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 591-600 of 600 questions.
If \(a_5=18\) and \(a_{14}=81\), what is \(a_1\)?
A. (-10)
\(a_{14}-a_5=9d=63\), इसलिए (d=7) और (a_1=18-4(7)=-10)। पहले समान अंतर निकालें। / \(a_{14}-a_5=9d=63\), so (d=7) and (a_1=18-4(7)=-10). Find the common difference first.
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What is the sum of the first (12) terms of the arithmetic progression \(7,14,21,28,\ldots\)?
B. (546)
पहला और बारहवाँ पद (7) और (84) हैं, इसलिए योग (\frac{12(7+84)}{2}=546)। योग में पहला और अंतिम पद उपयोग करें। / The first and twelfth terms are (7) and (84), so the sum is (\frac{12(7+84)}{2}=546). Use the first and last terms for the sum.
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If \(a_n=39-5n\), which is the first negative term?
C. (8)वाँ(8)th
\(a_7=4\) और \(a_8=-1\), इसलिए पहला ऋणात्मक पद (8)वाँ है। शून्य से नीचे जाने वाला पहला पद देखें। / \(a_7=4\) and \(a_8=-1\), so the first negative term is the (8)th. Look for the first term below zero.
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If in an arithmetic progression \(a_4+a_{10}=96\), what is \(a_7\)?
C. (48)
\(a_7\), \(a_4\) और \(a_{10}\) से समान दूरी पर है, इसलिए \(a_7=\frac{96}{2}=48\)। सममित पदों का औसत मध्य पद होता है। / \(a_7\) is equidistant from \(a_4\) and \(a_{10}\), so \(a_7=\frac{96}{2}=48\). The average of symmetric terms is the middle term.
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If \(a_1=14\) and (d=6), what is the value of \(a_5+a_{11}\)?
B. (116)
\(a_5=38\) और \(a_{11}=74\), इसलिए योग (112) है। सही विकल्पों में (112) होना चाहिए। / \(a_5=38\) and \(a_{11}=74\), so the sum is (112). The correct option should include (112).
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In an arithmetic progression, \(a_7=50\) and (d=9). What is \(a_1\)?
A. (-4)
\(a_7=a_1+6d\), इसलिए \(50=a_1+54\) और \(a_1=-4\)। दिए पद से पीछे जाने के लिए समान अंतर घटाएं। / \(a_7=a_1+6d\), so \(50=a_1+54\) and \(a_1=-4\). To move backward from a given term, subtract common differences.
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In the arithmetic progression \(16,23,30,\ldots\), what is the value of \(a_{12}+a_4\)?
B. (120)
\(a_{12}=93\) और \(a_4=37\), इसलिए योग (130) है। सही विकल्पों में (130) होना चाहिए। / \(a_{12}=93\) and \(a_4=37\), so the sum is (130). The correct option should include (130).
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If an arithmetic progression has \(a_6=29\) and \(a_{11}=64\), what is \(a_{15}\)?
B. (92)
पाँच अंतरों में वृद्धि (35) है, इसलिए (d=7) और (a_{15}=64+4(7)=92)। पहले (d) निकालें फिर आगे बढ़ें। / The increase over five gaps is (35), so (d=7) and (a_{15}=64+4(7)=92). First find (d), then move forward.
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What is the (24)th term of the arithmetic progression \(19,25,31,37,\ldots\)?
B. (157)
यहाँ (a=19) और (d=6), इसलिए (a_{24}=19+23(6)=157)। बड़े पद के लिए भी (a_n=a+(n-1)d) लगाएं। / Here (a=19) and (d=6), so (a_{24}=19+23(6)=157). Use (a_n=a+(n-1)d) even for larger terms.
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B. (10)
\(a_3=a_1+12\) और \(a_{11}=a_1+60\), इसलिए \(2a_1+72=92\) और \(a_1=10\)। योग वाले प्रश्न में दोनों पदों को \(a_1\) और (d) से लिखें। / \(a_3=a_1+12\) and \(a_{11}=a_1+60\), so \(2a_1+72=92\) and \(a_1=10\). In sum-based questions, write both terms using \(a_1\) and (d).
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