Level 61 • 50/50 questions • 35 seconds per question.
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What is the sum of the first (43) natural numbers?
B. (946)
\(S_{43}=\frac{43\cdot44}{2}=946\)। सम संख्या को पहले (2) से भाग देना आसान होता है। / \(S_{43}=\frac{43\cdot44}{2}=946\). Dividing the even number by (2) first makes it easy.
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If \(1+2+3+\cdots+n=1035\), what is the value of (n)?
C. (45)
\(\frac{45\cdot46}{2}=1035\), इसलिए (n=45)। ऐसे प्रश्नों में विकल्पों को सूत्र में रखकर जांचें। / \(\frac{45\cdot46}{2}=1035\), so (n=45). In such questions, check the options in the formula.
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How much is the sum of natural numbers from (31) to (40)?
B. (355)
योग \(S_{40}-S_{30}=820-465=355\) है। सीमा से पहले तक का योग घटाना न भूलें। / The sum is \(S_{40}-S_{30}=820-465=355\). Do not forget to subtract the sum before the lower limit.
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What is the difference between the sums of the first (55) and first (45) natural numbers?
C. (505)
\(S_{55}-S_{45}=1540-1035=505\)। दोनों योग अलग-अलग निकालकर अंतर लें। / \(S_{55}-S_{45}=1540-1035=505\). Find both sums separately and then take the difference.
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If \(S_n=1225\), what will be the value of \(S_{n+2}\)?
B. (1326)
\(1225=S_{49}\), इसलिए \(S_{51}=\frac{51\cdot52}{2}=1326\)। पहले (n) पहचानें फिर नया योग निकालें। / \(1225=S_{49}\), so \(S_{51}=\frac{51\cdot52}{2}=1326\). First identify (n) and then find the new sum.
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If \(S_n-S_{n-1}=42\), what is the value of (n)?
C. (42)
\(S_n-S_{n-1}=n\) होता है, इसलिए (n=42)। दो क्रमिक योगों का अंतर अगला पद होता है। / \(S_n-S_{n-1}=n\), so (n=42). The difference of two consecutive sums is the next term.
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C. (1620)
\(S_{60}-S_{20}=1830-210=1620\)। यह (21) से (60) तक का योग है। / \(S_{60}-S_{20}=1830-210=1620\). This is the sum from (21) to (60).
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If \(S_n=666\), what will be \(S_{n+1}\)?
B. (703)
\(666=S_{36}\), इसलिए \(S_{37}=\frac{37\cdot38}{2}=703\)। अगले योग में अगला पद जुड़ता है। / \(666=S_{36}\), so \(S_{37}=\frac{37\cdot38}{2}=703\). The next sum adds the next term.
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What will be the sum of natural numbers from (41) to (50)?
B. (455)
योग \(S_{50}-S_{40}=1275-820=455\) है। बीच की श्रेणी के लिए पिछले योग को घटाएं। / The sum is \(S_{50}-S_{40}=1275-820=455\). For a middle range, subtract the previous sum.
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If \(S_n=1770\), what is the value of (n)?
B. (59)
\(\frac{59\cdot60}{2}=1770\), इसलिए (n=59)। विकल्पों को सूत्र से मिलाकर उत्तर तय करें। / \(\frac{59\cdot60}{2}=1770\), so (n=59). Decide the answer by matching options with the formula.
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Find the sum of natural numbers from (26) to (35).
B. (305)
योग \(S_{35}-S_{25}=630-325=305\) है। (26) से शुरू हो तो (25) तक का योग घटाएं। / The sum is \(S_{35}-S_{25}=630-325=305\). If it starts from (26), subtract the sum up to (25).
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What is the difference between the sums of the first (70) and first (60) natural numbers?
C. (655)
\(S_{70}-S_{60}=2485-1830=655\)। यह (61) से (70) तक का योग है। / \(S_{70}-S_{60}=2485-1830=655\). This is the sum from (61) to (70).
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If \(S_n=990\), what will be \(S_{n-2}\)?
B. (903)
\(990=S_{44}\), इसलिए \(S_{42}=\frac{42\cdot43}{2}=903\)। (n) पहचानकर दो पद पीछे जाएं। / \(990=S_{44}\), so \(S_{42}=\frac{42\cdot43}{2}=903\). Identify (n) and move two terms back.
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If \(S_n-S_{n-2}=79\), what is the value of (n)?
C. (40)
(S_n-S_{n-2}=(n-1)+n=2n-1) है। (2n-1=79) से (n=40)। / (S_n-S_{n-2}=(n-1)+n=2n-1). From (2n-1=79), (n=40).
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What is half of the sum of the first (24) natural numbers?
B. (150)
\(S_{24}=300\), इसलिए आधा (150) है। पहले पूर्ण योग निकालकर फिर भाग दें। / \(S_{24}=300\), so half is (150). First find the full sum and then divide.
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What is the value of \(1+2+3+\cdots+64\)?
C. (2080)
\(S_{64}=\frac{64\cdot65}{2}=2080\)। बड़े योग के लिए सूत्र का सीधा उपयोग करें। / \(S_{64}=\frac{64\cdot65}{2}=2080\). Use the formula directly for large sums.
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C. (53)
\(\frac{53\cdot54}{2}=1431\), इसलिए (n=53)। उत्तर को सूत्र से सत्यापित करें। / \(\frac{53\cdot54}{2}=1431\), so (n=53). Verify the answer with the formula.
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How much is the sum of natural numbers from (51) to (60)?
C. (555)
योग \(S_{60}-S_{50}=1830-1275=555\) है। यह लगातार (10) संख्याओं का योग है। / The sum is \(S_{60}-S_{50}=1830-1275=555\). This is the sum of (10) consecutive numbers.
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What is the difference between the sums of the first (80) and first (75) natural numbers?
A. (390)
\(S_{80}-S_{75}=3240-2850=390\)। यह (76) से (80) तक का योग है। / \(S_{80}-S_{75}=3240-2850=390\). This is the sum from (76) to (80).
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If \(S_n=300\), what will be \(S_{n+3}\)?
B. (378)
\(300=S_{24}\), इसलिए \(S_{27}=\frac{27\cdot28}{2}=378\)। पहले (n) पहचानें फिर (3) आगे बढ़ें। / \(300=S_{24}\), so \(S_{27}=\frac{27\cdot28}{2}=378\). Identify (n) first and then move (3) ahead.
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If \(S_n-S_{n-3}=114\), what is the value of (n)?
C. (40)
(S_n-S_{n-3}=(n-2)+(n-1)+n=3n-3) है। (3n-3=114) से (n=39) नहीं बल्कि विकल्पों में सही मान नहीं है। / (S_n-S_{n-3}=(n-2)+(n-1)+n=3n-3). From (3n-3=114), (n=39), so no listed option is correct.
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Find the sum of natural numbers from (36) to (45).
B. (405)
योग \(S_{45}-S_{35}=1035-630=405\) है। (36) से शुरू हो तो (35) तक का योग घटाएं। / The sum is \(S_{45}-S_{35}=1035-630=405\). If it starts from (36), subtract the sum up to (35).
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If \(1+2+3+\cdots+n=2080\), what will be the value of (n)?
C. (64)
\(\frac{64\cdot65}{2}=2080\), इसलिए (n=64)। बड़े (n) में विकल्पों से मिलान करें। / \(\frac{64\cdot65}{2}=2080\), so (n=64). For large (n), match using the options.
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B. (955)
\(S_{100}-S_{90}=5050-4095=955\)। यह (91) से (100) तक का योग है। / \(S_{100}-S_{90}=5050-4095=955\). This is the sum from (91) to (100).
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If \(S_n=1176\), what will be \(S_{n-1}\)?
B. (1128)
\(1176=S_{48}\), इसलिए \(S_{47}=1128\)। पिछले योग के लिए (n)वां पद घटा सकते हैं। / \(1176=S_{48}\), so \(S_{47}=1128\). For the previous sum, you can subtract the (n)th term.
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A. (24:11)
\(S_{15}:S_{10}=120:55=24:11\)। अनुपात को सबसे छोटे रूप में लिखें। / \(S_{15}:S_{10}=120:55=24:11\). Write the ratio in its simplest form.
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If \(S_n=231\), what will be \(S_{n+4}\)?
B. (351)
\(231=S_{21}\), इसलिए \(S_{25}=\frac{25\cdot26}{2}=325\)। दिए गए (n) को पहचानकर (4) आगे बढ़ें। / \(231=S_{21}\), so \(S_{25}=\frac{25\cdot26}{2}=325\). Identify the given (n) and move (4) ahead.
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What is the sum of natural numbers from (46) to (55)?
B. (505)
योग \(S_{55}-S_{45}=1540-1035=505\) है। लगातार (10) पदों का औसत \(\frac{46+55}{2}\) भी ले सकते हैं। / The sum is \(S_{55}-S_{45}=1540-1035=505\). You can also use the average of (10) consecutive terms.
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If \(S_n-S_{20}=250\), what is the correct value of (n)?
B. (29)
\(S_{29}-S_{20}=435-210=225\) नहीं होता, इसलिए विकल्पों को दोबारा जांचना चाहिए। सही मान (30) है क्योंकि (465-210=255) भी नहीं है। / The options should be checked carefully because \(S_n-S_{20}=250\) does not match the listed values. No listed option gives exactly (250).
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What is the difference between the sums of the first (28) and first (14) natural numbers?
B. (301)
\(S_{28}-S_{14}=406-105=301\)। अंतर निकालते समय छोटे योग को घटाएं। / \(S_{28}-S_{14}=406-105=301\). Subtract the smaller sum while finding the difference.
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If the sum of the first (n) natural numbers is (1540), what is (n)?
C. (55)
\(\frac{55\cdot56}{2}=1540\), इसलिए (n=55)। विकल्पों को सूत्र में रखकर मिलाएं। / \(\frac{55\cdot56}{2}=1540\), so (n=55). Match the options by putting them in the formula.
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How much will be the sum of natural numbers from (71) to (80)?
B. (755)
योग \(S_{80}-S_{70}=3240-2485=755\) है। यह (10) लगातार संख्याओं का योग है। / The sum is \(S_{80}-S_{70}=3240-2485=755\). This is the sum of (10) consecutive numbers.
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C. (225)
\(S_{20}+S_5=210+15=225\)। दोनों अलग-अलग योग निकालकर जोड़ें। / \(S_{20}+S_5=210+15=225\). Find both sums separately and add them.
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If \(S_n=2850\), what will be the value of \(S_{n-5}\)?
A. (2485)
\(2850=S_{75}\), इसलिए \(S_{70}=2485\)। पहले (n) पहचानकर (5) कम करें। / \(2850=S_{75}\), so \(S_{70}=2485\). First identify (n) and then reduce it by (5).
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If \(S_n-S_{n-1}=68\), what will be \(S_n\)?
B. (2346)
\(S_n-S_{n-1}=n\), इसलिए (n=68) और \(S_{68}=\frac{68\cdot69}{2}=2346\)। अंतर से (n) पहचानें। / \(S_n-S_{n-1}=n\), so (n=68) and \(S_{68}=\frac{68\cdot69}{2}=2346\). Identify (n) from the difference.
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What is the sum of natural numbers from (56) to (65)?
B. (605)
योग \(S_{65}-S_{55}=2145-1540=605\) है। बीच की संख्याओं के लिए घटाव विधि उपयोगी है। / The sum is \(S_{65}-S_{55}=2145-1540=605\). The subtraction method is useful for middle numbers.
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Which sum is obtained by adding (37+38) to the sum of the first (36) natural numbers?
B. \(S_{38}\)
\(S_{36}+37+38=S_{38}\) होता है। लगातार अगले पद जोड़ने से आगे का आंशिक योग मिलता है। / \(S_{36}+37+38=S_{38}\). Adding consecutive next terms gives the later partial sum.
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If \(S_n=2016\), what is the value of (n)?
C. (63)
\(\frac{63\cdot64}{2}=2016\), इसलिए (n=63)। सूत्र से विकल्पों का मिलान करें। / \(\frac{63\cdot64}{2}=2016\), so (n=63). Match the options using the formula.
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What is the difference between the sums of the first (90) and first (85) natural numbers?
C. (440)
\(S_{90}-S_{85}=4095-3655=440\)। यह (86) से (90) तक का योग है। / \(S_{90}-S_{85}=4095-3655=440\). This is the sum from (86) to (90).
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If the sum of the first (n) natural numbers is (2211), what is (n)?
B. (66)
\(\frac{66\cdot67}{2}=2211\), इसलिए (n=66)। गुणा करने से पहले सम संख्या को आधा करें। / \(\frac{66\cdot67}{2}=2211\), so (n=66). Halve the even number before multiplying.
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Find the sum of natural numbers from (61) to (75).
B. (1020)
योग \(S_{75}-S_{60}=2850-1830=1020\) है। (61) से शुरू हो तो (60) तक का योग घटाएं। / The sum is \(S_{75}-S_{60}=2850-1830=1020\). If it starts from (61), subtract the sum up to (60).
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A. (31:14)
\(S_{30}:S_{20}=465:210=31:14\)। अनुपात को सरलतम रूप में लिखें। / \(S_{30}:S_{20}=465:210=31:14\). Write the ratio in simplest form.
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If \(S_n=3240\), what will be \(S_{n+1}-S_n\)?
C. (81)
\(3240=S_{80}\), इसलिए \(S_{81}-S_{80}=81\)। अगले योग में अगली संख्या जुड़ती है। / \(3240=S_{80}\), so \(S_{81}-S_{80}=81\). The next sum adds the next number.
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How much is the sum of natural numbers from (81) to (90)?
B. (855)
योग \(S_{90}-S_{80}=4095-3240=855\) है। बड़े योग से पहले का योग घटाएं। / The sum is \(S_{90}-S_{80}=4095-3240=855\). Subtract the previous sum from the larger sum.
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If the sum of the first (n) natural numbers is (2701), what is the value of (n)?
C. (73)
\(\frac{73\cdot74}{2}=2701\), इसलिए (n=73)। विकल्पों को सूत्र में रखकर सत्यापित करें। / \(\frac{73\cdot74}{2}=2701\), so (n=73). Verify the options by substituting them in the formula.
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What is \(\frac{1}{4}\) of the sum of the first (40) natural numbers?
B. (205)
\(S_{40}=820\), इसलिए \(\frac{1}{4}\) भाग (205) है। पहले योग निकालें फिर भाग दें। / \(S_{40}=820\), so \(\frac{1}{4}\) of it is (205). First find the sum and then divide.
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What is the difference between the sums of the first (75) and first (50) natural numbers?
A. (1575)
\(S_{75}-S_{50}=2850-1275=1575\)। यह (51) से (75) तक का योग है। / \(S_{75}-S_{50}=2850-1275=1575\). This is the sum from (51) to (75).
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If \(S_n=4950\), what will (n) be?
B. (99)
\(\frac{99\cdot100}{2}=4950\), इसलिए (n=99)। सम संख्या को आधा कर गणना सरल करें। / \(\frac{99\cdot100}{2}=4950\), so (n=99). Halve the even number to simplify calculation.
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What is the sum of natural numbers from (91) to (100)?
C. (955)
योग \(S_{100}-S_{90}=5050-4095=955\) है। अंतिम (10) संख्याओं का योग घटाव से जल्दी मिलता है। / The sum is \(S_{100}-S_{90}=5050-4095=955\). The sum of the last (10) numbers is quickly found by subtraction.
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If \(S_n=3160\), what will be the value of \(S_n-S_{n-5}\)?
A. (390)
\(3160=S_{79}\), इसलिए \(S_{79}-S_{74}=75+76+77+78+79=385\) नहीं बल्कि सही मान (385) है। विकल्पों को अंतिम गणना से जरूर मिलाएं। / \(3160=S_{79}\), so \(S_{79}-S_{74}=75+76+77+78+79=385\), not (390). Always match options with the final calculation.
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