यदि (S_n=\frac{n(n+1)}{2}) और \(S_n=7503\) है, तो (n) का मान क्या है?
If (S_n=\frac{n(n+1)}{2}) and \(S_n=7503\), what is the value of (n)?
#sequences
#progressions
#natural-numbers
#find-n
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A (120)
B (121)
C (122)
D (123)
Explanation opens after your attempt
Step 1
Concept
\(\frac{122\cdot123}{2}=7503\), so (n=122). For a large sum, check options in the formula.
Step 2
Why this answer is correct
The correct answer is C. (122). \(\frac{122\cdot123}{2}=7503\), so (n=122). For a large sum, check options in the formula.
Step 3
Exam Tip
\(\frac{122\cdot123}{2}=7503\), इसलिए (n=122)। बड़े योग में विकल्पों को सूत्र में जांचें।
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(56) से (120) तक प्राकृतिक संख्याओं का योग क्या है?
What is the sum of natural numbers from (56) to (120)?
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#progressions
#natural-numbers
#range-sum
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A (5620)
B (5720)
C (5820)
D (5920)
Explanation opens after your attempt
Step 1
Concept
The sum is \(S_{120}-S_{55}=7260-1540=5720\). Subtract the sum up to one less than the lower limit.
Step 2
Why this answer is correct
The correct answer is B. (5720). The sum is \(S_{120}-S_{55}=7260-1540=5720\). Subtract the sum up to one less than the lower limit.
Step 3
Exam Tip
योग \(S_{120}-S_{55}=7260-1540=5720\) है। निचली सीमा से एक कम तक का योग घटाएं।
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यदि \(S_n-S_{n-6}=813\), तो (n) का मान क्या होगा?
If \(S_n-S_{n-6}=813\), what will be the value of (n)?
#sequences
#progressions
#natural-numbers
#difference-equation
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A (135)
B (136)
C (137)
D (138)
Explanation opens after your attempt
Step 1
Concept
\(S_n-S_{n-6}=6n-15\). From (6n-15=813), (n=138).
Step 2
Why this answer is correct
The correct answer is D. (138). \(S_n-S_{n-6}=6n-15\). From (6n-15=813), (n=138).
Step 3
Exam Tip
\(S_n-S_{n-6}=6n-15\) होता है। (6n-15=813) से (n=138)।
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यदि \(S_{n+4}-S_{n-1}=485\), तो (n) का मान क्या है?
If \(S_{n+4}-S_{n-1}=485\), what is the value of (n)?
#sequences
#progressions
#natural-numbers
#algebra
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A (95)
B (96)
C (97)
D (98)
Explanation opens after your attempt
Step 1
Concept
This difference is (n+(n+1)+(n+2)+(n+3)+(n+4)=5n+10). From (5n+10=485), (n=95).
Step 2
Why this answer is correct
The correct answer is A. (95). This difference is (n+(n+1)+(n+2)+(n+3)+(n+4)=5n+10). From (5n+10=485), (n=95).
Step 3
Exam Tip
यह अंतर (n+(n+1)+(n+2)+(n+3)+(n+4)=5n+10) है। (5n+10=485) से (n=95)।
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यदि \(S_n=9870\), तो (n) का मान क्या है?
If \(S_n=9870\), what is the value of (n)?
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#natural-numbers
#find-n
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A (138)
B (140)
C (142)
D (144)
Explanation opens after your attempt
Step 1
Concept
\(\frac{140\cdot141}{2}=9870\), so (n=140). Halve the even number and multiply.
Step 2
Why this answer is correct
The correct answer is B. (140). \(\frac{140\cdot141}{2}=9870\), so (n=140). Halve the even number and multiply.
Step 3
Exam Tip
\(\frac{140\cdot141}{2}=9870\), इसलिए (n=140)। सम संख्या को आधा करके गुणा करें।
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यदि \(S_n=2701\), तो \(S_{n+7}-S_n\) का मान क्या होगा?
If \(S_n=2701\), what will be the value of \(S_{n+7}-S_n\)?
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#progressions
#natural-numbers
#next-terms
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A (525)
B (530)
C (535)
D (539)
Explanation opens after your attempt
Step 1
Concept
\(2701=S_{73}\), so the difference is \(74+75+\cdots+80=539\). Take the sum of the next seven terms.
Step 2
Why this answer is correct
The correct answer is D. (539). \(2701=S_{73}\), so the difference is \(74+75+\cdots+80=539\). Take the sum of the next seven terms.
Step 3
Exam Tip
\(2701=S_{73}\), इसलिए अंतर \(74+75+\cdots+80=539\) है। अगले सात पदों का योग लें।
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पहले (84) और पहले (56) प्राकृतिक संख्याओं के योगों का अनुपात क्या है?
What is the ratio of the sums of the first (84) and first (56) natural numbers?
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#natural-numbers
#ratio
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A (85:38)
B (84:56)
C (38:85)
D (3:2)
Explanation opens after your attempt
Correct Answer
A. (85:38)
Step 1
Concept
\(S_{84}:S_{56}=3570:1596=85:38\). Write the ratio in simplest form.
Step 2
Why this answer is correct
The correct answer is A. (85:38). \(S_{84}:S_{56}=3570:1596=85:38\). Write the ratio in simplest form.
Step 3
Exam Tip
\(S_{84}:S_{56}=3570:1596=85:38\)। अनुपात को सरलतम रूप में लिखें।
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यदि \(S_n+S_{n-1}=5625\) और \(S_n-S_{n-1}=75\), तो \(S_n\) का मान क्या है?
If \(S_n+S_{n-1}=5625\) and \(S_n-S_{n-1}=75\), what is the value of \(S_n\)?
#sequences
#progressions
#natural-numbers
#equation
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A (2775)
B (2850)
C (2925)
D (3000)
Explanation opens after your attempt
Step 1
Concept
Adding the two equations gives \(2S_n=5700\), so \(S_n=2850\). Adding equations is a quick method.
Step 2
Why this answer is correct
The correct answer is B. (2850). Adding the two equations gives \(2S_n=5700\), so \(S_n=2850\). Adding equations is a quick method.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर \(2S_n=5700\), इसलिए \(S_n=2850\)। समीकरणों को जोड़ना तेज तरीका है।
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(101) से (160) तक प्राकृतिक संख्याओं का योग कितना है?
How much is the sum of natural numbers from (101) to (160)?
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#progressions
#natural-numbers
#range-sum
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A (7730)
B (7780)
C (7830)
D (7880)
Explanation opens after your attempt
Step 1
Concept
The sum is \(S_{160}-S_{100}=12880-5050=7830\). Use the subtraction method for large intervals.
Step 2
Why this answer is correct
The correct answer is C. (7830). The sum is \(S_{160}-S_{100}=12880-5050=7830\). Use the subtraction method for large intervals.
Step 3
Exam Tip
योग \(S_{160}-S_{100}=12880-5050=7830\) है। बड़े अंतराल में घटाव विधि उपयोग करें।
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यदि \(S_n=16290\), तो \(S_{n-8}\) का मान क्या है?
If \(S_n=16290\), what is the value of \(S_{n-8}\)?
#sequences
#progressions
#natural-numbers
#previous-sum
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A (14628)
B (14753)
C (14800)
D (14878)
Explanation opens after your attempt
Correct Answer
D. (14878)
Step 1
Concept
\(16290=S_{180}\), so \(S_{172}=\frac{172\cdot173}{2}=14878\). Identify (n) first and then reduce it by (8).
Step 2
Why this answer is correct
The correct answer is D. (14878). \(16290=S_{180}\), so \(S_{172}=\frac{172\cdot173}{2}=14878\). Identify (n) first and then reduce it by (8).
Step 3
Exam Tip
\(16290=S_{180}\), इसलिए \(S_{172}=\frac{172\cdot173}{2}=14878\)। पहले (n) पहचानें फिर (8) कम करें।
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यदि \(S_{n+2}-S_{n-3}=625\), तो (n) का मान क्या है?
If \(S_{n+2}-S_{n-3}=625\), what is the value of (n)?
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#progressions
#natural-numbers
#difference-equation
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A (125)
B (126)
C (127)
D (128)
Explanation opens after your attempt
Step 1
Concept
This difference is ((n-2)+(n-1)+n+(n+1)+(n+2)=5n). So (5n=625) gives (n=125).
Step 2
Why this answer is correct
The correct answer is A. (125). This difference is ((n-2)+(n-1)+n+(n+1)+(n+2)=5n). So (5n=625) gives (n=125).
Step 3
Exam Tip
यह अंतर ((n-2)+(n-1)+n+(n+1)+(n+2)=5n) है। इसलिए (5n=625) से (n=125)।
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पहले (200) प्राकृतिक संख्याओं के योग का (30%) कितना है?
What is (30%) of the sum of the first (200) natural numbers?
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#percentage
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A (6000)
B (6015)
C (6030)
D (6045)
Explanation opens after your attempt
Step 1
Concept
\(S_{200}=20100\) and \(30%=\frac{3}{10}\), so the value is (6030). Convert the percentage into a fraction.
Step 2
Why this answer is correct
The correct answer is C. (6030). \(S_{200}=20100\) and \(30%=\frac{3}{10}\), so the value is (6030). Convert the percentage into a fraction.
Step 3
Exam Tip
\(S_{200}=20100\) और \(30%=\frac{3}{10}\), इसलिए मान (6030) है। प्रतिशत को भिन्न में बदलें।
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यदि \(S_n=11175\), तो (n) का मान क्या है?
If \(S_n=11175\), what is the value of (n)?
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#progressions
#natural-numbers
#find-n
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A (149)
B (150)
C (151)
D (152)
Explanation opens after your attempt
Step 1
Concept
\(\frac{149\cdot150}{2}=11175\), so (n=149). Check the options in the formula.
Step 2
Why this answer is correct
The correct answer is A. (149). \(\frac{149\cdot150}{2}=11175\), so (n=149). Check the options in the formula.
Step 3
Exam Tip
\(\frac{149\cdot150}{2}=11175\), इसलिए (n=149)। विकल्पों को सूत्र में रखकर जांचें।
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यदि \(S_n-S_{90}=5775\), तो (n) का मान क्या होगा?
If \(S_n-S_{90}=5775\), what will be the value of (n)?
#sequences
#progressions
#natural-numbers
#range-equation
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A (125)
B (130)
C (135)
D (140)
Explanation opens after your attempt
Step 1
Concept
\(S_{140}-S_{90}=9870-4095=5775\), so (n=140). Match the given difference with \(S_n-S_k\).
Step 2
Why this answer is correct
The correct answer is D. (140). \(S_{140}-S_{90}=9870-4095=5775\), so (n=140). Match the given difference with \(S_n-S_k\).
Step 3
Exam Tip
\(S_{140}-S_{90}=9870-4095=5775\), इसलिए (n=140)। दिए अंतर को \(S_n-S_k\) से मिलाएं।
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(151) से (210) तक प्राकृतिक संख्याओं का योग क्या है?
What is the sum of natural numbers from (151) to (210)?
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#progressions
#natural-numbers
#range-sum
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A (10730)
B (10830)
C (10930)
D (11030)
Explanation opens after your attempt
Correct Answer
B. (10830)
Step 1
Concept
The sum is \(S_{210}-S_{150}=22155-11325=10830\). Use the \(S_b-S_{a-1}\) method.
Step 2
Why this answer is correct
The correct answer is B. (10830). The sum is \(S_{210}-S_{150}=22155-11325=10830\). Use the \(S_b-S_{a-1}\) method.
Step 3
Exam Tip
योग \(S_{210}-S_{150}=22155-11325=10830\) है। \(S_b-S_{a-1}\) विधि का उपयोग करें।
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यदि \(S_{2n}=4095\), तो (n) का मान क्या है?
If \(S_{2n}=4095\), what is the value of (n)?
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#progressions
#natural-numbers
#index
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A (43)
B (44)
C (45)
D (46)
Explanation opens after your attempt
Step 1
Concept
\(4095=S_{90}\), so (2n=90) and (n=45). Identify the index first.
Step 2
Why this answer is correct
The correct answer is C. (45). \(4095=S_{90}\), so (2n=90) and (n=45). Identify the index first.
Step 3
Exam Tip
\(4095=S_{90}\), इसलिए (2n=90) और (n=45)। पहले सूचकांक पहचानें।
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यदि \(S_n-S_{n-4}=454\), तो (n) का मान क्या है?
If \(S_n-S_{n-4}=454\), what is the value of (n)?
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#progressions
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#difference-equation
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A (112)
B (113)
C (114)
D (115)
Explanation opens after your attempt
Step 1
Concept
\(S_n-S_{n-4}=4n-6\). From (4n-6=454), (n=115).
Step 2
Why this answer is correct
The correct answer is D. (115). \(S_n-S_{n-4}=4n-6\). From (4n-6=454), (n=115).
Step 3
Exam Tip
\(S_n-S_{n-4}=4n-6\) होता है। (4n-6=454) से (n=115)।
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पहले (225) और पहले (175) प्राकृतिक संख्याओं के योगों का अंतर क्या है?
What is the difference between the sums of the first (225) and first (175) natural numbers?
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#progressions
#natural-numbers
#difference
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A (10025)
B (10125)
C (10225)
D (10325)
Explanation opens after your attempt
Correct Answer
A. (10025)
Step 1
Concept
\(S_{225}-S_{175}=25425-15400=10025\). This is the sum from (176) to (225).
Step 2
Why this answer is correct
The correct answer is A. (10025). \(S_{225}-S_{175}=25425-15400=10025\). This is the sum from (176) to (225).
Step 3
Exam Tip
\(S_{225}-S_{175}=25425-15400=10025\)। यह (176) से (225) तक का योग है।
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पहले (150) और पहले (100) प्राकृतिक संख्याओं के योगों का अनुपात क्या है?
What is the ratio of the sums of the first (150) and first (100) natural numbers?
#sequences
#progressions
#natural-numbers
#ratio
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A (150:100)
B (453:202)
C (202:453)
D (3:2)
Explanation opens after your attempt
Correct Answer
B. (453:202)
Step 1
Concept
\(S_{150}:S_{100}=11325:5050=453:202\). Simplify the ratio fully.
Step 2
Why this answer is correct
The correct answer is B. (453:202). \(S_{150}:S_{100}=11325:5050=453:202\). Simplify the ratio fully.
Step 3
Exam Tip
\(S_{150}:S_{100}=11325:5050=453:202\)। अनुपात को पूरा सरल करें।
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यदि \(S_n=15400\), तो \(S_n-S_{n-10}\) का मान क्या होगा?
If \(S_n=15400\), what will be the value of \(S_n-S_{n-10}\)?
#sequences
#progressions
#natural-numbers
#last-terms
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A (1685)
B (1695)
C (1705)
D (1715)
Explanation opens after your attempt
Step 1
Concept
\(15400=S_{175}\), so the sum of the last ten terms is \(166+167+\cdots+175=1705\). Add the last terms directly.
Step 2
Why this answer is correct
The correct answer is C. (1705). \(15400=S_{175}\), so the sum of the last ten terms is \(166+167+\cdots+175=1705\). Add the last terms directly.
Step 3
Exam Tip
\(15400=S_{175}\), इसलिए अंतिम दस पदों का योग \(166+167+\cdots+175=1705\) है। अंतिम पदों को सीधे जोड़ें।
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यदि \(S_{n+1}-S_{n-4}=695\), तो (n) का मान क्या होगा?
If \(S_{n+1}-S_{n-4}=695\), what will be the value of (n)?
#sequences
#progressions
#natural-numbers
#algebra
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A (137)
B (138)
C (139)
D (140)
Explanation opens after your attempt
Step 1
Concept
This difference is ((n-3)+(n-2)+(n-1)+n+(n+1)=5n-5). From (5n-5=695), (n=140).
Step 2
Why this answer is correct
The correct answer is D. (140). This difference is ((n-3)+(n-2)+(n-1)+n+(n+1)=5n-5). From (5n-5=695), (n=140).
Step 3
Exam Tip
यह अंतर ((n-3)+(n-2)+(n-1)+n+(n+1)=5n-5) है। (5n-5=695) से (n=140)।
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(75) से (125) तक प्राकृतिक संख्याओं का योग क्या है?
What is the sum of natural numbers from (75) to (125)?
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#progressions
#natural-numbers
#range-sum
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A (5100)
B (5150)
C (5200)
D (5250)
Explanation opens after your attempt
Step 1
Concept
The sum is \(S_{125}-S_{74}=7875-2775=5100\). Subtract the sum before the lower limit.
Step 2
Why this answer is correct
The correct answer is A. (5100). The sum is \(S_{125}-S_{74}=7875-2775=5100\). Subtract the sum before the lower limit.
Step 3
Exam Tip
योग \(S_{125}-S_{74}=7875-2775=5100\) है। निचली सीमा से पहले का योग घटाएं।
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\(S_{120}-S_{80}+S_{40}\) का मान क्या है?
What is the value of \(S_{120}-S_{80}+S_{40}\)?
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#progressions
#natural-numbers
#combined-sum
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A (4740)
B (4840)
C (4940)
D (5040)
Explanation opens after your attempt
Step 1
Concept
\(S_{120}-S_{80}+S_{40}=7260-3240+820=4840\). Write each partial sum separately.
Step 2
Why this answer is correct
The correct answer is B. (4840). \(S_{120}-S_{80}+S_{40}=7260-3240+820=4840\). Write each partial sum separately.
Step 3
Exam Tip
\(S_{120}-S_{80}+S_{40}=7260-3240+820=4840\)। हर आंशिक योग अलग लिखें।
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यदि \(S_n=10440\), तो (n) का मान क्या है?
If \(S_n=10440\), what is the value of (n)?
#sequences
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#natural-numbers
#find-n
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A (141)
B (142)
C (144)
D (145)
Explanation opens after your attempt
Step 1
Concept
\(\frac{144\cdot145}{2}=10440\), so (n=144). Check the answer by substituting options in the formula.
Step 2
Why this answer is correct
The correct answer is C. (144). \(\frac{144\cdot145}{2}=10440\), so (n=144). Check the answer by substituting options in the formula.
Step 3
Exam Tip
\(\frac{144\cdot145}{2}=10440\), इसलिए (n=144)। सूत्र में विकल्प रखकर उत्तर जांचें।
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यदि \(S_n-S_{n-2}=257\), तो \(S_n\) का मान क्या है?
If \(S_n-S_{n-2}=257\), what is the value of \(S_n\)?
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#natural-numbers
#difference-equation
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A (8128)
B (8256)
C (8320)
D (8385)
Explanation opens after your attempt
Step 1
Concept
\(S_n-S_{n-2}=2n-1\). From (2n-1=257), (n=129), so \(S_{129}=8385\).
Step 2
Why this answer is correct
The correct answer is D. (8385). \(S_n-S_{n-2}=2n-1\). From (2n-1=257), (n=129), so \(S_{129}=8385\).
Step 3
Exam Tip
\(S_n-S_{n-2}=2n-1\) है। (2n-1=257) से (n=129), अतः \(S_{129}=8385\)।
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(181) से (240) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।
Find the sum of natural numbers from (181) to (240).
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#range-sum
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A (12630)
B (12730)
C (12830)
D (12930)
Explanation opens after your attempt
Correct Answer
A. (12630)
Step 1
Concept
The sum is \(S_{240}-S_{180}=28920-16290=12630\). The subtraction method is quick for large intervals.
Step 2
Why this answer is correct
The correct answer is A. (12630). The sum is \(S_{240}-S_{180}=28920-16290=12630\). The subtraction method is quick for large intervals.
Step 3
Exam Tip
योग \(S_{240}-S_{180}=28920-16290=12630\) है। बड़े अंतराल में घटाव विधि तेज होती है।
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पहले (128) और पहले (64) प्राकृतिक संख्याओं के योगों का अनुपात क्या है?
What is the ratio of the sums of the first (128) and first (64) natural numbers?
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#ratio
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A (129:64)
B (128:64)
C (258:65)
D (65:258)
Explanation opens after your attempt
Correct Answer
C. (258:65)
Step 1
Concept
\(S_{128}:S_{64}=8256:2080=258:65\). Write the ratio in simplest form.
Step 2
Why this answer is correct
The correct answer is C. (258:65). \(S_{128}:S_{64}=8256:2080=258:65\). Write the ratio in simplest form.
Step 3
Exam Tip
\(S_{128}:S_{64}=8256:2080=258:65\)। अनुपात को सरलतम रूप में लिखें।
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यदि \(S_n=8256\), तो \(S_{n+5}-S_n\) क्या होगा?
If \(S_n=8256\), what will be \(S_{n+5}-S_n\)?
#sequences
#progressions
#natural-numbers
#next-terms
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A (645)
B (655)
C (665)
D (675)
Explanation opens after your attempt
Step 1
Concept
\(8256=S_{128}\), so the difference is (129+130+131+132+133=655). Add the next five terms.
Step 2
Why this answer is correct
The correct answer is B. (655). \(8256=S_{128}\), so the difference is (129+130+131+132+133=655). Add the next five terms.
Step 3
Exam Tip
\(8256=S_{128}\), इसलिए अंतर (129+130+131+132+133=655) है। अगले पांच पदों को जोड़ें।
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यदि \(S_n+S_{n-1}=12544\) और \(S_n-S_{n-1}=112\), तो \(S_n\) का मान क्या है?
If \(S_n+S_{n-1}=12544\) and \(S_n-S_{n-1}=112\), what is the value of \(S_n\)?
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#equation
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A (6216)
B (6272)
C (6328)
D (6384)
Explanation opens after your attempt
Step 1
Concept
Adding the two equations gives \(2S_n=12656\), so \(S_n=6328\). Adding the equations is the fastest way.
Step 2
Why this answer is correct
The correct answer is C. (6328). Adding the two equations gives \(2S_n=12656\), so \(S_n=6328\). Adding the equations is the fastest way.
Step 3
Exam Tip
दोनों समीकरण जोड़ने पर \(2S_n=12656\), इसलिए \(S_n=6328\)। समीकरणों को जोड़ना सबसे तेज है।
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यदि \(S_n=1830\), तो \(S_{3n}\) का मान क्या होगा?
If \(S_n=1830\), what will be the value of \(S_{3n}\)?
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#index
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A (9870)
B (11325)
C (12880)
D (16290)
Explanation opens after your attempt
Correct Answer
D. (16290)
Step 1
Concept
\(1830=S_{60}\), so (3n=180) and \(S_{180}=16290\). Identify (n) first.
Step 2
Why this answer is correct
The correct answer is D. (16290). \(1830=S_{60}\), so (3n=180) and \(S_{180}=16290\). Identify (n) first.
Step 3
Exam Tip
\(1830=S_{60}\), इसलिए (3n=180) और \(S_{180}=16290\)। पहले (n) पहचानें।
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यदि \(S_{n+3}-S_{n-2}=760\), तो (n) का मान क्या है?
If \(S_{n+3}-S_{n-2}=760\), what is the value of (n)?
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#algebra
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A (151)
B (152)
C (153)
D (154)
Explanation opens after your attempt
Step 1
Concept
This difference is ((n-1)+n+(n+1)+(n+2)+(n+3)=5n+5). From (5n+5=760), (n=151).
Step 2
Why this answer is correct
The correct answer is A. (151). This difference is ((n-1)+n+(n+1)+(n+2)+(n+3)=5n+5). From (5n+5=760), (n=151).
Step 3
Exam Tip
यह अंतर ((n-1)+n+(n+1)+(n+2)+(n+3)=5n+5) है। (5n+5=760) से (n=151)।
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(90) से (150) तक प्राकृतिक संख्याओं का योग क्या है?
What is the sum of natural numbers from (90) to (150)?
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A (7220)
B (7320)
C (7420)
D (7520)
Explanation opens after your attempt
Step 1
Concept
The sum is \(S_{150}-S_{89}=11325-4005=7320\). If it starts from (90), subtract the sum up to (89).
Step 2
Why this answer is correct
The correct answer is B. (7320). The sum is \(S_{150}-S_{89}=11325-4005=7320\). If it starts from (90), subtract the sum up to (89).
Step 3
Exam Tip
योग \(S_{150}-S_{89}=11325-4005=7320\) है। (90) से शुरू हो तो (89) तक का योग घटाएं।
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पहले (175) प्राकृतिक संख्याओं के योग का (40%) कितना है?
What is (40%) of the sum of the first (175) natural numbers?
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A (5960)
B (6060)
C (6160)
D (6260)
Explanation opens after your attempt
Step 1
Concept
\(S_{175}=15400\) and \(40%=\frac{2}{5}\), so the value is (6160). Convert the percentage into a fraction.
Step 2
Why this answer is correct
The correct answer is C. (6160). \(S_{175}=15400\) and \(40%=\frac{2}{5}\), so the value is (6160). Convert the percentage into a fraction.
Step 3
Exam Tip
\(S_{175}=15400\) और \(40%=\frac{2}{5}\), इसलिए मान (6160) है। प्रतिशत को भिन्न में बदलें।
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यदि \(S_n=19900\), तो (n) का मान क्या है?
If \(S_n=19900\), what is the value of (n)?
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#find-n
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A (196)
B (197)
C (198)
D (199)
Explanation opens after your attempt
Step 1
Concept
\(\frac{199\cdot200}{2}=19900\), so (n=199). Halve the even number and multiply.
Step 2
Why this answer is correct
The correct answer is D. (199). \(\frac{199\cdot200}{2}=19900\), so (n=199). Halve the even number and multiply.
Step 3
Exam Tip
\(\frac{199\cdot200}{2}=19900\), इसलिए (n=199)। सम संख्या को आधा करके गुणा करें।
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यदि \(S_n-S_{n-7}=1330\), तो (n) का मान क्या होगा?
If \(S_n-S_{n-7}=1330\), what will be the value of (n)?
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A (193)
B (194)
C (195)
D (196)
Explanation opens after your attempt
Step 1
Concept
\(S_n-S_{n-7}=7n-21\). From (7n-21=1330), (n=193).
Step 2
Why this answer is correct
The correct answer is A. (193). \(S_n-S_{n-7}=7n-21\). From (7n-21=1330), (n=193).
Step 3
Exam Tip
\(S_n-S_{n-7}=7n-21\) होता है। (7n-21=1330) से (n=193)।
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(211) से (260) तक प्राकृतिक संख्याओं का योग कितना है?
How much is the sum of natural numbers from (211) to (260)?
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A (11675)
B (11775)
C (11875)
D (11975)
Explanation opens after your attempt
Correct Answer
B. (11775)
Step 1
Concept
The sum is \(S_{260}-S_{210}=33930-22155=11775\). For large intervals, use \(S_b-S_{a-1}\).
Step 2
Why this answer is correct
The correct answer is B. (11775). The sum is \(S_{260}-S_{210}=33930-22155=11775\). For large intervals, use \(S_b-S_{a-1}\).
Step 3
Exam Tip
योग \(S_{260}-S_{210}=33930-22155=11775\) है। बड़े अंतराल में \(S_b-S_{a-1}\) प्रयोग करें।
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पहले (100) और पहले (50) प्राकृतिक संख्याओं के योगों का अनुपात क्या है?
What is the ratio of the sums of the first (100) and first (50) natural numbers?
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A (2:1)
B (100:50)
C (202:51)
D (51:202)
Explanation opens after your attempt
Correct Answer
C. (202:51)
Step 1
Concept
\(S_{100}:S_{50}=5050:1275=202:51\). Simplify the ratio fully.
Step 2
Why this answer is correct
The correct answer is C. (202:51). \(S_{100}:S_{50}=5050:1275=202:51\). Simplify the ratio fully.
Step 3
Exam Tip
\(S_{100}:S_{50}=5050:1275=202:51\)। अनुपात को पूरी तरह सरल करें।
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यदि \(S_n=11175\), तो \(S_n-S_{n-4}\) क्या होगा?
If \(S_n=11175\), what will be \(S_n-S_{n-4}\)?
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#progressions
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#last-terms
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A (560)
B (570)
C (580)
D (590)
Explanation opens after your attempt
Step 1
Concept
\(11175=S_{149}\), so the difference is (146+147+148+149=590). Add the last four terms.
Step 2
Why this answer is correct
The correct answer is D. (590). \(11175=S_{149}\), so the difference is (146+147+148+149=590). Add the last four terms.
Step 3
Exam Tip
\(11175=S_{149}\), इसलिए अंतर (146+147+148+149=590) है। अंतिम चार पद जोड़ें।
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यदि (n=50), तो \(S_{2n}-S_n\) का मान क्या है?
If (n=50), what is the value of \(S_{2n}-S_n\)?
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#index
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A (3775)
B (3875)
C (3975)
D (4075)
Explanation opens after your attempt
Step 1
Concept
\(S_{2n}-S_n=S_{100}-S_{50}=5050-1275=3775\). Find (2n) first.
Step 2
Why this answer is correct
The correct answer is A. (3775). \(S_{2n}-S_n=S_{100}-S_{50}=5050-1275=3775\). Find (2n) first.
Step 3
Exam Tip
\(S_{2n}-S_n=S_{100}-S_{50}=5050-1275=3775\)। पहले (2n) निकालें।
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(301) से (350) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।
Find the sum of natural numbers from (301) to (350).
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A (16175)
B (16275)
C (16375)
D (16475)
Explanation opens after your attempt
Correct Answer
B. (16275)
Step 1
Concept
The sum is \(S_{350}-S_{300}=61425-45150=16275\). If it starts from (301), subtract the sum up to (300).
Step 2
Why this answer is correct
The correct answer is B. (16275). The sum is \(S_{350}-S_{300}=61425-45150=16275\). If it starts from (301), subtract the sum up to (300).
Step 3
Exam Tip
योग \(S_{350}-S_{300}=61425-45150=16275\) है। (301) से शुरू हो तो (300) तक का योग घटाएं।
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यदि \(S_n-S_{n-2}=199\), तो \(S_n\) का मान क्या होगा?
If \(S_n-S_{n-2}=199\), what will be the value of \(S_n\)?
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#difference-equation
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A (4851)
B (4950)
C (5050)
D (5151)
Explanation opens after your attempt
Step 1
Concept
\(S_n-S_{n-2}=2n-1\). From (2n-1=199), (n=100), so \(S_n=5050\).
Step 2
Why this answer is correct
The correct answer is C. (5050). \(S_n-S_{n-2}=2n-1\). From (2n-1=199), (n=100), so \(S_n=5050\).
Step 3
Exam Tip
\(S_n-S_{n-2}=2n-1\) है। (2n-1=199) से (n=100), इसलिए \(S_n=5050\)।
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यदि \(S_n=13041\), तो (n) का मान क्या है?
If \(S_n=13041\), what is the value of (n)?
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#natural-numbers
#find-n
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A (158)
B (159)
C (160)
D (161)
Explanation opens after your attempt
Step 1
Concept
\(\frac{161\cdot162}{2}=13041\), so (n=161). Check the options in the formula.
Step 2
Why this answer is correct
The correct answer is D. (161). \(\frac{161\cdot162}{2}=13041\), so (n=161). Check the options in the formula.
Step 3
Exam Tip
\(\frac{161\cdot162}{2}=13041\), इसलिए (n=161)। विकल्पों को सूत्र में रखकर जांचें।
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यदि \(S_{n+5}-S_{n-5}=1205\), तो (n) का मान क्या होगा?
If \(S_{n+5}-S_{n-5}=1205\), what will be the value of (n)?
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#progressions
#natural-numbers
#algebra
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A (120)
B (121)
C (122)
D (123)
Explanation opens after your attempt
Step 1
Concept
This difference is ((n-4)+(n-3)+\cdots+(n+5)=10n+5). From (10n+5=1205), (n=120).
Step 2
Why this answer is correct
The correct answer is A. (120). This difference is ((n-4)+(n-3)+\cdots+(n+5)=10n+5). From (10n+5=1205), (n=120).
Step 3
Exam Tip
यह अंतर ((n-4)+(n-3)+\cdots+(n+5)=10n+5) है। (10n+5=1205) से (n=120)।
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पहले (180) और पहले (120) प्राकृतिक संख्याओं के योगों का अंतर क्या है?
What is the difference between the sums of the first (180) and first (120) natural numbers?
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#progressions
#natural-numbers
#difference
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A (8930)
B (9030)
C (9130)
D (9230)
Explanation opens after your attempt
Step 1
Concept
\(S_{180}-S_{120}=16290-7260=9030\). This is the sum from (121) to (180).
Step 2
Why this answer is correct
The correct answer is B. (9030). \(S_{180}-S_{120}=16290-7260=9030\). This is the sum from (121) to (180).
Step 3
Exam Tip
\(S_{180}-S_{120}=16290-7260=9030\)। यह (121) से (180) तक का योग है।
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यदि \(S_n=2145\), तो \(S_{2n}-S_n\) का मान क्या होगा?
If \(S_n=2145\), what will be the value of \(S_{2n}-S_n\)?
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#progressions
#natural-numbers
#index
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A (6170)
B (6270)
C (6370)
D (6470)
Explanation opens after your attempt
Step 1
Concept
\(2145=S_{65}\), so \(S_{2n}-S_n=S_{130}-S_{65}=8515-2145=6370\). Identify (n) first.
Step 2
Why this answer is correct
The correct answer is C. (6370). \(2145=S_{65}\), so \(S_{2n}-S_n=S_{130}-S_{65}=8515-2145=6370\). Identify (n) first.
Step 3
Exam Tip
\(2145=S_{65}\), इसलिए \(S_{2n}-S_n=S_{130}-S_{65}=8515-2145=6370\)। पहले (n) पहचानें।
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(401) से (450) तक प्राकृतिक संख्याओं का योग क्या है?
What is the sum of natural numbers from (401) to (450)?
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#natural-numbers
#range-sum
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A (21275)
B (21375)
C (21475)
D (21575)
Explanation opens after your attempt
Correct Answer
A. (21275)
Step 1
Concept
The sum is \(S_{450}-S_{400}=101475-80200=21275\). Use the subtraction method for large intervals.
Step 2
Why this answer is correct
The correct answer is A. (21275). The sum is \(S_{450}-S_{400}=101475-80200=21275\). Use the subtraction method for large intervals.
Step 3
Exam Tip
योग \(S_{450}-S_{400}=101475-80200=21275\) है। बड़े अंतराल में घटाव विधि उपयोग करें।
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यदि \(S_n-S_{n-1}=225\), तो \(S_{n+1}\) का मान क्या होगा?
If \(S_n-S_{n-1}=225\), what will be the value of \(S_{n+1}\)?
#sequences
#progressions
#natural-numbers
#next-sum
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A (25425)
B (25651)
C (25878)
D (26106)
Explanation opens after your attempt
Correct Answer
B. (25651)
Step 1
Concept
\(S_n-S_{n-1}=n\), so (n=225) and \(S_{226}=25651\). For the next sum, take (n+1).
Step 2
Why this answer is correct
The correct answer is B. (25651). \(S_n-S_{n-1}=n\), so (n=225) and \(S_{226}=25651\). For the next sum, take (n+1).
Step 3
Exam Tip
\(S_n-S_{n-1}=n\), इसलिए (n=225) और \(S_{226}=25651\)। अगले योग के लिए (n+1) लें।
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यदि \(S_n=31375\), तो \(S_{n-12}\) का मान क्या है?
If \(S_n=31375\), what is the value of \(S_{n-12}\)?
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#progressions
#natural-numbers
#previous-sum
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A (28100)
B (28270)
C (28441)
D (28613)
Explanation opens after your attempt
Correct Answer
C. (28441)
Step 1
Concept
\(31375=S_{250}\), so \(S_{238}=\frac{238\cdot239}{2}=28441\). Identify (n) first and reduce it by (12).
Step 2
Why this answer is correct
The correct answer is C. (28441). \(31375=S_{250}\), so \(S_{238}=\frac{238\cdot239}{2}=28441\). Identify (n) first and reduce it by (12).
Step 3
Exam Tip
\(31375=S_{250}\), इसलिए \(S_{238}=\frac{238\cdot239}{2}=28441\)। पहले (n) पहचानकर (12) कम करें।
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यदि \(S_n-S_{n-8}=1228\), तो (n) का मान क्या होगा?
If \(S_n-S_{n-8}=1228\), what will be the value of (n)?
#sequences
#progressions
#natural-numbers
#difference-equation
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A (155)
B (156)
C (157)
D (158)
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Step 1
Concept
(S_n-S_{n-8}=(n-7)+(n-6)+\cdots+n=8n-28). From (8n-28=1228), (n=157).
Step 2
Why this answer is correct
The correct answer is C. (157). (S_n-S_{n-8}=(n-7)+(n-6)+\cdots+n=8n-28). From (8n-28=1228), (n=157).
Step 3
Exam Tip
(S_n-S_{n-8}=(n-7)+(n-6)+\cdots+n=8n-28) होता है। (8n-28=1228) से (n=157)।
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(251) से (300) तक प्राकृतिक संख्याओं का योग ज्ञात कीजिए।
Find the sum of natural numbers from (251) to (300).
#sequences
#progressions
#natural-numbers
#range-sum
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A (13675)
B (13775)
C (13875)
D (13975)
Explanation opens after your attempt
Correct Answer
B. (13775)
Step 1
Concept
The sum is \(S_{300}-S_{250}=45150-31375=13775\). The \(S_b-S_{a-1}\) method is fast for large intervals.
Step 2
Why this answer is correct
The correct answer is B. (13775). The sum is \(S_{300}-S_{250}=45150-31375=13775\). The \(S_b-S_{a-1}\) method is fast for large intervals.
Step 3
Exam Tip
योग \(S_{300}-S_{250}=45150-31375=13775\) है। \(S_b-S_{a-1}\) विधि बड़े अंतराल में तेज रहती है।
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