Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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If (10, 10+d, 10+2d, 10+4d) is an arithmetic progression, which conclusion is correct?
A. (d=0)
अंतर (d, d, 2d) हैं। तीनों बराबर तभी होंगे जब (d=0). / The differences are (d, d, 2d). All three are equal only when (d=0).
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In which option do the terms form an arithmetic progression with common difference (0)?
A. (6, 6, 6, 6)
सभी पद समान हों तो हर अंतर (0) होता है। स्थिर क्रम भी समांतर श्रेणी होता है। / When all terms are equal, every difference is (0). A constant sequence is also an arithmetic progression.
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If (3, 3+2m, 3+4m, 3+6m) is an arithmetic progression, what is the common difference?
B. (2m)
हर बार (2m) जुड़ रहा है। इसलिए सामान्य अंतर (2m) है। / Each time (2m) is added. Therefore the common difference is (2m).
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For which (y) are (5y+2, 3y+10, y+18) in an arithmetic progression?
A. हर (y) के लिएFor every (y)
पहला अंतर (-2y+8) और दूसरा अंतर (-2y+8) है। दोनों हर (y) के लिए बराबर हैं। / The first difference is (-2y+8), and the second difference is also (-2y+8). They are equal for every (y).
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A. (8) और (8)(8) and (8)
हर लगातार अंतर (8) है और (x) कट जाता है। समान चर वाले पदों में स्थिर भाग का अंतर देखें। / Every consecutive difference is (8), and (x) cancels out. For terms with the same variable part, compare the constant parts.
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For which (k) is (k+7, 2k+3, 4k-5) an arithmetic progression?
C. (4)
अंतर (k-4) और (2k-8) हैं। बराबर करने पर (k=4) मिलता है। / The differences are (k-4) and (2k-8). Equating them gives (k=4).
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If (13, 2x+1, 4x-5) are in an arithmetic progression, what is the common difference?
C. (7)
(2(2x+1)=13+(4x-5)) से (2=8) असंभव है। इसलिए ऐसा सामान्य अंतर नहीं होगा। / From (2(2x+1)=13+(4x-5)), we get (2=8), which is impossible. Therefore no such common difference exists.
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Which conclusion is correct for the sequence (13, 2x+1, 4x-5)?
D. यह किसी (x) पर समांतर श्रेणी नहीं हैIt is not an arithmetic progression for any (x)
समांतर श्रेणी के लिए (2(2x+1)=13+(4x-5)) चाहिए, जो (2=8) देता है। यह असंभव है। / For an arithmetic progression, (2(2x+1)=13+(4x-5)) is required, which gives (2=8). This is impossible.
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B. (p=3, d=2)
अंतर (2p-4) और (3p-7) हैं। बराबर करने पर (p=3), इसलिए (d=2). / The differences are (2p-4) and (3p-7). Equating them gives (p=3), so (d=2).
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B. (5, 9, 13, 20)
(5,9,13,20) में पहले दो अंतर (4,4) हैं लेकिन तीसरा अंतर (7) है। सभी लगातार अंतर जांचना जरूरी है। / In (5,9,13,20), the first two differences are (4,4), but the third difference is (7). It is necessary to check all consecutive differences.
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