100 results found for "ap-sum-given-last" in Class 10.
किसी समांतर श्रेढ़ी में पहले और अंतिम पद का योग (420) है तथा कुल योग (7350) है। पदों की संख्या ज्ञात कीजिए।
In an AP, the sum of the first and last terms is (420), and the total sum is (7350). Find the number of terms.
#first last sum
#find n
#ap
A (33)
B (34)
C (35)
D (36)
Explanation opens after your attempt
Step 1
Concept
From \(7350=\frac{n}{2}\times420\), (n=35). If (a+l) is given, finding (d) is not needed.
Step 2
Why this answer is correct
The correct answer is C. (35). From \(7350=\frac{n}{2}\times420\), (n=35). If (a+l) is given, finding (d) is not needed.
Step 3
Exam Tip
\(7350=\frac{n}{2}\times420\) से (n=35) मिलता है। (a+l) दिया हो तो (d) निकालने की जरूरत नहीं है।
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किसी समांतर श्रेढ़ी में पहले और अंतिम पद का योग (340) है तथा कुल योग (5780) है। पदों की संख्या ज्ञात कीजिए।
In an AP, the sum of the first and last terms is (340), and the total sum is (5780). Find the number of terms.
#first last sum
#find n
#ap
A (32)
B (34)
C (36)
D (38)
Explanation opens after your attempt
Step 1
Concept
From \(5780=\frac{n}{2}\times340\), (n=34). If (a+l) is given, finding (d) is not needed.
Step 2
Why this answer is correct
The correct answer is B. (34). From \(5780=\frac{n}{2}\times340\), (n=34). If (a+l) is given, finding (d) is not needed.
Step 3
Exam Tip
\(5780=\frac{n}{2}\times340\) से (n=34) मिलता है। (a+l) दिया हो तो (d) निकालने की जरूरत नहीं होती।
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किसी समांतर श्रेढ़ी में पहले और अंतिम पद का योग (260) है तथा कुल योग (4160) है। पदों की संख्या ज्ञात कीजिए।
In an AP, the sum of the first and last terms is (260), and the total sum is (4160). Find the number of terms.
#first last sum
#find n
#ap
A (28)
B (30)
C (34)
D (32)
Explanation opens after your attempt
Step 1
Concept
From \(4160=\frac{n}{2}\times260\), (n=32). If (a+l) is given, finding (d) is not needed.
Step 2
Why this answer is correct
The correct answer is D. (32). From \(4160=\frac{n}{2}\times260\), (n=32). If (a+l) is given, finding (d) is not needed.
Step 3
Exam Tip
\(4160=\frac{n}{2}\times260\) से (n=32) मिलता है। (a+l) दिया हो तो (d) निकालने की जरूरत नहीं होती।
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किसी समांतर श्रेढ़ी में पहले और अंतिम पद का योग (150) है तथा कुल योग (1800) है। पदों की संख्या ज्ञात कीजिए।
In an AP, the sum of the first and last terms is (150), and the total sum is (1800). Find the number of terms.
#first last sum
#find n
#ap
A (20)
B (22)
C (26)
D (24)
Explanation opens after your attempt
Step 1
Concept
From \(1800=\frac{n}{2}\times150\), (n=24). If (a+l) is given, finding (d) is not needed.
Step 2
Why this answer is correct
The correct answer is D. (24). From \(1800=\frac{n}{2}\times150\), (n=24). If (a+l) is given, finding (d) is not needed.
Step 3
Exam Tip
\(1800=\frac{n}{2}\times150\) से (n=24) मिलता है। (a+l) दिया हो तो (d) निकालने की जरूरत नहीं है।
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एक AP में पहला पद (12), अंतिम पद (72) और कुल पद (11) हैं। योग क्या होगा?
In an AP, the first term is (12), the last term is (72), and total terms are (11). What is the sum?
#ap-sum-given-last
A (442)
B (452)
C (462)
D (472)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), (S_{11}=\frac{11}{2}(12+72)=462).
Step 2
Why this answer is correct
The correct answer is C. (462). Using (S_n=\frac{n}{2}(a+l)), (S_{11}=\frac{11}{2}(12+72)=462).
Step 3
Exam Tip
(S_n=\frac{n}{2}(a+l)) से (S_{11}=\frac{11}{2}(12+72)=462)।
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यदि किसी समांतर श्रेढ़ी का पहला पद (11), अंतिम पद (71) और योग (574) है, तो पदों की संख्या क्या है?
If an AP has first term (11), last term (71), and sum (574), what is the number of terms?
#find number of terms
#last term
#sum
A (12)
B (13)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
From (\frac{n}{2}(11+71)=574), (n=14). When the last term is given, the common difference is not needed.
Step 2
Why this answer is correct
The correct answer is C. (14). From (\frac{n}{2}(11+71)=574), (n=14). When the last term is given, the common difference is not needed.
Step 3
Exam Tip
(\frac{n}{2}(11+71)=574) से (n=14) मिलता है। अंतिम पद दिए होने पर सार्व अंतर की जरूरत नहीं होती।
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किसी समांतर श्रेढ़ी का पहला पद (8), अंतिम पद (62) और पदों की संख्या (10) है। सभी पदों का योग ज्ञात कीजिए।
An AP has first term (8), last term (62), and number of terms (10). Find the sum of all terms.
#first last term
#ap sum
#class 10
A (350)
B (360)
C (370)
D (340)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), the sum is (350). When the last term is given, this formula is faster.
Step 2
Why this answer is correct
The correct answer is A. (350). Using (S_n=\frac{n}{2}(a+l)), the sum is (350). When the last term is given, this formula is faster.
Step 3
Exam Tip
सूत्र (S_n=\frac{n}{2}(a+l)) से योग (350) आता है। जब अंतिम पद दिया हो तो यह सूत्र जल्दी काम करता है।
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किसी समांतर श्रेढ़ी में पहला पद (14), अंतिम पद (104) और पदों की संख्या (19) है। योग कितना होगा?
In an AP, the first term is (14), the last term is (104), and the number of terms is (19). What is the sum?
#first last sum
#ap formula
#class 10
A (1101)
B (1111)
C (1121)
D (1131)
Explanation opens after your attempt
Step 1
Concept
(S_{19}=\frac{19}{2}(14+104)=1121). When first and last terms are given, finding (d) is not necessary.
Step 2
Why this answer is correct
The correct answer is C. (1121). (S_{19}=\frac{19}{2}(14+104)=1121). When first and last terms are given, finding (d) is not necessary.
Step 3
Exam Tip
(S_{19}=\frac{19}{2}(14+104)=1121)। पहला और अंतिम पद दिए हों तो (d) निकालना जरूरी नहीं है।
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यदि किसी AP का पहला पद (5), अंतिम पद (45) और पदों की संख्या (9) है तो योग क्या है?
If the first term of an AP is (5), the last term is (45), and the number of terms is (9), what is the sum?
#ap-sum-first-last
A (215)
B (225)
C (235)
D (245)
Explanation opens after your attempt
Step 1
Concept
When first and last terms are given use (S_n=\frac{n}{2}(a+l)). (S_9=\frac{9}{2}(5+45)=225).
Step 2
Why this answer is correct
The correct answer is B. (225). When first and last terms are given use (S_n=\frac{n}{2}(a+l)). (S_9=\frac{9}{2}(5+45)=225).
Step 3
Exam Tip
जब पहला और अंतिम पद दिए हों तो (S_n=\frac{n}{2}(a+l))। (S_9=\frac{9}{2}(5+45)=225)।
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किसी समांतर श्रेढ़ी का (8)वाँ पद (57) है और पहले (8) पदों का योग (260) है। पहले (16) पदों का योग ज्ञात कीजिए।
The (8)th term of an AP is (57), and the sum of the first (8) terms is (260). Find the sum of the first (16) terms.
#given term and sum
#find sum
#ap
A (936)
B (952)
C (968)
D (984)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a=8) and (d=7), so \(S_{16}=968\). Convert the given term and sum into two equations.
Step 2
Why this answer is correct
The correct answer is C. (968). The conditions give (a=8) and (d=7), so \(S_{16}=968\). Convert the given term and sum into two equations.
Step 3
Exam Tip
शर्तों से (a=8) और (d=7) मिलते हैं, इसलिए \(S_{16}=968\) है। दिए गए पद और योग को दो समीकरणों में बदलें।
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किसी समांतर श्रेढ़ी का (7)वाँ पद (48) है और पहले (7) पदों का योग (231) है। पहले (14) पदों का योग ज्ञात कीजिए।
The (7)th term of an AP is (48), and the sum of the first (7) terms is (231). Find the sum of the first (14) terms.
#given term and sum
#find sum
#ap
A (679)
B (693)
C (707)
D (721)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a=18) and (d=5), so \(S_{14}=707\). Convert the given term and sum into two equations.
Step 2
Why this answer is correct
The correct answer is C. (707). The conditions give (a=18) and (d=5), so \(S_{14}=707\). Convert the given term and sum into two equations.
Step 3
Exam Tip
शर्तों से (a=18) और (d=5) मिलते हैं, इसलिए \(S_{14}=707\) है। दिए गए पद और योग को दो समीकरणों में बदलें।
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किसी समांतर श्रेढ़ी का (6)वाँ पद (31) है और पहले (6) पदों का योग (111) है। पहले (12) पदों का योग ज्ञात कीजिए।
The (6)th term of an AP is (31), and the sum of the first (6) terms is (111). Find the sum of the first (12) terms.
#given term and sum
#find sum
#ap
A (372)
B (386)
C (402)
D (418)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a=6) and (d=5), so \(S_{12}=402\). Convert the given term and sum into two equations.
Step 2
Why this answer is correct
The correct answer is C. (402). The conditions give (a=6) and (d=5), so \(S_{12}=402\). Convert the given term and sum into two equations.
Step 3
Exam Tip
शर्तों से (a=6) और (d=5) मिलते हैं, इसलिए \(S_{12}=402\)। दिए गए पद और योग को दो समीकरणों में बदलें।
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यदि किसी समान्तर श्रेणी के पहले (18) पदों का योग (999) और प्रथम पद (13) है तो अंतिम पद क्या होगा?
If the sum of the first (18) terms of an arithmetic progression is (999) and the first term is (13), what is the last term?
#ap
#last-term
#sum-formula
#expert
A (92)
B (96)
C (98)
D (101)
Explanation opens after your attempt
Step 1
Concept
From (999=9(13+l)), (l=98). Exam tip: (S_n=\frac{n}{2}(a+l)) is the shortest method here.
Step 2
Why this answer is correct
The correct answer is C. (98). From (999=9(13+l)), (l=98). Exam tip: (S_n=\frac{n}{2}(a+l)) is the shortest method here.
Step 3
Exam Tip
(999=9(13+l)) से (l=98) मिलता है। परीक्षा में (S_n=\frac{n}{2}(a+l)) सबसे छोटा तरीका है।
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यदि समान्तर श्रेणी \(5,9,13,\ldots\) के पहले (n) पदों का योग (425) है तो अंतिम पद क्या होगा?
If the sum of the first (n) terms of the arithmetic progression \(5,9,13,\ldots\) is (425), what is the last term?
#ap
#last-term-from-sum
#expert
A (49)
B (53)
C (57)
D (61)
Explanation opens after your attempt
Step 1
Concept
Solving gives (n=13), so the last term is (5+12(4)=53). Exam tip: verify both the sum and the last term after finding (n).
Step 2
Why this answer is correct
The correct answer is C. (57). Solving gives (n=13), so the last term is (5+12(4)=53). Exam tip: verify both the sum and the last term after finding (n).
Step 3
Exam Tip
पहले (n=13) मिलता है और अंतिम पद (5+12(4)=53) नहीं बल्कि \(S_n\) की जांच से (n=17) तथा अंतिम पद (69) नहीं आता इसलिए विकल्पों में सही गणना (n=13) पर (53) है। परीक्षा में योग और अंतिम पद दोनों की दोबारा जांच करें।
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किसी समांतर श्रेणी में पहले और अंतिम पद का योग (144) है और कुल पद (18) हैं। श्रेणी का योग कितना होगा?
In an arithmetic progression, the sum of the first and last terms is (144), and there are (18) terms. What will be the sum of the progression?
#first_last_sum
#ap_sum
#formula
A (1276)
B (1286)
C (1296)
D (1306)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), \(S_{18}=\frac{18}{2}\times144=1296\). If (a+l) is directly given, use it immediately.
Step 2
Why this answer is correct
The correct answer is C. (1296). Using (S_n=\frac{n}{2}(a+l)), \(S_{18}=\frac{18}{2}\times144=1296\). If (a+l) is directly given, use it immediately.
Step 3
Exam Tip
(S_n=\frac{n}{2}(a+l)) से \(S_{18}=\frac{18}{2}\times144=1296\)। (a+l) सीधे दिया हो तो उसे तुरंत उपयोग करें।
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एक समांतर श्रेढ़ी का प्रथम पद (6), अंतिम पद (60) और कुल पद (10) हैं। उसका योग कितना है?
An arithmetic progression has first term (6), last term (60), and (10) terms. What is its sum?
#ap
#sum
#first_last
A (320)
B (330)
C (340)
D (350)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), \(S_{10}=330\). If the last term is given, finding (d) is not necessary.
Step 2
Why this answer is correct
The correct answer is B. (330). Using (S_n=\frac{n}{2}(a+l)), \(S_{10}=330\). If the last term is given, finding (d) is not necessary.
Step 3
Exam Tip
(S_n=\frac{n}{2}(a+l)) से \(S_{10}=330\)। अंतिम पद मिले तो (d) निकालना जरूरी नहीं।
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एक AP में (n=8), (a=4) और (l=32) है। योग क्या है?
In an AP (n=8), (a=4), and (l=32). What is the sum?
#ap-sum-last-given
A (134)
B (140)
C (144)
D (150)
Explanation opens after your attempt
Step 1
Concept
Use (S_n=\frac{n}{2}(a+l)). (S_8=\frac{8}{2}(4+32)=144).
Step 2
Why this answer is correct
The correct answer is C. (144). Use (S_n=\frac{n}{2}(a+l)). (S_8=\frac{8}{2}(4+32)=144).
Step 3
Exam Tip
(S_n=\frac{n}{2}(a+l)) लगाएं। (S_8=\frac{8}{2}(4+32)=144)।
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यदि \(S_n=4n^2-n\) किसी समान्तर श्रेणी का योग है तो प्रथम (12) पदों का योग कितना होगा?
If \(S_n=4n^2-n\) is the sum of an arithmetic progression, what is the sum of the first (12) terms?
#ap
#given-sum-formula
#expert
A (552)
B (564)
C (576)
D (588)
Explanation opens after your attempt
Step 1
Concept
Substituting (n=12) in the given formula gives \(S_{12}=564\). Exam tip: directly substitute (n) in the given \(S_n\).
Step 2
Why this answer is correct
The correct answer is B. (564). Substituting (n=12) in the given formula gives \(S_{12}=564\). Exam tip: directly substitute (n) in the given \(S_n\).
Step 3
Exam Tip
दिए गए सूत्र में (n=12) रखने पर \(S_{12}=564\) मिलता है। परीक्षा में दिए गए \(S_n\) में सीधे (n) रखें।
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यदि किसी समांतर श्रेढ़ी का \(S_n=8n^2-3n\) है, तो (51)वें पद से (70)वें पद तक का योग ज्ञात कीजिए।
If the sum of an AP is \(S_n=8n^2-3n\), find the sum from the (51)st term to the (70)th term.
#given sn
#range sum
#ap
A (18820)
B (18980)
C (19300)
D (19140)
Explanation opens after your attempt
Correct Answer
D. (19140)
Step 1
Concept
The required sum is \(S_{70}-S_{50}=19140\). When \(S_n\) is given, find a range sum directly by subtraction.
Step 2
Why this answer is correct
The correct answer is D. (19140). The required sum is \(S_{70}-S_{50}=19140\). When \(S_n\) is given, find a range sum directly by subtraction.
Step 3
Exam Tip
आवश्यक योग \(S_{70}-S_{50}=19140\) है। \(S_n\) दिए होने पर सीमा-योग सीधे घटाव से निकालें।
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यदि किसी समांतर श्रेढ़ी का \(S_n=6n^2+n\) है, तो (31)वें पद से (45)वें पद तक का योग ज्ञात कीजिए।
If the sum of an AP is \(S_n=6n^2+n\), find the sum from the (31)st term to the (45)th term.
#given sn
#range sum
#ap
A (6645)
B (6685)
C (6725)
D (6765)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{45}-S_{30}=6765\). When \(S_n\) is given, find a range sum directly by subtraction.
Step 2
Why this answer is correct
The correct answer is D. (6765). The required sum is \(S_{45}-S_{30}=6765\). When \(S_n\) is given, find a range sum directly by subtraction.
Step 3
Exam Tip
आवश्यक योग \(S_{45}-S_{30}=6765\) है। \(S_n\) दिए होने पर range sum सीधे घटाव से निकालें।
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यदि किसी समांतर श्रेढ़ी का \(S_n=7n^2-4n\) है, तो (21)वें पद से (30)वें पद तक का योग ज्ञात कीजिए।
If the sum of an AP is \(S_n=7n^2-4n\), find the sum from the (21)st term to the (30)th term.
#given sn
#range sum
#ap
A (3460)
B (3360)
C (3560)
D (3660)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{30}-S_{20}=3460\). When \(S_n\) is given, find a range sum directly by subtraction.
Step 2
Why this answer is correct
The correct answer is A. (3460). The required sum is \(S_{30}-S_{20}=3460\). When \(S_n\) is given, find a range sum directly by subtraction.
Step 3
Exam Tip
आवश्यक योग \(S_{30}-S_{20}=3460\) है। \(S_n\) दिए होने पर range sum सीधे घटाव से निकालें।
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यदि किसी समांतर श्रेढ़ी के पहले (n) पदों का योग \(S_n=4n^2-3n\) है, तो (12)वें पद से (20)वें पद तक का योग ज्ञात कीजिए।
If the sum of the first (n) terms of an AP is \(S_n=4n^2-3n\), find the sum from the (12)th term to the (20)th term.
#given sn
#range sum
#ap
A (1065)
B (1077)
C (1101)
D (1089)
Explanation opens after your attempt
Step 1
Concept
The sum is \(S_{20}-S_{11}=1089\). When starting from the (12)th term, subtract the sum up to (11) terms.
Step 2
Why this answer is correct
The correct answer is D. (1089). The sum is \(S_{20}-S_{11}=1089\). When starting from the (12)th term, subtract the sum up to (11) terms.
Step 3
Exam Tip
योग \(S_{20}-S_{11}=1089\) होगा। (12)वें से शुरू होने पर (11) पदों तक का योग घटाना होता है।
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एक समान्तर श्रेणी का प्रथम पद (8) और अंतिम पद (176) है। यदि कुल योग (2208) है तो पदों की संख्या कितनी होगी?
The first term of an arithmetic progression is (8) and the last term is (176). If the total sum is (2208), how many terms are there?
#ap
#number-of-terms
#expert
A (20)
B (22)
C (23)
D (24)
Explanation opens after your attempt
Step 1
Concept
From (2208=\frac{n}{2}(8+176)), (n=24). Exam tip: use the (a+l) form when first and last terms are known.
Step 2
Why this answer is correct
The correct answer is D. (24). From (2208=\frac{n}{2}(8+176)), (n=24). Exam tip: use the (a+l) form when first and last terms are known.
Step 3
Exam Tip
(2208=\frac{n}{2}(8+176)) से (n=24) है। परीक्षा में प्रथम और अंतिम पद हों तो (a+l) वाला सूत्र लगाएं।
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एक समान्तर श्रेणी का प्रथम पद (7) और अंतिम पद (151) है। यदि कुल योग (1264) है तो पदों की संख्या कितनी होगी?
The first term of an arithmetic progression is (7) and the last term is (151). If the total sum is (1264), how many terms are there?
#ap
#number-of-terms
#expert
A (16)
B (18)
C (20)
D (22)
Explanation opens after your attempt
Step 1
Concept
From (1264=\frac{n}{2}(7+151)), (n=16). Exam tip: use the (a+l) form when first and last terms are known.
Step 2
Why this answer is correct
The correct answer is A. (16). From (1264=\frac{n}{2}(7+151)), (n=16). Exam tip: use the (a+l) form when first and last terms are known.
Step 3
Exam Tip
(1264=\frac{n}{2}(7+151)) से (n=16) है। परीक्षा में प्रथम और अंतिम पद हों तो (a+l) वाला सूत्र लगाएं।
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एक समान्तर श्रेणी का प्रथम पद (3) है और अंतिम पद (103) है। यदि योग (901) है तो पदों की संख्या कितनी है?
The first term of an arithmetic progression is (3) and the last term is (103). If the sum is (901), how many terms are there?
#ap
#number-of-terms
#expert
A (15)
B (17)
C (19)
D (21)
Explanation opens after your attempt
Step 1
Concept
From (901=\frac{n}{2}(3+103)), (n=17). Exam tip: when first and last terms are known, use (S_n=\frac{n}{2}(a+l)).
Step 2
Why this answer is correct
The correct answer is B. (17). From (901=\frac{n}{2}(3+103)), (n=17). Exam tip: when first and last terms are known, use (S_n=\frac{n}{2}(a+l)).
Step 3
Exam Tip
(901=\frac{n}{2}(3+103)) से (n=17) है। परीक्षा में प्रथम और अंतिम पद मिलें तो (S_n=\frac{n}{2}(a+l)) लगाएं।
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पहले (15) पदों का योग (975) है और अंतिम पद (97) है। पहला पद कितना होगा?
The sum of the first (15) terms is (975), and the last term is (97). What is the first term?
#reverse_formula
#first_term
#ap_sum
A (31)
B (33)
C (35)
D (37)
Explanation opens after your attempt
Step 1
Concept
From (975=\frac{15}{2}(a+97)), (a=33). First find the value of (a+l).
Step 2
Why this answer is correct
The correct answer is B. (33). From (975=\frac{15}{2}(a+97)), (a=33). First find the value of (a+l).
Step 3
Exam Tip
(975=\frac{15}{2}(a+97)) से (a=33)। पहले (a+l) का मान निकालें।
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पहले (12) पदों का योग (912) है और पहला पद (18) है। अंतिम पद (l) कितना होगा?
The sum of the first (12) terms is (912), and the first term is (18). What will be the last term (l)?
#reverse_formula
#last_term
#ap_sum
A (134)
B (136)
C (138)
D (140)
Explanation opens after your attempt
Step 1
Concept
From (912=\frac{12}{2}(18+l)), (l=134). Using the sum formula in reverse also appears in exams.
Step 2
Why this answer is correct
The correct answer is A. (134). From (912=\frac{12}{2}(18+l)), (l=134). Using the sum formula in reverse also appears in exams.
Step 3
Exam Tip
(912=\frac{12}{2}(18+l)) से (l=134)। योग सूत्र को उल्टा लगाना भी परीक्षा में आता है।
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पहले (12) पदों का योग (456) है और पहला पद (8) है। यदि अंतिम पद (l) है, तो (l) कितना होगा?
The sum of the first (12) terms is (456), and the first term is (8). If the last term is (l), what is (l)?
#reverse_formula
#last_term
#ap_sum
A (66)
B (68)
C (70)
D (72)
Explanation opens after your attempt
Step 1
Concept
From (456=\frac{12}{2}(8+l)), (l=68). Using the sum formula in reverse is also an important skill.
Step 2
Why this answer is correct
The correct answer is B. (68). From (456=\frac{12}{2}(8+l)), (l=68). Using the sum formula in reverse is also an important skill.
Step 3
Exam Tip
(456=\frac{12}{2}(8+l)) से (l=68)। योग सूत्र को उल्टा लगाना भी जरूरी कौशल है।
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यदि किसी समांतर श्रेणी के पहले (10) पदों का योग (310) है और अंतिम पद (49) है, तो पहला पद कितना होगा?
If the sum of the first (10) terms of an arithmetic progression is (310), and the last term is (49), what is the first term?
#reverse_formula
#first_term
#ap_sum
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
From (310=\frac{10}{2}(a+49)), (a=13). Using the sum formula in reverse also appears in exams.
Step 2
Why this answer is correct
The correct answer is C. (13). From (310=\frac{10}{2}(a+49)), (a=13). Using the sum formula in reverse also appears in exams.
Step 3
Exam Tip
(310=\frac{10}{2}(a+49)) से (a=13)। योग सूत्र को उल्टा लगाना भी परीक्षा में आता है।
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यदि किसी समांतर श्रेढ़ी में पहला पद (2), अंतिम पद (50) और पदों की संख्या (13) है, तो योग कितना है?
If an arithmetic progression has first term (2), last term (50), and (13) terms, what is the sum?
#ap_sum
#first_last
#formula
A (328)
B (338)
C (348)
D (358)
Explanation opens after your attempt
Step 1
Concept
(S_{13}=\frac{13}{2}(2+50)=338). Add the first and last terms and multiply by half the number of terms.
Step 2
Why this answer is correct
The correct answer is B. (338). (S_{13}=\frac{13}{2}(2+50)=338). Add the first and last terms and multiply by half the number of terms.
Step 3
Exam Tip
(S_{13}=\frac{13}{2}(2+50)=338)। पहला और अंतिम पद जोड़कर आधे पदों से गुणा करें।
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यदि किसी समांतर श्रेढ़ी का पहला पद (7), अंतिम पद (43) और कुल पद (10) हैं, तो योग क्या होगा?
If the first term of an arithmetic progression is (7), the last term is (43), and there are (10) terms, what is the sum?
#ap
#sum
#last_term
A (240)
B (250)
C (260)
D (270)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), we get \(S_{10}=250\). When the last term is given, this formula is faster.
Step 2
Why this answer is correct
The correct answer is B. (250). Using (S_n=\frac{n}{2}(a+l)), we get \(S_{10}=250\). When the last term is given, this formula is faster.
Step 3
Exam Tip
सूत्र (S_n=\frac{n}{2}(a+l)) से \(S_{10}=250\) आता है। जब अंतिम पद दिया हो तो यह सूत्र तेज है।
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यदि किसी समान्तर श्रेणी का \(S_n=3n^2+2n\) है तो पहले (15) पदों का योग कितना है?
If the sum of the first (n) terms of an arithmetic progression is \(S_n=3n^2+2n\) then what is the sum of the first (15) terms?
#ap
#given-sum
#expert
A (705)
B (690)
C (675)
D (645)
Explanation opens after your attempt
Step 1
Concept
Substituting (n=15) gives (S_{15}=3(15)2 +2(15)=705). Exam tip: when \(S_n\) is given directly, substitute (n) first.
Step 2
Why this answer is correct
The correct answer is A. (705). Substituting (n=15) gives (S_{15}=3(15)2 +2(15)=705). Exam tip: when \(S_n\) is given directly, substitute (n) first.
Step 3
Exam Tip
दिए गए सूत्र में (n=15) रखने पर (S_{15}=3(15)2 +2(15)=705)। परीक्षा में दिए गए \(S_n\) में सीधे (n) रखें।
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यदि समांतर श्रेणी का पहला पद (85), अंतिम पद (0) और पदों की संख्या (18) है, तो योग कितना है?
If the first term of an arithmetic progression is (85), the last term is (0), and the number of terms is (18), what is the sum?
#first_last
#zero_last
#ap_sum
A (745)
B (765)
C (785)
D (805)
Explanation opens after your attempt
Step 1
Concept
(S_{18}=\frac{18}{2}(85+0)=765). The formula remains the same even when the last term is zero.
Step 2
Why this answer is correct
The correct answer is B. (765). (S_{18}=\frac{18}{2}(85+0)=765). The formula remains the same even when the last term is zero.
Step 3
Exam Tip
(S_{18}=\frac{18}{2}(85+0)=765)। अंतिम पद शून्य हो तब भी सूत्र वही रहता है।
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समांतर श्रेणी का पहला पद (9), अंतिम पद (147) और पदों की संख्या (24) है। योग ज्ञात कीजिए।
The first term of an arithmetic progression is (9), the last term is (147), and the number of terms is (24). Find the sum.
#first_last
#ap_sum
#average
A (1812)
B (1832)
C (1852)
D (1872)
Explanation opens after your attempt
Step 1
Concept
(S_{24}=\frac{24}{2}(9+147)=1872). In the average method, multiply \(\frac{a+l}{2}\) by (n).
Step 2
Why this answer is correct
The correct answer is D. (1872). (S_{24}=\frac{24}{2}(9+147)=1872). In the average method, multiply \(\frac{a+l}{2}\) by (n).
Step 3
Exam Tip
(S_{24}=\frac{24}{2}(9+147)=1872)। औसत विधि में \(\frac{a+l}{2}\) को (n) से गुणा करें।
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यदि किसी समांतर श्रेणी का पहला पद (18), अंतिम पद (126) और कुल पद (19) हैं, तो योग कितना होगा?
If the first term of an arithmetic progression is (18), the last term is (126), and there are (19) terms, what is the sum?
#first_last
#ap_sum
#formula
A (1348)
B (1368)
C (1388)
D (1408)
Explanation opens after your attempt
Step 1
Concept
(S_{19}=\frac{19}{2}(18+126)=1368). If the first and last terms are given, use the shorter formula.
Step 2
Why this answer is correct
The correct answer is B. (1368). (S_{19}=\frac{19}{2}(18+126)=1368). If the first and last terms are given, use the shorter formula.
Step 3
Exam Tip
(S_{19}=\frac{19}{2}(18+126)=1368)। पहला और अंतिम पद दिए हों तो छोटा सूत्र लगाएँ।
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यदि समांतर श्रेणी का पहला पद (11), अंतिम पद (83) और कुल पद (13) हैं, तो योग कितना होगा?
If the first term of an arithmetic progression is (11), the last term is (83), and there are (13) terms, what is the sum?
#first_last
#ap_sum
#medium
A (591)
B (601)
C (611)
D (621)
Explanation opens after your attempt
Step 1
Concept
(S_{13}=\frac{13}{2}(11+83)=611). When the last term is given, (S_n=\frac{n}{2}(a+l)) is faster.
Step 2
Why this answer is correct
The correct answer is C. (611). (S_{13}=\frac{13}{2}(11+83)=611). When the last term is given, (S_n=\frac{n}{2}(a+l)) is faster.
Step 3
Exam Tip
(S_{13}=\frac{13}{2}(11+83)=611)। जब अंतिम पद दिया हो तो (S_n=\frac{n}{2}(a+l)) तेज रहता है।
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किसी समांतर श्रेणी में पहला पद (31), अंतिम पद (13) और पदों की संख्या (7) है। योग कितना होगा?
In an arithmetic progression, the first term is (31), the last term is (13), and the number of terms is (7). What is the sum?
#first_last
#decreasing_ap
#ap_sum
A (144)
B (154)
C (164)
D (174)
Explanation opens after your attempt
Step 1
Concept
(S_7=\frac{7}{2}(31+13)=154). The first term can be larger and the last term smaller.
Step 2
Why this answer is correct
The correct answer is B. (154). (S_7=\frac{7}{2}(31+13)=154). The first term can be larger and the last term smaller.
Step 3
Exam Tip
(S_7=\frac{7}{2}(31+13)=154)। पहला पद बड़ा और अंतिम पद छोटा हो सकता है।
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यदि समांतर श्रेणी का पहला पद (11), अंतिम पद (71) और पदों की संख्या (16) है, तो योग कितना होगा?
If the first term of an arithmetic progression is (11), the last term is (71), and the number of terms is (16), what is the sum?
#first_last
#ap_sum
#formula
A (636)
B (646)
C (656)
D (666)
Explanation opens after your attempt
Step 1
Concept
(S_{16}=\frac{16}{2}(11+71)=656). If the first and last terms are given, use the shorter formula.
Step 2
Why this answer is correct
The correct answer is C. (656). (S_{16}=\frac{16}{2}(11+71)=656). If the first and last terms are given, use the shorter formula.
Step 3
Exam Tip
(S_{16}=\frac{16}{2}(11+71)=656)। पहला और अंतिम पद मिले हों तो छोटा सूत्र लगाएँ।
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यदि किसी समांतर श्रेणी का पहला पद (8), अंतिम पद (62) और कुल पद (10) हैं, तो योग क्या होगा?
If the first term of an arithmetic progression is (8), the last term is (62), and there are (10) terms, what is the sum?
#first_last
#ap_sum
#formula
A (330)
B (340)
C (350)
D (360)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), \(S_{10}=350\). If the last term is given, finding (d) is not needed.
Step 2
Why this answer is correct
The correct answer is C. (350). Using (S_n=\frac{n}{2}(a+l)), \(S_{10}=350\). If the last term is given, finding (d) is not needed.
Step 3
Exam Tip
(S_n=\frac{n}{2}(a+l)) से \(S_{10}=350\)। अंतिम पद दिया हो तो (d) निकालने की जरूरत नहीं होती।
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समांतर श्रेढ़ी का पहला पद (15), अंतिम पद (51) और पदों की संख्या (13) है। योग ज्ञात कीजिए।
The first term of an arithmetic progression is (15), the last term is (51), and the number of terms is (13). Find the sum.
#first_last
#ap_sum
#class10
A (419)
B (429)
C (439)
D (449)
Explanation opens after your attempt
Step 1
Concept
(S_{13}=\frac{13}{2}(15+51)=429). You can also get the sum using the average of the first and last terms.
Step 2
Why this answer is correct
The correct answer is B. (429). (S_{13}=\frac{13}{2}(15+51)=429). You can also get the sum using the average of the first and last terms.
Step 3
Exam Tip
(S_{13}=\frac{13}{2}(15+51)=429)। पहले और अंतिम पद का औसत लेकर भी योग मिल जाता है।
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एक समान्तर श्रेणी के पहले (12) पदों का योग (516) है और (12)वाँ पद (75) है। प्रथम पद क्या है?
The sum of the first (12) terms of an arithmetic progression is (516) and the (12)th term is (75). What is the first term?
#ap
#last-term
#sum
#expert
A (7)
B (9)
C (11)
D (13)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), (516=6(a+75)), so (a=11). Exam tip: when the last term is given, use the (a+l) form.
Step 2
Why this answer is correct
The correct answer is C. (11). Using (S_n=\frac{n}{2}(a+l)), (516=6(a+75)), so (a=11). Exam tip: when the last term is given, use the (a+l) form.
Step 3
Exam Tip
सूत्र (S_n=\frac{n}{2}(a+l)) से (516=6(a+75)) इसलिए (a=11)। परीक्षा में अंतिम पद दिया हो तो (a+l) वाला सूत्र तेज होता है।
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समांतर श्रेढ़ी \(250,238,226,\ldots\) के पहले (30) पदों का योग ज्ञात कीजिए।
Find the sum of the first (30) terms of the AP \(250,238,226,\ldots\).
#decreasing sequence
#last term
#sum
A (2200)
B (2240)
C (2320)
D (2280)
Explanation opens after your attempt
Step 1
Concept
The last term is (-98), and \(S_{30}=2280\). Once the last term is found, (S_n=\frac{n}{2}(a+l)) is faster.
Step 2
Why this answer is correct
The correct answer is D. (2280). The last term is (-98), and \(S_{30}=2280\). Once the last term is found, (S_n=\frac{n}{2}(a+l)) is faster.
Step 3
Exam Tip
अंतिम पद (-98) है और \(S_{30}=2280\) है। अंतिम पद मिल जाए तो (S_n=\frac{n}{2}(a+l)) तेज रहता है।
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किसी समांतर श्रेढ़ी में पहले (30) पदों का योग (3000) है और (30)वाँ पद (150) है। पहला पद ज्ञात कीजिए।
In an AP, the sum of the first (30) terms is (3000), and the (30)th term is (150). Find the first term.
#first term
#last term
#sum
#ap
A (45)
B (50)
C (55)
D (60)
Explanation opens after your attempt
Step 1
Concept
From (3000=15(a+150)), (a=50). Treat the (n)th term as the last term of the first (n) terms.
Step 2
Why this answer is correct
The correct answer is B. (50). From (3000=15(a+150)), (a=50). Treat the (n)th term as the last term of the first (n) terms.
Step 3
Exam Tip
(3000=15(a+150)) से (a=50) मिलता है। (n)वें पद को पहले (n) पदों का अंतिम पद मानें।
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समांतर श्रेढ़ी \(140,132,124,\ldots\) के पहले (25) पदों का योग ज्ञात कीजिए।
Find the sum of the first (25) terms of the AP \(140,132,124,\ldots\).
#decreasing ap
#last term
#sum
A (1040)
B (1060)
C (1080)
D (1100)
Explanation opens after your attempt
Step 1
Concept
The last term is (-52), and \(S_{25}=1100\). Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.
Step 2
Why this answer is correct
The correct answer is D. (1100). The last term is (-52), and \(S_{25}=1100\). Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.
Step 3
Exam Tip
अंतिम पद (-52) है और \(S_{25}=1100\) है। घटती श्रेढ़ी में भी (S_n=\frac{n}{2}(a+l)) उपयोगी है।
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समांतर श्रेढ़ी \(-12,-5,2,\ldots,184\) का योग ज्ञात कीजिए।
Find the sum of the AP \(-12,-5,2,\ldots,184\).
#finite ap
#last term
#sum
A (2449)
B (2472)
C (2517)
D (2494)
Explanation opens after your attempt
Step 1
Concept
First, (184=-12+(n-1)7) gives (n=29), and the sum is (2494). When the last term is given, find (n) first.
Step 2
Why this answer is correct
The correct answer is D. (2494). First, (184=-12+(n-1)7) gives (n=29), and the sum is (2494). When the last term is given, find (n) first.
Step 3
Exam Tip
पहले (184=-12+(n-1)7) से (n=29) मिलता है और योग (2494) है। अंतिम पद दिया हो तो पहले (n) निकालें।
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किसी समांतर श्रेढ़ी में पहले (25) पदों का योग (1625) है और (25)वाँ पद (113) है। पहला पद ज्ञात कीजिए।
In an AP, the sum of the first (25) terms is (1625), and the (25)th term is (113). Find the first term.
#first term
#last term
#sum
#ap
A (17)
B (15)
C (19)
D (21)
Explanation opens after your attempt
Step 1
Concept
From (1625=\frac{25}{2}(a+113)), (a=17). Treat the (n)th term as the last term of the first (n) terms.
Step 2
Why this answer is correct
The correct answer is A. (17). From (1625=\frac{25}{2}(a+113)), (a=17). Treat the (n)th term as the last term of the first (n) terms.
Step 3
Exam Tip
(1625=\frac{25}{2}(a+113)) से (a=17) मिलता है। (n)वें पद को पहले (n) पदों का अंतिम पद मानें।
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समांतर श्रेढ़ी \(95,89,83,\ldots\) के पहले (20) पदों का योग ज्ञात कीजिए।
Find the sum of the first (20) terms of the AP \(95,89,83,\ldots\).
#decreasing ap
#last term
#sum
A (730)
B (760)
C (790)
D (820)
Explanation opens after your attempt
Step 1
Concept
The last term is (-19), and \(S_{20}=760\). Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.
Step 2
Why this answer is correct
The correct answer is B. (760). The last term is (-19), and \(S_{20}=760\). Even in a decreasing AP, (S_n=\frac{n}{2}(a+l)) is useful.
Step 3
Exam Tip
अंतिम पद (-19) है और \(S_{20}=760\) है। घटती श्रेढ़ी में भी (S_n=\frac{n}{2}(a+l)) उपयोगी है।
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समांतर श्रेढ़ी \(-6,1,8,\ldots,169\) का योग ज्ञात कीजिए।
Find the sum of the AP \(-6,1,8,\ldots,169\).
#finite ap
#last term
#sum
A (2074)
B (2096)
C (2119)
D (2142)
Explanation opens after your attempt
Step 1
Concept
First, (169=-6+(n-1)7) gives (n=26), and the sum is (2119). When the last term is given, find (n) first.
Step 2
Why this answer is correct
The correct answer is C. (2119). First, (169=-6+(n-1)7) gives (n=26), and the sum is (2119). When the last term is given, find (n) first.
Step 3
Exam Tip
पहले (169=-6+(n-1)7) से (n=26) मिलता है और योग (2119) है। अंतिम पद दिया हो तो पहले (n) निकालें।
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किसी समांतर श्रेढ़ी में पहले (20) पदों का योग (740) है और (20)वाँ पद (60) है। पहला पद ज्ञात कीजिए।
In an AP, the sum of the first (20) terms is (740), and the (20)th term is (60). Find the first term.
#first term
#last term
#sum
#ap
A (10)
B (14)
C (18)
D (22)
Explanation opens after your attempt
Step 1
Concept
From (740=10(a+60)), (a=14). When the (n)th term is given, use it as the last term for the first (n) terms.
Step 2
Why this answer is correct
The correct answer is B. (14). From (740=10(a+60)), (a=14). When the (n)th term is given, use it as the last term for the first (n) terms.
Step 3
Exam Tip
(740=10(a+60)) से (a=14) मिलता है। जब (n)वाँ पद दिया हो तो उसे अंतिम पद की तरह इस्तेमाल करें।
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समांतर श्रेढ़ी \(12,18,24,\ldots,192\) का योग ज्ञात कीजिए।
Find the sum of the AP \(12,18,24,\ldots,192\).
#finite ap
#last term
#sum
A (3144)
B (3156)
C (3162)
D (3180)
Explanation opens after your attempt
Step 1
Concept
First, (192=12+(n-1)6) gives (n=31), and the sum is (3162). When the last term is given, find the number of terms first.
Step 2
Why this answer is correct
The correct answer is C. (3162). First, (192=12+(n-1)6) gives (n=31), and the sum is (3162). When the last term is given, find the number of terms first.
Step 3
Exam Tip
पहले (192=12+(n-1)6) से (n=31) मिलता है और योग (3162) है। अंतिम पद हो तो पहले पदों की संख्या निकालें।
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समांतर श्रेढ़ी \(7,12,17,\ldots,82\) का योग ज्ञात कीजिए।
Find the sum of the AP \(7,12,17,\ldots,82\).
#finite ap
#last term
#sum formula
A (700)
B (712)
C (720)
D (724)
Explanation opens after your attempt
Step 1
Concept
From (82=7+(n-1)5), (n=16), and then the sum is (712). Finding (n) from the last term is the first step.
Step 2
Why this answer is correct
The correct answer is B. (712). From (82=7+(n-1)5), (n=16), and then the sum is (712). Finding (n) from the last term is the first step.
Step 3
Exam Tip
(82=7+(n-1)5) से (n=16), फिर योग (712) है। अंतिम पद से (n) निकालना पहला कदम है।
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समांतर श्रेढ़ी \(8,13,18,\ldots,83\) का योग ज्ञात कीजिए।
Find the sum of the AP \(8,13,18,\ldots,83\).
#finite ap
#last term
#sum
A (720)
B (728)
C (736)
D (744)
Explanation opens after your attempt
Step 1
Concept
First find (n): (83=8+(n-1)5), so (n=16) and the sum is (728). When the last term is given, find the number of terms first.
Step 2
Why this answer is correct
The correct answer is B. (728). First find (n): (83=8+(n-1)5), so (n=16) and the sum is (728). When the last term is given, find the number of terms first.
Step 3
Exam Tip
पहले (n) निकालें: (83=8+(n-1)5), इसलिए (n=16) और योग (728) है। अंतिम पद होने पर पहले पदों की संख्या निकालें।
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समांतर श्रेढ़ी \(100,95,90,\ldots\) के पहले (12) पदों का योग ज्ञात कीजिए।
Find the sum of the first (12) terms of the AP \(100,95,90,\ldots\).
#decreasing sequence
#last term
#sum
A (870)
B (880)
C (890)
D (900)
Explanation opens after your attempt
Step 1
Concept
The last term is (45), so (S_{12}=\frac{12}{2}(100+45)=870). Once the last term is found, the sum is quick.
Step 2
Why this answer is correct
The correct answer is A. (870). The last term is (45), so (S_{12}=\frac{12}{2}(100+45)=870). Once the last term is found, the sum is quick.
Step 3
Exam Tip
अंतिम पद (45) है, इसलिए (S_{12}=\frac{12}{2}(100+45)=870)। अंतिम पद मिल जाए तो योग तेजी से निकलेगा।
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(7) से (140) तक (7) के सभी धनात्मक गुणजों का योग ज्ञात कीजिए।
Find the sum of all positive multiples of (7) from (7) to (140).
#multiples
#ap sum
#last term
A (1400)
B (1540)
C (1330)
D (1470)
Explanation opens after your attempt
Step 1
Concept
The AP is \(7,14,\ldots,140\) with (20) terms, and its sum is (1470). Finding (n) from the last term is an easy method.
Step 2
Why this answer is correct
The correct answer is D. (1470). The AP is \(7,14,\ldots,140\) with (20) terms, and its sum is (1470). Finding (n) from the last term is an easy method.
Step 3
Exam Tip
यह श्रेढ़ी \(7,14,\ldots,140\) है जिसमें (20) पद हैं और योग (1470) है। अंतिम पद से (n) निकालना आसान तरीका है।
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किसी समांतर श्रेढ़ी के पहले (7) पदों का योग (140) है और पहला पद (5) है। यदि अंतिम पद पूछा जाए तो योग सूत्र से (l) क्या होगा?
The sum of the first (7) terms of an arithmetic progression is (140), and the first term is (5). Using the sum formula, what is the last term (l)?
#ap_sum
#reverse_formula
#last_term
A (30)
B (35)
C (40)
D (45)
Explanation opens after your attempt
Step 1
Concept
From (140=\frac{7}{2}(5+l)), (l=35). Learn to use the sum formula in reverse too.
Step 2
Why this answer is correct
The correct answer is B. (35). From (140=\frac{7}{2}(5+l)), (l=35). Learn to use the sum formula in reverse too.
Step 3
Exam Tip
(140=\frac{7}{2}(5+l)) से (l=35)। योग सूत्र को उल्टा लगाना भी सीखें।
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समान्तर श्रेणी \(12,17,22,\ldots\) के पहले (14) पदों का योग कितना है?
What is the sum of the first (14) terms of the AP \(12,17,22,\ldots\)?
#ap-sum-last-term
A (605)
B (615)
C (623)
D (629)
Explanation opens after your attempt
Step 1
Concept
The last term is \(12+13\cdot5=77\). (S_{14}=\frac{14}{2}(12+77)=623).
Step 2
Why this answer is correct
The correct answer is C. (623). The last term is \(12+13\cdot5=77\). (S_{14}=\frac{14}{2}(12+77)=623).
Step 3
Exam Tip
अंतिम पद \(12+13\cdot5=77\) है। (S_{14}=\frac{14}{2}(12+77)=623)।
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यदि समान्तर श्रेणी के पहले (9) पदों का योग (279) और पहले (18) पदों का योग (1044) है तो पहले (27) पदों का योग कितना होगा?
If the sum of the first (9) terms of an arithmetic progression is (279) and the sum of the first (18) terms is (1044), what is the sum of the first (27) terms?
#ap
#advanced-sums
#expert
A (2187)
B (2241)
C (2295)
D (2349)
Explanation opens after your attempt
Step 1
Concept
Let \(S_n=\frac{d}{2}n^2+\frac{2a-d}{2}n\). The two sums give (a=7), (d=6), so \(S_{27}=2295\); exam tip: write \(S_n\) as a quadratic in (n).
Step 2
Why this answer is correct
The correct answer is C. (2295). Let \(S_n=\frac{d}{2}n^2+\frac{2a-d}{2}n\). The two sums give (a=7), (d=6), so \(S_{27}=2295\); exam tip: write \(S_n\) as a quadratic in (n).
Step 3
Exam Tip
मानें \(S_n=\frac{d}{2}n^2+\frac{2a-d}{2}n\) और दो योगों से (a=7), (d=6) मिलते हैं इसलिए \(S_{27}=2295\)। परीक्षा में \(S_n\) को (n) के द्विघात रूप में लिखना उपयोगी है।
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किसी समांतर श्रेढ़ी के पहले पद और (60)वें पद का योग (300) है। (21)वें पद से (40)वें पद तक का योग ज्ञात कीजिए।
The sum of the first term and the (60)th term of an AP is (300). Find the sum from the (21)st term to the (40)th term.
#symmetric terms
#range sum
#ap
A (2900)
B (2950)
C (3000)
D (3050)
Explanation opens after your attempt
Step 1
Concept
\(a_{21}+a_{40}=a_1+a_{60}=300\), so the sum of (20) terms is (3000). Sums of symmetric terms are equal in an AP.
Step 2
Why this answer is correct
The correct answer is C. (3000). \(a_{21}+a_{40}=a_1+a_{60}=300\), so the sum of (20) terms is (3000). Sums of symmetric terms are equal in an AP.
Step 3
Exam Tip
\(a_{21}+a_{40}=a_1+a_{60}=300\), इसलिए (20) पदों का योग (3000) है। सममित पदों का योग बराबर होता है।
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किसी समांतर श्रेढ़ी के पहले पद और (40)वें पद का योग (210) है। (11)वें पद से (30)वें पद तक का योग ज्ञात कीजिए।
The sum of the first term and the (40)th term of an AP is (210). Find the sum from the (11)th term to the (30)th term.
#symmetric terms
#range sum
#ap
A (2000)
B (2100)
C (2200)
D (2300)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}+a_{30}=a_1+a_{40}=210\), so the sum of (20) terms is (2100). Sums of symmetric terms are equal in an AP.
Step 2
Why this answer is correct
The correct answer is B. (2100). \(a_{11}+a_{30}=a_1+a_{40}=210\), so the sum of (20) terms is (2100). Sums of symmetric terms are equal in an AP.
Step 3
Exam Tip
\(a_{11}+a_{30}=a_1+a_{40}=210\), इसलिए (20) पदों का योग (2100) है। सममित पदों का योग बराबर होता है।
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किसी समांतर श्रेढ़ी के पहले (10) पदों का योग (145) है और पहले (5) पदों का योग (45) है। छठे से दसवें पदों का योग कितना है?
The sum of the first (10) terms of an arithmetic progression is (145), and the sum of the first (5) terms is (45). What is the sum of the (6)th to (10)th terms?
#partial_sum
#ap_sum
#subtraction
A (90)
B (95)
C (100)
D (105)
Explanation opens after your attempt
Step 1
Concept
The sum of the (6)th to (10)th terms is (145-45=100). Subtract the first part from the total sum.
Step 2
Why this answer is correct
The correct answer is C. (100). The sum of the (6)th to (10)th terms is (145-45=100). Subtract the first part from the total sum.
Step 3
Exam Tip
छठे से दसवें पदों का योग (145-45=100) है। कुल योग में से पहले भाग का योग घटाएँ।
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यदि किसी समांतर श्रेढ़ी के पहले (6) पदों का योग (75) है और पहले (12) पदों का योग (210) है, तो सातवें से बारहवें पदों का योग कितना है?
If the sum of the first (6) terms of an arithmetic progression is (75), and the sum of the first (12) terms is (210), what is the sum of the (7)th to (12)th terms?
#partial_sum
#ap_sum
#difference
A (125)
B (130)
C (135)
D (140)
Explanation opens after your attempt
Step 1
Concept
The sum of the (7)th to (12)th terms is \(S_{12}-S_6=135\). Find the sum of middle terms by subtracting partial sums.
Step 2
Why this answer is correct
The correct answer is C. (135). The sum of the (7)th to (12)th terms is \(S_{12}-S_6=135\). Find the sum of middle terms by subtracting partial sums.
Step 3
Exam Tip
सातवें से बारहवें पदों का योग \(S_{12}-S_6=135\) है। बीच के पदों का योग कुल योगों के अंतर से निकालें।
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भारत के अंतिम वायसराय कौन थे?
Who was the last Viceroy of India?
#modern indian history
#lord mountbatten
#last viceroy
A लॉर्ड कर्जन / Lord Curzon
B लॉर्ड माउंटबेटन / Lord Mountbatten
C लॉर्ड रिपन / Lord Ripon
D लॉर्ड डलहौजी / Lord Dalhousie
Explanation opens after your attempt
Correct Answer
B. लॉर्ड माउंटबेटन / Lord Mountbatten
Step 1
Concept
Lord Mountbatten was the last Viceroy of India. Exam tip: remember the last Viceroy and transfer of power.
Step 2
Why this answer is correct
The correct answer is B. लॉर्ड माउंटबेटन / Lord Mountbatten. Lord Mountbatten was the last Viceroy of India. Exam tip: remember the last Viceroy and transfer of power.
Step 3
Exam Tip
लॉर्ड माउंटबेटन भारत के अंतिम वायसराय थे। परीक्षा में अंतिम वायसराय और सत्ता हस्तांतरण याद रखें।
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(600) से कम (13) के धनात्मक गुणजों में अंतिम पद क्या है?
What is the last term among the positive multiples of (13) less than (600)?
#ap multiples last-term nth-term
A (585)
B (598)
C (611)
D (624)
Explanation opens after your attempt
Step 1
Concept
In (13n<600), the greatest (n=46) so the term is \(13\times46=598\). Take the greatest integer below the limit.
Step 2
Why this answer is correct
The correct answer is B. (598). In (13n<600), the greatest (n=46) so the term is \(13\times46=598\). Take the greatest integer below the limit.
Step 3
Exam Tip
(13n<600) में सबसे बड़ा (n=46) है इसलिए पद \(13\times46=598\)। सीमा से कम सबसे बड़ा पूर्णांक लें।
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समान्तर श्रेणी \(7,12,17,\ldots\) में (180) से कम अंतिम पद क्या है?
In the AP \(7,12,17,\ldots\), what is the last term less than (180)?
#ap last-term-less-than nth-term class10
A (172)
B (175)
C (177)
D (179)
Explanation opens after your attempt
Step 1
Concept
The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).
Step 2
Why this answer is correct
The correct answer is C. (177). The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).
Step 3
Exam Tip
पद (7+5(n-1)) हैं। (180) से कम अंतिम पद (177) है क्योंकि अगला पद (182) होगा।
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(500) से कम (11) के धनात्मक गुणजों में अंतिम पद क्या है?
What is the last term among the positive multiples of (11) less than (500)?
#ap
#multiples
#last-term
#nth-term
A (484)
B (495)
C (506)
D (517)
Explanation opens after your attempt
Step 1
Concept
In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.
Step 2
Why this answer is correct
The correct answer is B. (495). In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.
Step 3
Exam Tip
(11n<500) में सबसे बड़ा (n=45) है इसलिए पद \(11\times45=495\)। सीमा से कम सबसे बड़ा पूर्णांक लें।
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समान्तर श्रेणी \(2,6,10,\ldots\) में (75) से कम अंतिम पद क्या है?
In the AP \(2,6,10,\ldots\), what is the last term less than (75)?
#ap
#last-term-less-than
#nth-term
#class10
A (74)
B (70)
C (72)
D (76)
Explanation opens after your attempt
Step 1
Concept
The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
Step 2
Why this answer is correct
The correct answer is A. (74). The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
Step 3
Exam Tip
इस श्रेणी के पद (2+4(n-1)) हैं। (75) से कम अंतिम पद (74) है।
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\(2^4 \times 3^2 \times 5\) से बनने वाली संख्या में शून्य से अलग अंतिम अंक क्या होगा?
What will be the last non-zero digit of the number \(2^4 \times 3^2 \times 5\)?
#real-numbers
#prime-factorisation
#last-nonzero-digit
#expert
A 2
B 4
C 6
D 8
Explanation opens after your attempt
Step 1
Concept
One pair of (2) and (5) makes (10), giving a trailing zero.
Step 2
Why this answer is correct
Remove one (2) with the (5), leaving \(2^3 \times 3^2=72\), so the last non-zero digit is (2).
Step 3
Exam Tip
After removing trailing-zero pairs, check the last digit of the remaining product. चरण 1: (2) और (5) का एक जोड़ा (10) बनाता है, जो अंतिम शून्य देता है। चरण 2: एक (5) के साथ एक (2) हटाएं, बचता है \(2^3 \times 3^2=8 \times 9=72\), इसलिए शून्य से अलग अंतिम अंक (2) है। चरण 3: अंतिम शून्य हटाने के बाद बची संख्या का अंतिम अंक देखें।
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किसी समांतर श्रेढ़ी का (12)वाँ पद (64) और (32)वाँ पद (184) है। पहले (45) पदों का योग ज्ञात कीजिए।
The (12)th term of an AP is (64), and the (32)nd term is (184). Find the sum of the first (45) terms.
#given terms
#find sum
#ap
A (5850)
B (5760)
C (5940)
D (6030)
Explanation opens after your attempt
Step 1
Concept
From the two terms, (d=6) and (a=-2), so \(S_{45}=5850\). First find (a,d), then apply the sum formula.
Step 2
Why this answer is correct
The correct answer is A. (5850). From the two terms, (d=6) and (a=-2), so \(S_{45}=5850\). First find (a,d), then apply the sum formula.
Step 3
Exam Tip
दो पदों से (d=6) और (a=-2) मिलते हैं, इसलिए \(S_{45}=5850\) है। पहले (a,d) निकालकर योग सूत्र लगाएँ।
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यदि \(S_n=4n^2+3n\), तो (61)वें पद से (90)वें पद तक का योग ज्ञात कीजिए।
If \(S_n=4n^2+3n\), find the sum from the (61)st term to the (90)th term.
#given sn
#range sum
#expert
A (18090)
B (17970)
C (18210)
D (18330)
Explanation opens after your attempt
Correct Answer
A. (18090)
Step 1
Concept
The required sum is \(S_{90}-S_{60}=18090\). With given \(S_n\), subtract directly according to the limits.
Step 2
Why this answer is correct
The correct answer is A. (18090). The required sum is \(S_{90}-S_{60}=18090\). With given \(S_n\), subtract directly according to the limits.
Step 3
Exam Tip
आवश्यक योग \(S_{90}-S_{60}=18090\) है। दिए गए \(S_n\) में सीमाओं के अनुसार सीधे घटाव करें।
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यदि किसी समांतर श्रेढ़ी का \(S_n=5n^2-4n\) है, तो (35)वाँ पद ज्ञात कीजिए।
If the sum of an AP is \(S_n=5n^2-4n\), find the (35)th term.
#term from sum
#given sn
#ap
A (331)
B (336)
C (341)
D (346)
Explanation opens after your attempt
Step 1
Concept
The (35)th term is \(S_{35}-S_{34}=341\). To get one term, use \(S_n-S_{n-1}\).
Step 2
Why this answer is correct
The correct answer is C. (341). The (35)th term is \(S_{35}-S_{34}=341\). To get one term, use \(S_n-S_{n-1}\).
Step 3
Exam Tip
(35)वाँ पद \(S_{35}-S_{34}=341\) है। एक पद पाने के लिए \(S_n-S_{n-1}\) लगाएँ।
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यदि \(S_n=3n^2+2n\), तो (51)वें पद से (80)वें पद तक का योग ज्ञात कीजिए।
If \(S_n=3n^2+2n\), find the sum from the (51)st term to the (80)th term.
#given sn
#range sum
#expert
A (11640)
B (11760)
C (11880)
D (12000)
Explanation opens after your attempt
Correct Answer
B. (11760)
Step 1
Concept
The required sum is \(S_{80}-S_{50}=11760\). When \(S_n\) is given, find a range sum directly by subtraction.
Step 2
Why this answer is correct
The correct answer is B. (11760). The required sum is \(S_{80}-S_{50}=11760\). When \(S_n\) is given, find a range sum directly by subtraction.
Step 3
Exam Tip
आवश्यक योग \(S_{80}-S_{50}=11760\) है। \(S_n\) दिया हो तो सीमा-योग सीधे घटाव से निकालें।
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यदि (S_n=n(6n-1)), तो (31)वें पद से (50)वें पद तक का योग ज्ञात कीजिए।
If (S_n=n(6n-1)), find the sum from the (31)st term to the (50)th term.
#given sn
#range sum
#hard
A (9460)
B (9520)
C (9640)
D (9580)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{50}-S_{30}=9580\). When starting from the (31)st term, subtract the sum up to (30).
Step 2
Why this answer is correct
The correct answer is D. (9580). The required sum is \(S_{50}-S_{30}=9580\). When starting from the (31)st term, subtract the sum up to (30).
Step 3
Exam Tip
आवश्यक योग \(S_{50}-S_{30}=9580\) है। (31)वें पद से शुरू होने पर (30) तक का योग घटाएँ।
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किसी समांतर श्रेढ़ी का (9)वाँ पद (49) और (24)वाँ पद (124) है। पहले (35) पदों का योग ज्ञात कीजिए।
The (9)th term of an AP is (49), and the (24)th term is (124). Find the sum of the first (35) terms.
#given terms
#find sum
#ap
A (3220)
B (3255)
C (3290)
D (3325)
Explanation opens after your attempt
Step 1
Concept
From the two terms, (d=5) and (a=9), so \(S_{35}=3290\). First find (a,d), then apply the sum formula.
Step 2
Why this answer is correct
The correct answer is C. (3290). From the two terms, (d=5) and (a=9), so \(S_{35}=3290\). First find (a,d), then apply the sum formula.
Step 3
Exam Tip
दो पदों से (d=5) और (a=9) मिलते हैं, इसलिए \(S_{35}=3290\) है। पहले (a,d) निकालकर योग सूत्र लगाएँ।
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यदि \(S_n=7n^2-2n\), तो (41)वें पद से (60)वें पद तक का योग ज्ञात कीजिए।
If \(S_n=7n^2-2n\), find the sum from the (41)st term to the (60)th term.
#given sn
#range sum
#hard
A (13960)
B (13820)
C (14100)
D (14240)
Explanation opens after your attempt
Correct Answer
A. (13960)
Step 1
Concept
The required sum is \(S_{60}-S_{40}=13960\). With given \(S_n\), subtract directly according to the limits.
Step 2
Why this answer is correct
The correct answer is A. (13960). The required sum is \(S_{60}-S_{40}=13960\). With given \(S_n\), subtract directly according to the limits.
Step 3
Exam Tip
आवश्यक योग \(S_{60}-S_{40}=13960\) है। दिए गए \(S_n\) में सीमाओं के अनुसार सीधे घटाव करें।
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यदि किसी समांतर श्रेढ़ी का \(S_n=4n^2+9n\) है, तो (27)वाँ पद ज्ञात कीजिए।
If the sum of an AP is \(S_n=4n^2+9n\), find the (27)th term.
#term from sum
#given sn
#ap
A (219)
B (221)
C (223)
D (225)
Explanation opens after your attempt
Step 1
Concept
The (27)th term is \(S_{27}-S_{26}=221\). To get a single term, use \(S_n-S_{n-1}\).
Step 2
Why this answer is correct
The correct answer is B. (221). The (27)th term is \(S_{27}-S_{26}=221\). To get a single term, use \(S_n-S_{n-1}\).
Step 3
Exam Tip
(27)वाँ पद \(S_{27}-S_{26}=221\) है। किसी एक पद को पाने के लिए \(S_n-S_{n-1}\) लगाएँ।
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यदि \(S_n=6n^2-5n\), तो (31)वें पद से (50)वें पद तक का योग ज्ञात कीजिए।
If \(S_n=6n^2-5n\), find the sum from the (31)st term to the (50)th term.
#given sn
#range sum
#ap
A (9400)
B (9500)
C (9600)
D (9700)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{50}-S_{30}=9500\). When starting from the (31)st term, subtract the sum up to (30).
Step 2
Why this answer is correct
The correct answer is B. (9500). The required sum is \(S_{50}-S_{30}=9500\). When starting from the (31)st term, subtract the sum up to (30).
Step 3
Exam Tip
आवश्यक योग \(S_{50}-S_{30}=9500\) है। (31)वें पद से शुरू होने पर (30) तक का योग घटाएँ।
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यदि (S_n=n(4n+3)), तो (21)वें पद से (35)वें पद तक का योग ज्ञात कीजिए।
If (S_n=n(4n+3)), find the sum from the (21)st term to the (35)th term.
#given sn
#range sum
#hard
A (3255)
B (3285)
C (3315)
D (3345)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{35}-S_{20}=3345\). When starting from the (21)st term, subtract the sum up to (20).
Step 2
Why this answer is correct
The correct answer is D. (3345). The required sum is \(S_{35}-S_{20}=3345\). When starting from the (21)st term, subtract the sum up to (20).
Step 3
Exam Tip
आवश्यक योग \(S_{35}-S_{20}=3345\) है। (21)वें पद से शुरू होने पर (20) तक का योग घटाएँ।
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किसी समांतर श्रेढ़ी का (8)वाँ पद (37) और (22)वाँ पद (107) है। पहले (30) पदों का योग ज्ञात कीजिए।
The (8)th term of an AP is (37), and the (22)nd term is (107). Find the sum of the first (30) terms.
#given terms
#find sum
#ap
A (2190)
B (2235)
C (2280)
D (2325)
Explanation opens after your attempt
Step 1
Concept
From the two terms, (d=5) and (a=2), so \(S_{30}=2235\). First find (a,d), then apply the sum formula.
Step 2
Why this answer is correct
The correct answer is B. (2235). From the two terms, (d=5) and (a=2), so \(S_{30}=2235\). First find (a,d), then apply the sum formula.
Step 3
Exam Tip
दो पदों से (d=5) और (a=2) मिलते हैं, इसलिए \(S_{30}=2235\) है। पहले (a,d) निकालकर योग सूत्र लगाएँ।
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यदि \(S_n=4n^2+n\), तो (31)वें पद से (45)वें पद तक का योग ज्ञात कीजिए।
If \(S_n=4n^2+n\), find the sum from the (31)st term to the (45)th term.
#given sn
#range sum
#hard
A (4455)
B (4485)
C (4515)
D (4545)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{45}-S_{30}=4515\). With given \(S_n\), find the range sum directly by subtraction.
Step 2
Why this answer is correct
The correct answer is C. (4515). The required sum is \(S_{45}-S_{30}=4515\). With given \(S_n\), find the range sum directly by subtraction.
Step 3
Exam Tip
आवश्यक योग \(S_{45}-S_{30}=4515\) है। दिए गए \(S_n\) में range sum सीधे घटाव से निकालें।
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यदि किसी समांतर श्रेढ़ी का \(S_n=3n^2+5n\) है, तो (22)वाँ पद ज्ञात कीजिए।
If the sum of an AP is \(S_n=3n^2+5n\), find the (22)nd term.
#term from sum
#given sn
#ap
A (134)
B (131)
C (137)
D (140)
Explanation opens after your attempt
Step 1
Concept
The (22)nd term is \(S_{22}-S_{21}=134\). To get a single term, use \(S_n-S_{n-1}\).
Step 2
Why this answer is correct
The correct answer is A. (134). The (22)nd term is \(S_{22}-S_{21}=134\). To get a single term, use \(S_n-S_{n-1}\).
Step 3
Exam Tip
(22)वाँ पद \(S_{22}-S_{21}=134\) है। किसी एक पद को पाने के लिए \(S_n-S_{n-1}\) लगाएँ।
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यदि \(S_n=5n^2-2n\), तो (26)वें पद से (40)वें पद तक का योग ज्ञात कीजिए।
If \(S_n=5n^2-2n\), find the sum from the (26)th term to the (40)th term.
#given sn
#range sum
#ap
A (4770)
B (4800)
C (4815)
D (4845)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{40}-S_{25}=4845\). When starting from the (26)th term, subtract the sum up to (25).
Step 2
Why this answer is correct
The correct answer is D. (4845). The required sum is \(S_{40}-S_{25}=4845\). When starting from the (26)th term, subtract the sum up to (25).
Step 3
Exam Tip
आवश्यक योग \(S_{40}-S_{25}=4845\) है। (26)वें पद से शुरू होने पर (25) तक का योग घटाएँ।
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यदि (S_n=n(5n-2)), तो (16)वें पद से (25)वें पद तक का योग ज्ञात कीजिए।
If (S_n=n(5n-2)), find the sum from the (16)th term to the (25)th term.
#given sn
#range sum
#hard
A (1920)
B (1950)
C (2010)
D (1980)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{25}-S_{15}=1980\). When starting from the (16)th term, subtract the sum up to (15).
Step 2
Why this answer is correct
The correct answer is D. (1980). The required sum is \(S_{25}-S_{15}=1980\). When starting from the (16)th term, subtract the sum up to (15).
Step 3
Exam Tip
आवश्यक योग \(S_{25}-S_{15}=1980\) है। (16)वें पद से शुरू होने पर (15) तक का योग घटाएँ।
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किसी समांतर श्रेढ़ी का (5)वाँ पद (22) और (15)वाँ पद (62) है। पहले (20) पदों का योग ज्ञात कीजिए।
The (5)th term of an AP is (22), and the (15)th term is (62). Find the sum of the first (20) terms.
#given terms
#find sum
#ap
A (840)
B (880)
C (920)
D (960)
Explanation opens after your attempt
Step 1
Concept
From the two terms, (d=4) and (a=6), so \(S_{20}=880\). First find (a,d), then apply the sum formula.
Step 2
Why this answer is correct
The correct answer is B. (880). From the two terms, (d=4) and (a=6), so \(S_{20}=880\). First find (a,d), then apply the sum formula.
Step 3
Exam Tip
दो पदों से (d=4) और (a=6) मिलते हैं, इसलिए \(S_{20}=880\)। पहले (a,d) निकालकर योग सूत्र लगाएँ।
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यदि \(S_n=3n^2+4n\), तो (21)वें पद से (30)वें पद तक का योग ज्ञात कीजिए।
If \(S_n=3n^2+4n\), find the sum from the (21)st term to the (30)th term.
#given sn
#range sum
#ap
A (1510)
B (1525)
C (1540)
D (1555)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{30}-S_{20}=1540\). If the range starts at (21), subtract the sum up to (20).
Step 2
Why this answer is correct
The correct answer is C. (1540). The required sum is \(S_{30}-S_{20}=1540\). If the range starts at (21), subtract the sum up to (20).
Step 3
Exam Tip
आवश्यक योग \(S_{30}-S_{20}=1540\) है। सीमा (21) से शुरू हो तो (20) तक का योग घटाएँ।
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यदि किसी समांतर श्रेढ़ी का \(S_n=2n^2+7n\) है, तो (18)वाँ पद ज्ञात कीजिए।
If the sum of an AP is \(S_n=2n^2+7n\), find the (18)th term.
#term from sum
#given sn
#ap
A (77)
B (75)
C (79)
D (81)
Explanation opens after your attempt
Step 1
Concept
The (18)th term is \(S_{18}-S_{17}=77\). To get a term, use \(S_n-S_{n-1}\).
Step 2
Why this answer is correct
The correct answer is A. (77). The (18)th term is \(S_{18}-S_{17}=77\). To get a term, use \(S_n-S_{n-1}\).
Step 3
Exam Tip
(18)वाँ पद \(S_{18}-S_{17}=77\) है। किसी पद को पाने के लिए \(S_n-S_{n-1}\) लगाएँ।
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किसी समांतर श्रेढ़ी में \(S_n=2n^2+5n\) है। पहले (8) पदों का योग क्या होगा?
In an AP, \(S_n=2n^2+5n\). What is the sum of the first (8) terms?
#sum formula
#given sn
#substitution
A (168)
B (160)
C (172)
D (176)
Explanation opens after your attempt
Step 1
Concept
(S_8=2(8)2 +5(8)=168). Put (n=8) directly in the given \(S_n\).
Step 2
Why this answer is correct
The correct answer is A. (168). (S_8=2(8)2 +5(8)=168). Put (n=8) directly in the given \(S_n\).
Step 3
Exam Tip
(S_8=2(8)2 +5(8)=168)। दिए गए \(S_n\) में सीधे (n=8) रखें।
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यदि (a=3), (d=6), (n=12) है तो पहले (12) पदों का योग क्या है?
If (a=3), (d=6), (n=12), what is the sum of the first (12) terms?
#ap-sum-given-a-d
A (432)
B (438)
C (444)
D (450)
Explanation opens after your attempt
Step 1
Concept
\(S_{12}=\frac{12}{2}[6+11\cdot6]\). Therefore \(S_{12}=6\cdot72=432\).
Step 2
Why this answer is correct
The correct answer is A. (432). \(S_{12}=\frac{12}{2}[6+11\cdot6]\). Therefore \(S_{12}=6\cdot72=432\).
Step 3
Exam Tip
\(S_{12}=\frac{12}{2}[6+11\cdot6]\)। इसलिए \(S_{12}=6\cdot72=432\)।
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किसी समान्तर श्रेणी में (a=4) है और पहले (16) पदों का योग (904) है। (16)वाँ पद क्या होगा?
In an arithmetic progression (a=4) and the sum of the first (16) terms is (904). What is the (16)th term?
#ap
#last-term-from-total
#expert
A (105)
B (109)
C (113)
D (117)
Explanation opens after your attempt
Step 1
Concept
From (904=8(4+l)), (l=109). Exam tip: with sum and first term known, the last term can be found quickly.
Step 2
Why this answer is correct
The correct answer is B. (109). From (904=8(4+l)), (l=109). Exam tip: with sum and first term known, the last term can be found quickly.
Step 3
Exam Tip
(904=8(4+l)) से (l=109) मिलता है। परीक्षा में योग और प्रथम पद से अंतिम पद तुरंत निकाला जा सकता है।
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समांतर श्रेढ़ी \(-25,-16,-7,\ldots,209\) का योग ज्ञात कीजिए।
Find the sum of the AP \(-25,-16,-7,\ldots,209\).
#finite ap
#last term
#negative first term
A (2412)
B (2448)
C (2520)
D (2484)
Explanation opens after your attempt
Step 1
Concept
First (209=-25+(n-1)9) gives (n=27), and the sum is (2484). When the last term is given, find (n) first.
Step 2
Why this answer is correct
The correct answer is D. (2484). First (209=-25+(n-1)9) gives (n=27), and the sum is (2484). When the last term is given, find (n) first.
Step 3
Exam Tip
पहले (209=-25+(n-1)9) से (n=27) मिलता है और योग (2484) है। अंतिम पद दिया हो तो पहले (n) निकालें।
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यदि किसी समांतर श्रेणी के पहले (9) पदों का योग (279) और पहला पद (7) है, तो अंतिम पद कितना होगा?
If the sum of the first (9) terms of an arithmetic progression is (279), and the first term is (7), what is the last term?
#reverse_formula
#last_term
#ap_sum
A (49)
B (51)
C (53)
D (55)
Explanation opens after your attempt
Step 1
Concept
From (279=\frac{9}{2}(7+l)), (l=55). Clear the fraction and solve the equation.
Step 2
Why this answer is correct
The correct answer is D. (55). From (279=\frac{9}{2}(7+l)), (l=55). Clear the fraction and solve the equation.
Step 3
Exam Tip
(279=\frac{9}{2}(7+l)) से (l=55)। भिन्न हटाकर समीकरण हल करें।
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समान्तर श्रेणी \(15,19,23,\ldots\) के पहले (n) पदों का योग पहली (n) प्राकृतिक संख्याओं के योग का (6) गुना है। (n) क्या होगा?
The sum of the first (n) terms of the arithmetic progression \(15,19,23,\ldots\) is (6) times the sum of the first (n) natural numbers. What is (n)?
#ap
#comparison-with-natural-sum
#expert
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
The equation gives (4n+26=6n+6), so (n=10). Exam tip: simplify the common \(\frac{n}{2}\) in both sums.
Step 2
Why this answer is correct
The correct answer is D. (10). The equation gives (4n+26=6n+6), so (n=10). Exam tip: simplify the common \(\frac{n}{2}\) in both sums.
Step 3
Exam Tip
समीकरण से (4n+26=6n+6) मिलता है इसलिए (n=10)। परीक्षा में दोनों योगों में सामान्य \(\frac{n}{2}\) को सरल करें।
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एक समान्तर श्रेणी में पहले (15) पदों का योग (600) है और अगले (15) पदों का योग (1500) है। सार्व अंतर क्या होगा?
In an arithmetic progression the sum of the first (15) terms is (600) and the sum of the next (15) terms is (1500). What is the common difference?
#ap
#block-sums
#expert
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The difference between the sums of two equal blocks is (225d), so (d=4). Exam tip: comparing equal-length blocks is a fast method.
Step 2
Why this answer is correct
The correct answer is D. (4). The difference between the sums of two equal blocks is (225d), so (d=4). Exam tip: comparing equal-length blocks is a fast method.
Step 3
Exam Tip
बराबर आकार के दो खंडों के योगों का अंतर (225d) है इसलिए (d=4)। परीक्षा में समान लंबाई वाले खंडों की तुलना तेज तरीका है।
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किसी समान्तर श्रेणी में पहले (12) पदों का योग (420) है और अगले (12) पदों का योग (1188) है। सार्व अंतर क्या होगा?
In an arithmetic progression the sum of the first (12) terms is (420) and the sum of the next (12) terms is (1188). What is the common difference?
#ap
#block-sums
#expert
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The difference of the two equal block sums is (144d), so \(d=\frac{768}{144}=\frac{16}{3}\). Exam tip: recheck block-sum formulas carefully.
Step 2
Why this answer is correct
The correct answer is B. (5). The difference of the two equal block sums is (144d), so \(d=\frac{768}{144}=\frac{16}{3}\). Exam tip: recheck block-sum formulas carefully.
Step 3
Exam Tip
दो बराबर खंडों के योगों का अंतर (144d) है इसलिए \(d=\frac{768}{144}=5\frac{1}{3}\) नहीं बनता अतः सही संतुलित गणना से \(d=\frac{16}{3}\) है। परीक्षा में खंड सूत्र दोबारा जांचें।
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यदि \(S_n=2n^2+7n\) किसी समान्तर श्रेणी के पहले (n) पदों का योग है तो प्रथम पद और सार्व अंतर का योग क्या होगा?
If \(S_n=2n^2+7n\) is the sum of the first (n) terms of an arithmetic progression, what is the sum of the first term and common difference?
#ap
#sum-polynomial
#expert
A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
\(a_1=S_1=9\) and \(a_2=S_2-S_1=13\), so (d=4) and (a+d=13). Exam tip: start with \(S_1\) and \(S_2-S_1\).
Step 2
Why this answer is correct
The correct answer is C. (13). \(a_1=S_1=9\) and \(a_2=S_2-S_1=13\), so (d=4) and (a+d=13). Exam tip: start with \(S_1\) and \(S_2-S_1\).
Step 3
Exam Tip
\(a_1=S_1=9\) और \(a_2=S_2-S_1=13\) इसलिए (d=4) और (a+d=13)। परीक्षा में \(S_1\) और \(S_2-S_1\) से शुरुआत करें।
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किसी समान्तर श्रेणी में प्रथम पद (7) और सार्व अंतर (5) है। यदि पहले (n) पदों का योग (1470) है तो (n) का मान क्या होगा?
In an arithmetic progression the first term is (7) and the common difference is (5). If the sum of the first (n) terms is (1470) then what is (n)?
#ap
#sum
#nth-sum
#expert
A (21)
B (24)
C (28)
D (30)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}[2a+(n-1)d]) gives (n=24). Exam tip: first reduce the equation to a simple quadratic.
Step 2
Why this answer is correct
The correct answer is B. (24). Using (S_n=\frac{n}{2}[2a+(n-1)d]) gives (n=24). Exam tip: first reduce the equation to a simple quadratic.
Step 3
Exam Tip
सूत्र (S_n=\frac{n}{2}[2a+(n-1)d]) लगाने पर (n=24) मिलता है। परीक्षा में पहले समीकरण को सरल वर्ग समीकरण में बदलें।
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समांतर श्रेढ़ी \(4,11,18,\ldots\) में (25)वें पद से (60)वें पद तक का योग क्या होगा?
In the AP \(4,11,18,\ldots\), what is the sum from the (25)th term to the (60)th term?
#range sum
#partial sum
#ap
A (10602)
B (10542)
C (10662)
D (10722)
Explanation opens after your attempt
Correct Answer
A. (10602)
Step 1
Concept
The required sum is \(S_{60}-S_{24}=10602\). For a middle range, subtract the sum up to the term just before it.
Step 2
Why this answer is correct
The correct answer is A. (10602). The required sum is \(S_{60}-S_{24}=10602\). For a middle range, subtract the sum up to the term just before it.
Step 3
Exam Tip
आवश्यक योग \(S_{60}-S_{24}=10602\) है। बीच के पदों का योग निकालते समय ठीक पिछले पद तक का योग घटाएँ।
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समांतर श्रेढ़ी \(25,33,41,\ldots\) में (40)वें पद से (70)वें पद तक का योग ज्ञात कीजिए।
In the AP \(25,33,41,\ldots\), find the sum from the (40)th term to the (70)th term.
#range sum
#partial sum
#ap
A (14043)
B (14167)
C (14291)
D (14415)
Explanation opens after your attempt
Correct Answer
B. (14167)
Step 1
Concept
The required sum is \(S_{70}-S_{39}=14167\). Do not forget to subtract the sum just before the given range.
Step 2
Why this answer is correct
The correct answer is B. (14167). The required sum is \(S_{70}-S_{39}=14167\). Do not forget to subtract the sum just before the given range.
Step 3
Exam Tip
आवश्यक योग \(S_{70}-S_{39}=14167\) है। दी गई सीमा से ठीक पहले तक का योग घटाना न भूलें।
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यदि किसी समांतर श्रेढ़ी में \(S_{22}=1474\) और \(S_{11}=407\), तो (12)वें पद से (22)वें पद तक का योग क्या होगा?
If in an AP \(S_{22}=1474\) and \(S_{11}=407\), what is the sum from the (12)th term to the (22)nd term?
#partial sum difference
#range sum
#ap
A (1056)
B (1078)
C (1067)
D (1089)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{22}-S_{11}=1067\). The sum of consecutive terms is found by subtracting partial sums.
Step 2
Why this answer is correct
The correct answer is C. (1067). The required sum is \(S_{22}-S_{11}=1067\). The sum of consecutive terms is found by subtracting partial sums.
Step 3
Exam Tip
आवश्यक योग \(S_{22}-S_{11}=1067\) है। लगातार पदों का योग आंशिक योगों के अंतर से मिलता है।
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समांतर श्रेढ़ी \(8,14,20,\ldots\) में (18)वें पद से (36)वें पद तक का योग क्या होगा?
In the AP \(8,14,20,\ldots\), what is the sum from the (18)th term to the (36)th term?
#range sum
#partial sum
#ap
A (3116)
B (3098)
C (3134)
D (3152)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{36}-S_{17}=3116\). To find a middle block sum, subtract the previous partial sum.
Step 2
Why this answer is correct
The correct answer is A. (3116). The required sum is \(S_{36}-S_{17}=3116\). To find a middle block sum, subtract the previous partial sum.
Step 3
Exam Tip
आवश्यक योग \(S_{36}-S_{17}=3116\) है। बीच के पदों का योग निकालने के लिए पिछले आंशिक योग को घटाएँ।
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समांतर श्रेढ़ी \(18,25,32,\ldots\) में (30)वें पद से (55)वें पद तक का योग ज्ञात कीजिए।
In the AP \(18,25,32,\ldots\), find the sum from the (30)th term to the (55)th term.
#range sum
#partial sum
#ap
A (8021)
B (7943)
C (8099)
D (8177)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{55}-S_{29}=8021\). Do not forget to subtract the sum just before the given range.
Step 2
Why this answer is correct
The correct answer is A. (8021). The required sum is \(S_{55}-S_{29}=8021\). Do not forget to subtract the sum just before the given range.
Step 3
Exam Tip
आवश्यक योग \(S_{55}-S_{29}=8021\) है। दी गई सीमा से ठीक पहले तक का योग घटाना न भूलें।
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