100 results found for "ap-sum-zero-difference" in Class 10.
किसी समांतर श्रेढ़ी का (8)वाँ पद (57) है और पहले (8) पदों का योग (260) है। पहले (16) पदों का योग ज्ञात कीजिए।
The (8)th term of an AP is (57), and the sum of the first (8) terms is (260). Find the sum of the first (16) terms.
#given term and sum
#find sum
#ap
A (936)
B (952)
C (968)
D (984)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a=8) and (d=7), so \(S_{16}=968\). Convert the given term and sum into two equations.
Step 2
Why this answer is correct
The correct answer is C. (968). The conditions give (a=8) and (d=7), so \(S_{16}=968\). Convert the given term and sum into two equations.
Step 3
Exam Tip
शर्तों से (a=8) और (d=7) मिलते हैं, इसलिए \(S_{16}=968\) है। दिए गए पद और योग को दो समीकरणों में बदलें।
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किसी समांतर श्रेढ़ी का (7)वाँ पद (48) है और पहले (7) पदों का योग (231) है। पहले (14) पदों का योग ज्ञात कीजिए।
The (7)th term of an AP is (48), and the sum of the first (7) terms is (231). Find the sum of the first (14) terms.
#given term and sum
#find sum
#ap
A (679)
B (693)
C (707)
D (721)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a=18) and (d=5), so \(S_{14}=707\). Convert the given term and sum into two equations.
Step 2
Why this answer is correct
The correct answer is C. (707). The conditions give (a=18) and (d=5), so \(S_{14}=707\). Convert the given term and sum into two equations.
Step 3
Exam Tip
शर्तों से (a=18) और (d=5) मिलते हैं, इसलिए \(S_{14}=707\) है। दिए गए पद और योग को दो समीकरणों में बदलें।
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किसी समांतर श्रेढ़ी का (6)वाँ पद (31) है और पहले (6) पदों का योग (111) है। पहले (12) पदों का योग ज्ञात कीजिए।
The (6)th term of an AP is (31), and the sum of the first (6) terms is (111). Find the sum of the first (12) terms.
#given term and sum
#find sum
#ap
A (372)
B (386)
C (402)
D (418)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a=6) and (d=5), so \(S_{12}=402\). Convert the given term and sum into two equations.
Step 2
Why this answer is correct
The correct answer is C. (402). The conditions give (a=6) and (d=5), so \(S_{12}=402\). Convert the given term and sum into two equations.
Step 3
Exam Tip
शर्तों से (a=6) और (d=5) मिलते हैं, इसलिए \(S_{12}=402\)। दिए गए पद और योग को दो समीकरणों में बदलें।
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यदि किसी 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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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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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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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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कौन सा बहुपद (x=0) को शून्य बनाता है लेकिन शून्य बहुपद नहीं है?
Which polynomial makes (x=0) a zero but is not the zero polynomial?
#zero at zero
#constant term
#polynomial
A \(x^2+9\)
B \(4x^3-7x\)
C (5)
D \(x^4+1\)
Explanation opens after your attempt
Correct Answer
B. \(4x^3-7x\)
Step 1
Concept
Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(4x^3-7x\). Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 3
Exam Tip
\(4x^3-7x\) में (x=0) रखने पर (0) मिलता है और यह शून्य बहुपद नहीं है। (x=0) के लिए अचर पद (0) होना चाहिए।
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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 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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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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यदि (p(x)=x-2 -10x+r) का एक शून्यक (4) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=x-2 -10x+r) is (4), what is the other zero?
#one-zero-given
#sum-zeroes
#quadratic
A (6)
B (4)
C (10)
D -(6)
Explanation opens after your attempt
Step 1
Concept
The sum of zeroes is (10). Since one zero is (4), the other is (10-4=6).
Step 2
Why this answer is correct
The correct answer is A. (6). The sum of zeroes is (10). Since one zero is (4), the other is (10-4=6).
Step 3
Exam Tip
शून्यकों का योग (10) है। एक शून्यक (4) है, इसलिए दूसरा (10-4=6) है।
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यदि (p(x)=x-2 -2x-2) का एक शून्यक \(1+\sqrt{3}\) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=x-2 -2x-2) is \(1+\sqrt{3}\), what is the other zero?
#other-zero
#sum-of-zeroes
#conjugate
A \(1-\sqrt{3}\)
B \(-1+\sqrt{3}\)
C \(1+\sqrt{3}\)
D \(-1-\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(1-\sqrt{3}\)
Step 1
Concept
The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 2
Why this answer is correct
The correct answer is A. \(1-\sqrt{3}\). The sum of zeroes is (2), so the other zero is (2-\(1+\sqrt{3}\)=1-\sqrt{3}). With rational coefficients, the conjugate also appears.
Step 3
Exam Tip
शून्यकों का योग (2) है, इसलिए दूसरा शून्यक (2-\(1+\sqrt{3}\)=1-\sqrt{3}) है। परिमेय गुणांकों में संयुग्मी भी मिलता है।
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एक समांतर श्रेढ़ी का पहला पद (x) और सार्व अंतर (3x-2) है। यदि पहले (12) पदों का योग (1128) है, तो (x) का मान क्या है?
The first term of an AP is (x), and the common difference is (3x-2). If the sum of the first (12) terms is (1128), what is the value of (x)?
#variable ap
#find x
#sum
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
From (1128=6[2x+11(3x-2)]), (x=6). In variable-based questions, write (a) and (d) clearly first.
Step 2
Why this answer is correct
The correct answer is B. (6). From (1128=6[2x+11(3x-2)]), (x=6). In variable-based questions, write (a) and (d) clearly first.
Step 3
Exam Tip
(1128=6[2x+11(3x-2)]) से (x=6) मिलता है। चर वाले प्रश्न में पहले (a) और (d) स्पष्ट लिखें।
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एक समांतर श्रेढ़ी का पहला पद (x) और सार्व अंतर (2x+1) है। यदि पहले (10) पदों का योग (445) है, तो (x) का मान क्या है?
The first term of an AP is (x), and the common difference is (2x+1). If the sum of the first (10) terms is (445), what is the value of (x)?
#variable ap
#find x
#sum
A (2)
B (3)
C (5)
D (4)
Explanation opens after your attempt
Step 1
Concept
From (445=5[2x+9(2x+1)]), (x=4). In variable-based questions, write (a) and (d) clearly first.
Step 2
Why this answer is correct
The correct answer is D. (4). From (445=5[2x+9(2x+1)]), (x=4). In variable-based questions, write (a) and (d) clearly first.
Step 3
Exam Tip
(445=5[2x+9(2x+1)]) से (x=4) मिलता है। चर वाले प्रश्न में पहले (a) और (d) स्पष्ट लिखें।
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एक समांतर श्रेढ़ी का पहला पद (x) और सार्व अंतर (x+2) है। यदि पहले (10) पदों का योग (365) है, तो (x) का मान क्या है?
The first term of an AP is (x), and the common difference is (x+2). If the sum of the first (10) terms is (365), what is the value of (x)?
#variable ap
#find x
#sum
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
From (365=5[2x+9(x+2)]), (x=5). In variable-based questions, write (a) and (d) clearly first.
Step 2
Why this answer is correct
The correct answer is A. (5). From (365=5[2x+9(x+2)]), (x=5). In variable-based questions, write (a) and (d) clearly first.
Step 3
Exam Tip
(365=5[2x+9(x+2)]) से (x=5) मिलता है। चर वाले प्रश्न में पहले (a) और (d) को साफ लिखें।
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पहले (18) पदों का योग (441) और पहला पद (3) है। यदि श्रेढ़ी समांतर है, तो सार्व अंतर (d) क्या होगा?
The sum of the first (18) terms is (441), and the first term is (3). If the sequence is an AP, what is the common difference (d)?
#common difference
#ap sum
#unknown d
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (441=9[6+17d]), (d=3). In questions with unknown (d), simplify both sides first.
Step 2
Why this answer is correct
The correct answer is B. (3). From (441=9[6+17d]), (d=3). In questions with unknown (d), simplify both sides first.
Step 3
Exam Tip
(441=9[6+17d]) से (d=3) आता है। अज्ञात (d) वाले प्रश्नों में पहले दोनों पक्षों को सरल करें।
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यदि किसी समांतर श्रेढ़ी के पहले (20) पदों का योग (780) और पहला पद (5) है, तो सार्व अंतर (d) क्या होगा?
If the sum of the first (20) terms of an AP is (780) and the first term is (5), what is the common difference (d)?
#find common difference
#ap sum
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From (780=10[10+19d]), (d=4). When sum and first term are given, the common difference can be found directly.
Step 2
Why this answer is correct
The correct answer is B. (4). From (780=10[10+19d]), (d=4). When sum and first term are given, the common difference can be found directly.
Step 3
Exam Tip
(780=10[10+19d]) से (d=4) मिलता है। योग और पहला पद दिए हों तो सार्व अंतर सीधे निकाला जा सकता है।
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समान्तर श्रेणी \(0,4,8,\ldots\) के पहले (11) पदों का योग ज्ञात कीजिए।
Find the sum of the first (11) terms of the AP \(0,4,8,\ldots\).
#ap-sum-zero-first-term
A (210)
B (220)
C (230)
D (240)
Explanation opens after your attempt
Step 1
Concept
The last term is (40). (S_{11}=\frac{11}{2}(0+40)=220).
Step 2
Why this answer is correct
The correct answer is B. (220). The last term is (40). (S_{11}=\frac{11}{2}(0+40)=220).
Step 3
Exam Tip
अंतिम पद (40) है। (S_{11}=\frac{11}{2}(0+40)=220)।
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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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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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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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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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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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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 \(160,151,142,\ldots\) 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 \(120,113,106,\ldots\) 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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यदि किसी समांतर श्रेढ़ी में \(S_{12}=420\) और \(S_6=150\), तो (7)वें पद से (12)वें पद तक का योग क्या होगा?
If in an AP \(S_{12}=420\) and \(S_6=150\), what is the sum from the (7)th term to the (12)th term?
#partial sum difference
#ap
A (270)
B (260)
C (280)
D (290)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{12}-S_6=270\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 2
Why this answer is correct
The correct answer is A. (270). The required sum is \(S_{12}-S_6=270\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 3
Exam Tip
आवश्यक योग \(S_{12}-S_6=270\) है। लगातार पदों का योग partial sums के अंतर से तुरंत मिलता है।
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समांतर श्रेढ़ी \(80,75,70,\ldots\) के पहले (18) पदों का योग ज्ञात कीजिए।
Find the sum of the first (18) terms of the AP \(80,75,70,\ldots\).
#negative common difference
#ap sum
A (650)
B (675)
C (700)
D (725)
Explanation opens after your attempt
Step 1
Concept
Here (a=80), (d=-5), (n=18), and the sum is (675). Do not forget the negative sign of (d) in a decreasing AP.
Step 2
Why this answer is correct
The correct answer is B. (675). Here (a=80), (d=-5), (n=18), and the sum is (675). Do not forget the negative sign of (d) in a decreasing AP.
Step 3
Exam Tip
यहाँ (a=80), (d=-5), (n=18) है और योग (675) आता है। घटती श्रेढ़ी में (d) का ऋणात्मक चिह्न न भूलें।
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समांतर श्रेढ़ी \(9,16,23,\ldots\) के पहले (13) पदों का योग क्या है?
What is the sum of the first (13) terms of the AP \(9,16,23,\ldots\)?
#odd n
#ap sum
#common difference
A (650)
B (660)
C (663)
D (670)
Explanation opens after your attempt
Step 1
Concept
Here (a=9), (d=7), (n=13), so \(S_{13}=663\). Do not worry about \(\frac{n}{2}\) when (n) is odd.
Step 2
Why this answer is correct
The correct answer is C. (663). Here (a=9), (d=7), (n=13), so \(S_{13}=663\). Do not worry about \(\frac{n}{2}\) when (n) is odd.
Step 3
Exam Tip
यहाँ (a=9), (d=7), (n=13), इसलिए \(S_{13}=663\)। विषम (n) होने पर \(\frac{n}{2}\) से डरें नहीं।
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समांतर श्रेढ़ी \(4,10,16,\ldots\) के पहले (14) पदों का योग क्या है?
What is the sum of the first (14) terms of the AP \(4,10,16,\ldots\)?
#ap sum
#common difference
#medium
A (590)
B (602)
C (604)
D (610)
Explanation opens after your attempt
Step 1
Concept
Here (a=4), (d=6), (n=14), so the sum is (602). Calculate (2a) and ((n-1)d) separately.
Step 2
Why this answer is correct
The correct answer is B. (602). Here (a=4), (d=6), (n=14), so the sum is (602). Calculate (2a) and ((n-1)d) separately.
Step 3
Exam Tip
यहाँ (a=4), (d=6), (n=14), इसलिए योग (602) है। (2a) और ((n-1)d) को अलग-अलग निकालें।
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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 \(30,27,24,\ldots\) के पहले (10) पदों का योग ज्ञात कीजिए।
Find the sum of the first (10) terms of the AP \(30,27,24,\ldots\).
#ap-sum-negative-difference
A (155)
B (160)
C (165)
D (170)
Explanation opens after your attempt
Step 1
Concept
Here (d=-3). (S_{10}=5[60+9(-3)]=165).
Step 2
Why this answer is correct
The correct answer is C. (165). Here (d=-3). (S_{10}=5[60+9(-3)]=165).
Step 3
Exam Tip
यहां (d=-3) है। (S_{10}=5[60+9(-3)]=165)।
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यदि (p(x)=2x-2 +mx+18) का एक शून्यक (3) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=2x-2 +mx+18) is (3), what is the other zero?
#one-zero-given
#product-zeroes
#quadratic
A (3)
B -(3)
C (6)
D -(6)
Explanation opens after your attempt
Step 1
Concept
The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).
Step 3
Exam Tip
गुणनफल \(\frac{18}{2}=9\) है। एक शून्यक (3) है, इसलिए दूसरा (3) होगा।
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यदि (p(x)=x-2 +3x-18) का एक शून्यक (3) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=x-2 +3x-18) is (3), what is the other zero?
#one-zero-given
#product-zeroes
#quadratic
A -(6)
B (6)
C -(3)
D (9)
Explanation opens after your attempt
Step 1
Concept
The product of zeroes is (-18). Since one zero is (3), the other is \(-18\div3=-6\).
Step 2
Why this answer is correct
The correct answer is A. -(6). The product of zeroes is (-18). Since one zero is (3), the other is \(-18\div3=-6\).
Step 3
Exam Tip
शून्यकों का गुणनफल (-18) है। एक शून्यक (3) है, इसलिए दूसरा \(-18\div3=-6\) है।
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यदि (p(x)=x-2 -13x+k) का एक शून्यक (6) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होंगे?
If (p(x)=x-2 -13x+k) has one zero (6), what will be the other zero and the (x)-axis intersections?
#missing zero
#quadratic
#intercepts
A दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0))
B दूसरा (-7), कटान ((6,0)), ((-7,0)) / Other (-7), intersections ((6,0)), ((-7,0))
C दूसरा (13), कटान ((6,0)), ((13,0)) / Other (13), intersections ((6,0)), ((13,0))
D दूसरा (0), कटान ((6,0)), ((0,0)) / Other (0), intersections ((6,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0)). In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (13) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
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यदि परवलय का सममिति अक्ष (x=5) है और एक शून्यक (-1) है, तो दूसरा शून्यक क्या होगा?
If the axis of symmetry of a parabola is (x=5) and one zero is (-1), what will be the other zero?
#axis symmetry
#missing zero
#parabola
A (11)
B (9)
C (6)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (5), so the other zero is (11). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (11). The average of the two zeroes is (5), so the other zero is (11). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (5) है इसलिए दूसरा शून्यक (11) होगा। टिप: सममिति अक्ष शून्यकों के मध्य से गुजरता है।
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यदि (p(x)=x-2 -11x+k) का एक शून्यक (4) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होंगे?
If (p(x)=x-2 -11x+k) has one zero (4), what will be the other zero and the (x)-axis intersections?
#missing zero
#quadratic
#intercepts
A दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0))
B दूसरा (-7), कटान ((4,0)), ((-7,0)) / Other (-7), intersections ((4,0)), ((-7,0))
C दूसरा (11), कटान ((4,0)), ((11,0)) / Other (11), intersections ((4,0)), ((11,0))
D दूसरा (0), कटान ((4,0)), ((0,0)) / Other (0), intersections ((4,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0)). In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (11) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
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यदि परवलय का सममिति अक्ष (x=-2) है और एक शून्यक (5) है, तो दूसरा शून्यक क्या होगा?
If the axis of symmetry of a parabola is (x=-2) and one zero is (5), what will be the other zero?
#axis symmetry
#missing zero
#parabola
A (-9)
B (-7)
C (9)
D (7)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (-2), so the other zero is (-9). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (-9). The average of the two zeroes is (-2), so the other zero is (-9). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (-2) है, इसलिए दूसरा शून्यक (-9) होगा। टिप: सममिति अक्ष को शून्यकों के मध्य से जोड़ें।
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यदि (p(x)=x-2 -9x+k) का एक शून्यक (4) है तो दूसरा शून्यक और कटान बिंदु क्या होंगे?
If (p(x)=x-2 -9x+k) has one zero (4), what will be the other zero and intersection points?
#missing zero
#quadratic
#intercepts
A दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0))
B दूसरा (-5), कटान ((4,0)), ((-5,0)) / Other (-5), intersections ((4,0)), ((-5,0))
C दूसरा (9), कटान ((4,0)), ((9,0)) / Other (9), intersections ((4,0)), ((9,0))
D दूसरा (0), कटान ((4,0)), ((0,0)) / Other (0), intersections ((4,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (5), कटान ((4,0)), ((5,0)) / Other (5), intersections ((4,0)), ((5,0)). In the quadratic, the sum of zeroes is (9), so the other zero is (5). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (9) है इसलिए दूसरा शून्यक (5) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
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किसी परवलय का एक शून्यक (11) है और सममिति अक्ष (x=3) है। दूसरा शून्यक क्या होगा?
A parabola has one zero (11) and axis of symmetry (x=3). What will be the other zero?
#missing zero
#axis of symmetry
#parabola
A (-5)
B (5)
C (-8)
D (8)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (3), so the other zero is (-5). Tip: set \(\frac{a+b}{2}\) equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-5). The average of the two zeroes is (3), so the other zero is (-5). Tip: set \(\frac{a+b}{2}\) equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (3) है इसलिए दूसरा शून्यक (-5) होगा। टिप: \(\frac{a+b}{2}\) को सममिति अक्ष के बराबर रखें।
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किसी परवलय का सममिति अक्ष (x=4) है और एक शून्यक (-2) है। दूसरा शून्यक क्या होगा?
The axis of symmetry of a parabola is (x=4) and one zero is (-2). What will be the other zero?
#axis symmetry
#missing zero
#parabola
A (10)
B (6)
C (8)
D (-10)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (4), so the other zero is (10). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is A. (10). The average of the two zeroes is (4), so the other zero is (10). Tip: connect the axis of symmetry with the midpoint of zeroes.
Step 3
Exam Tip
दोनों शून्यकों का औसत (4) है इसलिए दूसरा शून्यक (10) होगा। टिप: सममिति अक्ष को शून्यकों के मध्य मान से जोड़ें।
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यदि (p(x)=x-2 -7x+k) का एक शून्यक (3) है, तो दूसरा शून्यक और कटान बिंदु क्या होंगे?
If (p(x)=x-2 -7x+k) has one zero (3), what will be the other zero and intersection points?
#missing zero
#quadratic
#intercepts
A दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0))
B दूसरा (-4), कटान ((3,0)), ((-4,0)) / Other (-4), intersections ((3,0)), ((-4,0))
C दूसरा (7), कटान ((3,0)), ((7,0)) / Other (7), intersections ((3,0)), ((7,0))
D दूसरा (0), कटान ((3,0)), ((0,0)) / Other (0), intersections ((3,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (4), कटान ((3,0)), ((4,0)) / Other (4), intersections ((3,0)), ((4,0)). In the quadratic, the sum of zeroes is (7), so the other zero is (4). Tip: quickly convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (7) है, इसलिए दूसरा शून्यक (4) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
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किसी परवलय का एक शून्यक (9) है और सममिति अक्ष (x=2) है। दूसरा शून्यक क्या होगा?
A parabola has one zero (9) and axis of symmetry (x=2). What is the other zero?
#missing zero
#axis of symmetry
#parabola
A (-5)
B (5)
C (-7)
D (7)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (2), so the other zero is (-5). Tip: set \( \frac{a+b}{2} \) equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-5). The average of the two zeroes is (2), so the other zero is (-5). Tip: set \( \frac{a+b}{2} \) equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (2) है, इसलिए दूसरा शून्यक (-5) होगा। टिप: \( \frac{a+b}{2} \) को सममिति अक्ष के बराबर रखें।
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किसी परवलय का सममिति अक्ष (x=1) है और एक शून्यक (-5) है। दूसरा शून्यक क्या होगा?
The axis of symmetry of a parabola is (x=1) and one zero is (-5). What will be the other zero?
#axis symmetry
#missing zero
#parabola
A (5)
B (6)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (1), so the other zero is (7). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 2
Why this answer is correct
The correct answer is C. (7). The average of the two zeroes is (1), so the other zero is (7). Tip: the axis of symmetry passes through the midpoint of zeroes.
Step 3
Exam Tip
दो शून्यकों का औसत (1) होगा इसलिए दूसरा शून्यक (7) है। टिप: सममिति अक्ष शून्यकों के मध्य से गुजरता है।
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यदि (p(x)=x-2 -5x+k) का एक शून्यक (2) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होगा?
If (p(x)=x-2 -5x+k) has one zero (2), what will be the other zero and the (x)-axis intersections?
#quadratic
#missing zero
#intercepts
A दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0))
B दूसरा (-3), कटान ((2,0)), ((-3,0)) / Other (-3), intersections ((2,0)), ((-3,0))
C दूसरा (5), कटान ((2,0)), ((5,0)) / Other (5), intersections ((2,0)), ((5,0))
D दूसरा (0), कटान ((2,0)), ((0,0)) / Other (0), intersections ((2,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0)). In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (5) है, इसलिए दूसरा शून्यक (3) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
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किसी परवलय का एक शून्यक (4) है और सममिति अक्ष (x=-1) है। दूसरा शून्यक क्या होगा?
A parabola has one zero (4) and axis of symmetry (x=-1). What will be the other zero?
#axis of symmetry
#missing zero
#parabola
A (-6)
B (-4)
C (2)
D (6)
Explanation opens after your attempt
Step 1
Concept
The average of the two zeroes is (-1), so the other zero is (-6). Tip: set the average equal to the axis of symmetry.
Step 2
Why this answer is correct
The correct answer is A. (-6). The average of the two zeroes is (-1), so the other zero is (-6). Tip: set the average equal to the axis of symmetry.
Step 3
Exam Tip
दो शून्यकों का औसत (-1) है, इसलिए दूसरा शून्यक (-6) होगा। टिप: औसत को सममिति अक्ष के बराबर रखें।
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एक समान्तर श्रेणी का प्रथम पद (14) है और पहले (16) पदों का योग (824) है। सार्व अंतर क्या होगा?
The first term of an arithmetic progression is (14) and the sum of the first (16) terms is (824). What is the common difference?
#ap
#find-difference
#expert
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (824=8[28+15d]), (d=5). Exam tip: solve directly for (d) when (n) is known.
Step 2
Why this answer is correct
The correct answer is B. (5). From (824=8[28+15d]), (d=5). Exam tip: solve directly for (d) when (n) is known.
Step 3
Exam Tip
(824=8[28+15d]) से (d=5) मिलता है। परीक्षा में ज्ञात (n) के साथ सीधे (d) के लिए हल करें।
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किसी समान्तर श्रेणी में प्रथम पद (15) और सार्व अंतर (6) है। पहले (28) पदों का योग कितना होगा?
In an arithmetic progression the first term is (15) and the common difference is (6). What is the sum of the first (28) terms?
#ap
#direct-sum
#expert
A (2592)
B (2646)
C (2688)
D (2730)
Explanation opens after your attempt
Step 1
Concept
(S_{28}=\frac{28}{2}[30+27(6)]=2688). Exam tip: simplify the bracket first.
Step 2
Why this answer is correct
The correct answer is C. (2688). (S_{28}=\frac{28}{2}[30+27(6)]=2688). Exam tip: simplify the bracket first.
Step 3
Exam Tip
(S_{28}=\frac{28}{2}[30+27(6)]=2688) है। परीक्षा में पहले कोष्ठक को सरल करें।
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किसी समान्तर श्रेणी में प्रथम पद (13) और सार्व अंतर (7) है। पहले (22) पदों का योग कितना होगा?
In an arithmetic progression the first term is (13) and the common difference is (7). What is the sum of the first (22) terms?
#ap
#direct-sum
#expert
A (1859)
B (1892)
C (1903)
D (1914)
Explanation opens after your attempt
Step 1
Concept
(S_{22}=\frac{22}{2}[26+21(7)]=1903). Exam tip: simplify the bracket first.
Step 2
Why this answer is correct
The correct answer is C. (1903). (S_{22}=\frac{22}{2}[26+21(7)]=1903). Exam tip: simplify the bracket first.
Step 3
Exam Tip
(S_{22}=\frac{22}{2}[26+21(7)]=1903) है। परीक्षा में पहले कोष्ठक को सरल करें।
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एक समान्तर श्रेणी का प्रथम पद (12) है और पहले (10) पदों का योग (345) है। सार्व अंतर क्या होगा?
The first term of an arithmetic progression is (12) and the sum of the first (10) terms is (345). What is the common difference?
#ap
#find-difference
#expert
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (345=5[24+9d]), (d=5). Exam tip: solve directly for (d) when (n) is known.
Step 2
Why this answer is correct
The correct answer is B. (5). From (345=5[24+9d]), (d=5). Exam tip: solve directly for (d) when (n) is known.
Step 3
Exam Tip
(345=5[24+9d]) से (d=5) मिलता है। परीक्षा में ज्ञात (n) के साथ सीधे (d) के लिए हल करें।
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किसी समान्तर श्रेणी में प्रथम पद (9) और सार्व अंतर (4) है। पहले (30) पदों का योग कितना होगा?
In an arithmetic progression the first term is (9) and the common difference is (4). What is the sum of the first (30) terms?
#ap
#direct-sum
#expert
A (1950)
B (1980)
C (2010)
D (2040)
Explanation opens after your attempt
Step 1
Concept
(S_{30}=\frac{30}{2}[18+29(4)]=2010). Exam tip: simplify the bracket first.
Step 2
Why this answer is correct
The correct answer is C. (2010). (S_{30}=\frac{30}{2}[18+29(4)]=2010). Exam tip: simplify the bracket first.
Step 3
Exam Tip
(S_{30}=\frac{30}{2}[18+29(4)]=2010) मिलता है। परीक्षा में कोष्ठक को पहले सरल करें।
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एक समान्तर श्रेणी का प्रथम पद (18) है। यदि पहले (10) पदों का योग (315) है तो सार्व अंतर क्या होगा?
The first term of an arithmetic progression is (18). If the sum of the first (10) terms is (315) then what is the common difference?
#ap
#find-difference
#expert
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (315=5[36+9d]), (d=3). Exam tip: when (n) is known, solve the sum formula directly for (d).
Step 2
Why this answer is correct
The correct answer is B. (3). From (315=5[36+9d]), (d=3). Exam tip: when (n) is known, solve the sum formula directly for (d).
Step 3
Exam Tip
(315=5[36+9d]) से (d=3) मिलता है। परीक्षा में (n) ज्ञात होने पर सूत्र को सीधे (d) के लिए हल करें।
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समांतर श्रेढ़ी में पहला पद (3), सार्व अंतर (5) और पदों की संख्या (20) है। पहले (20) पदों का योग क्या होगा?
In an AP, the first term is (3), common difference is (5), and number of terms is (20). What is the sum of the first (20) terms?
#arithmetic progression
#ap sum
#class 10
A (1010)
B (1000)
C (990)
D (1030)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}[2a+(n-1)d]), the sum is (1010). In exams, handle (n-1) carefully.
Step 2
Why this answer is correct
The correct answer is A. (1010). Using (S_n=\frac{n}{2}[2a+(n-1)d]), the sum is (1010). In exams, handle (n-1) carefully.
Step 3
Exam Tip
सूत्र (S_n=\frac{n}{2}[2a+(n-1)d]) लगाने पर योग (1010) आता है। परीक्षा में (n-1) को ध्यान से रखें।
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यदि किसी समांतर श्रेणी में पहला पद (4), अंतर (5) और पदों की संख्या (13) है, तो पहले (13) पदों का योग कितना होगा?
If an arithmetic progression has first term (4), common difference (5), and (13) terms, what is the sum of the first (13) terms?
#ap
#sum
#formula
A (422)
B (432)
C (442)
D (452)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{13}=442\). Write ((n-1)d) carefully in the formula.
Step 2
Why this answer is correct
The correct answer is C. (442). Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{13}=442\). Write ((n-1)d) carefully in the formula.
Step 3
Exam Tip
सूत्र (S_n=\frac{n}{2}[2a+(n-1)d]) से \(S_{13}=442\) मिलता है। सूत्र में ((n-1)d) ध्यान से लिखें।
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यदि किसी समांतर श्रेढ़ी में प्रथम पद (a=3), अंतर (d=2) और पदों की संख्या (n=10) है, तो पहले (10) पदों का योग कितना होगा?
If an arithmetic progression has first term (a=3), common difference (d=2), and number of terms (n=10), what is the sum of the first (10) terms?
#ap
#sum
#n_terms
#class10
A (120)
B (110)
C (100)
D (90)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{10}=120\). In exams, first identify (a), (d), and (n).
Step 2
Why this answer is correct
The correct answer is A. (120). Using (S_n=\frac{n}{2}[2a+(n-1)d]), we get \(S_{10}=120\). In exams, first identify (a), (d), and (n).
Step 3
Exam Tip
सूत्र (S_n=\frac{n}{2}[2a+(n-1)d]) लगाने पर \(S_{10}=120\) मिलता है। परीक्षा में पहले (a), (d), (n) पहचानें।
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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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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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