Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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The sequence (2, 2+k, 2+4k, 2+9k) can be an arithmetic progression. Under what condition?
A. (k=0)
अंतर (k, 3k, 5k) हैं। ये सभी बराबर केवल (k=0) पर होंगे। / The differences are (k, 3k, 5k). They are all equal only when (k=0).
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If (14, 14-d, 14-2d, 14-3d) is an arithmetic progression, what is the common difference?
B. (-d)
हर अगला पद पिछले पद से (d) कम है। इसलिए सामान्य अंतर (-d) है। / Each next term is (d) less than the previous term. Therefore the common difference is (-d).
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For which (n) will (n+2, 2n+5, 4n+8) form an arithmetic progression?
A. (0)
लगातार अंतर (n+3) और (2n+3) हैं। बराबर करने पर (n=0) मिलता है। / The consecutive differences are (n+3) and (2n+3). Equating them gives (n=0).
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If (3z, z+10, 22-z) are in an arithmetic progression, what is the first term?
C. (12)
(2(z+10)=3z+(22-z)) से (z=4). पहला पद (3z=12) है। / From (2(z+10)=3z+(22-z)), (z=4). The first term is (3z=12).
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What mistake is made if (81, 27, 9, 3) is considered an arithmetic progression?
B. अनुपात समान है, अंतर समान नहींThe ratio is constant, not the difference
इस क्रम में अनुपात \(\frac{1}{3}\) है, पर अंतर (-54, -18, -6) बराबर नहीं हैं। समांतर श्रेणी में अनुपात नहीं, अंतर देखें। / This sequence has ratio \(\frac{1}{3}\), but differences (-54, -18, -6) are not equal. In an arithmetic progression, check difference, not ratio.
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If (2, 5, 10, 17) is called an arithmetic progression, what does the correct check show?
C. यह समांतर श्रेणी नहीं है क्योंकि अंतर (3,5,7) हैंIt is not an arithmetic progression because the differences are (3,5,7)
समांतर श्रेणी के लिए हर लगातार अंतर समान होना चाहिए। यहाँ (3,5,7) समान नहीं हैं। / For an arithmetic progression, every consecutive difference must be equal. Here (3,5,7) are not equal.
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A. (r=-2, d=1)
अंतर (r+3) और (2r+5) हैं। बराबर करने पर (r=-2) और (d=1) मिलता है। / The differences are (r+3) and (2r+5). Equating them gives (r=-2) and (d=1).
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If (x, x+6, 3x-2) are in an arithmetic progression, what is the third term?
B. (16)
(2(x+6)=x+(3x-2)) से (x=9). तीसरा पद (3x-2=25) नहीं, इसलिए विकल्पों में सही मान नहीं है। / From (2(x+6)=x+(3x-2)), (x=7). The third term is (3x-2=19), so none of the options is correct.
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If (x, x+6, 3x-2) are in an arithmetic progression, what is the correct value of (x)?
C. (7)
अंतर (6) और (2x-8) बराबर होने चाहिए। इसलिए (2x-8=6) से (x=7). / The differences (6) and (2x-8) must be equal. Thus (2x-8=6), giving (x=7).
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For which (s) will \(\frac{s}{2}, s+3, 3s-1\) form an arithmetic progression?
C. (8)
पहला अंतर \(\frac{s}{2}+3\) और दूसरा अंतर (2s-4) है। बराबर करने पर (s=8) मिलता है। / The first difference is \(\frac{s}{2}+3\), and the second is (2s-4). Equating them gives (s=8).
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