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 281-290 of 600 questions.
If \(a_n=8\cdot2^{n-1}\), which sequence does it form?
C. \(8,16,32,64,\ldots\)
(n=1,2,3,4) रखने पर (8,16,32,64) मिलते हैं। नियम से शुरू के पद बनाकर विकल्प मिलाएं। / Putting (n=1,2,3,4) gives (8,16,32,64). Form the initial terms from the rule and match the option.
Login to save your score, XP, coins and progress.
If (x,20,100) are consecutive terms of a geometric progression, what is (x)?
B. (4)
\(\frac{100}{20}=5\), इसलिए \(\frac{20}{x}=5\) और (x=4)। लगातार अनुपात बराबर रखें। / \(\frac{100}{20}=5\), so \(\frac{20}{x}=5\) and (x=4). Keep consecutive ratios equal.
Login to save your score, XP, coins and progress.
What is the (6)th term of the geometric progression \(6,18,54,\ldots\)?
C. (1458)
यहाँ (r=3), इसलिए \(a_6=6\cdot3^5=1458\)। (6)वें पद में (5) बार अनुपात लगता है। / Here (r=3), so \(a_6=6\cdot3^5=1458\). The sixth term uses the ratio (5) times.
Login to save your score, XP, coins and progress.
Which sequence has common ratio (6)?
B. \(2,12,72,432,\ldots\)
\(2,12,72,432,\ldots\) में हर बार (6) से गुणा हो रहा है। अनुपात के लिए अगले पद को पिछले पद से भाग दें। / In \(2,12,72,432,\ldots\), each term is multiplied by (6). For the ratio divide the next term by the previous term.
Login to save your score, XP, coins and progress.
If \(a_1=\frac{7}{4}\) and (r=2), what is \(a_4\)?
D. (14)
\(a_4=\frac{7}{4}\cdot2^3=14\)। भिन्न पहले पद के साथ घात को सावधानी से गुणा करें। / \(a_4=\frac{7}{4}\cdot2^3=14\). Multiply the power carefully with the fractional first term.
Login to save your score, XP, coins and progress.
What is the sum of the first (6) terms of the geometric progression \(4,8,16,32,\ldots\)?
C. (252)
पहले (6) पद (4,8,16,32,64,128) हैं और योग (252) है। पदों को क्रम से लिखकर जोड़ें। / The first (6) terms are (4,8,16,32,64,128), and their sum is (252). Write the terms in order and add.
Login to save your score, XP, coins and progress.
If \(a_1=5\) and (r=-2), what are the first four terms?
B. (5,-10,20,-40)
हर बार (-2) से गुणा करने पर (5,-10,20,-40) मिलते हैं। ऋणात्मक अनुपात से चिह्न बदलते हैं। / Multiplying by (-2) each time gives (5,-10,20,-40). A negative ratio makes the signs alternate.
Login to save your score, XP, coins and progress.
For which (x) will (16,x,81) be consecutive terms of a positive geometric progression?
C. (36)
\(x^2=16\cdot81=1296\), इसलिए धनात्मक (x=36)। मध्य पद ज्यामितीय माध्य होता है। / \(x^2=16\cdot81=1296\), so positive (x=36). The middle term is the geometric mean.
Login to save your score, XP, coins and progress.
What is the (n)th term of the sequence \(13,39,117,351,\ldots\)?
A. \(a_n=13\cdot3^{n-1}\)
पहला पद (13) और अनुपात (3) है, इसलिए \(a_n=13\cdot3^{n-1}\)। सामान्य पद में पहला पद और अनुपात रखें। / The first term is (13) and the ratio is (3), so \(a_n=13\cdot3^{n-1}\). Use the first term and ratio in the general term.
Login to save your score, XP, coins and progress.
If \(a_2=40\) and \(a_5=320\), and the ratio is positive, what is (r)?
A. (2)
\(a_5=a_2r^3\), इसलिए \(320=40r^3\) और \(r^3=8\), अतः (r=2)। पदों की दूरी घात तय करती है। / \(a_5=a_2r^3\), so \(320=40r^3\) and \(r^3=8\), hence (r=2). The gap between positions decides the exponent.
Login to save your score, XP, coins and progress.
Use Google login or mobile OTP. Admin can block users and control login providers.