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)?
#sequences
#progressions
#natural-numbers
#find-n
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A (110)
B (112)
C (115)
D (116)
Explanation opens after your attempt
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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(41) से (95) तक प्राकृतिक संख्याओं का योग क्या है?
What is the sum of natural numbers from (41) to (95)?
#sequences
#progressions
#natural-numbers
#range-sum
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A (3740)
B (3720)
C (3760)
D (3800)
Explanation opens after your attempt
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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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)?
#sequences
#progressions
#natural-numbers
#difference-equation
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A (96)
B (98)
C (100)
D (102)
Explanation opens after your attempt
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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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)?
#sequences
#progressions
#natural-numbers
#algebra
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A (70)
B (72)
C (74)
D (76)
Explanation opens after your attempt
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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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?
#sequences
#progressions
#natural-numbers
#difference
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A (3505)
B (3585)
C (3605)
D (3625)
Explanation opens after your attempt
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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यदि \(S_n=5050\), तो \(S_{n+4}-S_n\) का मान क्या है?
If \(S_n=5050\), what is the value of \(S_{n+4}-S_n\)?
#sequences
#progressions
#natural-numbers
#next-terms
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A (406)
B (410)
C (414)
D (418)
Explanation opens after your attempt
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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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?
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#progressions
#natural-numbers
#ratio
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A (65:33)
B (64:32)
C (33:65)
D (2:1)
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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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 \(S_n\)?
#sequences
#progressions
#natural-numbers
#equation
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A (2138.5)
B (2073.5)
C (2112)
D (2145)
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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(126) से (175) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।
Find the sum of natural numbers from (126) to (175).
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#progressions
#natural-numbers
#range-sum
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A (7525)
B (7475)
C (7575)
D (7625)
Explanation opens after your attempt
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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यदि \(S_n=7875\), तो \(S_{n-7}\) का मान क्या होगा?
If \(S_n=7875\), what is the value of \(S_{n-7}\)?
#sequences
#progressions
#natural-numbers
#previous-sum
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A (7260)
B (7381)
C (7503)
D (7626)
Explanation opens after your attempt
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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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)?
#sequences
#progressions
#natural-numbers
#difference-equation
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A (99)
B (100)
C (101)
D (102)
Explanation opens after your attempt
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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पहले (150) प्राकृतिक संख्याओं के योग का (20%) कितना है?
What is (20%) of the sum of the first (150) natural numbers?
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#natural-numbers
#percentage
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A (2225)
B (2255)
C (2265)
D (2285)
Explanation opens after your attempt
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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यदि \(S_n=12246\), तो (n) का मान क्या है?
If \(S_n=12246\), what is the value of (n)?
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#progressions
#natural-numbers
#find-n
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A (154)
B (155)
C (156)
D (157)
Explanation opens after your attempt
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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यदि \(S_n-S_{70}=5250\), तो (n) का मान क्या है?
If \(S_n-S_{70}=5250\), what is the value of (n)?
#sequences
#progressions
#natural-numbers
#range-equation
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A (120)
B (125)
C (130)
D (135)
Explanation opens after your attempt
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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(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)?
#sequences
#progressions
#natural-numbers
#difference
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A (8725)
B (8775)
C (8825)
D (8875)
Explanation opens after your attempt
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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यदि \(S_n=20100\), तो \(S_n-S_{n-8}\) का मान क्या होगा?
If \(S_n=20100\), what will be the value of \(S_n-S_{n-8}\)?
#sequences
#progressions
#natural-numbers
#last-terms
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A (1572)
B (1576)
C (1580)
D (1584)
Explanation opens after your attempt
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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यदि \(S_{3n}=1770\), तो (n) का मान क्या है?
If \(S_{3n}=1770\), what is the value of (n)?
#sequences
#progressions
#natural-numbers
#index
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A (18)
B (19)
C (20)
D (21)
Explanation opens after your attempt
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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(50) से (150) तक प्राकृतिक संख्याओं का योग क्या है?
What is the sum of natural numbers from (50) to (150)?
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#progressions
#natural-numbers
#range-sum
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A (10100)
B (10050)
C (10000)
D (9950)
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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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 \(S_n\)?
#sequences
#progressions
#natural-numbers
#difference-equation
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A (6670)
B (6786)
C (6903)
D (7021)
Explanation opens after your attempt
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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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?
#sequences
#progressions
#natural-numbers
#ratio
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A (388:219)
B (194:109)
C (129:73)
D (96:72)
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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यदि \(S_n=15400\), तो \(S_{n-10}\) का मान क्या होगा?
If \(S_n=15400\), what is the value of \(S_{n-10}\)?
#sequences
#progressions
#natural-numbers
#previous-sum
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A (13366)
B (13455)
C (13545)
D (13636)
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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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?
#sequences
#progressions
#natural-numbers
#equation
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A (4999.5)
B (5099.5)
C (5199.5)
D (5299.5)
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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(201) से (250) तक प्राकृतिक संख्याओं का योग कितना है?
How much is the sum of natural numbers from (201) to (250)?
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#progressions
#natural-numbers
#range-sum
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A (11275)
B (11375)
C (11475)
D (11575)
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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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)?
#sequences
#progressions
#natural-numbers
#algebra
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A (117)
B (118)
C (119)
D (120)
Explanation opens after your attempt
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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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?
#sequences
#progressions
#natural-numbers
#difference
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A (12195)
B (12295)
C (12395)
D (12495)
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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यदि \(S_n=8911\), तो (n) का मान क्या है?
If \(S_n=8911\), what is the value of (n)?
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#progressions
#natural-numbers
#find-n
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A (132)
B (133)
C (134)
D (135)
Explanation opens after your attempt
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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यदि \(S_n=7140\), तो \(S_{n+5}-S_n\) का मान क्या है?
If \(S_n=7140\), what is the value of \(S_{n+5}-S_n\)?
#sequences
#progressions
#natural-numbers
#next-terms
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A (595)
B (600)
C (605)
D (610)
Explanation opens after your attempt
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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(81) से (144) तक प्राकृतिक संख्याओं का योग क्या होगा?
What will be the sum of natural numbers from (81) to (144)?
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#range-sum
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A (7200)
B (7240)
C (7280)
D (7320)
Explanation opens after your attempt
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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यदि \(S_n-S_{100}=15150\), तो (n) का मान क्या है?
If \(S_n-S_{100}=15150\), what is the value of (n)?
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A (180)
B (190)
C (200)
D (210)
Explanation opens after your attempt
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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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?
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#progressions
#natural-numbers
#combined-sum
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A (2054)
B (2059)
C (2064)
D (2069)
Explanation opens after your attempt
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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यदि \(S_n=1225\), तो \(S_{2n}\) का मान क्या होगा?
If \(S_n=1225\), what will be the value of \(S_{2n}\)?
#sequences
#progressions
#natural-numbers
#index
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A (4753)
B (4851)
C (4950)
D (5050)
Explanation opens after your attempt
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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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)?
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#natural-numbers
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A (120)
B (121)
C (122)
D (123)
Explanation opens after your attempt
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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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?
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A (7425)
B (7475)
C (7525)
D (7575)
Explanation opens after your attempt
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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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?
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A (3:2)
B (121:81)
C (120:80)
D (81:121)
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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यदि \(S_n=11325\), तो \(S_n-S_{n-6}\) क्या होगा?
If \(S_n=11325\), what will be \(S_n-S_{n-6}\)?
#sequences
#progressions
#natural-numbers
#last-terms
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A (885)
B (895)
C (905)
D (915)
Explanation opens after your attempt
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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\(1+2+3+\cdots+n=8256\) हो, तो (n) का मान क्या है?
If \(1+2+3+\cdots+n=8256\), what is the value of (n)?
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#progressions
#natural-numbers
#find-n
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A (127)
B (128)
C (129)
D (130)
Explanation opens after your attempt
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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(63) से (150) तक प्राकृतिक संख्याओं का योग क्या है?
What is the sum of natural numbers from (63) to (150)?
#sequences
#progressions
#natural-numbers
#range-sum
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A (9369)
B (9379)
C (9389)
D (9399)
Explanation opens after your attempt
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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यदि \(S_n-S_{n-3}=420\), तो (n) क्या होगा?
If \(S_n-S_{n-3}=420\), what is (n)?
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#progressions
#natural-numbers
#difference-equation
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A (139)
B (140)
C (141)
D (142)
Explanation opens after your attempt
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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पहले (144) प्राकृतिक संख्याओं के योग का आधा क्या है?
What is half of the sum of the first (144) natural numbers?
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#half-sum
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A (5200)
B (5220)
C (5240)
D (5260)
Explanation opens after your attempt
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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यदि \(S_n=6903\), तो \(S_{n+5}-S_n\) का मान क्या है?
If \(S_n=6903\), what is the value of \(S_{n+5}-S_n\)?
#sequences
#progressions
#natural-numbers
#next-terms
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A (590)
B (600)
C (610)
D (620)
Explanation opens after your attempt
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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(151) से (225) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।
Find the sum of natural numbers from (151) to (225).
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A (14050)
B (14100)
C (14150)
D (14200)
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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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 \(S_n\)?
#sequences
#progressions
#natural-numbers
#equation
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A (630)
B (648)
C (666)
D (684)
Explanation opens after your attempt
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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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)?
#sequences
#progressions
#natural-numbers
#algebra
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A (108)
B (109)
C (110)
D (111)
Explanation opens after your attempt
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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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?
#sequences
#progressions
#natural-numbers
#concept
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A (179)
B (180)
C (181)
D (16290)
Explanation opens after your attempt
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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(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)?
#sequences
#progressions
#natural-numbers
#difference
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A (11175)
B (11275)
C (11375)
D (11475)
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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यदि \(S_n=7626\), तो \(S_{n+2}\) का मान क्या होगा?
If \(S_n=7626\), what is the value of \(S_{n+2}\)?
#sequences
#progressions
#natural-numbers
#next-sum
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A (7875)
B (8001)
C (8128)
D (8256)
Explanation opens after your attempt
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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यदि \(S_n-S_{n-1}=150\), तो \(S_{n-1}\) क्या होगा?
If \(S_n-S_{n-1}=150\), what will be \(S_{n-1}\)?
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A (11175)
B (11275)
C (11325)
D (11475)
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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पहले (125) प्राकृतिक संख्याओं के योग का (40%) कितना है?
What is (40%) of the sum of the first (125) natural numbers?
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A (3150)
B (3250)
C (3350)
D (3450)
Explanation opens after your attempt
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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यदि \(S_n=25425\), तो (n) का मान क्या होगा?
If \(S_n=25425\), what will be the value of (n)?
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A (223)
B (224)
C (225)
D (226)
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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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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)?
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A (143)
B (144)
C (145)
D (146)
Explanation opens after your attempt
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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