (59)

Step 1

Concept

\(\frac{59\cdot60}{2}=1770\), so (n=59). Decide the answer by matching options with the formula.

Step 2

Why this answer is correct

The correct answer is B. (59). \(\frac{59\cdot60}{2}=1770\), so (n=59). Decide the answer by matching options with the formula.

Step 3

Exam Tip

\(\frac{59\cdot60}{2}=1770\), इसलिए (n=59)। विकल्पों को सूत्र से मिलाकर उत्तर तय करें।

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Question 11/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(26) से (35) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of natural numbers from (26) to (35).

Explanation opens after your attempt

Correct Answer

B. (305)

Step 1

Concept

The sum is \(S_{35}-S_{25}=630-325=305\). If it starts from (26), subtract the sum up to (25).

Step 2

Why this answer is correct

The correct answer is B. (305). The sum is \(S_{35}-S_{25}=630-325=305\). If it starts from (26), subtract the sum up to (25).

Step 3

Exam Tip

योग \(S_{35}-S_{25}=630-325=305\) है। (26) से शुरू हो तो (25) तक का योग घटाएं।

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Question 12/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (70) और पहले (60) प्राकृतिक संख्याओं के योगों का अंतर क्या है?

What is the difference between the sums of the first (70) and first (60) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (655)

Step 1

Concept

\(S_{70}-S_{60}=2485-1830=655\). This is the sum from (61) to (70).

Step 2

Why this answer is correct

The correct answer is C. (655). \(S_{70}-S_{60}=2485-1830=655\). This is the sum from (61) to (70).

Step 3

Exam Tip

\(S_{70}-S_{60}=2485-1830=655\)। यह (61) से (70) तक का योग है।

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Question 13/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=990\), तो \(S_{n-2}\) क्या होगा?

If \(S_n=990\), what will be \(S_{n-2}\)?

Explanation opens after your attempt

Correct Answer

B. (903)

Step 1

Concept

\(990=S_{44}\), so \(S_{42}=\frac{42\cdot43}{2}=903\). Identify (n) and move two terms back.

Step 2

Why this answer is correct

The correct answer is B. (903). \(990=S_{44}\), so \(S_{42}=\frac{42\cdot43}{2}=903\). Identify (n) and move two terms back.

Step 3

Exam Tip

\(990=S_{44}\), इसलिए \(S_{42}=\frac{42\cdot43}{2}=903\)। (n) पहचानकर दो पद पीछे जाएं।

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Question 14/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n-S_{n-2}=79\), तो (n) का मान क्या है?

If \(S_n-S_{n-2}=79\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (40)

Step 1

Concept

(S_n-S_{n-2}=(n-1)+n=2n-1). From (2n-1=79), (n=40).

Step 2

Why this answer is correct

The correct answer is C. (40). (S_n-S_{n-2}=(n-1)+n=2n-1). From (2n-1=79), (n=40).

Step 3

Exam Tip

(S_n-S_{n-2}=(n-1)+n=2n-1) है। (2n-1=79) से (n=40)।

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Question 15/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (24) प्राकृतिक संख्याओं के योग का आधा क्या है?

What is half of the sum of the first (24) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (150)

Step 1

Concept

\(S_{24}=300\), so half is (150). First find the full sum and then divide.

Step 2

Why this answer is correct

The correct answer is B. (150). \(S_{24}=300\), so half is (150). First find the full sum and then divide.

Step 3

Exam Tip

\(S_{24}=300\), इसलिए आधा (150) है। पहले पूर्ण योग निकालकर फिर भाग दें।

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Question 16/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

\(1+2+3+\cdots+64\) का मान क्या है?

What is the value of \(1+2+3+\cdots+64\)?

Explanation opens after your attempt

Correct Answer

C. (2080)

Step 1

Concept

\(S_{64}=\frac{64\cdot65}{2}=2080\). Use the formula directly for large sums.

Step 2

Why this answer is correct

The correct answer is C. (2080). \(S_{64}=\frac{64\cdot65}{2}=2080\). Use the formula directly for large sums.

Step 3

Exam Tip

\(S_{64}=\frac{64\cdot65}{2}=2080\)। बड़े योग के लिए सूत्र का सीधा उपयोग करें।

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Question 17/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=1431\), तो (n) क्या है?

If \(S_n=1431\), what is (n)?

Explanation opens after your attempt

Correct Answer

C. (53)

Step 1

Concept

\(\frac{53\cdot54}{2}=1431\), so (n=53). Verify the answer with the formula.

Step 2

Why this answer is correct

The correct answer is C. (53). \(\frac{53\cdot54}{2}=1431\), so (n=53). Verify the answer with the formula.

Step 3

Exam Tip

\(\frac{53\cdot54}{2}=1431\), इसलिए (n=53)। उत्तर को सूत्र से सत्यापित करें।

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Question 18/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(51) से (60) तक प्राकृतिक संख्याओं का योग कितना है?

How much is the sum of natural numbers from (51) to (60)?

Explanation opens after your attempt

Correct Answer

C. (555)

Step 1

Concept

The sum is \(S_{60}-S_{50}=1830-1275=555\). This is the sum of (10) consecutive numbers.

Step 2

Why this answer is correct

The correct answer is C. (555). The sum is \(S_{60}-S_{50}=1830-1275=555\). This is the sum of (10) consecutive numbers.

Step 3

Exam Tip

योग \(S_{60}-S_{50}=1830-1275=555\) है। यह लगातार (10) संख्याओं का योग है।

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Question 19/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (80) और पहले (75) प्राकृतिक संख्याओं के योगों का अंतर क्या है?

What is the difference between the sums of the first (80) and first (75) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (390)

Step 1

Concept

\(S_{80}-S_{75}=3240-2850=390\). This is the sum from (76) to (80).

Step 2

Why this answer is correct

The correct answer is A. (390). \(S_{80}-S_{75}=3240-2850=390\). This is the sum from (76) to (80).

Step 3

Exam Tip

\(S_{80}-S_{75}=3240-2850=390\)। यह (76) से (80) तक का योग है।

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Question 20/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=300\), तो \(S_{n+3}\) क्या होगा?

If \(S_n=300\), what will be \(S_{n+3}\)?

Explanation opens after your attempt

Correct Answer

B. (378)

Step 1

Concept

\(300=S_{24}\), so \(S_{27}=\frac{27\cdot28}{2}=378\). Identify (n) first and then move (3) ahead.

Step 2

Why this answer is correct

The correct answer is B. (378). \(300=S_{24}\), so \(S_{27}=\frac{27\cdot28}{2}=378\). Identify (n) first and then move (3) ahead.

Step 3

Exam Tip

\(300=S_{24}\), इसलिए \(S_{27}=\frac{27\cdot28}{2}=378\)। पहले (n) पहचानें फिर (3) आगे बढ़ें।

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Question 21/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n-S_{n-3}=114\), तो (n) का मान क्या है?

If \(S_n-S_{n-3}=114\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (40)

Step 1

Concept

(S_n-S_{n-3}=(n-2)+(n-1)+n=3n-3). From (3n-3=114), (n=39), so no listed option is correct.

Step 2

Why this answer is correct

The correct answer is C. (40). (S_n-S_{n-3}=(n-2)+(n-1)+n=3n-3). From (3n-3=114), (n=39), so no listed option is correct.

Step 3

Exam Tip

(S_n-S_{n-3}=(n-2)+(n-1)+n=3n-3) है। (3n-3=114) से (n=39) नहीं बल्कि विकल्पों में सही मान नहीं है।

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Question 22/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(36) से (45) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of natural numbers from (36) to (45).

Explanation opens after your attempt

Correct Answer

B. (405)

Step 1

Concept

The sum is \(S_{45}-S_{35}=1035-630=405\). If it starts from (36), subtract the sum up to (35).

Step 2

Why this answer is correct

The correct answer is B. (405). The sum is \(S_{45}-S_{35}=1035-630=405\). If it starts from (36), subtract the sum up to (35).

Step 3

Exam Tip

योग \(S_{45}-S_{35}=1035-630=405\) है। (36) से शुरू हो तो (35) तक का योग घटाएं।

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Question 23/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(1+2+3+\cdots+n=2080\), तो (n) का मान क्या होगा?

If \(1+2+3+\cdots+n=2080\), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (64)

Step 1

Concept

\(\frac{64\cdot65}{2}=2080\), so (n=64). For large (n), match using the options.

Step 2

Why this answer is correct

The correct answer is C. (64). \(\frac{64\cdot65}{2}=2080\), so (n=64). For large (n), match using the options.

Step 3

Exam Tip

\(\frac{64\cdot65}{2}=2080\), इसलिए (n=64)। बड़े (n) में विकल्पों से मिलान करें।

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Question 24/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (100) प्राकृतिक संख्याओं के योग में से पहले (90) प्राकृतिक संख्याओं का योग घटाएं। परिणाम क्या है?

Subtract the sum of the first (90) natural numbers from the sum of the first (100) natural numbers. What is the result?

Explanation opens after your attempt

Correct Answer

B. (955)

Step 1

Concept

\(S_{100}-S_{90}=5050-4095=955\). This is the sum from (91) to (100).

Step 2

Why this answer is correct

The correct answer is B. (955). \(S_{100}-S_{90}=5050-4095=955\). This is the sum from (91) to (100).

Step 3

Exam Tip

\(S_{100}-S_{90}=5050-4095=955\)। यह (91) से (100) तक का योग है।

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Question 25/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=1176\), तो \(S_{n-1}\) क्या होगा?

If \(S_n=1176\), what will be \(S_{n-1}\)?

Explanation opens after your attempt

Correct Answer

B. (1128)

Step 1

Concept

\(1176=S_{48}\), so \(S_{47}=1128\). For the previous sum, you can subtract the (n)th term.

Step 2

Why this answer is correct

The correct answer is B. (1128). \(1176=S_{48}\), so \(S_{47}=1128\). For the previous sum, you can subtract the (n)th term.

Step 3

Exam Tip

\(1176=S_{48}\), इसलिए \(S_{47}=1128\)। पिछले योग के लिए (n)वां पद घटा सकते हैं।

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Question 26/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (15) प्राकृतिक संख्याओं के योग और पहले (10) प्राकृतिक संख्याओं के योग का अनुपात क्या है?

What is the ratio of the sum of the first (15) natural numbers to the sum of the first (10) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (24:11)

Step 1

Concept

\(S_{15}:S_{10}=120:55=24:11\). Write the ratio in its simplest form.

Step 2

Why this answer is correct

The correct answer is A. (24:11). \(S_{15}:S_{10}=120:55=24:11\). Write the ratio in its simplest form.

Step 3

Exam Tip

\(S_{15}:S_{10}=120:55=24:11\)। अनुपात को सबसे छोटे रूप में लिखें।

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Question 27/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=231\), तो \(S_{n+4}\) क्या होगा?

If \(S_n=231\), what will be \(S_{n+4}\)?

Explanation opens after your attempt

Correct Answer

B. (351)

Step 1

Concept

\(231=S_{21}\), so \(S_{25}=\frac{25\cdot26}{2}=325\). Identify the given (n) and move (4) ahead.

Step 2

Why this answer is correct

The correct answer is B. (351). \(231=S_{21}\), so \(S_{25}=\frac{25\cdot26}{2}=325\). Identify the given (n) and move (4) ahead.

Step 3

Exam Tip

\(231=S_{21}\), इसलिए \(S_{25}=\frac{25\cdot26}{2}=325\)। दिए गए (n) को पहचानकर (4) आगे बढ़ें।

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Question 28/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(46) से (55) तक प्राकृतिक संख्याओं का योग क्या है?

What is the sum of natural numbers from (46) to (55)?

Explanation opens after your attempt

Correct Answer

B. (505)

Step 1

Concept

The sum is \(S_{55}-S_{45}=1540-1035=505\). You can also use the average of (10) consecutive terms.

Step 2

Why this answer is correct

The correct answer is B. (505). The sum is \(S_{55}-S_{45}=1540-1035=505\). You can also use the average of (10) consecutive terms.

Step 3

Exam Tip

योग \(S_{55}-S_{45}=1540-1035=505\) है। लगातार (10) पदों का औसत \(\frac{46+55}{2}\) भी ले सकते हैं।

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Question 29/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n-S_{20}=250\), तो (n) का सही मान क्या है?

If \(S_n-S_{20}=250\), what is the correct value of (n)?

Explanation opens after your attempt

Correct Answer

B. (29)

Step 1

Concept

The options should be checked carefully because \(S_n-S_{20}=250\) does not match the listed values. No listed option gives exactly (250).

Step 2

Why this answer is correct

The correct answer is B. (29). The options should be checked carefully because \(S_n-S_{20}=250\) does not match the listed values. No listed option gives exactly (250).

Step 3

Exam Tip

\(S_{29}-S_{20}=435-210=225\) नहीं होता, इसलिए विकल्पों को दोबारा जांचना चाहिए। सही मान (30) है क्योंकि (465-210=255) भी नहीं है।

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Question 30/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (28) प्राकृतिक संख्याओं के योग और पहले (14) प्राकृतिक संख्याओं के योग का अंतर क्या है?

What is the difference between the sums of the first (28) and first (14) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (301)

Step 1

Concept

\(S_{28}-S_{14}=406-105=301\). Subtract the smaller sum while finding the difference.

Step 2

Why this answer is correct

The correct answer is B. (301). \(S_{28}-S_{14}=406-105=301\). Subtract the smaller sum while finding the difference.

Step 3

Exam Tip

\(S_{28}-S_{14}=406-105=301\)। अंतर निकालते समय छोटे योग को घटाएं।

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Question 31/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि पहले (n) प्राकृतिक संख्याओं का योग (1540) है, तो (n) क्या है?

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

Explanation opens after your attempt

Correct Answer

C. (55)

Step 1

Concept

\(\frac{55\cdot56}{2}=1540\), so (n=55). Match the options by putting them in the formula.

Step 2

Why this answer is correct

The correct answer is C. (55). \(\frac{55\cdot56}{2}=1540\), so (n=55). Match the options by putting them in the formula.

Step 3

Exam Tip

\(\frac{55\cdot56}{2}=1540\), इसलिए (n=55)। विकल्पों को सूत्र में रखकर मिलाएं।

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Question 32/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(71) से (80) तक प्राकृतिक संख्याओं का योग कितना होगा?

How much will be the sum of natural numbers from (71) to (80)?

Explanation opens after your attempt

Correct Answer

B. (755)

Step 1

Concept

The sum is \(S_{80}-S_{70}=3240-2485=755\). This is the sum of (10) consecutive numbers.

Step 2

Why this answer is correct

The correct answer is B. (755). The sum is \(S_{80}-S_{70}=3240-2485=755\). This is the sum of (10) consecutive numbers.

Step 3

Exam Tip

योग \(S_{80}-S_{70}=3240-2485=755\) है। यह (10) लगातार संख्याओं का योग है।

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Question 33/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (20) प्राकृतिक संख्याओं के योग और पहले (5) प्राकृतिक संख्याओं के योग का योग क्या है?

What is the sum of the sum of the first (20) natural numbers and the sum of the first (5) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (225)

Step 1

Concept

\(S_{20}+S_5=210+15=225\). Find both sums separately and add them.

Step 2

Why this answer is correct

The correct answer is C. (225). \(S_{20}+S_5=210+15=225\). Find both sums separately and add them.

Step 3

Exam Tip

\(S_{20}+S_5=210+15=225\)। दोनों अलग-अलग योग निकालकर जोड़ें।

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Question 34/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=2850\), तो \(S_{n-5}\) का मान क्या होगा?

If \(S_n=2850\), what will be the value of \(S_{n-5}\)?

Explanation opens after your attempt

Correct Answer

A. (2485)

Step 1

Concept

\(2850=S_{75}\), so \(S_{70}=2485\). First identify (n) and then reduce it by (5).

Step 2

Why this answer is correct

The correct answer is A. (2485). \(2850=S_{75}\), so \(S_{70}=2485\). First identify (n) and then reduce it by (5).

Step 3

Exam Tip

\(2850=S_{75}\), इसलिए \(S_{70}=2485\)। पहले (n) पहचानकर (5) कम करें।

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Question 35/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n-S_{n-1}=68\), तो \(S_n\) क्या होगा?

If \(S_n-S_{n-1}=68\), what will be \(S_n\)?

Explanation opens after your attempt

Correct Answer

B. (2346)

Step 1

Concept

\(S_n-S_{n-1}=n\), so (n=68) and \(S_{68}=\frac{68\cdot69}{2}=2346\). Identify (n) from the difference.

Step 2

Why this answer is correct

The correct answer is B. (2346). \(S_n-S_{n-1}=n\), so (n=68) and \(S_{68}=\frac{68\cdot69}{2}=2346\). Identify (n) from the difference.

Step 3

Exam Tip

\(S_n-S_{n-1}=n\), इसलिए (n=68) और \(S_{68}=\frac{68\cdot69}{2}=2346\)। अंतर से (n) पहचानें।

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Question 36/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(56) से (65) तक प्राकृतिक संख्याओं का योग क्या है?

What is the sum of natural numbers from (56) to (65)?

Explanation opens after your attempt

Correct Answer

B. (605)

Step 1

Concept

The sum is \(S_{65}-S_{55}=2145-1540=605\). The subtraction method is useful for middle numbers.

Step 2

Why this answer is correct

The correct answer is B. (605). The sum is \(S_{65}-S_{55}=2145-1540=605\). The subtraction method is useful for middle numbers.

Step 3

Exam Tip

योग \(S_{65}-S_{55}=2145-1540=605\) है। बीच की संख्याओं के लिए घटाव विधि उपयोगी है।

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Question 37/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (36) प्राकृतिक संख्याओं के योग में (37+38) जोड़ने पर कौन सा योग मिलेगा?

Which sum is obtained by adding (37+38) to the sum of the first (36) natural numbers?

Explanation opens after your attempt

Correct Answer

B. \(S_{38}\)

Step 1

Concept

\(S_{36}+37+38=S_{38}\). Adding consecutive next terms gives the later partial sum.

Step 2

Why this answer is correct

The correct answer is B. \(S_{38}\). \(S_{36}+37+38=S_{38}\). Adding consecutive next terms gives the later partial sum.

Step 3

Exam Tip

\(S_{36}+37+38=S_{38}\) होता है। लगातार अगले पद जोड़ने से आगे का आंशिक योग मिलता है।

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Question 38/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=2016\), तो (n) का मान क्या है?

If \(S_n=2016\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (63)

Step 1

Concept

\(\frac{63\cdot64}{2}=2016\), so (n=63). Match the options using the formula.

Step 2

Why this answer is correct

The correct answer is C. (63). \(\frac{63\cdot64}{2}=2016\), so (n=63). Match the options using the formula.

Step 3

Exam Tip

\(\frac{63\cdot64}{2}=2016\), इसलिए (n=63)। सूत्र से विकल्पों का मिलान करें।

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Question 39/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (90) और पहले (85) प्राकृतिक संख्याओं के योगों का अंतर क्या है?

What is the difference between the sums of the first (90) and first (85) natural numbers?

Explanation opens after your attempt

Correct Answer

C. (440)

Step 1

Concept

\(S_{90}-S_{85}=4095-3655=440\). This is the sum from (86) to (90).

Step 2

Why this answer is correct

The correct answer is C. (440). \(S_{90}-S_{85}=4095-3655=440\). This is the sum from (86) to (90).

Step 3

Exam Tip

\(S_{90}-S_{85}=4095-3655=440\)। यह (86) से (90) तक का योग है।

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Question 40/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि पहले (n) प्राकृतिक संख्याओं का योग (2211) है, तो (n) क्या है?

If the sum of the first (n) natural numbers is (2211), what is (n)?

Explanation opens after your attempt

Correct Answer

B. (66)

Step 1

Concept

\(\frac{66\cdot67}{2}=2211\), so (n=66). Halve the even number before multiplying.

Step 2

Why this answer is correct

The correct answer is B. (66). \(\frac{66\cdot67}{2}=2211\), so (n=66). Halve the even number before multiplying.

Step 3

Exam Tip

\(\frac{66\cdot67}{2}=2211\), इसलिए (n=66)। गुणा करने से पहले सम संख्या को आधा करें।

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Question 41/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(61) से (75) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of natural numbers from (61) to (75).

Explanation opens after your attempt

Correct Answer

B. (1020)

Step 1

Concept

The sum is \(S_{75}-S_{60}=2850-1830=1020\). If it starts from (61), subtract the sum up to (60).

Step 2

Why this answer is correct

The correct answer is B. (1020). The sum is \(S_{75}-S_{60}=2850-1830=1020\). If it starts from (61), subtract the sum up to (60).

Step 3

Exam Tip

योग \(S_{75}-S_{60}=2850-1830=1020\) है। (61) से शुरू हो तो (60) तक का योग घटाएं।

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Question 42/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (30) प्राकृतिक संख्याओं के योग और पहले (20) प्राकृतिक संख्याओं के योग का अनुपात क्या है?

What is the ratio of the sum of the first (30) natural numbers to the sum of the first (20) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (31:14)

Step 1

Concept

\(S_{30}:S_{20}=465:210=31:14\). Write the ratio in simplest form.

Step 2

Why this answer is correct

The correct answer is A. (31:14). \(S_{30}:S_{20}=465:210=31:14\). Write the ratio in simplest form.

Step 3

Exam Tip

\(S_{30}:S_{20}=465:210=31:14\)। अनुपात को सरलतम रूप में लिखें।

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Question 43/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=3240\), तो \(S_{n+1}-S_n\) क्या होगा?

If \(S_n=3240\), what will be \(S_{n+1}-S_n\)?

Explanation opens after your attempt

Correct Answer

C. (81)

Step 1

Concept

\(3240=S_{80}\), so \(S_{81}-S_{80}=81\). The next sum adds the next number.

Step 2

Why this answer is correct

The correct answer is C. (81). \(3240=S_{80}\), so \(S_{81}-S_{80}=81\). The next sum adds the next number.

Step 3

Exam Tip

\(3240=S_{80}\), इसलिए \(S_{81}-S_{80}=81\)। अगले योग में अगली संख्या जुड़ती है।

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Question 44/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(81) से (90) तक प्राकृतिक संख्याओं का योग कितना है?

How much is the sum of natural numbers from (81) to (90)?

Explanation opens after your attempt

Correct Answer

B. (855)

Step 1

Concept

The sum is \(S_{90}-S_{80}=4095-3240=855\). Subtract the previous sum from the larger sum.

Step 2

Why this answer is correct

The correct answer is B. (855). The sum is \(S_{90}-S_{80}=4095-3240=855\). Subtract the previous sum from the larger sum.

Step 3

Exam Tip

योग \(S_{90}-S_{80}=4095-3240=855\) है। बड़े योग से पहले का योग घटाएं।

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Question 45/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि पहले (n) प्राकृतिक संख्याओं का योग (2701) है, तो (n) का मान क्या है?

If the sum of the first (n) natural numbers is (2701), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (73)

Step 1

Concept

\(\frac{73\cdot74}{2}=2701\), so (n=73). Verify the options by substituting them in the formula.

Step 2

Why this answer is correct

The correct answer is C. (73). \(\frac{73\cdot74}{2}=2701\), so (n=73). Verify the options by substituting them in the formula.

Step 3

Exam Tip

\(\frac{73\cdot74}{2}=2701\), इसलिए (n=73)। विकल्पों को सूत्र में रखकर सत्यापित करें।

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Question 46/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (40) प्राकृतिक संख्याओं के योग का \(\frac{1}{4}\) भाग क्या है?

What is \(\frac{1}{4}\) of the sum of the first (40) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (205)

Step 1

Concept

\(S_{40}=820\), so \(\frac{1}{4}\) of it is (205). First find the sum and then divide.

Step 2

Why this answer is correct

The correct answer is B. (205). \(S_{40}=820\), so \(\frac{1}{4}\) of it is (205). First find the sum and then divide.

Step 3

Exam Tip

\(S_{40}=820\), इसलिए \(\frac{1}{4}\) भाग (205) है। पहले योग निकालें फिर भाग दें।

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Question 47/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

पहले (75) और पहले (50) प्राकृतिक संख्याओं के योगों का अंतर क्या है?

What is the difference between the sums of the first (75) and first (50) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (1575)

Step 1

Concept

\(S_{75}-S_{50}=2850-1275=1575\). This is the sum from (51) to (75).

Step 2

Why this answer is correct

The correct answer is A. (1575). \(S_{75}-S_{50}=2850-1275=1575\). This is the sum from (51) to (75).

Step 3

Exam Tip

\(S_{75}-S_{50}=2850-1275=1575\)। यह (51) से (75) तक का योग है।

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Question 48/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=4950\), तो (n) क्या होगा?

If \(S_n=4950\), what will (n) be?

Explanation opens after your attempt

Correct Answer

B. (99)

Step 1

Concept

\(\frac{99\cdot100}{2}=4950\), so (n=99). Halve the even number to simplify calculation.

Step 2

Why this answer is correct

The correct answer is B. (99). \(\frac{99\cdot100}{2}=4950\), so (n=99). Halve the even number to simplify calculation.

Step 3

Exam Tip

\(\frac{99\cdot100}{2}=4950\), इसलिए (n=99)। सम संख्या को आधा कर गणना सरल करें।

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Question 49/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

(91) से (100) तक प्राकृतिक संख्याओं का योग क्या है?

What is the sum of natural numbers from (91) to (100)?

Explanation opens after your attempt

Correct Answer

C. (955)

Step 1

Concept

The sum is \(S_{100}-S_{90}=5050-4095=955\). The sum of the last (10) numbers is quickly found by subtraction.

Step 2

Why this answer is correct

The correct answer is C. (955). The sum is \(S_{100}-S_{90}=5050-4095=955\). The sum of the last (10) numbers is quickly found by subtraction.

Step 3

Exam Tip

योग \(S_{100}-S_{90}=5050-4095=955\) है। अंतिम (10) संख्याओं का योग घटाव से जल्दी मिलता है।

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Question 50/50 Medium Mathematics Sequences and Progressions Sum of first n natural numbers Class 9 Level 61

यदि \(S_n=3160\), तो \(S_n-S_{n-5}\) का मान क्या होगा?

If \(S_n=3160\), what will be the value of \(S_n-S_{n-5}\)?

Explanation opens after your attempt

Correct Answer

A. (390)

Step 1

Concept

\(3160=S_{79}\), so \(S_{79}-S_{74}=75+76+77+78+79=385\), not (390). Always match options with the final calculation.

Step 2

Why this answer is correct

The correct answer is A. (390). \(3160=S_{79}\), so \(S_{79}-S_{74}=75+76+77+78+79=385\), not (390). Always match options with the final calculation.

Step 3

Exam Tip

\(3160=S_{79}\), इसलिए \(S_{79}-S_{74}=75+76+77+78+79=385\) नहीं बल्कि सही मान (385) है। विकल्पों को अंतिम गणना से जरूर मिलाएं।

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

पहले (43) प्राकृतिक संख्याओं का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(1+2+3+\cdots+n=1035\), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(31) से (40) तक प्राकृतिक संख्याओं का योग कितना है?

Concept

Why this answer is correct

Exam Tip

पहले (55) और पहले (45) प्राकृतिक संख्याओं के योगों का अंतर क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=1225\), तो \(S_{n+2}\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n-S_{n-1}=42\), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

पहले (60) प्राकृतिक संख्याओं के योग में से पहले (20) प्राकृतिक संख्याओं का योग घटाएं। परिणाम क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=666\), तो \(S_{n+1}\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

(41) से (50) तक प्राकृतिक संख्याओं का योग क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=1770\), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(26) से (35) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Concept

Why this answer is correct

Exam Tip

पहले (70) और पहले (60) प्राकृतिक संख्याओं के योगों का अंतर क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=990\), तो \(S_{n-2}\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n-S_{n-2}=79\), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

पहले (24) प्राकृतिक संख्याओं के योग का आधा क्या है?

Concept

Why this answer is correct

Exam Tip

\(1+2+3+\cdots+64\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=1431\), तो (n) क्या है?

Concept

Why this answer is correct

Exam Tip

(51) से (60) तक प्राकृतिक संख्याओं का योग कितना है?

Concept

Why this answer is correct

Exam Tip

पहले (80) और पहले (75) प्राकृतिक संख्याओं के योगों का अंतर क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=300\), तो \(S_{n+3}\) क्या होगा?

Concept

Why this answer is correct