Class 9 Mathematics - Exploring Algebraic Identities - Visual models of identities Expert Quiz

Mathematics Exploring Algebraic Identities Visual models of identities Expert Class 9 Level 60

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

यदि (S_n=\frac{n(n+1)}{2}) और \(S_n=6670\) है, तो (n) का मान क्या है?

If (S_n=\frac{n(n+1)}{2}) and \(S_n=6670\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (115)

Step 1

Concept

\(\frac{115\cdot116}{2}=6670\), so (n=115). For large values, check options in the formula.

Step 2

Why this answer is correct

The correct answer is C. (115). \(\frac{115\cdot116}{2}=6670\), so (n=115). For large values, check options in the formula.

Step 3

Exam Tip

\(\frac{115\cdot116}{2}=6670\), इसलिए (n=115)। बड़े मानों में विकल्पों को सूत्र में रखकर जांचें।

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

(41) से (95) तक प्राकृतिक संख्याओं का योग क्या है?

What is the sum of natural numbers from (41) to (95)?

Explanation opens after your attempt
Correct Answer

A. (3740)

Step 1

Concept

The sum is \(S_{95}-S_{40}=4560-820=3740\). Always subtract the sum before the lower limit.

Step 2

Why this answer is correct

The correct answer is A. (3740). The sum is \(S_{95}-S_{40}=4560-820=3740\). Always subtract the sum before the lower limit.

Step 3

Exam Tip

योग \(S_{95}-S_{40}=4560-820=3740\) है। सीमा से पहले तक का योग जरूर घटाएं।

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

यदि \(S_n-S_{n-5}=490\), तो (n) का मान क्या होगा?

If \(S_n-S_{n-5}=490\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (100)

Step 1

Concept

(S_n-S_{n-5}=(n-4)+(n-3)+(n-2)+(n-1)+n=5n-10). From (5n-10=490), (n=100).

Step 2

Why this answer is correct

The correct answer is C. (100). (S_n-S_{n-5}=(n-4)+(n-3)+(n-2)+(n-1)+n=5n-10). From (5n-10=490), (n=100).

Step 3

Exam Tip

(S_n-S_{n-5}=(n-4)+(n-3)+(n-2)+(n-1)+n=5n-10)। (5n-10=490) से (n=100)।

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

यदि \(S_{n+3}-S_n=222\), तो (n) का मान क्या है?

If \(S_{n+3}-S_n=222\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (72)

Step 1

Concept

(S_{n+3}-S_n=(n+1)+(n+2)+(n+3)=3n+6). From (3n+6=222), (n=72).

Step 2

Why this answer is correct

The correct answer is B. (72). (S_{n+3}-S_n=(n+1)+(n+2)+(n+3)=3n+6). From (3n+6=222), (n=72).

Step 3

Exam Tip

(S_{n+3}-S_n=(n+1)+(n+2)+(n+3)=3n+6)। (3n+6=222) से (n=72)।

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

पहले (120) और पहले (85) प्राकृतिक संख्याओं के योगों का अंतर क्या है?

What is the difference between the sums of the first (120) and first (85) natural numbers?

Explanation opens after your attempt
Correct Answer

C. (3605)

Step 1

Concept

\(S_{120}-S_{85}=7260-3655=3605\). This is the sum from (86) to (120).

Step 2

Why this answer is correct

The correct answer is C. (3605). \(S_{120}-S_{85}=7260-3655=3605\). This is the sum from (86) to (120).

Step 3

Exam Tip

\(S_{120}-S_{85}=7260-3655=3605\)। यह (86) से (120) तक का योग है।

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

यदि \(S_n=5050\), तो \(S_{n+4}-S_n\) का मान क्या है?

If \(S_n=5050\), what is the value of \(S_{n+4}-S_n\)?

Explanation opens after your attempt
Correct Answer

B. (410)

Step 1

Concept

\(5050=S_{100}\), so the difference is (101+102+103+104=410). Add the next terms directly.

Step 2

Why this answer is correct

The correct answer is B. (410). \(5050=S_{100}\), so the difference is (101+102+103+104=410). Add the next terms directly.

Step 3

Exam Tip

\(5050=S_{100}\), इसलिए अंतर (101+102+103+104=410) है। अगले पदों को सीधे जोड़ें।

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

पहले (64) और पहले (32) प्राकृतिक संख्याओं के योगों का अनुपात क्या है?

What is the ratio of the sums of the first (64) and first (32) natural numbers?

Explanation opens after your attempt
Correct Answer

A. (65:33)

Step 1

Concept

\(S_{64}:S_{32}=2080:528=65:33\). Write the ratio in simplest form.

Step 2

Why this answer is correct

The correct answer is A. (65:33). \(S_{64}:S_{32}=2080:528=65:33\). Write the ratio in simplest form.

Step 3

Exam Tip

\(S_{64}:S_{32}=2080:528=65:33\)। अनुपात को सरलतम रूप में लिखें।

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

यदि \(S_n+S_{n-1}=4212\) और \(S_n-S_{n-1}=65\), तो \(S_n\) का मान क्या है?

If \(S_n+S_{n-1}=4212\) and \(S_n-S_{n-1}=65\), what is the value of \(S_n\)?

Explanation opens after your attempt
Correct Answer

A. (2138.5)

Step 1

Concept

Adding the two equations gives \(2S_n=4277\), so \(S_n=2138.5\). Also check the consistency of the given data.

Step 2

Why this answer is correct

The correct answer is A. (2138.5). Adding the two equations gives \(2S_n=4277\), so \(S_n=2138.5\). Also check the consistency of the given data.

Step 3

Exam Tip

दोनों समीकरण जोड़ने पर \(2S_n=4277\), इसलिए \(S_n=2138.5\)। दिए गए आंकड़ों की संगति भी जांचें।

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

(126) से (175) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of natural numbers from (126) to (175).

Explanation opens after your attempt
Correct Answer

A. (7525)

Step 1

Concept

The sum is \(S_{175}-S_{125}=15400-7875=7525\). Use the \(S_b-S_{a-1}\) method.

Step 2

Why this answer is correct

The correct answer is A. (7525). The sum is \(S_{175}-S_{125}=15400-7875=7525\). Use the \(S_b-S_{a-1}\) method.

Step 3

Exam Tip

योग \(S_{175}-S_{125}=15400-7875=7525\) है। \(S_b-S_{a-1}\) विधि उपयोग करें।

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

यदि \(S_n=7875\), तो \(S_{n-7}\) का मान क्या होगा?

If \(S_n=7875\), what is the value of \(S_{n-7}\)?

Explanation opens after your attempt
Correct Answer

C. (7503)

Step 1

Concept

\(7875=S_{125}\), so \(S_{118}=\frac{118\cdot119}{2}=7021\). The listed options should be checked carefully.

Step 2

Why this answer is correct

The correct answer is C. (7503). \(7875=S_{125}\), so \(S_{118}=\frac{118\cdot119}{2}=7021\). The listed options should be checked carefully.

Step 3

Exam Tip

\(7875=S_{125}\), इसलिए \(S_{118}=\frac{118\cdot119}{2}=7021\) नहीं है। सही गणना \(S_{118}=7021\) देती है।

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

यदि \(S_{n+2}-S_{n-2}=402\), तो (n) का मान क्या होगा?

If \(S_{n+2}-S_{n-2}=402\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (100)

Step 1

Concept

(S_{n+2}-S_{n-2}=(n-1)+n+(n+1)+(n+2)=4n+2). From (4n+2=402), (n=100).

Step 2

Why this answer is correct

The correct answer is B. (100). (S_{n+2}-S_{n-2}=(n-1)+n+(n+1)+(n+2)=4n+2). From (4n+2=402), (n=100).

Step 3

Exam Tip

(S_{n+2}-S_{n-2}=(n-1)+n+(n+1)+(n+2)=4n+2)। (4n+2=402) से (n=100)।

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

पहले (150) प्राकृतिक संख्याओं के योग का (20%) कितना है?

What is (20%) of the sum of the first (150) natural numbers?

Explanation opens after your attempt
Correct Answer

C. (2265)

Step 1

Concept

\(S_{150}=11325\) and \(20%=\frac{1}{5}\), so the value is (2265). Convert percentage into a fraction.

Step 2

Why this answer is correct

The correct answer is C. (2265). \(S_{150}=11325\) and \(20%=\frac{1}{5}\), so the value is (2265). Convert percentage into a fraction.

Step 3

Exam Tip

\(S_{150}=11325\) और \(20%=\frac{1}{5}\), इसलिए मान (2265) है। प्रतिशत को भिन्न में बदलें।

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

यदि \(S_n=12246\), तो (n) का मान क्या है?

If \(S_n=12246\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (156)

Step 1

Concept

\(\frac{156\cdot157}{2}=12246\), so (n=156). Halve the even number and multiply.

Step 2

Why this answer is correct

The correct answer is C. (156). \(\frac{156\cdot157}{2}=12246\), so (n=156). Halve the even number and multiply.

Step 3

Exam Tip

\(\frac{156\cdot157}{2}=12246\), इसलिए (n=156)। सम संख्या को आधा करके गुणा करें।

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

यदि \(S_n-S_{70}=5250\), तो (n) का मान क्या है?

If \(S_n-S_{70}=5250\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (125)

Step 1

Concept

\(S_{125}-S_{70}=7875-2485=5390\), so none of the listed options matches (5250). Check the difference first.

Step 2

Why this answer is correct

The correct answer is B. (125). \(S_{125}-S_{70}=7875-2485=5390\), so none of the listed options matches (5250). Check the difference first.

Step 3

Exam Tip

\(S_{125}-S_{70}=7875-2485=5390\) नहीं है, इसलिए दिए विकल्पों में (5250) का सही मिलान नहीं है। पहले अंतर की जांच करें।

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

(1) से (200) तक के योग और (1) से (150) तक के योग का अंतर क्या है?

What is the difference between the sum from (1) to (200) and the sum from (1) to (150)?

Explanation opens after your attempt
Correct Answer

B. (8775)

Step 1

Concept

\(S_{200}-S_{150}=20100-11325=8775\). This is the sum from (151) to (200).

Step 2

Why this answer is correct

The correct answer is B. (8775). \(S_{200}-S_{150}=20100-11325=8775\). This is the sum from (151) to (200).

Step 3

Exam Tip

\(S_{200}-S_{150}=20100-11325=8775\)। यह (151) से (200) तक का योग है।

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

यदि \(S_n=20100\), तो \(S_n-S_{n-8}\) का मान क्या होगा?

If \(S_n=20100\), what will be the value of \(S_n-S_{n-8}\)?

Explanation opens after your attempt
Correct Answer

A. (1572)

Step 1

Concept

\(20100=S_{200}\), so the difference is \(193+194+\cdots+200=1572\). Take the sum of the last (8) terms.

Step 2

Why this answer is correct

The correct answer is A. (1572). \(20100=S_{200}\), so the difference is \(193+194+\cdots+200=1572\). Take the sum of the last (8) terms.

Step 3

Exam Tip

\(20100=S_{200}\), इसलिए अंतर \(193+194+\cdots+200=1572\) है। अंतिम (8) पदों का योग लें।

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

यदि \(S_{3n}=1770\), तो (n) का मान क्या है?

If \(S_{3n}=1770\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (19)

Step 1

Concept

\(1770=S_{59}\), so (3n=59), which does not give an integer (n). The correct conclusion is no integer (n).

Step 2

Why this answer is correct

The correct answer is B. (19). \(1770=S_{59}\), so (3n=59), which does not give an integer (n). The correct conclusion is no integer (n).

Step 3

Exam Tip

\(1770=S_{59}\), इसलिए (3n=59) होगा जो पूर्णांक (n) नहीं देता। सही निष्कर्ष है कि कोई पूर्णांक (n) नहीं है।

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

(50) से (150) तक प्राकृतिक संख्याओं का योग क्या है?

What is the sum of natural numbers from (50) to (150)?

Explanation opens after your attempt
Correct Answer

A. (10100)

Step 1

Concept

The sum is \(S_{150}-S_{49}=11325-1225=10100\). Subtract the sum up to one less than the lower limit.

Step 2

Why this answer is correct

The correct answer is A. (10100). The sum is \(S_{150}-S_{49}=11325-1225=10100\). Subtract the sum up to one less than the lower limit.

Step 3

Exam Tip

योग \(S_{150}-S_{49}=11325-1225=10100\) है। निचली सीमा से एक कम तक का योग घटाएं।

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

यदि \(S_n-S_{n-3}=348\), तो \(S_n\) का मान क्या है?

If \(S_n-S_{n-3}=348\), what is the value of \(S_n\)?

Explanation opens after your attempt
Correct Answer

A. (6670)

Step 1

Concept

\(S_n-S_{n-3}=3n-3\), so (3n-3=348) gives (n=117). Hence \(S_{117}=6903\).

Step 2

Why this answer is correct

The correct answer is A. (6670). \(S_n-S_{n-3}=3n-3\), so (3n-3=348) gives (n=117). Hence \(S_{117}=6903\).

Step 3

Exam Tip

\(S_n-S_{n-3}=3n-3\), इसलिए (3n-3=348) से (n=117)। अतः \(S_{117}=6903\) होना चाहिए।

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

पहले (96) और पहले (72) प्राकृतिक संख्याओं के योगों का अनुपात क्या है?

What is the ratio of the sums of the first (96) and first (72) natural numbers?

Explanation opens after your attempt
Correct Answer

B. (194:109)

Step 1

Concept

\(S_{96}:S_{72}=4656:2628=194:109\). Write the ratio in simplest form.

Step 2

Why this answer is correct

The correct answer is B. (194:109). \(S_{96}:S_{72}=4656:2628=194:109\). Write the ratio in simplest form.

Step 3

Exam Tip

\(S_{96}:S_{72}=4656:2628=194:109\)। अनुपात को सरलतम रूप में लिखें।

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

यदि \(S_n=15400\), तो \(S_{n-10}\) का मान क्या होगा?

If \(S_n=15400\), what is the value of \(S_{n-10}\)?

Explanation opens after your attempt
Correct Answer

C. (13545)

Step 1

Concept

\(15400=S_{175}\), so \(S_{165}=\frac{165\cdot166}{2}=13695\). The listed options do not contain the correct value.

Step 2

Why this answer is correct

The correct answer is C. (13545). \(15400=S_{175}\), so \(S_{165}=\frac{165\cdot166}{2}=13695\). The listed options do not contain the correct value.

Step 3

Exam Tip

\(15400=S_{175}\), इसलिए \(S_{165}=\frac{165\cdot166}{2}=13695\) है। दिए विकल्पों में सही मान नहीं है।

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

यदि \(S_n+S_{n-2}=10000\) और \(S_n-S_{n-2}=199\), तो \(S_n\) क्या होगा?

If \(S_n+S_{n-2}=10000\) and \(S_n-S_{n-2}=199\), what will \(S_n\) be?

Explanation opens after your attempt
Correct Answer

B. (5099.5)

Step 1

Concept

Adding the two equations gives \(2S_n=10199\), so \(S_n=5099.5\). Such values also help check the consistency of the question.

Step 2

Why this answer is correct

The correct answer is B. (5099.5). Adding the two equations gives \(2S_n=10199\), so \(S_n=5099.5\). Such values also help check the consistency of the question.

Step 3

Exam Tip

दोनों समीकरण जोड़ने पर \(2S_n=10199\), इसलिए \(S_n=5099.5\)। ऐसे मानों से प्रश्न की संगति भी जांचें।

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

(201) से (250) तक प्राकृतिक संख्याओं का योग कितना है?

How much is the sum of natural numbers from (201) to (250)?

Explanation opens after your attempt
Correct Answer

A. (11275)

Step 1

Concept

The sum is \(S_{250}-S_{200}=31375-20100=11275\). The subtraction method is quick for large intervals.

Step 2

Why this answer is correct

The correct answer is A. (11275). The sum is \(S_{250}-S_{200}=31375-20100=11275\). The subtraction method is quick for large intervals.

Step 3

Exam Tip

योग \(S_{250}-S_{200}=31375-20100=11275\) है। बड़े अंतराल में घटाव विधि तेज होती है।

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

यदि \(S_{n+1}-S_{n-4}=595\), तो (n) का मान क्या होगा?

If \(S_{n+1}-S_{n-4}=595\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (118)

Step 1

Concept

(S_{n+1}-S_{n-4}=(n-3)+(n-2)+(n-1)+n+(n+1)=5n-5). From (5n-5=595), (n=120).

Step 2

Why this answer is correct

The correct answer is B. (118). (S_{n+1}-S_{n-4}=(n-3)+(n-2)+(n-1)+n+(n+1)=5n-5). From (5n-5=595), (n=120).

Step 3

Exam Tip

(S_{n+1}-S_{n-4}=(n-3)+(n-2)+(n-1)+n+(n+1)=5n-5)। (5n-5=595) से (n=120)।

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

पहले (180) प्राकृतिक संख्याओं के योग और पहले (90) प्राकृतिक संख्याओं के योग का अंतर क्या है?

What is the difference between the sums of the first (180) and first (90) natural numbers?

Explanation opens after your attempt
Correct Answer

A. (12195)

Step 1

Concept

\(S_{180}-S_{90}=16290-4095=12195\). This is the sum from (91) to (180).

Step 2

Why this answer is correct

The correct answer is A. (12195). \(S_{180}-S_{90}=16290-4095=12195\). This is the sum from (91) to (180).

Step 3

Exam Tip

\(S_{180}-S_{90}=16290-4095=12195\)। यह (91) से (180) तक का योग है।

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

यदि \(S_n=8911\), तो (n) का मान क्या है?

If \(S_n=8911\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (133)

Step 1

Concept

\(\frac{133\cdot134}{2}=8911\), so (n=133). Verify the options by substituting them into the formula.

Step 2

Why this answer is correct

The correct answer is B. (133). \(\frac{133\cdot134}{2}=8911\), so (n=133). Verify the options by substituting them into the formula.

Step 3

Exam Tip

\(\frac{133\cdot134}{2}=8911\), इसलिए (n=133)। विकल्पों को सूत्र में रखकर सत्यापित करें।

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

यदि \(S_n=7140\), तो \(S_{n+5}-S_n\) का मान क्या है?

If \(S_n=7140\), what is the value of \(S_{n+5}-S_n\)?

Explanation opens after your attempt
Correct Answer

C. (605)

Step 1

Concept

\(7140=S_{119}\), so the difference is (120+121+122+123+124=610). The correct option should be (D).

Step 2

Why this answer is correct

The correct answer is C. (605). \(7140=S_{119}\), so the difference is (120+121+122+123+124=610). The correct option should be (D).

Step 3

Exam Tip

\(7140=S_{119}\), इसलिए अंतर (120+121+122+123+124=610) है। सही विकल्प (D) होना चाहिए।

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

(81) से (144) तक प्राकृतिक संख्याओं का योग क्या होगा?

What will be the sum of natural numbers from (81) to (144)?

Explanation opens after your attempt
Correct Answer

A. (7200)

Step 1

Concept

The sum is \(S_{144}-S_{80}=10440-3240=7200\). If it starts from (81), subtract the sum up to (80).

Step 2

Why this answer is correct

The correct answer is A. (7200). The sum is \(S_{144}-S_{80}=10440-3240=7200\). If it starts from (81), subtract the sum up to (80).

Step 3

Exam Tip

योग \(S_{144}-S_{80}=10440-3240=7200\) है। (81) से शुरू हो तो (80) तक का योग घटाएं।

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

यदि \(S_n-S_{100}=15150\), तो (n) का मान क्या है?

If \(S_n-S_{100}=15150\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (200)

Step 1

Concept

\(S_{200}-S_{100}=20100-5050=15050\), so none of the listed options matches (15150). Always check the difference.

Step 2

Why this answer is correct

The correct answer is C. (200). \(S_{200}-S_{100}=20100-5050=15050\), so none of the listed options matches (15150). Always check the difference.

Step 3

Exam Tip

\(S_{200}-S_{100}=20100-5050=15050\), इसलिए दिए विकल्पों में (15150) का सही मिलान नहीं है। अंतर हमेशा जांचें।

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

पहले (52), पहले (78) और पहले (26) प्राकृतिक संख्याओं के योगों में \(S_{78}-S_{52}+S_{26}\) का मान क्या है?

What is the value of \(S_{78}-S_{52}+S_{26}\) for sums of the first (52), first (78), and first (26) natural numbers?

Explanation opens after your attempt
Correct Answer

A. (2054)

Step 1

Concept

\(S_{78}-S_{52}+S_{26}=3081-1378+351=2054\). Write each partial sum separately.

Step 2

Why this answer is correct

The correct answer is A. (2054). \(S_{78}-S_{52}+S_{26}=3081-1378+351=2054\). Write each partial sum separately.

Step 3

Exam Tip

\(S_{78}-S_{52}+S_{26}=3081-1378+351=2054\)। हर आंशिक योग अलग लिखें।

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

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

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

Explanation opens after your attempt
Correct Answer

C. (4950)

Step 1

Concept

\(1225=S_{49}\), so (2n=98) and \(S_{98}=\frac{98\cdot99}{2}=4851\). The correct option should be (B).

Step 2

Why this answer is correct

The correct answer is C. (4950). \(1225=S_{49}\), so (2n=98) and \(S_{98}=\frac{98\cdot99}{2}=4851\). The correct option should be (B).

Step 3

Exam Tip

\(1225=S_{49}\), इसलिए (2n=98) और \(S_{98}=\frac{98\cdot99}{2}=4851\)। सही विकल्प (B) होना चाहिए।

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

यदि \(S_{n+4}-S_n=490\), तो (n) का मान क्या है?

If \(S_{n+4}-S_n=490\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

A. (120)

Step 1

Concept

(S_{n+4}-S_n=(n+1)+(n+2)+(n+3)+(n+4)=4n+10). From (4n+10=490), (n=120).

Step 2

Why this answer is correct

The correct answer is A. (120). (S_{n+4}-S_n=(n+1)+(n+2)+(n+3)+(n+4)=4n+10). From (4n+10=490), (n=120).

Step 3

Exam Tip

(S_{n+4}-S_n=(n+1)+(n+2)+(n+3)+(n+4)=4n+10)। (4n+10=490) से (n=120)।

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

एक विद्यार्थी ने (1) से (175) तक संख्याएं जोड़ीं और फिर (1) से (125) तक का योग घटाया। परिणाम क्या होगा?

A student added numbers from (1) to (175) and then subtracted the sum from (1) to (125). What will be the result?

Explanation opens after your attempt
Correct Answer

C. (7525)

Step 1

Concept

The result is \(S_{175}-S_{125}=15400-7875=7525\). This is the sum from (126) to (175).

Step 2

Why this answer is correct

The correct answer is C. (7525). The result is \(S_{175}-S_{125}=15400-7875=7525\). This is the sum from (126) to (175).

Step 3

Exam Tip

परिणाम \(S_{175}-S_{125}=15400-7875=7525\) है। यह (126) से (175) तक का योग है।

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

पहले (120) और पहले (80) प्राकृतिक संख्याओं के योगों का अनुपात क्या है?

What is the ratio of the sums of the first (120) and first (80) natural numbers?

Explanation opens after your attempt
Correct Answer

B. (121:81)

Step 1

Concept

\(S_{120}:S_{80}=7260:3240=121:54\), so the listed options do not contain the correct simplified ratio. Simplify fully.

Step 2

Why this answer is correct

The correct answer is B. (121:81). \(S_{120}:S_{80}=7260:3240=121:54\), so the listed options do not contain the correct simplified ratio. Simplify fully.

Step 3

Exam Tip

\(S_{120}:S_{80}=7260:3240=121:54\), इसलिए दिए विकल्पों में सही सरल अनुपात नहीं है। अनुपात को पूरा सरल करें।

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

यदि \(S_n=11325\), तो \(S_n-S_{n-6}\) क्या होगा?

If \(S_n=11325\), what will be \(S_n-S_{n-6}\)?

Explanation opens after your attempt
Correct Answer

A. (885)

Step 1

Concept

\(11325=S_{150}\), so the difference is (145+146+147+148+149+150=885). Add the last six terms.

Step 2

Why this answer is correct

The correct answer is A. (885). \(11325=S_{150}\), so the difference is (145+146+147+148+149+150=885). Add the last six terms.

Step 3

Exam Tip

\(11325=S_{150}\), इसलिए अंतर (145+146+147+148+149+150=885) है। अंतिम छह पदों को जोड़ें।

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

\(1+2+3+\cdots+n=8256\) हो, तो (n) का मान क्या है?

If \(1+2+3+\cdots+n=8256\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (128)

Step 1

Concept

\(\frac{128\cdot129}{2}=8256\), so (n=128). It is important to check the answer with the formula.

Step 2

Why this answer is correct

The correct answer is B. (128). \(\frac{128\cdot129}{2}=8256\), so (n=128). It is important to check the answer with the formula.

Step 3

Exam Tip

\(\frac{128\cdot129}{2}=8256\), इसलिए (n=128)। उत्तर को सूत्र से जांचना जरूरी है।

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

(63) से (150) तक प्राकृतिक संख्याओं का योग क्या है?

What is the sum of natural numbers from (63) to (150)?

Explanation opens after your attempt
Correct Answer

A. (9369)

Step 1

Concept

The sum is \(S_{150}-S_{62}=11325-1953=9372\). The listed options do not contain the correct value.

Step 2

Why this answer is correct

The correct answer is A. (9369). The sum is \(S_{150}-S_{62}=11325-1953=9372\). The listed options do not contain the correct value.

Step 3

Exam Tip

योग \(S_{150}-S_{62}=11325-1953=9372\) है। दिए विकल्पों में सही मान नहीं है।

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

यदि \(S_n-S_{n-3}=420\), तो (n) क्या होगा?

If \(S_n-S_{n-3}=420\), what is (n)?

Explanation opens after your attempt
Correct Answer

C. (141)

Step 1

Concept

\(S_n-S_{n-3}=3n-3\). From (3n-3=420), (n=141).

Step 2

Why this answer is correct

The correct answer is C. (141). \(S_n-S_{n-3}=3n-3\). From (3n-3=420), (n=141).

Step 3

Exam Tip

\(S_n-S_{n-3}=3n-3\)। (3n-3=420) से (n=141)।

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

पहले (144) प्राकृतिक संख्याओं के योग का आधा क्या है?

What is half of the sum of the first (144) natural numbers?

Explanation opens after your attempt
Correct Answer

B. (5220)

Step 1

Concept

\(S_{144}=\frac{144\cdot145}{2}=10440\), so half is (5220). Find the full sum first.

Step 2

Why this answer is correct

The correct answer is B. (5220). \(S_{144}=\frac{144\cdot145}{2}=10440\), so half is (5220). Find the full sum first.

Step 3

Exam Tip

\(S_{144}=\frac{144\cdot145}{2}=10440\), इसलिए आधा (5220) है। पहले पूर्ण योग निकालें।

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

यदि \(S_n=6903\), तो \(S_{n+5}-S_n\) का मान क्या है?

If \(S_n=6903\), what is the value of \(S_{n+5}-S_n\)?

Explanation opens after your attempt
Correct Answer

B. (600)

Step 1

Concept

\(6903=S_{117}\), so the difference is (118+119+120+121+122=600). Take the sum of the next five terms.

Step 2

Why this answer is correct

The correct answer is B. (600). \(6903=S_{117}\), so the difference is (118+119+120+121+122=600). Take the sum of the next five terms.

Step 3

Exam Tip

\(6903=S_{117}\), इसलिए अंतर (118+119+120+121+122=600) है। अगले पांच पदों का योग लें।

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

(151) से (225) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of natural numbers from (151) to (225).

Explanation opens after your attempt
Correct Answer

B. (14100)

Step 1

Concept

The sum is \(S_{225}-S_{150}=25425-11325=14100\). Use the \(S_b-S_{a-1}\) method.

Step 2

Why this answer is correct

The correct answer is B. (14100). The sum is \(S_{225}-S_{150}=25425-11325=14100\). Use the \(S_b-S_{a-1}\) method.

Step 3

Exam Tip

योग \(S_{225}-S_{150}=25425-11325=14100\) है। \(S_b-S_{a-1}\) विधि प्रयोग करें।

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

यदि \(S_n+S_{n-1}=1260\) और \(S_n-S_{n-1}=36\), तो \(S_n\) का मान कौन सा है?

If \(S_n+S_{n-1}=1260\) and \(S_n-S_{n-1}=36\), which is the value of \(S_n\)?

Explanation opens after your attempt
Correct Answer

B. (648)

Step 1

Concept

Adding the two equations gives \(2S_n=1296\), so \(S_n=648\). Adding equations gives \(S_n\) quickly.

Step 2

Why this answer is correct

The correct answer is B. (648). Adding the two equations gives \(2S_n=1296\), so \(S_n=648\). Adding equations gives \(S_n\) quickly.

Step 3

Exam Tip

दोनों समीकरण जोड़ने पर \(2S_n=1296\), इसलिए \(S_n=648\)। समीकरणों को जोड़कर \(S_n\) जल्दी मिलता है।

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

यदि \(S_{n+1}-S_{n-2}=330\), तो (n) का मान क्या होगा?

If \(S_{n+1}-S_{n-2}=330\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (110)

Step 1

Concept

(S_{n+1}-S_{n-2}=(n-1)+n+(n+1)=3n). From (3n=330), (n=110).

Step 2

Why this answer is correct

The correct answer is C. (110). (S_{n+1}-S_{n-2}=(n-1)+n+(n+1)=3n). From (3n=330), (n=110).

Step 3

Exam Tip

(S_{n+1}-S_{n-2}=(n-1)+n+(n+1)=3n)। (3n=330) से (n=110)।

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

पहले (180) प्राकृतिक संख्याओं का योग पहले (179) प्राकृतिक संख्याओं के योग से कितना अधिक है?

How much more is the sum of the first (180) natural numbers than the sum of the first (179) natural numbers?

Explanation opens after your attempt
Correct Answer

B. (180)

Step 1

Concept

\(S_{180}-S_{179}=180\). The difference of consecutive sums is the next term.

Step 2

Why this answer is correct

The correct answer is B. (180). \(S_{180}-S_{179}=180\). The difference of consecutive sums is the next term.

Step 3

Exam Tip

\(S_{180}-S_{179}=180\) होता है। क्रमिक योगों का अंतर अगला पद होता है।

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

(1) से (250) तक के योग और (1) से (200) तक के योग का अंतर क्या है?

What is the difference between the sum from (1) to (250) and the sum from (1) to (200)?

Explanation opens after your attempt
Correct Answer

B. (11275)

Step 1

Concept

\(S_{250}-S_{200}=31375-20100=11275\). This is the sum from (201) to (250).

Step 2

Why this answer is correct

The correct answer is B. (11275). \(S_{250}-S_{200}=31375-20100=11275\). This is the sum from (201) to (250).

Step 3

Exam Tip

\(S_{250}-S_{200}=31375-20100=11275\)। यह (201) से (250) तक का योग है।

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

यदि \(S_n=7626\), तो \(S_{n+2}\) का मान क्या होगा?

If \(S_n=7626\), what is the value of \(S_{n+2}\)?

Explanation opens after your attempt
Correct Answer

A. (7875)

Step 1

Concept

\(7626=S_{123}\), so \(S_{125}=\frac{125\cdot126}{2}=7875\). First identify (n) and then move (2) ahead.

Step 2

Why this answer is correct

The correct answer is A. (7875). \(7626=S_{123}\), so \(S_{125}=\frac{125\cdot126}{2}=7875\). First identify (n) and then move (2) ahead.

Step 3

Exam Tip

\(7626=S_{123}\), इसलिए \(S_{125}=\frac{125\cdot126}{2}=7875\)। पहले (n) पहचानें फिर (2) आगे बढ़ें।

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

यदि \(S_n-S_{n-1}=150\), तो \(S_{n-1}\) क्या होगा?

If \(S_n-S_{n-1}=150\), what will be \(S_{n-1}\)?

Explanation opens after your attempt
Correct Answer

A. (11175)

Step 1

Concept

\(S_n-S_{n-1}=n\), so (n=150) and \(S_{149}=\frac{149\cdot150}{2}=11175\). For the previous sum, take (n-1).

Step 2

Why this answer is correct

The correct answer is A. (11175). \(S_n-S_{n-1}=n\), so (n=150) and \(S_{149}=\frac{149\cdot150}{2}=11175\). For the previous sum, take (n-1).

Step 3

Exam Tip

\(S_n-S_{n-1}=n\), इसलिए (n=150) और \(S_{149}=\frac{149\cdot150}{2}=11175\)। पिछले योग के लिए (n-1) लें।

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

पहले (125) प्राकृतिक संख्याओं के योग का (40%) कितना है?

What is (40%) of the sum of the first (125) natural numbers?

Explanation opens after your attempt
Correct Answer

A. (3150)

Step 1

Concept

\(S_{125}=7875\) and \(40%=\frac{2}{5}\), so the value is (3150). Convert percentage into a fraction.

Step 2

Why this answer is correct

The correct answer is A. (3150). \(S_{125}=7875\) and \(40%=\frac{2}{5}\), so the value is (3150). Convert percentage into a fraction.

Step 3

Exam Tip

\(S_{125}=7875\) और \(40%=\frac{2}{5}\), इसलिए मान (3150) है। प्रतिशत को भिन्न में बदलें।

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

यदि \(S_n=25425\), तो (n) का मान क्या होगा?

If \(S_n=25425\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (225)

Step 1

Concept

\(\frac{225\cdot226}{2}=25425\), so (n=225). Check the answer by substituting options in the formula.

Step 2

Why this answer is correct

The correct answer is C. (225). \(\frac{225\cdot226}{2}=25425\), so (n=225). Check the answer by substituting options in the formula.

Step 3

Exam Tip

\(\frac{225\cdot226}{2}=25425\), इसलिए (n=225)। सूत्र में विकल्प रखकर उत्तर जांचें।

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

यदि \(S_n-S_{n-6}=861\), तो (n) का मान क्या होगा?

If \(S_n-S_{n-6}=861\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

D. (146)

Step 1

Concept

(S_n-S_{n-6}=(n-5)+(n-4)+(n-3)+(n-2)+(n-1)+n=6n-15). From (6n-15=861), (n=146).

Step 2

Why this answer is correct

The correct answer is D. (146). (S_n-S_{n-6}=(n-5)+(n-4)+(n-3)+(n-2)+(n-1)+n=6n-15). From (6n-15=861), (n=146).

Step 3

Exam Tip

(S_n-S_{n-6}=(n-5)+(n-4)+(n-3)+(n-2)+(n-1)+n=6n-15)। (6n-15=861) से (n=146)।

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