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 171-180 of 600 questions.
If (2,6,x,54) is a geometric progression, what is (x)?
B. (18)
सार्व अनुपात \(\frac{6}{2}=3\) है, इसलिए \(x=6\cdot3=18\)। समान अनुपात को हर अगले पद पर लगाएं। / The common ratio is \(\frac{6}{2}=3\), so \(x=6\cdot3=18\). Apply the same ratio to each next term.
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Which sequence has a negative common ratio?
C. \(5,-10,20,-40,\ldots\)
\(5,-10,20,-40,\ldots\) में सार्व अनुपात (-2) है। ऋणात्मक अनुपात से पदों के चिह्न बदलते हैं। / In \(5,-10,20,-40,\ldots\), the common ratio is (-2). A negative ratio changes the signs of terms.
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What is the sum of the first (4) terms of the geometric progression \(10,20,40,80,\ldots\)?
B. (150)
योग (10+20+40+80=150) है। कम पद हों तो सीधे जोड़ना आसान है। / The sum is (10+20+40+80=150). For a small number of terms direct addition is easy.
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If a geometric progression has \(a_3=20\) and (r=2), what is \(a_1\)?
B. (5)
\(a_3=a_1r^2\), इसलिए \(20=a_1\cdot4\) और \(a_1=5\)। दो पद पीछे जाने के लिए \(r^2\) से भाग दें। / \(a_3=a_1r^2\), so \(20=a_1\cdot4\) and \(a_1=5\). Divide by \(r^2\) to move two terms backward.
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What is the (n)th term of the sequence \(6,18,54,162,\ldots\)?
A. \(a_n=6\cdot3^{n-1}\)
पहला पद (6) और अनुपात (3) है, इसलिए \(a_n=6\cdot3^{n-1}\)। सामान्य पद में पहला पद और अनुपात दोनों रखें। / The first term is (6) and the ratio is (3), so \(a_n=6\cdot3^{n-1}\). Use both first term and ratio in the general term.
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If (a=1) and (r=2), what will be the sum of the first (6) terms?
B. (63)
पहले (6) पद (1,2,4,8,16,32) हैं और योग (63) है। (2) की घातों के योग को ध्यान से जोड़ें। / The first (6) terms are (1,2,4,8,16,32), and their sum is (63). Add powers of (2) carefully.
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If \(a_1=12\) and \(r=\frac{1}{2}\), what is \(a_4\)?
A. \(\frac{3}{2}\)
(a_4=12\left\(\frac{1}{2}\right\)3=\frac{3}{2})। भिन्न अनुपात में हर बार आधा होता है। / (a_4=12\left\(\frac{1}{2}\right\)3=\frac{3}{2}). With a fractional ratio each term becomes half.
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Which value of (x) makes (4,20,x) a geometric progression?
C. (100)
सार्व अनुपात \(\frac{20}{4}=5\) है, इसलिए \(x=20\cdot5=100\)। तीसरे पद के लिए दूसरे पद को अनुपात से गुणा करें। / The common ratio is \(\frac{20}{4}=5\), so \(x=20\cdot5=100\). Multiply the second term by the ratio to get the third term.
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In the sequence \(2,8,32,128,\ldots\), which term is (512)?
B. (5)वाँ(5)th
सार्व अनुपात (4) है और पद (2,8,32,128,512) हैं। पद-संख्या के लिए क्रम से पद बनाएं। / The common ratio is (4), and the terms are (2,8,32,128,512). For position form terms in order.
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If a geometric progression has \(a_2=18\) and \(a_4=162\), what is (r)?
B. (3)
\(a_4=a_2r^2\), इसलिए \(162=18r^2\) और \(r^2=9\), धनात्मक अनुपात (r=3) है। पदों के बीच दूरी को घात बनाएं। / \(a_4=a_2r^2\), so \(162=18r^2\) and \(r^2=9\), giving positive ratio (r=3). Use the gap between terms as the exponent.
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