100 results found for "ap-sum-multiples" in Class 10.
(44) से (297) तक (11) के गुणजों का योग कितना होगा?
What is the sum of the multiples of (11) from (44) to (297)?
#ap
#multiples-sum
#expert
A (4092)
B (4212)
C (4332)
D (4452)
Explanation opens after your attempt
Step 1
Concept
This is the AP \(44,55,\ldots,297\) with (24) terms. Exam tip: find the number of terms first.
Step 2
Why this answer is correct
The correct answer is A. (4092). This is the AP \(44,55,\ldots,297\) with (24) terms. Exam tip: find the number of terms first.
Step 3
Exam Tip
यह समान्तर श्रेणी \(44,55,\ldots,297\) है जिसमें (24) पद हैं। परीक्षा में पहले पदों की संख्या निकालें।
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(21) से (210) तक (7) के गुणजों का योग कितना होगा?
What is the sum of the multiples of (7) from (21) to (210)?
#ap
#multiples-sum
#expert
A (3178)
B (3192)
C (3210)
D (3234)
Explanation opens after your attempt
Step 1
Concept
This is the AP \(21,28,\ldots,210\) with (28) terms. Exam tip: find the number of terms first.
Step 2
Why this answer is correct
The correct answer is D. (3234). This is the AP \(21,28,\ldots,210\) with (28) terms. Exam tip: find the number of terms first.
Step 3
Exam Tip
यह समान्तर श्रेणी \(21,28,\ldots,210\) है जिसमें (28) पद हैं। परीक्षा में पहले पदों की संख्या निकालें।
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(50) से कम (4) के सभी धनात्मक गुणजों का योग कितना है?
What is the sum of all positive multiples of (4) less than (50)?
#multiples less than
#ap sum
#class 10
A (300)
B (304)
C (312)
D (320)
Explanation opens after your attempt
Step 1
Concept
The AP is \(4,8,\ldots,48\) with (12) terms, and the sum is (312). Identifying the last allowed multiple is important.
Step 2
Why this answer is correct
The correct answer is C. (312). The AP is \(4,8,\ldots,48\) with (12) terms, and the sum is (312). Identifying the last allowed multiple is important.
Step 3
Exam Tip
श्रेढ़ी \(4,8,\ldots,48\) है जिसमें (12) पद हैं और योग (312) है। अंतिम स्वीकार्य गुणज पहचानना जरूरी है।
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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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(3) के दो क्रमागत धनात्मक गुणजों का गुणनफल (270) है। वे गुणज कौन से हैं?
The product of two consecutive positive multiples of (3) is (270). Which multiples are they?
#quadratic equations
#multiples
#application
A (9) और (12) / (9) and (12)
B (12) और (15) / (12) and (15)
C (15) और (18) / (15) and (18)
D (18) और (21) / (18) and (21)
Explanation opens after your attempt
Correct Answer
C. (15) और (18) / (15) and (18)
Step 1
Concept
Let the multiples be (x) and (x+3). From (x(x+3)=270), we get (x=15).
Step 2
Why this answer is correct
The correct answer is C. (15) और (18) / (15) and (18). Let the multiples be (x) and (x+3). From (x(x+3)=270), we get (x=15).
Step 3
Exam Tip
गुणज (x) और (x+3) मानें। (x(x+3)=270) से (x=15) मिलता है।
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(300) से कम (25) के सभी तीन अंकों वाले गुणजों का योग कितना है?
What is the sum of all three-digit multiples of (25) less than (300)?
#three_digit_numbers
#multiples
#ap_sum
A (1500)
B (1525)
C (1550)
D (1575)
Explanation opens after your attempt
Step 1
Concept
The multiples are \(100,125,\ldots,275\), and there are (8) terms, so the sum is (1500). Decide the first and last terms according to the limit.
Step 2
Why this answer is correct
The correct answer is A. (1500). The multiples are \(100,125,\ldots,275\), and there are (8) terms, so the sum is (1500). Decide the first and last terms according to the limit.
Step 3
Exam Tip
गुणज \(100,125,\ldots,275\) हैं और (8) पद हैं, इसलिए योग (1500) है। सीमा के अनुसार पहला और अंतिम पद तय करें।
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(4) से (100) तक (4) के गुणजों का योग कितना है?
What is the sum of the multiples of (4) from (4) to (100)?
#multiples
#ap_sum
#natural_numbers
A (1280)
B (1300)
C (1320)
D (1340)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (25) multiples of (4), so \(4\times\frac{25\times26}{2}=1300\). Use the sum of natural numbers for multiples.
Step 2
Why this answer is correct
The correct answer is B. (1300). This is the sum of the first (25) multiples of (4), so \(4\times\frac{25\times26}{2}=1300\). Use the sum of natural numbers for multiples.
Step 3
Exam Tip
यह (4) के पहले (25) गुणजों का योग है, इसलिए \(4\times\frac{25\times26}{2}=1300\)। गुणजों में प्राकृतिक संख्याओं का योग लगाएँ।
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(20) से (200) तक (10) के गुणजों का योग कितना है?
What is the sum of the multiples of (10) from (20) to (200)?
#multiples
#range
#ap_sum
A (2090)
B (2100)
C (2110)
D (2120)
Explanation opens after your attempt
Step 1
Concept
The sequence is \(20,30,\ldots,200\) with (19) terms, so the sum is (2090). Include both boundary terms.
Step 2
Why this answer is correct
The correct answer is A. (2090). The sequence is \(20,30,\ldots,200\) with (19) terms, so the sum is (2090). Include both boundary terms.
Step 3
Exam Tip
यह श्रेणी \(20,30,\ldots,200\) है जिसमें (19) पद हैं, इसलिए योग (2090) है। सीमा के दोनों सिरों को शामिल करें।
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(100) से कम (6) के सभी धनात्मक गुणजों का योग ज्ञात कीजिए।
Find the sum of all positive multiples of (6) less than (100).
#multiples
#ap_sum
#less_than
A (816)
B (826)
C (836)
D (846)
Explanation opens after your attempt
Step 1
Concept
The multiples are from (6) to (96), and there are (16) terms, so the sum is (816). In boundary questions, decide the last term first.
Step 2
Why this answer is correct
The correct answer is A. (816). The multiples are from (6) to (96), and there are (16) terms, so the sum is (816). In boundary questions, decide the last term first.
Step 3
Exam Tip
गुणज (6) से (96) तक हैं और (16) पद हैं, इसलिए योग (816) है। सीमा वाले प्रश्न में अंतिम पद पहले तय करें।
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समांतर श्रेढ़ी \(2,9,16,\ldots\) के पहले (50) पदों में उन पदों का योग ज्ञात कीजिए जिनके क्रमांक (5) के गुणज हैं।
In the first (50) terms of the AP \(2,9,16,\ldots\), find the sum of the terms whose positions are multiples of (5).
#position multiples
#selected terms
#ap
A (1825)
B (1875)
C (1925)
D (1975)
Explanation opens after your attempt
Step 1
Concept
The selected terms are \(a_5,a_{10},\ldots,a_{50}\), and their sum is (1875). In position-based questions, form the new AP of selected terms.
Step 2
Why this answer is correct
The correct answer is B. (1875). The selected terms are \(a_5,a_{10},\ldots,a_{50}\), and their sum is (1875). In position-based questions, form the new AP of selected terms.
Step 3
Exam Tip
चुने गए पद \(a_5,a_{10},\ldots,a_{50}\) हैं और उनका योग (1875) है। क्रमांक आधारित प्रश्न में चुने गए पदों की नई श्रेढ़ी बनाएँ।
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समांतर श्रेढ़ी \(1,6,11,\ldots\) के पहले (40) पदों में उन पदों का योग ज्ञात कीजिए जिनके क्रमांक (4) के गुणज हैं।
In the first (40) terms of the AP \(1,6,11,\ldots\), find the sum of the terms whose positions are multiples of (4).
#position multiples
#selected terms
#ap
A (1060)
B (1020)
C (1100)
D (1140)
Explanation opens after your attempt
Step 1
Concept
The selected terms are \(a_4,a_8,\ldots,a_{40}\), and their sum is (1060). In position-based questions, form the new AP of selected terms.
Step 2
Why this answer is correct
The correct answer is A. (1060). The selected terms are \(a_4,a_8,\ldots,a_{40}\), and their sum is (1060). In position-based questions, form the new AP of selected terms.
Step 3
Exam Tip
चुने गए पद \(a_4,a_8,\ldots,a_{40}\) हैं और उनका योग (1060) है। क्रमांक आधारित प्रश्न में चुने गए पदों की नई श्रेढ़ी बनाएँ।
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समांतर श्रेढ़ी \(2,5,8,\ldots\) के पहले (30) पदों में उन पदों का योग ज्ञात कीजिए जिनके क्रमांक (3) के गुणज हैं।
In the first (30) terms of the AP \(2,5,8,\ldots\), find the sum of the terms whose positions are multiples of (3).
#position multiples
#selected terms
#ap
A (485)
B (475)
C (495)
D (505)
Explanation opens after your attempt
Step 1
Concept
The selected terms are \(a_3,a_6,\ldots,a_{30}\), and their sum is (485). In position-based questions, form the new AP of selected terms.
Step 2
Why this answer is correct
The correct answer is A. (485). The selected terms are \(a_3,a_6,\ldots,a_{30}\), and their sum is (485). In position-based questions, form the new AP of selected terms.
Step 3
Exam Tip
चुने गए पद \(a_3,a_6,\ldots,a_{30}\) हैं और उनका योग (485) है। क्रमांक आधारित प्रश्न में चुने गए पदों की नई श्रेढ़ी बनाएँ।
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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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(75) और (255) के बीच (12) से विभाज्य संख्याओं का योग कितना होगा?
What is the sum of numbers divisible by (12) between (75) and (255)?
#ap
#multiples-sum
#expert
A (2304)
B (2448)
C (2592)
D (2736)
Explanation opens after your attempt
Step 1
Concept
The terms are \(84,96,\ldots,252\), making (15) terms. Exam tip: choose the first and last valid terms carefully.
Step 2
Why this answer is correct
The correct answer is C. (2592). The terms are \(84,96,\ldots,252\), making (15) terms. Exam tip: choose the first and last valid terms carefully.
Step 3
Exam Tip
पद \(84,96,\ldots,252\) हैं और कुल (15) पद बनते हैं। परीक्षा में पहला और अंतिम मान सावधानी से चुनें।
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(200) से (1200) तक (19) से विभाज्य सभी संख्याओं का योग ज्ञात कीजिए।
Find the sum of all numbers divisible by (19) from (200) to (1200).
#multiples
#ap sum
#limits
A (37259)
B (37107)
C (37411)
D (37563)
Explanation opens after your attempt
Correct Answer
A. (37259)
Step 1
Concept
The first multiple is (209), the last is (1197), and there are (53) terms, so the sum is (37259). Choose the first multiple within the range correctly.
Step 2
Why this answer is correct
The correct answer is A. (37259). The first multiple is (209), the last is (1197), and there are (53) terms, so the sum is (37259). Choose the first multiple within the range correctly.
Step 3
Exam Tip
पहला गुणज (209), अंतिम (1197) और (53) पद हैं, इसलिए योग (37259) है। सीमा के अंदर पहला गुणज सही चुनें।
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(1) से (1500) तक उन सभी संख्याओं का योग ज्ञात कीजिए जो (9) से विभाज्य हैं लेकिन (12) से विभाज्य नहीं हैं।
Find the sum of all numbers from (1) to (1500) that are divisible by (9) but not by (12).
#multiples
#overlap
#lcm
#ap sum
A (93753)
B (93393)
C (94113)
D (94473)
Explanation opens after your attempt
Correct Answer
A. (93753)
Step 1
Concept
Subtracting the sum of multiples of (36) from the sum of multiples of (9) gives (93753). Numbers divisible by both are multiples of (\operatorname{lcm}(9,12)).
Step 2
Why this answer is correct
The correct answer is A. (93753). Subtracting the sum of multiples of (36) from the sum of multiples of (9) gives (93753). Numbers divisible by both are multiples of (\operatorname{lcm}(9,12)).
Step 3
Exam Tip
(9) के गुणजों के योग से (36) के गुणजों का योग घटाने पर (93753) मिलता है। दोनों से विभाज्य संख्याएँ (\operatorname{lcm}(9,12)) की गुणज होती हैं।
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(1) से (1000) तक उन सभी संख्याओं का योग ज्ञात कीजिए जो (5) या (8) से विभाज्य हैं।
Find the sum of all numbers from (1) to (1000) that are divisible by (5) or (8).
#inclusion exclusion
#multiples
#ap sum
A (149500)
B (150500)
C (151500)
D (152500)
Explanation opens after your attempt
Correct Answer
B. (150500)
Step 1
Concept
Adding sums of multiples of (5) and (8), then subtracting multiples of (40), gives (150500). Avoiding double counting is important.
Step 2
Why this answer is correct
The correct answer is B. (150500). Adding sums of multiples of (5) and (8), then subtracting multiples of (40), gives (150500). Avoiding double counting is important.
Step 3
Exam Tip
(5) और (8) के गुणजों के योग जोड़कर (40) के गुणजों का योग घटाने से (150500) मिलता है। दोहरी गिनती से बचना जरूरी है।
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(120) से (900) तक (16) से विभाज्य सभी संख्याओं का योग ज्ञात कीजिए।
Find the sum of all numbers divisible by (16) from (120) to (900).
#multiples
#ap sum
#limits
A (25088)
B (24896)
C (25280)
D (25472)
Explanation opens after your attempt
Correct Answer
A. (25088)
Step 1
Concept
The first multiple is (128), the last is (896), and there are (49) terms, so the sum is (25088). Choose the first term according to the range carefully.
Step 2
Why this answer is correct
The correct answer is A. (25088). The first multiple is (128), the last is (896), and there are (49) terms, so the sum is (25088). Choose the first term according to the range carefully.
Step 3
Exam Tip
पहला गुणज (128), अंतिम (896) और कुल (49) पद हैं, इसलिए योग (25088) है। सीमा के अनुसार पहला पद ध्यान से चुनें।
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(150) से (750) तक (17) से विभाज्य सभी संख्याओं का योग ज्ञात कीजिए।
Find the sum of all numbers divisible by (17) from (150) to (750).
#multiples
#ap sum
#divisibility
A (16110)
B (16218)
C (16326)
D (16434)
Explanation opens after your attempt
Correct Answer
B. (16218)
Step 1
Concept
The numbers are \(153,170,\ldots,748\), and their sum is (16218). Choose the first and last multiples within the limits correctly.
Step 2
Why this answer is correct
The correct answer is B. (16218). The numbers are \(153,170,\ldots,748\), and their sum is (16218). Choose the first and last multiples within the limits correctly.
Step 3
Exam Tip
संख्याएँ \(153,170,\ldots,748\) हैं और उनका योग (16218) है। सीमा के अंदर पहला और अंतिम गुणज सही चुनें।
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(1) से (1000) तक उन सभी संख्याओं का योग ज्ञात कीजिए जो (6) से विभाज्य हैं लेकिन (15) से विभाज्य नहीं हैं।
Find the sum of all numbers from (1) to (1000) that are divisible by (6) but not by (15).
#multiples
#overlap
#lcm
#ap sum
A (65976)
B (66156)
C (66336)
D (66516)
Explanation opens after your attempt
Correct Answer
C. (66336)
Step 1
Concept
Subtracting the sum of multiples of (30) from the sum of multiples of (6) gives (66336). Numbers divisible by both (6) and (15) are multiples of (30).
Step 2
Why this answer is correct
The correct answer is C. (66336). Subtracting the sum of multiples of (30) from the sum of multiples of (6) gives (66336). Numbers divisible by both (6) and (15) are multiples of (30).
Step 3
Exam Tip
(6) के गुणजों के योग से (30) के गुणजों का योग घटाने पर (66336) मिलता है। (6) और (15) दोनों से विभाज्य संख्याएँ (30) की गुणज होती हैं।
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(1) से (700) तक उन सभी संख्याओं का योग ज्ञात कीजिए जो (4) या (7) से विभाज्य हैं।
Find the sum of all numbers from (1) to (700) that are divisible by (4) or (7).
#inclusion exclusion
#multiples
#ap sum
A (87850)
B (87450)
C (88250)
D (88650)
Explanation opens after your attempt
Correct Answer
A. (87850)
Step 1
Concept
Adding sums of multiples of (4) and (7), then subtracting multiples of (28), gives (87850). Avoiding double counting is important.
Step 2
Why this answer is correct
The correct answer is A. (87850). Adding sums of multiples of (4) and (7), then subtracting multiples of (28), gives (87850). Avoiding double counting is important.
Step 3
Exam Tip
(4) और (7) के गुणजों के योग जोड़कर (28) के गुणजों का योग घटाने से (87850) मिलता है। दोहरी गिनती से बचना जरूरी है।
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(80) से (600) तक (13) से विभाज्य सभी संख्याओं का योग ज्ञात कीजिए।
Find the sum of all numbers divisible by (13) from (80) to (600).
#multiples
#ap sum
#limits
A (13650)
B (13715)
C (13780)
D (13845)
Explanation opens after your attempt
Correct Answer
C. (13780)
Step 1
Concept
The first multiple is (91), the last is (598), and there are (40) terms, so the sum is (13780). Choose the first term according to the range carefully.
Step 2
Why this answer is correct
The correct answer is C. (13780). The first multiple is (91), the last is (598), and there are (40) terms, so the sum is (13780). Choose the first term according to the range carefully.
Step 3
Exam Tip
पहला गुणज (91), अंतिम (598) और कुल (40) पद हैं, इसलिए योग (13780) है। सीमा के अनुसार पहला पद ध्यान से चुनें।
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(200) से (800) तक (14) से विभाज्य सभी संख्याओं का योग ज्ञात कीजिए।
Find the sum of all numbers divisible by (14) from (200) to (800).
#multiples
#ap sum
#divisibility
A (21462)
B (21588)
C (21630)
D (21672)
Explanation opens after your attempt
Correct Answer
D. (21672)
Step 1
Concept
The numbers are \(210,224,\ldots,798\), and their sum is (21672). Choose the first and last multiples within the limits correctly.
Step 2
Why this answer is correct
The correct answer is D. (21672). The numbers are \(210,224,\ldots,798\), and their sum is (21672). Choose the first and last multiples within the limits correctly.
Step 3
Exam Tip
संख्याएँ \(210,224,\ldots,798\) हैं और उनका योग (21672) है। सीमा के अंदर पहला और अंतिम गुणज सही चुनें।
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(1) से (1000) तक उन सभी संख्याओं का योग ज्ञात कीजिए जो (4) से विभाज्य हैं लेकिन (10) से विभाज्य नहीं हैं।
Find the sum of all numbers from (1) to (1000) that are divisible by (4) but not by (10).
#multiples
#overlap
#lcm
#ap sum
A (98500)
B (99500)
C (101000)
D (100000)
Explanation opens after your attempt
Correct Answer
D. (100000)
Step 1
Concept
The sum of multiples of (4) is (125500), and the sum of multiples of (20) is (25500), so the answer is (100000). Remove overlap using \(\operatorname{lcm}\).
Step 2
Why this answer is correct
The correct answer is D. (100000). The sum of multiples of (4) is (125500), and the sum of multiples of (20) is (25500), so the answer is (100000). Remove overlap using \(\operatorname{lcm}\).
Step 3
Exam Tip
(4) के गुणजों का योग (125500) और (20) के गुणजों का योग (25500) है, इसलिए उत्तर (100000) है। \(\operatorname{lcm}\) से overlap हटाएँ।
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(1) से (500) तक उन सभी संख्याओं का योग ज्ञात कीजिए जो (3) या (5) से विभाज्य हैं।
Find the sum of all numbers from (1) to (500) that are divisible by (3) or (5).
#inclusion exclusion
#multiples
#ap sum
A (58418)
B (58518)
C (58318)
D (58618)
Explanation opens after your attempt
Correct Answer
A. (58418)
Step 1
Concept
Adding sums of multiples of (3) and (5), then subtracting multiples of (15), gives (58418). Avoiding double counting is important.
Step 2
Why this answer is correct
The correct answer is A. (58418). Adding sums of multiples of (3) and (5), then subtracting multiples of (15), gives (58418). Avoiding double counting is important.
Step 3
Exam Tip
(3) और (5) के गुणजों के योग जोड़कर (15) के गुणजों का योग घटाने से (58418) मिलता है। दोहरी गिनती से बचना जरूरी है।
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तीन अंकों वाली उन सभी विषम संख्याओं का योग ज्ञात कीजिए जो (9) से विभाज्य हैं।
Find the sum of all three-digit odd numbers that are divisible by (9).
#odd multiples
#three digit
#ap sum
A (27600)
B (27900)
C (28100)
D (28350)
Explanation opens after your attempt
Correct Answer
B. (27900)
Step 1
Concept
The numbers are \(117,135,\ldots,999\), and the sum of (50) terms is (27900). For odd multiples, the common difference is (18).
Step 2
Why this answer is correct
The correct answer is B. (27900). The numbers are \(117,135,\ldots,999\), and the sum of (50) terms is (27900). For odd multiples, the common difference is (18).
Step 3
Exam Tip
संख्याएँ \(117,135,\ldots,999\) हैं और (50) पदों का योग (27900) है। विषम गुणजों में अंतर (18) होगा।
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(100) और (500) के बीच (11) से विभाज्य सभी संख्याओं का योग ज्ञात कीजिए।
Find the sum of all numbers divisible by (11) between (100) and (500).
#multiples
#between numbers
#ap sum
A (10835)
B (10860)
C (10920)
D (10890)
Explanation opens after your attempt
Correct Answer
D. (10890)
Step 1
Concept
The numbers are \(110,121,\ldots,495\), and their sum is (10890). When between is written, check carefully whether endpoints are included.
Step 2
Why this answer is correct
The correct answer is D. (10890). The numbers are \(110,121,\ldots,495\), and their sum is (10890). When between is written, check carefully whether endpoints are included.
Step 3
Exam Tip
संख्याएँ \(110,121,\ldots,495\) हैं और उनका योग (10890) है। between लिखे होने पर सिरों को शामिल करना है या नहीं यह ध्यान से देखें।
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एक AP में (a=11), (d=11), (n=20) है। योग क्या है?
In an AP (a=11), (d=11), (n=20). What is the sum?
#ap-sum-multiples-eleven
A (2310)
B (2320)
C (2330)
D (2340)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (20) multiples of (11). (S_{20}=\frac{20}{2}(11+220)=2310).
Step 2
Why this answer is correct
The correct answer is A. (2310). This is the sum of the first (20) multiples of (11). (S_{20}=\frac{20}{2}(11+220)=2310).
Step 3
Exam Tip
यह (11) के पहले (20) गुणजों का योग है। (S_{20}=\frac{20}{2}(11+220)=2310)।
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समान्तर श्रेणी \(9,18,27,\ldots\) के पहले (12) पदों का योग कितना है?
What is the sum of the first (12) terms of the AP \(9,18,27,\ldots\)?
#ap-sum-nine-multiples
A (692)
B (702)
C (712)
D (722)
Explanation opens after your attempt
Step 1
Concept
The last term is (108). (S_{12}=\frac{12}{2}(9+108)=702).
Step 2
Why this answer is correct
The correct answer is B. (702). The last term is (108). (S_{12}=\frac{12}{2}(9+108)=702).
Step 3
Exam Tip
अंतिम पद (108) है। (S_{12}=\frac{12}{2}(9+108)=702)।
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समान्तर श्रेणी \(11,22,33,\ldots\) के पहले (9) पदों का योग कितना है?
What is the sum of the first (9) terms of the AP \(11,22,33,\ldots\)?
#ap-sum-eleven-multiples
A (485)
B (495)
C (505)
D (515)
Explanation opens after your attempt
Step 1
Concept
The last term is (99). (S_9=\frac{9}{2}(11+99)=495).
Step 2
Why this answer is correct
The correct answer is B. (495). The last term is (99). (S_9=\frac{9}{2}(11+99)=495).
Step 3
Exam Tip
अंतिम पद (99) है। (S_9=\frac{9}{2}(11+99)=495)।
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समान्तर श्रेणी \(5,10,15,\ldots\) के पहले (18) पदों का योग क्या होगा?
What will be the sum of the first (18) terms of the AP \(5,10,15,\ldots\)?
#ap-sum-five-multiples
A (845)
B (855)
C (865)
D (875)
Explanation opens after your attempt
Step 1
Concept
Here the last term is (90). (S_{18}=\frac{18}{2}(5+90)=855).
Step 2
Why this answer is correct
The correct answer is B. (855). Here the last term is (90). (S_{18}=\frac{18}{2}(5+90)=855).
Step 3
Exam Tip
यहां अंतिम पद (90) है। (S_{18}=\frac{18}{2}(5+90)=855)।
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समान्तर श्रेणी \(7,14,21,\ldots\) के पहले (10) पदों का योग क्या होगा?
What will be the sum of the first (10) terms of the AP \(7,14,21,\ldots\)?
#ap-sum-multiples-seven
A (365)
B (375)
C (385)
D (395)
Explanation opens after your attempt
Step 1
Concept
This is the sequence of multiples of (7). (S_{10}=\frac{10}{2}(7+70)=385).
Step 2
Why this answer is correct
The correct answer is C. (385). This is the sequence of multiples of (7). (S_{10}=\frac{10}{2}(7+70)=385).
Step 3
Exam Tip
यह (7) के गुणजों की श्रेणी है। (S_{10}=\frac{10}{2}(7+70)=385)।
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समान्तर श्रेणी \(10,20,30,\ldots\) के पहले (12) पदों का योग कितना है?
What is the sum of the first (12) terms of the AP \(10,20,30,\ldots\)?
#ap-sum-multiples
A (760)
B (780)
C (800)
D (820)
Explanation opens after your attempt
Step 1
Concept
Here (a=10), (d=10), (n=12). \(S_{12}=6[20+110]=780\).
Step 2
Why this answer is correct
The correct answer is B. (780). Here (a=10), (d=10), (n=12). \(S_{12}=6[20+110]=780\).
Step 3
Exam Tip
यहां (a=10), (d=10), (n=12)। \(S_{12}=6[20+110]=780\)।
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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 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 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 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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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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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 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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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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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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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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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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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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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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(5000) से कम (41) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या होगा?
What will be the last term in the AP of positive multiples of (41) less than (5000)?
#ap expert multiples
A (4920)
B (4961)
C (5002)
D (5043)
Explanation opens after your attempt
Step 1
Concept
In (41n<5000), the greatest (n=121). The last term will be \(41\times121=4961\).
Step 2
Why this answer is correct
The correct answer is B. (4961). In (41n<5000), the greatest (n=121). The last term will be \(41\times121=4961\).
Step 3
Exam Tip
(41n<5000) में सबसे बड़ा (n=121) है। अंतिम पद \(41\times121=4961\) होगा।
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(3600) से कम (37) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या होगा?
What will be the last term in the AP of positive multiples of (37) less than (3600)?
#ap expert multiples
A (3515)
B (3552)
C (3589)
D (3626)
Explanation opens after your attempt
Step 1
Concept
In (37n<3600), the greatest (n=97). The last term will be \(37\times97=3589\).
Step 2
Why this answer is correct
The correct answer is C. (3589). In (37n<3600), the greatest (n=97). The last term will be \(37\times97=3589\).
Step 3
Exam Tip
(37n<3600) में सबसे बड़ा (n=97) है। अंतिम पद \(37\times97=3589\) होगा।
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(2500) से कम (29) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या होगा?
What will be the last term in the AP of positive multiples of (29) less than (2500)?
#ap-multiples-expert
A (2465)
B (2494)
C (2523)
D (2552)
Explanation opens after your attempt
Step 1
Concept
In (29n<2500), the greatest (n=86). The last term will be \(29\times86=2494\).
Step 2
Why this answer is correct
The correct answer is B. (2494). In (29n<2500), the greatest (n=86). The last term will be \(29\times86=2494\).
Step 3
Exam Tip
(29n<2500) में सबसे बड़ा (n=86) है। अंतिम पद \(29\times86=2494\) होगा।
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(2000) से कम (23) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या है?
What is the last term in the AP of positive multiples of (23) less than (2000)?
#ap multiples hard
A (1955)
B (1978)
C (2001)
D (2024)
Explanation opens after your attempt
Step 1
Concept
In (23n<2000), the greatest (n=86). The last term will be \(23\times86=1978\).
Step 2
Why this answer is correct
The correct answer is B. (1978). In (23n<2000), the greatest (n=86). The last term will be \(23\times86=1978\).
Step 3
Exam Tip
(23n<2000) में सबसे बड़ा (n=86) है। अंतिम पद \(23\times86=1978\) होगा।
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(1500) से कम (19) के धनात्मक गुणजों की समान्तर श्रेणी में अंतिम पद क्या है?
What is the last term in the AP of positive multiples of (19) less than (1500)?
#ap-multiples-hard
A (1482)
B (1501)
C (1463)
D (1444)
Explanation opens after your attempt
Step 1
Concept
In (19n<1500), the greatest (n=78). The last term will be \(19\times78=1482\).
Step 2
Why this answer is correct
The correct answer is A. (1482). In (19n<1500), the greatest (n=78). The last term will be \(19\times78=1482\).
Step 3
Exam Tip
(19n<1500) में सबसे बड़ा (n=78) है। अंतिम पद \(19\times78=1482\) होगा।
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(1000) से कम (17) के धनात्मक गुणजों की AP में अंतिम पद क्या है?
What is the last term in the AP of positive multiples of (17) less than (1000)?
#ap-multiples-hard
A (969)
B (986)
C (1003)
D (1020)
Explanation opens after your attempt
Step 1
Concept
In (17n<1000), the greatest (n=58). The last term will be \(17\times58=986\).
Step 2
Why this answer is correct
The correct answer is B. (986). In (17n<1000), the greatest (n=58). The last term will be \(17\times58=986\).
Step 3
Exam Tip
(17n<1000) में सबसे बड़ा (n=58) है। अंतिम पद \(17\times58=986\) होगा।
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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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(400) से बड़े (12) के गुणजों की AP \(408,420,432,\ldots\) है। इसका (18)वां पद क्या होगा?
The AP of multiples of (12) greater than (400) is \(408,420,432,\ldots\). What is its (18)th term?
#ap multiples nth-term class10
A (612)
B (624)
C (636)
D (648)
Explanation opens after your attempt
Step 1
Concept
Here (a=408) and (d=12) so \(a_{18}=408+17\times12=612\). Choose the first correct multiple after the limit.
Step 2
Why this answer is correct
The correct answer is A. (612). Here (a=408) and (d=12) so \(a_{18}=408+17\times12=612\). Choose the first correct multiple after the limit.
Step 3
Exam Tip
यहां (a=408) और (d=12) है इसलिए \(a_{18}=408+17\times12=612\)। सीमा के बाद पहला सही गुणज चुनें।
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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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(300) से बड़े (8) के गुणजों की समान्तर श्रेणी \(304,312,320,\ldots\) है। इसका (25)वां पद क्या होगा?
The AP of multiples of (8) greater than (300) is \(304,312,320,\ldots\). What is its (25)th term?
#ap
#multiples
#nth-term
#class10
A (496)
B (488)
C (492)
D (500)
Explanation opens after your attempt
Step 1
Concept
Here (a=304) and (d=8) so \(a_{25}=304+24\times8=496\). Choose the first correct multiple after the limit.
Step 2
Why this answer is correct
The correct answer is A. (496). Here (a=304) and (d=8) so \(a_{25}=304+24\times8=496\). Choose the first correct multiple after the limit.
Step 3
Exam Tip
यहां (a=304) और (d=8) है इसलिए \(a_{25}=304+24\times8=496\)। सीमा के बाद पहला सही गुणज चुनें।
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(200) से कम (9) के धनात्मक गुणजों में अंतिम पद क्या है?
What is the last term among the positive multiples of (9) less than (200)?
#ap
#multiples
#less-than
#nth-term
A (189)
B (196)
C (198)
D (199)
Explanation opens after your attempt
Step 1
Concept
In \(9,18,27,\ldots\), (9n<200), so the greatest (n=22) and the term is (198). For multiples, take the largest integer below the limit.
Step 2
Why this answer is correct
The correct answer is C. (198). In \(9,18,27,\ldots\), (9n<200), so the greatest (n=22) and the term is (198). For multiples, take the largest integer below the limit.
Step 3
Exam Tip
\(9,18,27,\ldots\) में (9n<200), इसलिए सबसे बड़ा (n=22) और पद (198) है। गुणजों में सीमा से कम सबसे बड़ा पूर्णांक लें।
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तीन अंकों वाली (19) से विभाज्य सभी संख्याओं का योग कितना होगा?
What is the sum of all three-digit numbers divisible by (19)?
#ap
#three-digit-multiples
#expert
A (24945)
B (25421)
C (26373)
D (25897)
Explanation opens after your attempt
Correct Answer
D. (25897)
Step 1
Concept
The numbers are \(114,133,\ldots,988\), and there are (47) terms. Exam tip: find the first and last three-digit multiples.
Step 2
Why this answer is correct
The correct answer is D. (25897). The numbers are \(114,133,\ldots,988\), and there are (47) terms. Exam tip: find the first and last three-digit multiples.
Step 3
Exam Tip
संख्याएँ \(114,133,\ldots,988\) हैं और कुल (47) पद हैं। परीक्षा में पहला और अंतिम तीन अंकीय गुणज निकालें।
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(10) और (130) के बीच (4) और (6) दोनों से विभाज्य संख्याओं का योग कितना होगा?
What is the sum of numbers between (10) and (130) that are divisible by both (4) and (6)?
#ap
#lcm-multiples
#expert
A (780)
B (840)
C (900)
D (960)
Explanation opens after your attempt
Step 1
Concept
The numbers are \(12,24,\ldots,120\), and there are (10) terms. Exam tip: divisible by both means use the least common multiple.
Step 2
Why this answer is correct
The correct answer is B. (840). The numbers are \(12,24,\ldots,120\), and there are (10) terms. Exam tip: divisible by both means use the least common multiple.
Step 3
Exam Tip
ऐसी संख्याएँ \(12,24,\ldots,120\) हैं और कुल (10) पद हैं। परीक्षा में दोनों से विभाज्य का अर्थ लघुत्तम समापवर्त्य लें।
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तीन अंकों वाली (17) से विभाज्य सभी संख्याओं का योग कितना होगा?
What is the sum of all three-digit numbers divisible by (17)?
#ap
#three-digit-multiples
#expert
A (30498)
B (31008)
C (31518)
D (32028)
Explanation opens after your attempt
Correct Answer
C. (31518)
Step 1
Concept
The numbers are \(102,119,\ldots,986\), and there are (53) terms. Exam tip: find the first and last three-digit multiples.
Step 2
Why this answer is correct
The correct answer is C. (31518). The numbers are \(102,119,\ldots,986\), and there are (53) terms. Exam tip: find the first and last three-digit multiples.
Step 3
Exam Tip
संख्याएँ \(102,119,\ldots,986\) हैं और कुल (53) पद हैं। परीक्षा में पहला और अंतिम तीन अंकीय गुणज निकालें।
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(50) से (250) तक (7) से विभाज्य सभी संख्याओं का योग ज्ञात कीजिए।
Find the sum of all numbers divisible by (7) from (50) to (250).
#multiples
#closed interval
#ap
A (4172)
B (4196)
C (4214)
D (4242)
Explanation opens after your attempt
Step 1
Concept
The AP is \(56,63,\ldots,245\) with (28) terms, and the sum is (4214). Choose the first and last multiples within the limits correctly.
Step 2
Why this answer is correct
The correct answer is C. (4214). The AP is \(56,63,\ldots,245\) with (28) terms, and the sum is (4214). Choose the first and last multiples within the limits correctly.
Step 3
Exam Tip
श्रेढ़ी \(56,63,\ldots,245\) है जिसमें (28) पद हैं और योग (4214) है। सीमा के अंदर पहला और अंतिम गुणज सही चुनें।
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समांतर श्रेणी \(11,22,33,\ldots\) के पहले (14) पदों का योग ज्ञात कीजिए।
Find the sum of the first (14) terms of the arithmetic progression \(11,22,33,\ldots\).
#multiples
#ap_sum
#natural_numbers
A (1135)
B (1155)
C (1175)
D (1195)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (14) multiples of (11), so \(11\times\frac{14\times15}{2}=1155\). For multiples, use the sum of natural numbers.
Step 2
Why this answer is correct
The correct answer is B. (1155). This is the sum of the first (14) multiples of (11), so \(11\times\frac{14\times15}{2}=1155\). For multiples, use the sum of natural numbers.
Step 3
Exam Tip
यह (11) के पहले (14) गुणजों का योग है, इसलिए \(11\times\frac{14\times15}{2}=1155\)। गुणजों में प्राकृतिक संख्याओं के योग का उपयोग करें।
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यदि (a=9), (d=9), और (n=8) है, तो समांतर श्रेणी के पहले (8) पदों का योग क्या होगा?
If (a=9), (d=9), and (n=8), what will be the sum of the first (8) terms of the arithmetic progression?
#multiples
#ap_sum
#nine
A (304)
B (314)
C (324)
D (334)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (8) multiples of (9), so \(9\times36=324\). If (a=d), the multiples method is faster.
Step 2
Why this answer is correct
The correct answer is C. (324). This is the sum of the first (8) multiples of (9), so \(9\times36=324\). If (a=d), the multiples method is faster.
Step 3
Exam Tip
यह (9) के पहले (8) गुणजों का योग है, इसलिए \(9\times36=324\)। (a=d) हो तो गुणज वाला तरीका तेज है।
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समांतर श्रेणी \(16,32,48,\ldots\) के पहले (6) पदों का योग ज्ञात करें।
Find the sum of the first (6) terms of the arithmetic progression \(16,32,48,\ldots\).
#multiples
#ap_sum
#six_terms
A (336)
B (346)
C (356)
D (366)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (6) multiples of (16), so \(16\times21=336\). For multiples, use \(1+2+\cdots+n\).
Step 2
Why this answer is correct
The correct answer is A. (336). This is the sum of the first (6) multiples of (16), so \(16\times21=336\). For multiples, use \(1+2+\cdots+n\).
Step 3
Exam Tip
यह (16) के पहले (6) गुणजों का योग है, इसलिए \(16\times21=336\)। गुणजों में \(1+2+\cdots+n\) का उपयोग करें।
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समांतर श्रेणी \(8,16,24,\ldots\) के पहले (11) पदों का योग क्या है?
What is the sum of the first (11) terms of the arithmetic progression \(8,16,24,\ldots\)?
#multiples
#ap_sum
#eight
A (518)
B (528)
C (538)
D (548)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (11) multiples of (8), so \(8\times66=528\). For multiples, use the sum of natural numbers.
Step 2
Why this answer is correct
The correct answer is B. (528). This is the sum of the first (11) multiples of (8), so \(8\times66=528\). For multiples, use the sum of natural numbers.
Step 3
Exam Tip
यह (8) के पहले (11) गुणजों का योग है, इसलिए \(8\times66=528\)। गुणजों में प्राकृतिक संख्याओं के योग का उपयोग करें।
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समांतर श्रेढ़ी \(21,28,35,\ldots\) के पहले (6) पदों का योग कितना होगा?
What will be the sum of the first (6) terms of the arithmetic progression \(21,28,35,\ldots\)?
#ap_sum
#multiples
#first_term
A (231)
B (238)
C (245)
D (252)
Explanation opens after your attempt
Step 1
Concept
These are the (3)rd to (8)th multiples of (7), or directly (a=21), (d=7), (n=6) gives (231). Look carefully at the first term.
Step 2
Why this answer is correct
The correct answer is A. (231). These are the (3)rd to (8)th multiples of (7), or directly (a=21), (d=7), (n=6) gives (231). Look carefully at the first term.
Step 3
Exam Tip
यह (7) के (3)वें से (8)वें गुणजों का योग है, या सीधे (a=21), (d=7), (n=6) से (231) मिलता है। प्रश्न में पहले पद को ध्यान से देखें।
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समांतर श्रेढ़ी \(11,22,33,\ldots\) के पहले (5) पदों का योग ज्ञात करें।
Find the sum of the first (5) terms of the arithmetic progression \(11,22,33,\ldots\).
#multiples
#ap_sum
#eleven
A (155)
B (165)
C (175)
D (185)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (5) multiples of (11), so \(11\times15=165\). For multiples, the sum of the first (n) natural numbers is useful.
Step 2
Why this answer is correct
The correct answer is B. (165). This is the sum of the first (5) multiples of (11), so \(11\times15=165\). For multiples, the sum of the first (n) natural numbers is useful.
Step 3
Exam Tip
यह (11) के पहले (5) गुणजों का योग है, इसलिए \(11\times15=165\)। गुणजों में पहले (n) प्राकृतिक संख्याओं का योग काम आता है।
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समांतर श्रेढ़ी \(7,14,21,\ldots\) के पहले (8) पदों का योग क्या है?
What is the sum of the first (8) terms of the arithmetic progression \(7,14,21,\ldots\)?
#multiples
#seven
#ap_sum
A (240)
B (252)
C (264)
D (276)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (8) multiples of (7), so \(7\times36=252\). For multiples, use the sum of natural numbers.
Step 2
Why this answer is correct
The correct answer is B. (252). This is the sum of the first (8) multiples of (7), so \(7\times36=252\). For multiples, use the sum of natural numbers.
Step 3
Exam Tip
यह (7) के पहले (8) गुणजों का योग है, इसलिए \(7\times36=252\)। गुणजों के प्रश्न में प्राकृतिक संख्याओं के योग का उपयोग करें।
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समांतर श्रेढ़ी \(6,12,18,\ldots\) के पहले (10) पदों का योग क्या है?
What is the sum of the first (10) terms of the arithmetic progression \(6,12,18,\ldots\)?
#multiples
#ap_sum
#class10
A (300)
B (320)
C (330)
D (360)
Explanation opens after your attempt
Step 1
Concept
These are the first (10) multiples of (6), whose sum is (330). Treat multiples as an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is C. (330). These are the first (10) multiples of (6), whose sum is (330). Treat multiples as an arithmetic progression.
Step 3
Exam Tip
यह (6) के पहले (10) गुणज हैं, जिनका योग (330) है। गुणजों को भी समांतर श्रेढ़ी की तरह 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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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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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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यदि किसी समांतर श्रेढ़ी में \(S_{18}=810\) और \(S_9=270\), तो (10)वें पद से (18)वें पद तक का योग क्या होगा?
If in an AP \(S_{18}=810\) and \(S_9=270\), what is the sum from the (10)th term to the (18)th term?
#partial sum difference
#range sum
#ap
A (510)
B (520)
C (530)
D (540)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{18}-S_9=540\). The sum of consecutive terms is found by subtracting partial sums.
Step 2
Why this answer is correct
The correct answer is D. (540). The required sum is \(S_{18}-S_9=540\). The sum of consecutive terms is found by subtracting partial sums.
Step 3
Exam Tip
आवश्यक योग \(S_{18}-S_9=540\) है। लगातार पदों का योग आंशिक योगों के अंतर से मिलता है।
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समांतर श्रेढ़ी \(3,10,17,\ldots\) में (15)वें पद से (32)वें पद तक का योग क्या होगा?
In the AP \(3,10,17,\ldots\), what is the sum from the (15)th term to the (32)nd term?
#range sum
#partial sum
#ap
A (2862)
B (2889)
C (2916)
D (2943)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{32}-S_{14}=2889\). To find a middle block sum, subtract the previous partial sum.
Step 2
Why this answer is correct
The correct answer is B. (2889). The required sum is \(S_{32}-S_{14}=2889\). To find a middle block sum, subtract the previous partial sum.
Step 3
Exam Tip
मांगा गया योग \(S_{32}-S_{14}=2889\) है। बीच के पदों का योग निकालने के लिए पिछले आंशिक योग को घटाएँ।
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समांतर श्रेढ़ी \(12,17,22,\ldots\) में (21)वें पद से (40)वें पद तक का योग ज्ञात कीजिए।
In the AP \(12,17,22,\ldots\), find the sum from the (21)st term to the (40)th term.
#range sum
#partial sum
#ap
A (3190)
B (3150)
C (3230)
D (3270)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{40}-S_{20}=3190\). Do not forget to subtract the sum just before the given range.
Step 2
Why this answer is correct
The correct answer is A. (3190). The required sum is \(S_{40}-S_{20}=3190\). Do not forget to subtract the sum just before the given range.
Step 3
Exam Tip
आवश्यक योग \(S_{40}-S_{20}=3190\) है। दी गई सीमा से ठीक पहले तक का योग घटाना न भूलें।
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समांतर श्रेढ़ी \(6,10,14,\ldots\) में (4)वें पद से (25)वें पद तक का योग कितना है?
In the AP \(6,10,14,\ldots\), what is the sum from the (4)th term to the (25)th term?
#range sum
#ap
#partial sum
A (1296)
B (1320)
C (1344)
D (1368)
Explanation opens after your attempt
Step 1
Concept
This sum is \(S_{25}-S_3=1320\). When starting from the (4)th term, subtract the sum of the first (3) terms.
Step 2
Why this answer is correct
The correct answer is B. (1320). This sum is \(S_{25}-S_3=1320\). When starting from the (4)th term, subtract the sum of the first (3) terms.
Step 3
Exam Tip
यह योग \(S_{25}-S_3=1320\) है। (4)वें पद से शुरू होने पर पहले (3) पदों का योग घटाएँ।
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एक सड़क पर खंभों की दूरी के क्रम \(6,12,18,\ldots\) मीटर हैं। पहले (25) अंतरालों की कुल दूरी कितनी होगी?
On a road, the distances of intervals are \(6,12,18,\ldots\) meters. What is the total distance of the first (25) intervals?
#road distance
#multiples
#ap sum
A (1900)
B (1925)
C (1950)
D (1975)
Explanation opens after your attempt
Step 1
Concept
This is the sum of the first (25) multiples of (6), so the total distance is (1950) meters. In sums of multiples, (a=d).
Step 2
Why this answer is correct
The correct answer is C. (1950). This is the sum of the first (25) multiples of (6), so the total distance is (1950) meters. In sums of multiples, (a=d).
Step 3
Exam Tip
यह (6) के पहले (25) गुणजों का योग है, इसलिए कुल दूरी (1950) मीटर है। गुणजों के योग में (a=d) होता है।
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यदि किसी समान्तर श्रेणी का \(S_n=7n^2+2n\) है तो (9)वें से (18)वें पदों का योग कितना होगा?
If \(S_n=7n^2+2n\) for an arithmetic progression, what is the sum from the (9)th to the (18)th terms?
#ap
#range-sum-from-sn
#expert
A (1780)
B (1840)
C (1900)
D (1960)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{18}-S_8=2304-464=1840\). Exam tip: the sum from the (m)th to (n)th term is \(S_n-S_{m-1}\).
Step 2
Why this answer is correct
The correct answer is B. (1840). The required sum is \(S_{18}-S_8=2304-464=1840\). Exam tip: the sum from the (m)th to (n)th term is \(S_n-S_{m-1}\).
Step 3
Exam Tip
वांछित योग \(S_{18}-S_8=2304-464=1840\) है। परीक्षा में (m)वें से (n)वें तक का योग \(S_n-S_{m-1}\) होता है।
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समान्तर श्रेणी \(80,76,72,\ldots\) में (5)वें पद से (20)वें पद तक का योग कितना होगा?
In the arithmetic progression \(80,76,72,\ldots\), what is the sum from the (5)th term to the (20)th term?
#ap
#selected-terms-sum
#expert
A (544)
B (560)
C (576)
D (592)
Explanation opens after your attempt
Step 1
Concept
\(t_5=64\) and \(t_{20}=4\), so the sum is (\frac{16}{2}(64+4)=544). Exam tip: count the selected terms correctly.
Step 2
Why this answer is correct
The correct answer is A. (544). \(t_5=64\) and \(t_{20}=4\), so the sum is (\frac{16}{2}(64+4)=544). Exam tip: count the selected terms correctly.
Step 3
Exam Tip
\(t_5=64\) और \(t_{20}=4\) हैं इसलिए योग (\frac{16}{2}(64+4)=544) है। परीक्षा में चुने गए पदों की संख्या सही गिनें।
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एक समान्तर श्रेणी में (29) पद हैं और मध्य पद (48) है। सभी पदों का योग कितना होगा?
An arithmetic progression has (29) terms and its middle term is (48). What is the sum of all terms?
#ap
#middle-term-sum
#expert
A (1392)
B (1421)
C (1450)
D (1479)
Explanation opens after your attempt
Step 1
Concept
For an AP with an odd number of terms, the sum is the product of the number of terms and the middle term. Exam tip: remember the middle-term property.
Step 2
Why this answer is correct
The correct answer is A. (1392). For an AP with an odd number of terms, the sum is the product of the number of terms and the middle term. Exam tip: remember the middle-term property.
Step 3
Exam Tip
विषम संख्या पदों वाली समान्तर श्रेणी में योग पदों की संख्या और मध्य पद का गुणनफल होता है। परीक्षा में मध्य पद की संपत्ति याद रखें।
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एक समान्तर श्रेणी का प्रथम पद (96) है और पहले (25) पदों का योग (0) है। सार्व अंतर क्या होगा?
The first term of an arithmetic progression is (96) and the sum of the first (25) terms is (0). What is the common difference?
#ap
#zero-sum
#expert
A ( -7 )
B ( -8 )
C ( -9 )
D ( -10 )
Explanation opens after your attempt
Step 1
Concept
From \(0=\frac{25}{2}[192+24d]\), (d=-8). Exam tip: in zero-sum questions, set the bracket equal to zero.
Step 2
Why this answer is correct
The correct answer is B. ( -8 ). From \(0=\frac{25}{2}[192+24d]\), (d=-8). Exam tip: in zero-sum questions, set the bracket equal to zero.
Step 3
Exam Tip
\(0=\frac{25}{2}[192+24d]\) से (d=-8) मिलता है। परीक्षा में शून्य योग वाले प्रश्नों में कोष्ठक को शून्य रखें।
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समान्तर श्रेणी \(90,84,78,\ldots\) के आरम्भिक पदों के योग का अधिकतम मान क्या होगा?
What is the maximum value of the sum of initial terms of the arithmetic progression \(90,84,78,\ldots\)?
#ap
#maximum-sum
#expert
A (690)
B (705)
C (735)
D (720)
Explanation opens after your attempt
Step 1
Concept
(S_n=3n(31-n)), and the maximum (720) occurs at (n=15) or (n=16). Exam tip: check integer values near the vertex.
Step 2
Why this answer is correct
The correct answer is D. (720). (S_n=3n(31-n)), and the maximum (720) occurs at (n=15) or (n=16). Exam tip: check integer values near the vertex.
Step 3
Exam Tip
(S_n=3n(31-n)) है और (n=15) या (n=16) पर अधिकतम (720) मिलता है। परीक्षा में शीर्ष के पास वाले पूर्णांक जांचें।
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(1) से (140) तक उन प्राकृतिक संख्याओं का योग कितना है जो (7) से विभाज्य नहीं हैं?
What is the sum of natural numbers from (1) to (140) that are not divisible by (7)?
#ap
#complement-sum
#expert
A (8400)
B (8500)
C (8600)
D (8700)
Explanation opens after your attempt
Step 1
Concept
The total sum is (9870), and the sum of multiples of (7) is (1470), so the answer is (8400). Exam tip: subtract the complementary sum.
Step 2
Why this answer is correct
The correct answer is A. (8400). The total sum is (9870), and the sum of multiples of (7) is (1470), so the answer is (8400). Exam tip: subtract the complementary sum.
Step 3
Exam Tip
कुल योग (9870) है और (7) के गुणजों का योग (1470) है इसलिए उत्तर (8400) है। परीक्षा में पूरक योग घटाना आसान होता है।
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एक समान्तर श्रेणी में (d=7) है और (13)वें से (24)वें पदों का योग (1602) है। प्रथम पद क्या होगा?
In an arithmetic progression (d=7) and the sum of the (13)th to (24)th terms is (1602). What is the first term?
#ap
#middle-terms-sum
#expert
A (9)
B (11)
C (13)
D (15)
Explanation opens after your attempt
Step 1
Concept
The selected (12) terms give (6(2a+245)=1602), so (a=11). Exam tip: treat the selected part as a separate AP.
Step 2
Why this answer is correct
The correct answer is B. (11). The selected (12) terms give (6(2a+245)=1602), so (a=11). Exam tip: treat the selected part as a separate AP.
Step 3
Exam Tip
चुने गए (12) पदों का योग (6(2a+245)=1602) देता है इसलिए (a=11)। परीक्षा में चयनित भाग को अलग समान्तर श्रेणी मानें।
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एक समान्तर श्रेणी में \(t_4+t_{10}=68\) और \(t_7+t_{17}=128\) है। पहले (20) पदों का योग कितना होगा?
In an arithmetic progression \(t_4+t_{10}=68\) and \(t_7+t_{17}=128\). What is the sum of the first (20) terms?
#ap
#term-pair-sum
#expert
A (1060)
B (1080)
C (1120)
D (1100)
Explanation opens after your attempt
Step 1
Concept
The two equations give (a=-2) and (d=6), so \(S_{20}=1100\). Exam tip: convert term sums into (a) and (d).
Step 2
Why this answer is correct
The correct answer is D. (1100). The two equations give (a=-2) and (d=6), so \(S_{20}=1100\). Exam tip: convert term sums into (a) and (d).
Step 3
Exam Tip
दो समीकरणों से (a=-2) और (d=6) मिलते हैं इसलिए \(S_{20}=1100\)। परीक्षा में पदों के योग को (a) और (d) में बदलें।
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समान्तर श्रेणी \(150,141,132,\ldots\) के कितने आरम्भिक पदों का योग धनात्मक रहेगा?
For the arithmetic progression \(150,141,132,\ldots\), the sum of how many initial terms will remain positive?
#ap
#positive-sum
#expert
A (32)
B (34)
C (35)
D (36)
Explanation opens after your attempt
Step 1
Concept
(S_n=\frac{n}{2}(309-9n)) is positive up to (n=34). Exam tip: solve the inequality and then take the integer limit.
Step 2
Why this answer is correct
The correct answer is B. (34). (S_n=\frac{n}{2}(309-9n)) is positive up to (n=34). Exam tip: solve the inequality and then take the integer limit.
Step 3
Exam Tip
(S_n=\frac{n}{2}(309-9n)) धनात्मक होने पर अधिकतम (n=34) है। परीक्षा में असमानता हल करके पूर्णांक सीमा लें।
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समान्तर श्रेणी \(18,25,32,\ldots\) में (8)वें पद से (26)वें पद तक का योग कितना होगा?
In the arithmetic progression \(18,25,32,\ldots\), what is the sum from the (8)th term to the (26)th term?
#ap
#range-sum
#expert
A (2470)
B (2546)
C (2622)
D (2698)
Explanation opens after your attempt
Step 1
Concept
\(t_8=67\), \(t_{26}=193\), and there are (19) terms, so the sum is (2470). Exam tip: count the selected terms correctly.
Step 2
Why this answer is correct
The correct answer is A. (2470). \(t_8=67\), \(t_{26}=193\), and there are (19) terms, so the sum is (2470). Exam tip: count the selected terms correctly.
Step 3
Exam Tip
\(t_8=67\), \(t_{26}=193\) और कुल (19) पद हैं इसलिए योग (2470) है। परीक्षा में चुने गए पदों की संख्या सही गिनें।
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यदि किसी समान्तर श्रेणी के पहले (n) पदों का योग \(S_n=6n^2-5n\) है तो (18)वाँ पद क्या होगा?
If the sum of the first (n) terms of an arithmetic progression is \(S_n=6n^2-5n\), what is the (18)th term?
#ap
#sum-to-term
#expert
A (181)
B (187)
C (205)
D (211)
Explanation opens after your attempt
Step 1
Concept
\(a_{18}=S_{18}-S_{17}=1854-1649=205\). Exam tip: subtract two consecutive sums to find a term.
Step 2
Why this answer is correct
The correct answer is C. (205). \(a_{18}=S_{18}-S_{17}=1854-1649=205\). Exam tip: subtract two consecutive sums to find a term.
Step 3
Exam Tip
\(a_{18}=S_{18}-S_{17}=1854-1649=205\) है। परीक्षा में किसी पद के लिए लगातार दो योग घटाएं।
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एक समान्तर श्रेणी का (6)वाँ पद (29) और (19)वाँ पद (94) है। पहले (19) पदों का योग कितना होगा?
The (6)th term of an arithmetic progression is (29) and the (19)th term is (94). What is the sum of the first (19) terms?
#ap
#two-terms-sum
#expert
A (931)
B (950)
C (969)
D (988)
Explanation opens after your attempt
Step 1
Concept
The two terms give (d=5) and (a=4), so \(S_{19}=931\). Exam tip: find (a) and (d) first.
Step 2
Why this answer is correct
The correct answer is A. (931). The two terms give (d=5) and (a=4), so \(S_{19}=931\). Exam tip: find (a) and (d) first.
Step 3
Exam Tip
दो पदों से (d=5) और (a=4) मिलता है इसलिए \(S_{19}=931\)। परीक्षा में पहले (a) और (d) निकालें।
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