class10 se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
2084 questions tagged with class10.
Find the (7)th term of the AP \(-3,1,5,9,\ldots\).
C. (21)
यहाँ (a=-3) और (d=4) है इसलिए \(a_7=-3+6\times4=21\)। ऋणात्मक प्रथम पद से सावधानी रखें। / Here (a=-3) and (d=4), so \(a_7=-3+6\times4=21\). Be careful with a negative first term.
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What is the (9)th term of the AP \(20,18,16,14,\ldots\)?
B. (4)
यहाँ (d=-2) है इसलिए (a_9=20+8(-2)=4)। घटती एपी में (d) ऋणात्मक होता है। / Here (d=-2), so (a_9=20+8(-2)=4). In a decreasing AP, (d) is negative.
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If (a=12), (d=5), and (n=6), what is the value of \(a_n\)?
C. (37)
(a_n=12+(6-1)\times5=37)। सूत्र में सीधे मान रखने से गलती कम होती है। / (a_n=12+(6-1)\times5=37). Substituting values directly reduces mistakes.
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What is the (10)th term in the AP \(7,11,15,19,\ldots\)?
C. (43)
यहाँ (d=4) है इसलिए \(a_{10}=7+9\times4=43\)। पद संख्या से (1) घटाकर गुणा करें। / Here (d=4), so \(a_{10}=7+9\times4=43\). Multiply by one less than the term number.
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Find the (12)th term of the AP \(2,6,10,14,\ldots\).
B. (46)
यहाँ (a=2) और (d=4) है इसलिए \(a_{12}=2+11\times4=46\)। पहले सार्व अंतर निकालें। / Here (a=2) and (d=4), so \(a_{12}=2+11\times4=46\). First find the common difference.
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If the first term of an AP is (5) and common difference is (3), what is the (8)th term?
C. (26)
सूत्र (a_n=a+(n-1)d) लगाएं तो \(5+7\times3=26\)। परीक्षा में (n-1) लेना न भूलें। / Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).
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In which sequence are the first three consecutive differences (4,4,4)?
A. \(2,6,10,14,\ldots\)
\(2,6,10,14,\ldots\) में अंतर (4,4,4) हैं। समान अंतर समांतर श्रेढ़ी की पहचान है। / In \(2,6,10,14,\ldots\), the differences are (4,4,4). Equal differences identify an arithmetic progression.
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What is the common difference of \(5m,5m-4,5m-8,5m-12,\ldots\)?
B. (-4)
लगातार पदों का अंतर ((5m-4)-5m=-4) है। बीजीय पदों में समान पद काटकर अंतर निकालें। / The difference of consecutive terms is ((5m-4)-5m=-4). In algebraic terms, cancel like terms to find the difference.
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If an arithmetic progression has (a=28) and second term (19), what is the common difference?
B. (-9)
सार्व अंतर (19-28=-9) है। दूसरे पद से पहले पद को घटाकर (d) निकालें। / The common difference is (19-28=-9). Find (d) by subtracting the first term from the second term.
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What will be the sixth term in \(-18,-12,-6,0,\ldots\)?
B. (12)
यहाँ सार्व अंतर (6) है। पाँचवाँ पद (6) और छठा पद (12) होगा। / The common difference is (6). The fifth term is (6) and the sixth term is (12).
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If (a=2.5) and (d=1.5), what are the first three terms?
A. (2.5,4.0,5.5)
पहला पद (2.5) है और हर बार (1.5) जोड़ना है। इसलिए पद (2.5,4.0,5.5) हैं। / The first term is (2.5), and (1.5) is added each time. Hence the terms are (2.5,4.0,5.5).
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In the sequence \(25,21,17,13,\ldots\), which term is (21)?
B. दूसरा पदSecond term
लिखे क्रम में (25) पहला और (21) दूसरा पद है। पद की स्थिति के लिए क्रम से गिनें। / In the written order, (25) is the first term and (21) is the second term. Count in order to find the position.
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B. (7)
सार्व अंतर (18-11=7) है। (d) के लिए दूसरा पद घटा पहला पद करें। / The common difference is (18-11=7). For (d), subtract the first term from the second term.
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In which sequence are the consecutive differences not equal?
D. \(2,3,5,8,\ldots\)
\(2,3,5,8,\ldots\) में अंतर (1,2,3) हैं। इसलिए लगातार अंतर बराबर नहीं हैं। / In \(2,3,5,8,\ldots\), the differences are (1,2,3). Hence the consecutive differences are not equal.
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What is the common difference of the arithmetic progression \(a-2,a+1,a+4,a+7,\ldots\)?
B. (3)
लगातार पदों का अंतर ((a+1)-(a-2)=3) है। चर वाले पदों में समान पद कट जाते हैं। / The difference of consecutive terms is ((a+1)-(a-2)=3). Like terms cancel in variable terms.
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If a sequence is \(1,4,7,10,\ldots\), what is the difference between the third and second terms?
B. (3)
तीसरा पद (7) और दूसरा पद (4) है। इसलिए अंतर (7-4=3) है। / The third term is (7) and the second term is (4). Therefore, the difference is (7-4=3).
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What is the common difference in \(7,7.5,8,8.5,\ldots\)?
B. (0.5)
सार्व अंतर (7.5-7=0.5) है। दशमलव पदों में भी नियमित अंतर देखें। / The common difference is (7.5-7=0.5). For decimal terms also, check the regular difference.
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Which sequence is an arithmetic progression with (d=0.25)?
B. \(0.25,0.5,0.75,1.0,\ldots\)
(0.5-0.25=0.25) और आगे भी यही अंतर है। इसलिए यह सही समांतर श्रेढ़ी है। / (0.5-0.25=0.25), and the same difference continues. Hence this is the correct arithmetic progression.
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If (a=4) and (a+d=13), what is the value of (d)?
B. (9)
(d=13-4=9) है। दूसरे पद से पहले पद को घटाने पर सार्व अंतर मिलता है। / (d=13-4=9). Subtracting the first term from the second term gives the common difference.
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What will be the fifth term in \(64,57,50,43,\ldots\)?
A. (36)
यहाँ (d=-7) है। पाँचवाँ पद (43-7=36) होगा। / Here (d=-7). The fifth term will be (43-7=36).
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Rooms on the floors of a building increase as \(18,22,26,30,\ldots\). What is the common difference?
B. (4)
हर अगली मंजिल पर (4) कमरे बढ़ रहे हैं। इसलिए सार्व अंतर (4) है। / Each next floor has (4) more rooms. Therefore, the common difference is (4).
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What is (d) in the arithmetic progression \(\frac{1}{3},\frac{2}{3},1,\frac{4}{3},\ldots\)?
A. \(\frac{1}{3}\)
\(\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\) है। भिन्नों में पहले दो पदों का अंतर निकालें। / \(\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\). For fractions, find the difference of the first two terms.
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If an arithmetic progression has (d=-1.5) and first term (10), what is the second term?
A. (8.5)
दूसरा पद (10+(-1.5)=8.5) है। दशमलव और ऋणात्मक चिन्ह दोनों का ध्यान रखें। / The second term is (10+(-1.5)=8.5). Take care of both decimals and negative signs.
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What is the common difference of \(2k,2k+3,2k+6,2k+9,\ldots\)?
B. (3)
लगातार पदों का अंतर ((2k+3)-2k=3) है। बीजीय पदों में समान पद काट दें। / The difference of consecutive terms is ((2k+3)-2k=3). In algebraic terms, cancel like terms.
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If (a=15) and (d=-4), what are the first four terms?
B. (15,11,7,3)
पहला पद (15) है और हर बार (4) घटता है। इसलिए पद (15,11,7,3) होंगे। / The first term is (15), and (4) is subtracted each time. Hence the terms are (15,11,7,3).
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In an arithmetic progression, (a=3) and (d=0). What are the first three terms?
C. (3,3,3)
(d=0) होने पर हर पद समान रहता है। इसलिए पहले तीन पद (3,3,3) हैं। / When (d=0), every term remains equal. Therefore, the first three terms are (3,3,3).
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A. (7) और (7)(7) and (7)
पहला अंतर (12-5=7) और दूसरा (26-19=7) है। समान अंतर समांतर श्रेढ़ी की पुष्टि करता है। / The first difference is (12-5=7), and the second is (26-19=7). Equal differences confirm an arithmetic progression.
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If the consecutive differences of a sequence are (2,4,6), what is the correct conclusion?
B. यह समांतर श्रेढ़ी नहीं हैIt is not an arithmetic progression
अंतर समान नहीं हैं इसलिए सार्व अंतर स्थिर नहीं है। अतः यह समांतर श्रेढ़ी नहीं है। / The differences are not equal, so the common difference is not constant. Hence it is not an arithmetic progression.
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B. (-68)
यहाँ पहला पद (17) और (d=-4) है। इसलिए गुणनफल \(17\times(-4)=-68\) होगा। / Here the first term is (17) and (d=-4). Therefore, the product is \(17\times(-4)=-68\).
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In the sequence \(14,20,26,32,\ldots\), which term is (20)?
B. दूसरा पदSecond term
लिखे क्रम में (14) पहला और (20) दूसरा पद है। पद संख्या के लिए क्रम से गिनें। / In the written order, (14) is the first term and (20) is the second term. Count in order to find the term number.
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