Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 251-260 of 600 questions.
What is the common difference in the sequence \(6,13,20,27,\ldots\)?
C. (7)
लगातार पदों का अंतर (13-6=7) है। समान अंतर के लिए दूसरे पद से पहला पद घटाएं। / The difference between consecutive terms is (13-6=7). To find the common difference, subtract the first term from the second term.
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If an arithmetic progression has first term (8) and common difference (5), what is the (7)th term?
C. (38)
(a_7=8+(7-1)5=38)। (n)वें पद के लिए (a_n=a+(n-1)d) लगाएं। / (a_7=8+(7-1)5=38). Use (a_n=a+(n-1)d) for the (n)th term.
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What is the (n)th term of the arithmetic progression \(42,36,30,24,\ldots\)?
A. \(a_n=48-6n\)
पहला पद (42) और अंतर (-6) है इसलिए (a_n=42+(n-1)(-6)=48-6n)। घटती श्रेढ़ी में समान अंतर ऋणात्मक होता है। / The first term is (42) and the difference is (-6), so (a_n=42+(n-1)(-6)=48-6n). In a decreasing progression, the common difference is negative.
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If (a=15) and (d=4), what will be the (9)th term of the arithmetic progression?
B. (47)
(a_9=15+8(4)=47)। (9)वें पद तक (8) समान अंतर जुड़ते हैं। / (a_9=15+8(4)=47). Up to the (9)th term, (8) common differences are added.
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In the arithmetic progression \(3,11,19,27,\ldots\), which term is (67)?
C. (9)वाँ(9)th
(3+(n-1)8=67) से (8(n-1)=64) और (n=9)। पद का स्थान निकालने के लिए दिए पद को \(a_n\) के बराबर रखें। / From (3+(n-1)8=67), (8(n-1)=64) and (n=9). To find the position, set the given term equal to \(a_n\).
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If \(a_n=4n+3\), what will be the first four terms?
A. (7,11,15,19)
(n=1,2,3,4) रखने पर (7,11,15,19) मिलते हैं। नियम से पद बनाते समय (n) को (1) से शुरू करें। / Putting (n=1,2,3,4) gives (7,11,15,19). When forming terms from a rule, start (n) from (1).
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In an arithmetic progression, \(a_1=17\) and \(a_6=47\). What is the common difference?
B. (6)
\(a_6=a_1+5d\), इसलिए (47=17+5d) और (d=6)। दो पदों के बीच अंतरालों की संख्या गिनें। / \(a_6=a_1+5d\), so (47=17+5d) and (d=6). Count the number of gaps between the two terms.
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What is the sum of the first (5) terms of the arithmetic progression \(7,15,23,31,\ldots\)?
C. (115)
पहले (5) पद (7,15,23,31,39) हैं और योग (115) है। कम पद हों तो पद लिखकर जोड़ना सरल है। / The first (5) terms are (7,15,23,31,39), and their sum is (115). For a small number of terms, listing and adding is simple.
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If \(a_n=55-5n\), what is the common difference of this arithmetic progression?
A. (-5)
रैखिक रूप में (n) का गुणांक (-5) है, इसलिए समान अंतर (-5) है। गुणांक का चिह्न जरूर देखें। / In the linear form, the coefficient of (n) is (-5), so the common difference is (-5). Always check the sign of the coefficient.
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C. (5)
\(a_4=21+3d=36\) से (3d=15) और (d=5)। चौथे पद तक तीन अंतर होते हैं। / From \(a_4=21+3d=36\), (3d=15) and (d=5). Up to the fourth term, there are three gaps.
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