100 results found for "ap-sum-five-decreasing" in Class 10.
एक घटती समान्तर श्रेणी में प्रथम पद (72) और सार्व अंतर (-4) है। पहले (24) पदों का योग कितना होगा?
In a decreasing arithmetic progression the first term is (72) and the common difference is (-4). What is the sum of the first (24) terms?
#ap
#decreasing-ap
#expert
A (576)
B (600)
C (612)
D (624)
Explanation opens after your attempt
Step 1
Concept
(S_{24}=\frac{24}{2}[144+23(-4)]=624). Exam tip: handle the negative common difference carefully.
Step 2
Why this answer is correct
The correct answer is D. (624). (S_{24}=\frac{24}{2}[144+23(-4)]=624). Exam tip: handle the negative common difference carefully.
Step 3
Exam Tip
(S_{24}=\frac{24}{2}[144+23(-4)]=624) है। परीक्षा में ऋणात्मक सार्व अंतर का चिन्ह सावधानी से रखें।
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एक घटती समान्तर श्रेणी में प्रथम पद (65) और सार्व अंतर (-5) है। पहले (15) पदों का योग कितना होगा?
In a decreasing arithmetic progression the first term is (65) and the common difference is (-5). What is the sum of the first (15) terms?
#ap
#decreasing-ap
#expert
A (450)
B (475)
C (500)
D (525)
Explanation opens after your attempt
Step 1
Concept
(S_{15}=\frac{15}{2}[130+14(-5)]=450). Exam tip: handle the negative common difference carefully.
Step 2
Why this answer is correct
The correct answer is A. (450). (S_{15}=\frac{15}{2}[130+14(-5)]=450). Exam tip: handle the negative common difference carefully.
Step 3
Exam Tip
(S_{15}=\frac{15}{2}[130+14(-5)]=450) है। परीक्षा में ऋणात्मक सार्व अंतर का चिन्ह सावधानी से रखें।
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समान्तर श्रेणी \(60,54,48,\ldots\) के पहले (5) पदों का योग क्या होगा?
What will be the sum of the first (5) terms of the AP \(60,54,48,\ldots\)?
#ap-sum-five-decreasing
A (230)
B (240)
C (250)
D (260)
Explanation opens after your attempt
Step 1
Concept
The fifth term is (36). (S_5=\frac{5}{2}(60+36)=240).
Step 2
Why this answer is correct
The correct answer is B. (240). The fifth term is (36). (S_5=\frac{5}{2}(60+36)=240).
Step 3
Exam Tip
पांचवां पद (36) है। (S_5=\frac{5}{2}(60+36)=240)।
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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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दांतों की सड़न में मुंह का पीएच पाँच दशमलव पाँच से कम होना क्यों हानिकारक है?
Why is mouth pH below five point five harmful in tooth decay?
#science
#class10
#medium
#tooth-decay
#ph
A अम्ल दांतों के आवरण को कमजोर करता है / Acid weakens tooth enamel
B क्षार दांतों को पिघलाता है / Base melts teeth
C लवण दांतों को गैस बनाता है / Salt turns teeth into gas
D जल दांतों को रंगहीन करता है / Water makes teeth colourless
Explanation opens after your attempt
Correct Answer
A. अम्ल दांतों के आवरण को कमजोर करता है / Acid weakens tooth enamel
Step 1
Concept
Lower pH indicates higher acidity.
Step 2
Why this answer is correct
Acid can damage the hard enamel of teeth.
Step 3
Exam Tip
Therefore low pH can increase tooth decay. चरण 1: कम पीएच अधिक अम्लीयता बताता है। चरण 2: अम्ल दांतों के कठोर आवरण को नुकसान पहुंचा सकता है। चरण 3: इसलिए कम पीएच दांतों की सड़न बढ़ा सकता 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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समांतर श्रेढ़ी \(300,287,274,\ldots\) के पहले (35) पदों का योग ज्ञात कीजिए।
Find the sum of the first (35) terms of the AP \(300,287,274,\ldots\).
#decreasing ap
#negative difference
#sum
A (2715)
B (2735)
C (2755)
D (2765)
Explanation opens after your attempt
Step 1
Concept
Here (d=-13), and \(S_{35}=2765\). Do not forget the negative sign of the common difference in a decreasing AP.
Step 2
Why this answer is correct
The correct answer is D. (2765). Here (d=-13), and \(S_{35}=2765\). Do not forget the negative sign of the common difference in a decreasing AP.
Step 3
Exam Tip
यहाँ (d=-13) है और \(S_{35}=2765\) आता है। घटती श्रेढ़ी में सार्व अंतर का ऋणात्मक चिह्न न भूलें।
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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 \(160,151,142,\ldots\) के पहले (22) पदों का योग ज्ञात कीजिए।
Find the sum of the first (22) terms of the AP \(160,151,142,\ldots\).
#decreasing ap
#negative difference
#sum
A (1397)
B (1419)
C (1463)
D (1441)
Explanation opens after your attempt
Step 1
Concept
Here (d=-9), and the formula gives \(S_{22}=1441\). In a decreasing AP, write the common difference as negative.
Step 2
Why this answer is correct
The correct answer is D. (1441). Here (d=-9), and the formula gives \(S_{22}=1441\). In a decreasing AP, write the common difference as negative.
Step 3
Exam Tip
यहाँ (d=-9) है और सूत्र से \(S_{22}=1441\) मिलता है। घटती श्रेढ़ी में सार्व अंतर ऋणात्मक लिखें।
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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 \(120,113,106,\ldots\) के पहले (25) पदों का योग ज्ञात कीजिए।
Find the sum of the first (25) terms of the AP \(120,113,106,\ldots\).
#decreasing ap
#negative difference
#sum
A (850)
B (875)
C (900)
D (925)
Explanation opens after your attempt
Step 1
Concept
Here (d=-7), and the formula gives \(S_{25}=900\). In a decreasing AP, write the common difference as negative.
Step 2
Why this answer is correct
The correct answer is C. (900). Here (d=-7), and the formula gives \(S_{25}=900\). In a decreasing AP, write the common difference as negative.
Step 3
Exam Tip
यहाँ (d=-7) है और सूत्र से \(S_{25}=900\) मिलता है। घटती श्रेढ़ी में सार्व अंतर ऋणात्मक लिखें।
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समांतर श्रेढ़ी \(50,47,44,\ldots\) में (6)वें पद से (20)वें पद तक का योग क्या है?
In the AP \(50,47,44,\ldots\), what is the sum from the (6)th term to the (20)th term?
#decreasing ap
#middle terms
#partial sum
A (180)
B (195)
C (210)
D (225)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{20}-S_5=210\). The same partial-sum method works for a decreasing AP.
Step 2
Why this answer is correct
The correct answer is C. (210). The required sum is \(S_{20}-S_5=210\). The same partial-sum method works for a decreasing AP.
Step 3
Exam Tip
आवश्यक योग \(S_{20}-S_5=210\) है। घटती श्रेढ़ी में भी आंशिक योग का वही तरीका लागू होता है।
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समांतर श्रेढ़ी \(24,21,18,\ldots\) के पहले (16) पदों का योग कितना है?
What is the sum of the first (16) terms of the AP \(24,21,18,\ldots\)?
#decreasing ap
#small sum
#ap
A (20)
B (22)
C (24)
D (26)
Explanation opens after your attempt
Step 1
Concept
The last term is (-21), and (S_{16}=\frac{16}{2}(24-21)=24). Positive and negative terms can greatly reduce the sum.
Step 2
Why this answer is correct
The correct answer is C. (24). The last term is (-21), and (S_{16}=\frac{16}{2}(24-21)=24). Positive and negative terms can greatly reduce the sum.
Step 3
Exam Tip
अंतिम पद (-21) है और (S_{16}=\frac{16}{2}(24-21)=24)। धनात्मक और ऋणात्मक पद एक-दूसरे को काफी घटा सकते हैं।
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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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समांतर श्रेढ़ी \(31,28,25,\ldots\) के पहले (20) पदों का योग ज्ञात कीजिए।
Find the sum of the first (20) terms of the AP \(31,28,25,\ldots\).
#decreasing ap
#negative terms
#sum
A (50)
B (55)
C (60)
D (65)
Explanation opens after your attempt
Step 1
Concept
Here the last term is (-26), and \(S_{20}=50\). In a decreasing AP, the sum can become quite small.
Step 2
Why this answer is correct
The correct answer is A. (50). Here the last term is (-26), and \(S_{20}=50\). In a decreasing AP, the sum can become quite small.
Step 3
Exam Tip
यहाँ अंतिम पद (-26) है और \(S_{20}=50\) मिलता है। घटती श्रेढ़ी में योग बहुत छोटा भी हो सकता है।
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समांतर श्रेढ़ी \(50,47,44,\ldots\) के पहले (18) पदों का योग ज्ञात कीजिए।
Find the sum of the first (18) terms of the AP \(50,47,44,\ldots\).
#decreasing ap
#ap sum
#common difference
A (441)
B (459)
C (468)
D (450)
Explanation opens after your attempt
Step 1
Concept
Here (d=-3), and the formula gives \(S_{18}=441\). In a decreasing AP, write the common difference as negative.
Step 2
Why this answer is correct
The correct answer is A. (441). Here (d=-3), and the formula gives \(S_{18}=441\). In a decreasing AP, write the common difference as negative.
Step 3
Exam Tip
यहाँ (d=-3) है और सूत्र से \(S_{18}=441\) मिलता है। घटती श्रेढ़ी में सार्व अंतर ऋणात्मक लिखें।
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समान्तर श्रेणी \(50,45,40,\ldots\) के पहले (9) पदों का योग क्या है?
What is the sum of the first (9) terms of the AP \(50,45,40,\ldots\)?
#ap-sum-decreasing-nine
A (260)
B (270)
C (280)
D (290)
Explanation opens after your attempt
Step 1
Concept
The ninth term is (10). (S_9=\frac{9}{2}(50+10)=270).
Step 2
Why this answer is correct
The correct answer is B. (270). The ninth term is (10). (S_9=\frac{9}{2}(50+10)=270).
Step 3
Exam Tip
नौवां पद (10) है। (S_9=\frac{9}{2}(50+10)=270)।
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समान्तर श्रेणी \(100,90,80,\ldots\) के पहले (6) पदों का योग क्या है?
What is the sum of the first (6) terms of the AP \(100,90,80,\ldots\)?
#ap-sum-decreasing-six
A (430)
B (440)
C (450)
D (460)
Explanation opens after your attempt
Step 1
Concept
The sixth term is (50). (S_6=\frac{6}{2}(100+50)=450).
Step 2
Why this answer is correct
The correct answer is C. (450). The sixth term is (50). (S_6=\frac{6}{2}(100+50)=450).
Step 3
Exam Tip
छठा पद (50) है। (S_6=\frac{6}{2}(100+50)=450)।
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समान्तर श्रेणी \(20,18,16,\ldots\) के पहले (8) पदों का योग क्या है?
What is the sum of the first (8) terms of the AP \(20,18,16,\ldots\)?
#ap-sum-decreasing
A (100)
B (104)
C (108)
D (112)
Explanation opens after your attempt
Step 1
Concept
This is a decreasing AP with (d=-2). (S_8=\frac{8}{2}[40+7(-2)]=104).
Step 2
Why this answer is correct
The correct answer is B. (104). This is a decreasing AP with (d=-2). (S_8=\frac{8}{2}[40+7(-2)]=104).
Step 3
Exam Tip
यह घटती AP है जिसमें (d=-2) है। (S_8=\frac{8}{2}[40+7(-2)]=104)।
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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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समान्तर श्रेणी \(14,18,22,\ldots\) के पहले (25) पदों का योग कितना है?
What is the sum of the first (25) terms of the AP \(14,18,22,\ldots\)?
#ap-sum-twenty-five
A (1535)
B (1550)
C (1565)
D (1575)
Explanation opens after your attempt
Step 1
Concept
The last term is \(14+24\cdot4=110\). (S_{25}=\frac{25}{2}(14+110)=1550).
Step 2
Why this answer is correct
The correct answer is B. (1550). The last term is \(14+24\cdot4=110\). (S_{25}=\frac{25}{2}(14+110)=1550).
Step 3
Exam Tip
अंतिम पद \(14+24\cdot4=110\) है। (S_{25}=\frac{25}{2}(14+110)=1550)।
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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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किस अनुक्रम में पद समान मात्रा से घट रहे हैं लेकिन (d=-4) नहीं है?
In which sequence are terms decreasing by an equal amount but (d) is not (-4)?
#ap
#decreasing sequence
#negative difference
#medium
A \(30,26,22,18,\ldots\)
B \(45,40,35,30,\ldots\)
C \(16,12,8,4,\ldots\)
D \(9,5,1,-3,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(45,40,35,30,\ldots\)
Step 1
Concept
In \(45,40,35,30,\ldots\), (d=-5), not (-4). Check both value and sign in the options.
Step 2
Why this answer is correct
The correct answer is B. \(45,40,35,30,\ldots\). In \(45,40,35,30,\ldots\), (d=-5), not (-4). Check both value and sign in the options.
Step 3
Exam Tip
\(45,40,35,30,\ldots\) में (d=-5) है, (-4) नहीं। विकल्पों में मान और चिह्न दोनों जांचें।
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किस अनुक्रम में पद समान मात्रा से घट रहे हैं लेकिन (d=-2) नहीं है?
In which sequence are the terms decreasing by an equal amount but (d) is not (-2)?
#ap
#decreasing sequence
#negative difference
#medium
A \(20,17,14,11,\ldots\)
B \(9,7,5,3,\ldots\)
C \(8,6,4,2,\ldots\)
D \(5,3,1,-1,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(20,17,14,11,\ldots\)
Step 1
Concept
In \(20,17,14,11,\ldots\), (d=-3), not (-2). Check both sign and value in options.
Step 2
Why this answer is correct
The correct answer is A. \(20,17,14,11,\ldots\). In \(20,17,14,11,\ldots\), (d=-3), not (-2). Check both sign and value in options.
Step 3
Exam Tip
\(20,17,14,11,\ldots\) में (d=-3) है, (-2) नहीं। विकल्पों में चिह्न और मान दोनों जांचें।
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निम्न में से कौन सा अनुक्रम घटती अंकगणितीय श्रेणी है?
Which of the following is a decreasing arithmetic progression?
#ap
#decreasing ap
#negative difference
#easy
A \(50,45,40,35,\ldots\)
B \(2,4,8,16,\ldots\)
C \(5,5,5,5,\ldots\)
D \(1,4,9,16,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(50,45,40,35,\ldots\)
Step 1
Concept
In \(50,45,40,35,\ldots\), the equal difference is (-5). A decreasing arithmetic progression has negative (d).
Step 2
Why this answer is correct
The correct answer is A. \(50,45,40,35,\ldots\). In \(50,45,40,35,\ldots\), the equal difference is (-5). A decreasing arithmetic progression has negative (d).
Step 3
Exam Tip
\(50,45,40,35,\ldots\) में समान अंतर (-5) है। घटती अंकगणितीय श्रेणी का (d) ऋणात्मक होता है।
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एक समान्तर श्रेणी में (a=18) और (d=-4) है। पहले कितने पदों का योग (144) होगा?
In an arithmetic progression (a=18) and (d=-4). How many first terms have sum (144)?
#ap
#find-n
#decreasing
#expert
A (8)
B (9)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
Using the sum formula gives (n=9). Exam tip: even in a decreasing AP, take the positive value of (n).
Step 2
Why this answer is correct
The correct answer is B. (9). Using the sum formula gives (n=9). Exam tip: even in a decreasing AP, take the positive value of (n).
Step 3
Exam Tip
योग सूत्र रखने पर समीकरण से (n=9) मिलता है। परीक्षा में घटती श्रेणी में भी धनात्मक (n) ही लें।
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समान्तर श्रेणी \(81,75,69,\ldots\) के कितने आरम्भिक पदों का योग (315) होगा?
How many initial terms of the arithmetic progression \(81,75,69,\ldots\) have sum (315)?
#ap
#decreasing-ap
#expert
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
Solving (\frac{n}{2}[162-6(n-1)]=315) gives (n=7). Exam tip: the same sum formula works for decreasing progressions too.
Step 2
Why this answer is correct
The correct answer is C. (7). Solving (\frac{n}{2}[162-6(n-1)]=315) gives (n=7). Exam tip: the same sum formula works for decreasing progressions too.
Step 3
Exam Tip
(\frac{n}{2}[162-6(n-1)]=315) हल करने पर (n=7) मिलता है। परीक्षा में घटती श्रेणी में भी वही योग सूत्र लागू होता है।
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यदि (S_n=\frac{n}{2}(a+l)), (a=25), (l=5), और (n=7) है, तो योग क्या होगा?
If (S_n=\frac{n}{2}(a+l)), (a=25), (l=5), and (n=7), what is the sum?
#ap_sum
#first_last
#decreasing
A (95)
B (100)
C (105)
D (110)
Explanation opens after your attempt
Step 1
Concept
(S_7=\frac{7}{2}(25+5)=105). The first term may be larger, but the formula remains the same.
Step 2
Why this answer is correct
The correct answer is C. (105). (S_7=\frac{7}{2}(25+5)=105). The first term may be larger, but the formula remains the same.
Step 3
Exam Tip
(S_7=\frac{7}{2}(25+5)=105)। पहला पद बड़ा हो सकता है, फिर भी सूत्र वही रहता है।
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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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मार्टिन लूथर द्वारा पंचानबे थीसिस किस आंदोलन से जुड़ी थी?
Martin Luther's Ninety Five Theses were linked with which movement?
#martin-luther
#reformation
#ninety-five-theses
A औद्योगिक क्रांति / Industrial Revolution
B अमेरिकी क्रांति / American Revolution
C प्रोटेस्टेंट सुधार / Protestant Reformation
D रूसी क्रांति / Russian Revolution
Explanation opens after your attempt
Correct Answer
C. प्रोटेस्टेंट सुधार / Protestant Reformation
Step 1
Concept
The Ninety Five Theses were linked with the Protestant Reformation. For exams remember Martin Luther with religious reform.
Step 2
Why this answer is correct
The correct answer is C. प्रोटेस्टेंट सुधार / Protestant Reformation. The Ninety Five Theses were linked with the Protestant Reformation. For exams remember Martin Luther with religious reform.
Step 3
Exam Tip
पंचानबे थीसिस प्रोटेस्टेंट सुधार से जुड़ी थीं। परीक्षा में मार्टिन लूथर और धार्मिक सुधार साथ याद रखें।
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जोसेफ स्टालिन की पंचवर्षीय योजनाएं किस क्षेत्र से जुड़ी थीं?
Joseph Stalin's Five Year Plans were linked with which field?
#world-leaders
#stalin
#five-year-plans
A समुद्री खोज / Sea exploration
B धार्मिक सुधार / Religious reform
C तेज औद्योगिकीकरण और केंद्रीकृत अर्थव्यवस्था / Rapid industrialization and centralized economy
D कला पुनर्जागरण / Art Renaissance
Explanation opens after your attempt
Correct Answer
C. तेज औद्योगिकीकरण और केंद्रीकृत अर्थव्यवस्था / Rapid industrialization and centralized economy
Step 1
Concept
Stalin's Five Year Plans stressed Soviet industrialization. For exams connect them with state controlled economy.
Step 2
Why this answer is correct
The correct answer is C. तेज औद्योगिकीकरण और केंद्रीकृत अर्थव्यवस्था / Rapid industrialization and centralized economy. Stalin's Five Year Plans stressed Soviet industrialization. For exams connect them with state controlled economy.
Step 3
Exam Tip
स्टालिन की पंचवर्षीय योजनाओं ने सोवियत औद्योगिकीकरण पर जोर दिया। परीक्षा में इन्हें राज्य नियंत्रित अर्थव्यवस्था से जोड़ें।
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दूसरी पंचवर्षीय योजना किस वर्ष शुरू हुई थी?
The Second Five-Year Plan began in which year?
#indian-history
#important-dates
#second-five-year-plan
A सन् 1951 / 1951
B सन् 1956 / 1956
C सन् 1961 / 1961
D सन् 1965 / 1965
Explanation opens after your attempt
Correct Answer
B. सन् 1956 / 1956
Step 1
Concept
The Second Five-Year Plan began in 1956. In exams remember its focus on heavy industries.
Step 2
Why this answer is correct
The correct answer is B. सन् 1956 / 1956. The Second Five-Year Plan began in 1956. In exams remember its focus on heavy industries.
Step 3
Exam Tip
दूसरी पंचवर्षीय योजना 1956 में शुरू हुई थी। परीक्षा में भारी उद्योगों पर इसका जोर याद रखें।
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प्रथम पंचवर्षीय योजना किस वर्ष शुरू हुई थी?
The First Five-Year Plan began in which year?
#indian-history
#important-dates
#five-year-plan
A सन् 1950 / 1950
B सन् 1951 / 1951
C सन् 1956 / 1956
D सन् 1961 / 1961
Explanation opens after your attempt
Correct Answer
B. सन् 1951 / 1951
Step 1
Concept
The First Five-Year Plan began in 1951. In exams remember its focus on agriculture and irrigation.
Step 2
Why this answer is correct
The correct answer is B. सन् 1951 / 1951. The First Five-Year Plan began in 1951. In exams remember its focus on agriculture and irrigation.
Step 3
Exam Tip
प्रथम पंचवर्षीय योजना 1951 में शुरू हुई थी। परीक्षा में कृषि और सिंचाई पर इसके जोर को याद रखें।
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यदि (a=25), (d=-2), (n=15) है तो \(S_{15}\) क्या होगा?
If (a=25), (d=-2), (n=15), what is \(S_{15}\)?
#ap-sum-decreasing-values
A (155)
B (160)
C (165)
D (170)
Explanation opens after your attempt
Step 1
Concept
In a decreasing AP use (d=-2). (S_{15}=\frac{15}{2}[50+14(-2)]=165).
Step 2
Why this answer is correct
The correct answer is C. (165). In a decreasing AP use (d=-2). (S_{15}=\frac{15}{2}[50+14(-2)]=165).
Step 3
Exam Tip
घटती AP में (d=-2) रखें। (S_{15}=\frac{15}{2}[50+14(-2)]=165)।
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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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(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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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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एक समान्तर श्रेणी में (31) पद हैं और मध्य पद (44) है। सभी पदों का योग कितना होगा?
An arithmetic progression has (31) terms and the middle term is (44). What is the sum of all terms?
#ap
#middle-term-sum
#expert
A (1324)
B (1364)
C (1404)
D (1444)
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 B. (1364). 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 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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समान्तर श्रेणी \(30,34,38,\ldots\) में (6)वें पद से (25)वें पद तक का योग कितना होगा?
In the arithmetic progression \(30,34,38,\ldots\), what is the sum from the (6)th term to the (25)th term?
#ap
#selected-range-sum
#expert
A (1420)
B (1480)
C (1540)
D (1600)
Explanation opens after your attempt
Step 1
Concept
\(t_6=50\) and \(t_{25}=126\), so the sum is (\frac{20}{2}(50+126)=1760). Exam tip: count the selected terms correctly.
Step 2
Why this answer is correct
The correct answer is D. (1600). \(t_6=50\) and \(t_{25}=126\), so the sum is (\frac{20}{2}(50+126)=1760). Exam tip: count the selected terms correctly.
Step 3
Exam Tip
\(t_6=50\) और \(t_{25}=126\) हैं इसलिए योग (\frac{20}{2}(50+126)=1760) है। परीक्षा में चुने गए पदों की संख्या सही गिनें।
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समान्तर श्रेणी \(2,8,14,\ldots\) के पहले (n) पदों का योग (n)वें पद के (12) गुना के बराबर है। (n) क्या होगा?
The sum of the first (n) terms of the arithmetic progression \(2,8,14,\ldots\) equals (12) times the (n)th term. What is (n)?
#ap
#sum-nth-term-relation
#expert
A (21)
B (22)
C (23)
D (24)
Explanation opens after your attempt
Step 1
Concept
The equation (\frac{n}{2}[4+6(n-1)]=12[2+6(n-1)]) gives (n=23). Exam tip: write \(S_n\) and \(t_n\) separately.
Step 2
Why this answer is correct
The correct answer is C. (23). The equation (\frac{n}{2}[4+6(n-1)]=12[2+6(n-1)]) gives (n=23). Exam tip: write \(S_n\) and \(t_n\) separately.
Step 3
Exam Tip
समीकरण (\frac{n}{2}[4+6(n-1)]=12[2+6(n-1)]) से (n=23) है। परीक्षा में \(S_n\) और \(t_n\) दोनों अलग लिखें।
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(1) से (150) तक उन प्राकृतिक संख्याओं का योग कितना है जो (6) से विभाज्य नहीं हैं?
What is the sum of natural numbers from (1) to (150) that are not divisible by (6)?
#ap
#complement-sum
#expert
A (9300)
B (9450)
C (9600)
D (9750)
Explanation opens after your attempt
Step 1
Concept
The total sum is (11325), and the sum of multiples of (6) is (1875), so the answer is (9450). Exam tip: subtract the complementary sum.
Step 2
Why this answer is correct
The correct answer is B. (9450). The total sum is (11325), and the sum of multiples of (6) is (1875), so the answer is (9450). Exam tip: subtract the complementary sum.
Step 3
Exam Tip
कुल योग (11325) है और (6) के गुणजों का योग (1875) है इसलिए उत्तर (9450) है। परीक्षा में पूरक योग घटाना आसान होता है।
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समान्तर श्रेणी \(100,94,88,\ldots\) 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 \(100,94,88,\ldots\)?
#ap
#maximum-sum
#expert
A (850)
B (867)
C (884)
D (901)
Explanation opens after your attempt
Step 1
Concept
The sum is (S_n=n(103-3n)), and the maximum (901) occurs at (n=17). Exam tip: check integer values near the vertex.
Step 2
Why this answer is correct
The correct answer is D. (901). The sum is (S_n=n(103-3n)), and the maximum (901) occurs at (n=17). Exam tip: check integer values near the vertex.
Step 3
Exam Tip
योग (S_n=n(103-3n)) है और (n=17) पर अधिकतम (901) मिलता है। परीक्षा में शीर्ष के पास वाले पूर्णांक जांचें।
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समान्तर श्रेणी \(8,13,18,\ldots\) के पहले (n) पदों का योग (775) है। (n) का मान क्या होगा?
The sum of the first (n) terms of the arithmetic progression \(8,13,18,\ldots\) is (775). What is (n)?
#ap
#quadratic-sum
#expert
A (14)
B (15)
C (16)
D (17)
Explanation opens after your attempt
Step 1
Concept
Solving (\frac{n}{2}[16+5(n-1)]=775) gives (n=17). Exam tip: choose the positive integer root.
Step 2
Why this answer is correct
The correct answer is D. (17). Solving (\frac{n}{2}[16+5(n-1)]=775) gives (n=17). Exam tip: choose the positive integer root.
Step 3
Exam Tip
(\frac{n}{2}[16+5(n-1)]=775) हल करने पर (n=17) मिलता है। परीक्षा में धनात्मक पूर्णांक मूल चुनें।
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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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किसी समान्तर श्रेणी में \(S_{10}=310\) और \(S_{20}=1120\) है। (11)वें से (20)वें पद तक का योग कितना होगा?
In an arithmetic progression \(S_{10}=310\) and \(S_{20}=1120\). What is the sum from the (11)th term to the (20)th term?
#ap
#partial-sum
#expert
A (780)
B (800)
C (810)
D (830)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{20}-S_{10}=1120-310=810\). Exam tip: use the difference of cumulative sums for middle terms.
Step 2
Why this answer is correct
The correct answer is C. (810). The required sum is \(S_{20}-S_{10}=1120-310=810\). Exam tip: use the difference of cumulative sums for middle terms.
Step 3
Exam Tip
वांछित योग \(S_{20}-S_{10}=1120-310=810\) है। परीक्षा में बीच के पदों के लिए कुल योगों का अंतर लें।
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एक समान्तर श्रेणी का (9)वाँ पद (46) और (21)वाँ पद (106) है। पहले (21) पदों का योग कितना होगा?
The (9)th term of an arithmetic progression is (46) and the (21)th term is (106). What is the sum of the first (21) terms?
#ap
#two-terms-sum
#expert
A (1176)
B (1188)
C (1197)
D (1218)
Explanation opens after your attempt
Step 1
Concept
The two terms give (d=5) and (a=6), so \(S_{21}=1176\). Exam tip: find (a) and (d) first.
Step 2
Why this answer is correct
The correct answer is A. (1176). The two terms give (d=5) and (a=6), so \(S_{21}=1176\). Exam tip: find (a) and (d) first.
Step 3
Exam Tip
दो पदों से (d=5) और (a=6) मिलता है इसलिए \(S_{21}=1176\)। परीक्षा में पहले (a) और (d) निकालें।
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यदि किसी समान्तर श्रेणी के पहले (n) पदों का योग \(S_n=5n^2+4n\) है तो (18)वाँ पद क्या होगा?
If the sum of the first (n) terms of an arithmetic progression is \(S_n=5n^2+4n\), what is the (18)th term?
#ap
#sum-to-term
#expert
A (169)
B (174)
C (179)
D (184)
Explanation opens after your attempt
Step 1
Concept
\(a_{18}=S_{18}-S_{17}=1692-1513=179\). Exam tip: subtract two consecutive sums to find a term.
Step 2
Why this answer is correct
The correct answer is C. (179). \(a_{18}=S_{18}-S_{17}=1692-1513=179\). Exam tip: subtract two consecutive sums to find a term.
Step 3
Exam Tip
\(a_{18}=S_{18}-S_{17}=1692-1513=179\) है। परीक्षा में किसी पद के लिए लगातार दो योग घटाएं।
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एक समान्तर श्रेणी में \(t_3+t_9=70\) और \(t_5+t_{15}=110\) है। पहले (20) पदों का योग कितना होगा?
In an arithmetic progression \(t_3+t_9=70\) and \(t_5+t_{15}=110\). What is the sum of the first (20) terms?
#ap
#term-pair-sum
#expert
A (1150)
B (1200)
C (1250)
D (1300)
Explanation opens after your attempt
Step 1
Concept
The two equations give (a=10) and (d=5). Exam tip: convert term sums into (a) and (d).
Step 2
Why this answer is correct
The correct answer is A. (1150). The two equations give (a=10) and (d=5). Exam tip: convert term sums into (a) and (d).
Step 3
Exam Tip
दो समीकरणों से (a=10) और (d=5) मिलते हैं। परीक्षा में पदों के योग को (a) और (d) में बदलें।
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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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समान्तर श्रेणी \(120,113,106,\ldots\) के कितने आरम्भिक पदों का योग धनात्मक रहेगा?
For the arithmetic progression \(120,113,106,\ldots\), the sum of how many initial terms will remain positive?
#ap
#positive-sum
#expert
A (33)
B (34)
C (35)
D (36)
Explanation opens after your attempt
Step 1
Concept
(S_n=\frac{n}{2}(247-7n)) is positive up to (n=35). Exam tip: solve the inequality and then take the integer limit.
Step 2
Why this answer is correct
The correct answer is C. (35). (S_n=\frac{n}{2}(247-7n)) is positive up to (n=35). Exam tip: solve the inequality and then take the integer limit.
Step 3
Exam Tip
(S_n=\frac{n}{2}(247-7n)) धनात्मक होने पर अधिकतम (n=35) है। परीक्षा में असमानता हल करके पूर्णांक सीमा लें।
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समान्तर श्रेणी \(14,20,26,\ldots\) में (5)वें पद से (20)वें पद तक का योग कितना होगा?
In the arithmetic progression \(14,20,26,\ldots\), what is the sum from the (5)th term to the (20)th term?
#ap
#partial-sum
#expert
A (1264)
B (1288)
C (1304)
D (1328)
Explanation opens after your attempt
Step 1
Concept
This is the sum of (16) terms with \(t_5=38\) and \(t_{20}=128\). Exam tip: treat the required middle part as a smaller AP.
Step 2
Why this answer is correct
The correct answer is D. (1328). This is the sum of (16) terms with \(t_5=38\) and \(t_{20}=128\). Exam tip: treat the required middle part as a smaller AP.
Step 3
Exam Tip
यह योग (16) पदों का है जिसमें \(t_5=38\) और \(t_{20}=128\) हैं। परीक्षा में बीच के पदों का योग छोटे भाग के रूप में निकालें।
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यदि किसी समान्तर श्रेणी के पहले (n) पदों का योग \(S_n=4n^2+3n\) है तो (25)वाँ पद क्या होगा?
If the sum of the first (n) terms of an arithmetic progression is \(S_n=4n^2+3n\), what is the (25)th term?
#ap
#sum-to-term
#expert
A (191)
B (195)
C (199)
D (203)
Explanation opens after your attempt
Step 1
Concept
\(a_{25}=S_{25}-S_{24}=199\). Exam tip: subtract two consecutive sums to get a term.
Step 2
Why this answer is correct
The correct answer is C. (199). \(a_{25}=S_{25}-S_{24}=199\). Exam tip: subtract two consecutive sums to get a term.
Step 3
Exam Tip
\(a_{25}=S_{25}-S_{24}=199\) है। परीक्षा में किसी पद के लिए लगातार दो योग घटाएं।
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एक समान्तर श्रेणी का (7)वाँ पद (34) और (18)वाँ पद (89) है। पहले (18) पदों का योग कितना होगा?
The (7)th term of an arithmetic progression is (34) and the (18)th term is (89). What is the sum of the first (18) terms?
#ap
#two-terms-sum
#expert
A (801)
B (819)
C (828)
D (837)
Explanation opens after your attempt
Step 1
Concept
The two terms give (d=5) and (a=4), so \(S_{18}=837\). Exam tip: find (a) and (d) first.
Step 2
Why this answer is correct
The correct answer is D. (837). The two terms give (d=5) and (a=4), so \(S_{18}=837\). Exam tip: find (a) and (d) first.
Step 3
Exam Tip
दो पदों से (d=5) और (a=4) मिलता है इसलिए \(S_{18}=837\)। परीक्षा में पहले (a) और (d) निकालें।
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किसी समान्तर श्रेणी के पहले (n) पदों का योग (S_n=n(4n-1)) है। (20)वाँ पद क्या होगा?
The sum of the first (n) terms of an arithmetic progression is (S_n=n(4n-1)). What is the (20)th term?
#ap
#nth-term-from-sum
#expert
A (151)
B (155)
C (159)
D (163)
Explanation opens after your attempt
Step 1
Concept
\(a_{20}=S_{20}-S_{19}=1580-1425=155\). Exam tip: subtract two consecutive sums to find a term.
Step 2
Why this answer is correct
The correct answer is B. (155). \(a_{20}=S_{20}-S_{19}=1580-1425=155\). Exam tip: subtract two consecutive sums to find a term.
Step 3
Exam Tip
\(a_{20}=S_{20}-S_{19}=1580-1425=155\) है। परीक्षा में पद निकालने के लिए दो लगातार योग घटाएं।
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एक समान्तर श्रेणी में \(S_{10}=220\) और \(S_{20}=840\) है। (11)वें से (20)वें पद तक का योग कितना होगा?
In an arithmetic progression \(S_{10}=220\) and \(S_{20}=840\). What is the sum from the (11)th term to the (20)th term?
#ap
#partial-sum
#expert
A (600)
B (610)
C (620)
D (640)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{20}-S_{10}=840-220=620\). Exam tip: find sums of middle terms by subtracting cumulative sums.
Step 2
Why this answer is correct
The correct answer is C. (620). The required sum is \(S_{20}-S_{10}=840-220=620\). Exam tip: find sums of middle terms by subtracting cumulative sums.
Step 3
Exam Tip
वांछित योग \(S_{20}-S_{10}=840-220=620\) है। परीक्षा में बीच के पदों का योग कुल योगों के अंतर से निकालें।
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एक समान्तर श्रेणी का (5)वाँ पद (22) और (15)वाँ पद (62) है। पहले (15) पदों का योग कितना है?
The (5)th term of an arithmetic progression is (22) and the (15)th term is (62). What is the sum of the first (15) terms?
#ap
#two-terms-sum
#expert
A (510)
B (525)
C (540)
D (555)
Explanation opens after your attempt
Step 1
Concept
The two terms give (d=4) and (a=6), so \(S_{15}=510\). Exam tip: first find (d) from the difference of two given terms.
Step 2
Why this answer is correct
The correct answer is A. (510). The two terms give (d=4) and (a=6), so \(S_{15}=510\). Exam tip: first find (d) from the difference of two given terms.
Step 3
Exam Tip
इन पदों से (d=4) और (a=6) मिलता है इसलिए \(S_{15}=510\)। परीक्षा में दो पदों का अंतर लेकर पहले (d) निकालें।
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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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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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एक समान्तर श्रेणी का (8)वाँ पद (31) और (20)वाँ पद (79) है। पहले (20) पदों का योग कितना होगा?
The (8)th term of an arithmetic progression is (31) and the (20)th term is (79). What is the sum of the first (20) terms?
#ap
#term-sum
#expert
A (900)
B (940)
C (980)
D (1020)
Explanation opens after your attempt
Step 1
Concept
From the two terms (d=4) and (a=3). Hence \(S_{20}=980\); exam tip: find (a) and (d) before applying the sum formula.
Step 2
Why this answer is correct
The correct answer is C. (980). From the two terms (d=4) and (a=3). Hence \(S_{20}=980\); exam tip: find (a) and (d) before applying the sum formula.
Step 3
Exam Tip
दो पदों से (d=4) और (a=3) मिलता है इसलिए \(S_{20}=980\)। परीक्षा में पहले (a) और (d) निकालें फिर योग लगाएं।
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किसी समांतर श्रेढ़ी का (n)वाँ पद \(a_n=7n-4\) है। पहले (80) पदों का योग ज्ञात कीजिए।
The (n)th term of an AP is \(a_n=7n-4\). Find the sum of the first (80) terms.
#nth term
#sum
#ap
A (22080)
B (22220)
C (22360)
D (22500)
Explanation opens after your attempt
Correct Answer
C. (22360)
Step 1
Concept
The first term is (3), and the (80)th term is (556), so the sum is (22360). Finding the first and last terms from \(a_n\) is an easy method.
Step 2
Why this answer is correct
The correct answer is C. (22360). The first term is (3), and the (80)th term is (556), so the sum is (22360). Finding the first and last terms from \(a_n\) is an easy method.
Step 3
Exam Tip
पहला पद (3) और (80)वाँ पद (556) है, इसलिए योग (22360) है। \(a_n\) से पहला और अंतिम पद निकालना आसान तरीका है।
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