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

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

यदि (S_n=\frac{n(n+1)}{2}) और \(S_n=861\) है, तो (n) का मान क्या है?

If (S_n=\frac{n(n+1)}{2}) and \(S_n=861\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (41)

Step 1

Concept

\(\frac{41\cdot42}{2}=861\), so (n=41). Check options quickly using the formula.

Step 2

Why this answer is correct

The correct answer is C. (41). \(\frac{41\cdot42}{2}=861\), so (n=41). Check options quickly using the formula.

Step 3

Exam Tip

\(\frac{41\cdot42}{2}=861\), इसलिए (n=41)। विकल्पों को सूत्र में रखकर जल्दी जांचें।

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

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

What is the sum of natural numbers from (26) to (50)?

Explanation opens after your attempt

Correct Answer

B. (950)

Step 1

Concept

The sum is \(S_{50}-S_{25}=1275-325=950\). Do not forget to subtract the sum before the lower limit.

Step 2

Why this answer is correct

The correct answer is B. (950). The sum is \(S_{50}-S_{25}=1275-325=950\). Do not forget to subtract the sum before the lower limit.

Step 3

Exam Tip

योग \(S_{50}-S_{25}=1275-325=950\) है। सीमा से पहले तक का योग घटाना न भूलें।

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

यदि \(S_n-S_{n-4}=250\), तो (n) का मान क्या होगा?

If \(S_n-S_{n-4}=250\), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

D. (64)

Step 1

Concept

(S_n-S_{n-4}=(n-3)+(n-2)+(n-1)+n=4n-6). From (4n-6=250), (n=64).

Step 2

Why this answer is correct

The correct answer is D. (64). (S_n-S_{n-4}=(n-3)+(n-2)+(n-1)+n=4n-6). From (4n-6=250), (n=64).

Step 3

Exam Tip

(S_n-S_{n-4}=(n-3)+(n-2)+(n-1)+n=4n-6)। (4n-6=250) से (n=64)।

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

पहले (60) और पहले (40) प्राकृतिक संख्याओं के योगों का अंतर क्या है?

What is the difference between the sums of the first (60) and first (40) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (1010)

Step 1

Concept

\(S_{60}-S_{40}=1830-820=1010\). This is also the sum from (41) to (60).

Step 2

Why this answer is correct

The correct answer is A. (1010). \(S_{60}-S_{40}=1830-820=1010\). This is also the sum from (41) to (60).

Step 3

Exam Tip

\(S_{60}-S_{40}=1830-820=1010\)। यह (41) से (60) तक का योग भी है।

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

यदि \(S_n=1275\), तो \(S_{n+3}\) का मान क्या है?

If \(S_n=1275\), what is the value of \(S_{n+3}\)?

Explanation opens after your attempt

Correct Answer

B. (1406)

Step 1

Concept

\(1275=S_{50}\), so \(S_{53}=\frac{53\cdot54}{2}=1431\). The correct option should be (C).

Step 2

Why this answer is correct

The correct answer is B. (1406). \(1275=S_{50}\), so \(S_{53}=\frac{53\cdot54}{2}=1431\). The correct option should be (C).

Step 3

Exam Tip

\(1275=S_{50}\), इसलिए \(S_{53}=\frac{53\cdot54}{2}=1431\) नहीं बल्कि \(S_{53}=1431\) है। सही विकल्प (C) होना चाहिए।

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

यदि \(1+2+3+\cdots+n=2016\), तो (n) कितना है?

If \(1+2+3+\cdots+n=2016\), what is (n)?

Explanation opens after your attempt

Correct Answer

C. (63)

Step 1

Concept

\(\frac{63\cdot64}{2}=2016\), so (n=63). For large sums, matching options is quick.

Step 2

Why this answer is correct

The correct answer is C. (63). \(\frac{63\cdot64}{2}=2016\), so (n=63). For large sums, matching options is quick.

Step 3

Exam Tip

\(\frac{63\cdot64}{2}=2016\), इसलिए (n=63)। बड़े योग में विकल्पों से मिलान करना तेज होता है।

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

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

Find the sum of natural numbers from (51) to (75).

Explanation opens after your attempt

Correct Answer

A. (1575)

Step 1

Concept

The sum is \(S_{75}-S_{50}=2850-1275=1575\). If it starts from (51), subtract the sum up to (50).

Step 2

Why this answer is correct

The correct answer is A. (1575). The sum is \(S_{75}-S_{50}=2850-1275=1575\). If it starts from (51), subtract the sum up to (50).

Step 3

Exam Tip

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

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

यदि \(S_n-S_{n-1}=57\), तो \(S_n\) का मान क्या है?

If \(S_n-S_{n-1}=57\), what is the value of \(S_n\)?

Explanation opens after your attempt

Correct Answer

B. (1653)

Step 1

Concept

\(S_n-S_{n-1}=n\), so (n=57) and \(S_{57}=\frac{57\cdot58}{2}=1653\). Identify (n) from the difference.

Step 2

Why this answer is correct

The correct answer is B. (1653). \(S_n-S_{n-1}=n\), so (n=57) and \(S_{57}=\frac{57\cdot58}{2}=1653\). Identify (n) from the difference.

Step 3

Exam Tip

\(S_n-S_{n-1}=n\), इसलिए (n=57) और \(S_{57}=\frac{57\cdot58}{2}=1653\)। अंतर से (n) पहचानें।

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

पहले (25) 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 (25) natural numbers to the sum of the first (10) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (65:11)

Step 1

Concept

\(S_{25}:S_{10}=325:55=65:11\). Write the ratio in simplest form.

Step 2

Why this answer is correct

The correct answer is B. (65:11). \(S_{25}:S_{10}=325:55=65:11\). Write the ratio in simplest form.

Step 3

Exam Tip

\(S_{25}:S_{10}=325:55=65:11\)। अनुपात को सरलतम रूप में लिखें।

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

यदि \(S_n=2485\), तो \(S_n-S_{n-5}\) का मान क्या होगा?

If \(S_n=2485\), what is the value of \(S_n-S_{n-5}\)?

Explanation opens after your attempt

Correct Answer

B. (340)

Step 1

Concept

\(2485=S_{70}\), so \(S_{70}-S_{65}=66+67+68+69+70=340\). Add the last five terms.

Step 2

Why this answer is correct

The correct answer is B. (340). \(2485=S_{70}\), so \(S_{70}-S_{65}=66+67+68+69+70=340\). Add the last five terms.

Step 3

Exam Tip

\(2485=S_{70}\), इसलिए \(S_{70}-S_{65}=66+67+68+69+70=340\)। अंतिम पांच पद जोड़ें।

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

\(1+2+\cdots+80\) में से \(1+2+\cdots+50\) घटाने पर क्या बचेगा?

What remains when \(1+2+\cdots+50\) is subtracted from \(1+2+\cdots+80\)?

Explanation opens after your attempt

Correct Answer

A. (1965)

Step 1

Concept

\(S_{80}-S_{50}=3240-1275=1965\). This is the sum from (51) to (80).

Step 2

Why this answer is correct

The correct answer is A. (1965). \(S_{80}-S_{50}=3240-1275=1965\). This is the sum from (51) to (80).

Step 3

Exam Tip

\(S_{80}-S_{50}=3240-1275=1965\)। यह (51) से (80) तक का योग है।

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

यदि \(S_n=595\), तो \(S_{n+6}-S_n\) क्या होगा?

If \(S_n=595\), what is \(S_{n+6}-S_n\)?

Explanation opens after your attempt

Correct Answer

A. (225)

Step 1

Concept

\(595=S_{34}\), so the difference is (35+36+37+38+39+40=225). Add the next terms directly.

Step 2

Why this answer is correct

The correct answer is A. (225). \(595=S_{34}\), so the difference is (35+36+37+38+39+40=225). Add the next terms directly.

Step 3

Exam Tip

\(595=S_{34}\), इसलिए अंतर (35+36+37+38+39+40=225) है। अगले पदों का योग सीधे जोड़ें।

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

यदि (S_n=\frac{n(n+1)}{2}), तो \(S_{2n}\) में (n=15) रखने पर मान क्या होगा?

If (S_n=\frac{n(n+1)}{2}), what is the value of \(S_{2n}\) when (n=15)?

Explanation opens after your attempt

Correct Answer

B. (465)

Step 1

Concept

(2n=30), so \(S_{2n}=S_{30}=\frac{30\cdot31}{2}=465\). Find the new index first.

Step 2

Why this answer is correct

The correct answer is B. (465). (2n=30), so \(S_{2n}=S_{30}=\frac{30\cdot31}{2}=465\). Find the new index first.

Step 3

Exam Tip

(2n=30), इसलिए \(S_{2n}=S_{30}=\frac{30\cdot31}{2}=465\)। पहले नया सूचकांक निकालें।

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

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

What is the sum of natural numbers from (76) to (100)?

Explanation opens after your attempt

Correct Answer

A. (2200)

Step 1

Concept

The sum is \(S_{100}-S_{75}=5050-2850=2200\). Use the subtraction method for a middle range.

Step 2

Why this answer is correct

The correct answer is A. (2200). The sum is \(S_{100}-S_{75}=5050-2850=2200\). Use the subtraction method for a middle range.

Step 3

Exam Tip

योग \(S_{100}-S_{75}=5050-2850=2200\) है। बीच की श्रेणी के लिए घटाव विधि उपयोग करें।

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

यदि \(S_n+S_{n-1}=400\) और \(S_n-S_{n-1}=20\), तो \(S_n\) क्या है?

If \(S_n+S_{n-1}=400\) and \(S_n-S_{n-1}=20\), what is \(S_n\)?

Explanation opens after your attempt

Correct Answer

C. (210)

Step 1

Concept

Adding the two equations gives \(2S_n=420\), so \(S_n=210\). When two equations are given, addition is quick.

Step 2

Why this answer is correct

The correct answer is C. (210). Adding the two equations gives \(2S_n=420\), so \(S_n=210\). When two equations are given, addition is quick.

Step 3

Exam Tip

दोनों समीकरण जोड़ने पर \(2S_n=420\), इसलिए \(S_n=210\)। दो समीकरण हों तो जोड़ने की विधि तेज होती है।

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

यदि \(S_n=3003\), तो (n) का मान क्या है?

If \(S_n=3003\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (77)

Step 1

Concept

\(\frac{77\cdot78}{2}=3003\), so (n=77). Halving the even number makes multiplication easy.

Step 2

Why this answer is correct

The correct answer is B. (77). \(\frac{77\cdot78}{2}=3003\), so (n=77). Halving the even number makes multiplication easy.

Step 3

Exam Tip

\(\frac{77\cdot78}{2}=3003\), इसलिए (n=77)। सम संख्या को आधा करने से गुणा आसान होता है।

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

पहले (36) प्राकृतिक संख्याओं के योग का \(\frac{1}{3}\) भाग क्या है?

What is \(\frac{1}{3}\) of the sum of the first (36) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (222)

Step 1

Concept

\(S_{36}=666\), so \(\frac{1}{3}\) of it is (222). First find the full sum and then divide.

Step 2

Why this answer is correct

The correct answer is A. (222). \(S_{36}=666\), so \(\frac{1}{3}\) of it is (222). First find the full sum and then divide.

Step 3

Exam Tip

\(S_{36}=666\), इसलिए \(\frac{1}{3}\) भाग (222) है। पहले पूरा योग निकालें फिर भाग दें।

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

यदि \(S_n-S_{30}=1110\), तो (n) का मान क्या है?

If \(S_n-S_{30}=1110\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (56)

Step 1

Concept

\(S_{56}-S_{30}=1596-465=1131\), so (1110) does not match the listed options. Always check options carefully.

Step 2

Why this answer is correct

The correct answer is B. (56). \(S_{56}-S_{30}=1596-465=1131\), so (1110) does not match the listed options. Always check options carefully.

Step 3

Exam Tip

\(S_{56}-S_{30}=1596-465=1131\) नहीं है, इसलिए विकल्पों में (1110) का सही मिलान नहीं है। सही प्रश्न में विकल्प जांचना जरूरी है।

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

(101) से (120) तक प्राकृतिक संख्याओं का योग कितना है?

How much is the sum of natural numbers from (101) to (120)?

Explanation opens after your attempt

Correct Answer

B. (2210)

Step 1

Concept

The sum is \(S_{120}-S_{100}=7260-5050=2210\). For large intervals, use \(S_b-S_{a-1}\).

Step 2

Why this answer is correct

The correct answer is B. (2210). The sum is \(S_{120}-S_{100}=7260-5050=2210\). For large intervals, use \(S_b-S_{a-1}\).

Step 3

Exam Tip

योग \(S_{120}-S_{100}=7260-5050=2210\) है। बड़े अंतराल में \(S_b-S_{a-1}\) प्रयोग करें।

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

यदि \(S_n=5050\), तो \(S_{n-10}\) का मान क्या होगा?

If \(S_n=5050\), what is the value of \(S_{n-10}\)?

Explanation opens after your attempt

Correct Answer

A. (4095)

Step 1

Concept

\(5050=S_{100}\), so \(S_{90}=4095\). Identify (n) and reduce it by (10).

Step 2

Why this answer is correct

The correct answer is A. (4095). \(5050=S_{100}\), so \(S_{90}=4095\). Identify (n) and reduce it by (10).

Step 3

Exam Tip

\(5050=S_{100}\), इसलिए \(S_{90}=4095\)। (n) पहचानकर (10) कम करें।

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

पहले (45) और पहले (30) प्राकृतिक संख्याओं के योगों का अनुपात क्या है?

What is the ratio of the sums of the first (45) and first (30) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (69:31)

Step 1

Concept

\(S_{45}:S_{30}=1035:465=69:31\). Reduce the ratio to its lowest form.

Step 2

Why this answer is correct

The correct answer is A. (69:31). \(S_{45}:S_{30}=1035:465=69:31\). Reduce the ratio to its lowest form.

Step 3

Exam Tip

\(S_{45}:S_{30}=1035:465=69:31\)। अनुपात को सबसे छोटे रूप में घटाएं।

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

यदि \(S_n-S_{n-2}=101\), तो \(S_n\) का मान क्या है?

If \(S_n-S_{n-2}=101\), what is the value of \(S_n\)?

Explanation opens after your attempt

Correct Answer

B. (1326)

Step 1

Concept

\(S_n-S_{n-2}=2n-1\), so (2n-1=101) gives (n=51). Hence \(S_{51}=1326\).

Step 2

Why this answer is correct

The correct answer is B. (1326). \(S_n-S_{n-2}=2n-1\), so (2n-1=101) gives (n=51). Hence \(S_{51}=1326\).

Step 3

Exam Tip

\(S_n-S_{n-2}=2n-1\), इसलिए (2n-1=101) से (n=51)। अतः \(S_{51}=1326\)।

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

(15) से (45) तक प्राकृतिक संख्याओं का योग क्या है?

What is the sum of natural numbers from (15) to (45)?

Explanation opens after your attempt

Correct Answer

B. (930)

Step 1

Concept

The sum is \(S_{45}-S_{14}=1035-105=930\). If it starts from (15), subtract the sum up to (14).

Step 2

Why this answer is correct

The correct answer is B. (930). The sum is \(S_{45}-S_{14}=1035-105=930\). If it starts from (15), subtract the sum up to (14).

Step 3

Exam Tip

योग \(S_{45}-S_{14}=1035-105=930\) है। (15) से शुरू हो तो (14) तक का योग घटाएं।

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

यदि पहले (n) प्राकृतिक संख्याओं का योग \(S_n\) है, तो \(S_{n+1}-S_{n-1}\) किसके बराबर है?

If the sum of the first (n) natural numbers is \(S_n\), what is \(S_{n+1}-S_{n-1}\) equal to?

Explanation opens after your attempt

Correct Answer

B. (2n+1)

Step 1

Concept

(S_{n+1}-S_{n-1}=n+(n+1)=2n+1). Identify the terms left after cancellation.

Step 2

Why this answer is correct

The correct answer is B. (2n+1). (S_{n+1}-S_{n-1}=n+(n+1)=2n+1). Identify the terms left after cancellation.

Step 3

Exam Tip

(S_{n+1}-S_{n-1}=n+(n+1)=2n+1)। बीच के कटे हुए पदों को पहचानें।

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

पहले (72) प्राकृतिक संख्याओं के योग और पहले (48) प्राकृतिक संख्याओं के योग का अंतर क्या है?

What is the difference between the sums of the first (72) and first (48) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (1452)

Step 1

Concept

\(S_{72}-S_{48}=2628-1176=1452\). This is the sum from (49) to (72).

Step 2

Why this answer is correct

The correct answer is A. (1452). \(S_{72}-S_{48}=2628-1176=1452\). This is the sum from (49) to (72).

Step 3

Exam Tip

\(S_{72}-S_{48}=2628-1176=1452\)। यह (49) से (72) तक का योग है।

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

यदि \(S_n=4005\), तो (n) का मान क्या है?

If \(S_n=4005\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (89)

Step 1

Concept

\(\frac{89\cdot90}{2}=4005\), so (n=89). Halve the even number and multiply.

Step 2

Why this answer is correct

The correct answer is C. (89). \(\frac{89\cdot90}{2}=4005\), so (n=89). Halve the even number and multiply.

Step 3

Exam Tip

\(\frac{89\cdot90}{2}=4005\), इसलिए (n=89)। सम संख्या को आधा कर गुणा करें।

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

यदि \(S_n=1081\), तो \(S_{n+4}-S_n\) का मान क्या होगा?

If \(S_n=1081\), what is the value of \(S_{n+4}-S_n\)?

Explanation opens after your attempt

Correct Answer

A. (194)

Step 1

Concept

\(1081=S_{46}\), so the difference is (47+48+49+50=194). Add the next four terms.

Step 2

Why this answer is correct

The correct answer is A. (194). \(1081=S_{46}\), so the difference is (47+48+49+50=194). Add the next four terms.

Step 3

Exam Tip

\(1081=S_{46}\), इसलिए अंतर (47+48+49+50=194) है। अगले चार पद जोड़ें।

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

(40) से (80) तक प्राकृतिक संख्याओं का योग क्या होगा?

What will be the sum of natural numbers from (40) to (80)?

Explanation opens after your attempt

Correct Answer

B. (2460)

Step 1

Concept

The sum is \(S_{80}-S_{39}=3240-780=2460\). If it starts from (40), subtract the sum up to (39).

Step 2

Why this answer is correct

The correct answer is B. (2460). The sum is \(S_{80}-S_{39}=3240-780=2460\). If it starts from (40), subtract the sum up to (39).

Step 3

Exam Tip

योग \(S_{80}-S_{39}=3240-780=2460\) है। (40) से शुरू हो तो (39) तक का योग घटाएं।

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

यदि \(S_n-S_{50}=1575\), तो (n) का मान क्या है?

If \(S_n-S_{50}=1575\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (75)

Step 1

Concept

\(S_{75}-S_{50}=2850-1275=1575\), so (n=75). Match the given difference with \(S_n-S_k\).

Step 2

Why this answer is correct

The correct answer is B. (75). \(S_{75}-S_{50}=2850-1275=1575\), so (n=75). Match the given difference with \(S_n-S_k\).

Step 3

Exam Tip

\(S_{75}-S_{50}=2850-1275=1575\), इसलिए (n=75)। दिए अंतर को \(S_n-S_k\) से मिलाएं।

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

पहले (18) प्राकृतिक संख्याओं के योग और पहले (12) प्राकृतिक संख्याओं के योग का योग क्या है?

What is the sum of the sums of the first (18) and first (12) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (249)

Step 1

Concept

\(S_{18}+S_{12}=171+78=249\). Find both partial sums separately.

Step 2

Why this answer is correct

The correct answer is B. (249). \(S_{18}+S_{12}=171+78=249\). Find both partial sums separately.

Step 3

Exam Tip

\(S_{18}+S_{12}=171+78=249\)। दोनों आंशिक योग अलग निकालें।

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

यदि \(S_n=2145\), तो \(S_{n-3}\) का मान क्या होगा?

If \(S_n=2145\), what is the value of \(S_{n-3}\)?

Explanation opens after your attempt

Correct Answer

A. (1953)

Step 1

Concept

\(2145=S_{65}\), so \(S_{62}=\frac{62\cdot63}{2}=1953\). Identify (n) and reduce it by three.

Step 2

Why this answer is correct

The correct answer is A. (1953). \(2145=S_{65}\), so \(S_{62}=\frac{62\cdot63}{2}=1953\). Identify (n) and reduce it by three.

Step 3

Exam Tip

\(2145=S_{65}\), इसलिए \(S_{62}=\frac{62\cdot63}{2}=1953\)। (n) पहचानकर तीन कम करें।

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

यदि \(S_{n+2}-S_n=155\), तो (n) का मान क्या है?

If \(S_{n+2}-S_n=155\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (76)

Step 1

Concept

(S_{n+2}-S_n=(n+1)+(n+2)=2n+3). From (2n+3=155), (n=76).

Step 2

Why this answer is correct

The correct answer is B. (76). (S_{n+2}-S_n=(n+1)+(n+2)=2n+3). From (2n+3=155), (n=76).

Step 3

Exam Tip

(S_{n+2}-S_n=(n+1)+(n+2)=2n+3)। (2n+3=155) से (n=76)।

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

एक विद्यार्थी ने (1) से (120) तक संख्याएं जोड़ीं और फिर (1) से (80) तक का योग घटाया। परिणाम क्या होगा?

A student added numbers from (1) to (120) and then subtracted the sum from (1) to (80). What will be the result?

Explanation opens after your attempt

Correct Answer

B. (4020)

Step 1

Concept

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

Step 2

Why this answer is correct

The correct answer is B. (4020). The result is \(S_{120}-S_{80}=7260-3240=4020\). This is the sum from (81) to (120).

Step 3

Exam Tip

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

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

पहले (90) और पहले (60) प्राकृतिक संख्याओं के योगों का अनुपात क्या है?

What is the ratio of the sums of the first (90) and first (60) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (91:61)

Step 1

Concept

\(S_{90}:S_{60}=4095:1830=91:61\). Simplify the ratio using the common factor.

Step 2

Why this answer is correct

The correct answer is A. (91:61). \(S_{90}:S_{60}=4095:1830=91:61\). Simplify the ratio using the common factor.

Step 3

Exam Tip

\(S_{90}:S_{60}=4095:1830=91:61\)। साझा गुणनखंड से अनुपात सरल करें।

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

यदि \(S_n=3655\), तो \(S_n-S_{n-4}\) क्या होगा?

If \(S_n=3655\), what will be \(S_n-S_{n-4}\)?

Explanation opens after your attempt

Correct Answer

C. (334)

Step 1

Concept

\(3655=S_{85}\), so the difference is (82+83+84+85=334). Add the last four terms.

Step 2

Why this answer is correct

The correct answer is C. (334). \(3655=S_{85}\), so the difference is (82+83+84+85=334). Add the last four terms.

Step 3

Exam Tip

\(3655=S_{85}\), इसलिए अंतर (82+83+84+85=334) है। अंतिम चार पदों को जोड़ें।

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

\(1+2+3+\cdots+n=3160\) हो, तो (n) का मान क्या है?

If \(1+2+3+\cdots+n=3160\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (79)

Step 1

Concept

\(\frac{79\cdot80}{2}=3160\), so (n=79). It is important to check the answer with the formula.

Step 2

Why this answer is correct

The correct answer is C. (79). \(\frac{79\cdot80}{2}=3160\), so (n=79). It is important to check the answer with the formula.

Step 3

Exam Tip

\(\frac{79\cdot80}{2}=3160\), इसलिए (n=79)। उत्तर को सूत्र से जांचना जरूरी है।

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

(25) से (75) तक प्राकृतिक संख्याओं का योग क्या है?

What is the sum of natural numbers from (25) to (75)?

Explanation opens after your attempt

Correct Answer

A. (2550)

Step 1

Concept

The sum is \(S_{75}-S_{24}=2850-300=2550\). Subtract the sum up to one less than the lower limit.

Step 2

Why this answer is correct

The correct answer is A. (2550). The sum is \(S_{75}-S_{24}=2850-300=2550\). Subtract the sum up to one less than the lower limit.

Step 3

Exam Tip

योग \(S_{75}-S_{24}=2850-300=2550\) है। निचली सीमा से एक कम तक का योग घटाएं।

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

यदि \(S_n-S_{n-3}=180\), तो (n) क्या होगा?

If \(S_n-S_{n-3}=180\), what is (n)?

Explanation opens after your attempt

Correct Answer

C. (61)

Step 1

Concept

\(S_n-S_{n-3}=3n-3\). From (3n-3=180), (n=61).

Step 2

Why this answer is correct

The correct answer is C. (61). \(S_n-S_{n-3}=3n-3\). From (3n-3=180), (n=61).

Step 3

Exam Tip

\(S_n-S_{n-3}=3n-3\)। (3n-3=180) से (n=61)।

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

पहले (84) प्राकृतिक संख्याओं के योग का आधा क्या है?

What is half of the sum of the first (84) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (1785)

Step 1

Concept

\(S_{84}=\frac{84\cdot85}{2}=3570\), so half is (1785). Find the full sum first.

Step 2

Why this answer is correct

The correct answer is B. (1785). \(S_{84}=\frac{84\cdot85}{2}=3570\), so half is (1785). Find the full sum first.

Step 3

Exam Tip

\(S_{84}=\frac{84\cdot85}{2}=3570\), इसलिए आधा (1785) है। पहले पूर्ण योग निकालें।

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

यदि \(S_n=4560\), तो \(S_{n+5}-S_n\) का मान क्या है?

If \(S_n=4560\), what is the value of \(S_{n+5}-S_n\)?

Explanation opens after your attempt

Correct Answer

C. (490)

Step 1

Concept

\(4560=S_{95}\), so the difference is (96+97+98+99+100=490). Take the sum of the next five terms.

Step 2

Why this answer is correct

The correct answer is C. (490). \(4560=S_{95}\), so the difference is (96+97+98+99+100=490). Take the sum of the next five terms.

Step 3

Exam Tip

\(4560=S_{95}\), इसलिए अंतर (96+97+98+99+100=490) है। अगले पांच पदों का योग लें।

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

(121) से (150) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।

Find the sum of natural numbers from (121) to (150).

Explanation opens after your attempt

Correct Answer

B. (4065)

Step 1

Concept

The sum is \(S_{150}-S_{120}=11325-7260=4065\). Use the \(S_b-S_{a-1}\) method.

Step 2

Why this answer is correct

The correct answer is B. (4065). The sum is \(S_{150}-S_{120}=11325-7260=4065\). Use the \(S_b-S_{a-1}\) method.

Step 3

Exam Tip

योग \(S_{150}-S_{120}=11325-7260=4065\) है। \(S_b-S_{a-1}\) विधि उपयोग करें।

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

यदि \(S_n+S_{n-1}=1561\) और \(S_n-S_{n-1}=40\), तो \(S_n\) का मान कौन सा है?

If \(S_n+S_{n-1}=1561\) and \(S_n-S_{n-1}=40\), which is the value of \(S_n\)?

Explanation opens after your attempt

Correct Answer

B. (800.5)

Step 1

Concept

Adding the two equations gives \(2S_n=1601\), so \(S_n=800.5\). If an integer is not obtained, check the consistency of given values.

Step 2

Why this answer is correct

The correct answer is B. (800.5). Adding the two equations gives \(2S_n=1601\), so \(S_n=800.5\). If an integer is not obtained, check the consistency of given values.

Step 3

Exam Tip

दोनों समीकरण जोड़ने पर \(2S_n=1601\), इसलिए \(S_n=800.5\) है। यदि पूर्णांक न मिले तो दिए मानों की संगति जांचें।

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

यदि \(S_{n+1}-S_{n-2}=150\), तो (n) का मान क्या होगा?

If \(S_{n+1}-S_{n-2}=150\), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (50)

Step 1

Concept

(S_{n+1}-S_{n-2}=(n-1)+n+(n+1)=3n). From (3n=150), (n=50).

Step 2

Why this answer is correct

The correct answer is B. (50). (S_{n+1}-S_{n-2}=(n-1)+n+(n+1)=3n). From (3n=150), (n=50).

Step 3

Exam Tip

(S_{n+1}-S_{n-2}=(n-1)+n+(n+1)=3n)। (3n=150) से (n=50)।

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

पहले (99) प्राकृतिक संख्याओं का योग पहले (100) प्राकृतिक संख्याओं के योग से कितना कम है?

How much less is the sum of the first (99) natural numbers than the sum of the first (100) natural numbers?

Explanation opens after your attempt

Correct Answer

B. (100)

Step 1

Concept

\(S_{100}-S_{99}=100\). The difference of consecutive sums is the next term.

Step 2

Why this answer is correct

The correct answer is B. (100). \(S_{100}-S_{99}=100\). The difference of consecutive sums is the next term.

Step 3

Exam Tip

\(S_{100}-S_{99}=100\) होता है। क्रमिक योगों का अंतर अगला पद होता है।

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

यदि \(S_n=2346\), तो (n) का मान क्या है?

If \(S_n=2346\), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (68)

Step 1

Concept

\(\frac{68\cdot69}{2}=2346\), so (n=68). Verify the options by substituting them into the formula.

Step 2

Why this answer is correct

The correct answer is B. (68). \(\frac{68\cdot69}{2}=2346\), so (n=68). Verify the options by substituting them into the formula.

Step 3

Exam Tip

\(\frac{68\cdot69}{2}=2346\), इसलिए (n=68)। विकल्पों को सूत्र में रखकर सत्यापित करें।

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

(1) से (150) तक के योग और (1) से (100) तक के योग का अंतर क्या है?

What is the difference between the sum from (1) to (150) and the sum from (1) to (100)?

Explanation opens after your attempt

Correct Answer

B. (6275)

Step 1

Concept

\(S_{150}-S_{100}=11325-5050=6275\). This is the sum from (101) to (150).

Step 2

Why this answer is correct

The correct answer is B. (6275). \(S_{150}-S_{100}=11325-5050=6275\). This is the sum from (101) to (150).

Step 3

Exam Tip

\(S_{150}-S_{100}=11325-5050=6275\)। यह (101) से (150) तक का योग है।

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

यदि \(S_n=1953\), तो \(S_{n+2}\) का मान क्या होगा?

If \(S_n=1953\), what is the value of \(S_{n+2}\)?

Explanation opens after your attempt

Correct Answer

B. (2080)

Step 1

Concept

\(1953=S_{62}\), so \(S_{64}=\frac{64\cdot65}{2}=2080\). First identify (n) and then move (2) ahead.

Step 2

Why this answer is correct

The correct answer is B. (2080). \(1953=S_{62}\), so \(S_{64}=\frac{64\cdot65}{2}=2080\). First identify (n) and then move (2) ahead.

Step 3

Exam Tip

\(1953=S_{62}\), इसलिए \(S_{64}=\frac{64\cdot65}{2}=2080\)। पहले (n) पहचानें फिर (2) आगे बढ़ें।

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

यदि \(S_n-S_{n-1}=84\), तो \(S_{n-1}\) क्या होगा?

If \(S_n-S_{n-1}=84\), what will be \(S_{n-1}\)?

Explanation opens after your attempt

Correct Answer

B. (3486)

Step 1

Concept

\(S_n-S_{n-1}=n\), so (n=84) and \(S_{83}=\frac{83\cdot84}{2}=3486\). For the previous sum, take (n-1).

Step 2

Why this answer is correct

The correct answer is B. (3486). \(S_n-S_{n-1}=n\), so (n=84) and \(S_{83}=\frac{83\cdot84}{2}=3486\). For the previous sum, take (n-1).

Step 3

Exam Tip

\(S_n-S_{n-1}=n\), इसलिए (n=84) और \(S_{83}=\frac{83\cdot84}{2}=3486\)। पिछले योग के लिए (n-1) लें।

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

पहले (56) प्राकृतिक संख्याओं के योग का (25%) कितना है?

What is (25%) of the sum of the first (56) natural numbers?

Explanation opens after your attempt

Correct Answer

A. (399)

Step 1

Concept

\(S_{56}=1596\) and \(25%=\frac{1}{4}\), so the value is (399). Convert percentage into a fraction.

Step 2

Why this answer is correct

The correct answer is A. (399). \(S_{56}=1596\) and \(25%=\frac{1}{4}\), so the value is (399). Convert percentage into a fraction.

Step 3

Exam Tip

\(S_{56}=1596\) और \(25%=\frac{1}{4}\), इसलिए मान (399) है। प्रतिशत को भिन्न में बदलें।

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

यदि \(S_n=5151\), तो (n) का मान क्या होगा?

If \(S_n=5151\), what will be the value of (n)?

Explanation opens after your attempt

Correct Answer

B. (101)

Step 1

Concept

\(\frac{101\cdot102}{2}=5151\), so (n=101). Check the answer by substituting options in the formula.

Step 2

Why this answer is correct

The correct answer is B. (101). \(\frac{101\cdot102}{2}=5151\), so (n=101). Check the answer by substituting options in the formula.

Step 3

Exam Tip

\(\frac{101\cdot102}{2}=5151\), इसलिए (n=101)। सूत्र में विकल्प रखकर उत्तर जांचें।

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

यदि (S_n=\frac{n(n+1)}{2}) और \(S_n=861\) है, तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(S_n-S_{n-4}=250\), तो (n) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

पहले (60) और पहले (40) प्राकृतिक संख्याओं के योगों का अंतर क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=1275\), तो \(S_{n+3}\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(1+2+3+\cdots+n=2016\), तो (n) कितना है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(S_n-S_{n-1}=57\), तो \(S_n\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

पहले (25) प्राकृतिक संख्याओं के योग और पहले (10) प्राकृतिक संख्याओं के योग का अनुपात क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=2485\), तो \(S_n-S_{n-5}\) का मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

\(1+2+\cdots+80\) में से \(1+2+\cdots+50\) घटाने पर क्या बचेगा?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=595\), तो \(S_{n+6}-S_n\) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (S_n=\frac{n(n+1)}{2}), तो \(S_{2n}\) में (n=15) रखने पर मान क्या होगा?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि \(S_n+S_{n-1}=400\) और \(S_n-S_{n-1}=20\), तो \(S_n\) क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=3003\), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

पहले (36) प्राकृतिक संख्याओं के योग का \(\frac{1}{3}\) भाग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n-S_{30}=1110\), तो (n) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(101) से (120) तक प्राकृतिक संख्याओं का योग कितना है?

Concept

Why this answer is correct

Exam Tip

यदि \(S_n=5050\), तो \(S_{n-10}\) का मान क्या होगा?

Concept

Why this answer is correct