किसी गुणोत्तर श्रेणी में \(a_3=24\) और \(a_6=192\) हैं। यदि (r>0) है, तो पहले (5) पदों का योग क्या होगा?
In a geometric progression, \(a_3=24\) and \(a_6=192\). If (r>0), what is the sum of the first (5) terms?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (180)
B (186)
C (192)
D (198)
Explanation opens after your attempt
Step 1
Concept
From \(\frac{192}{24}=r^3=8\), (r=2) and (a=6). Therefore (S_5=6\(2^5-1\)=186).
Step 2
Why this answer is correct
The correct answer is B. (186). From \(\frac{192}{24}=r^3=8\), (r=2) and (a=6). Therefore (S_5=6\(2^5-1\)=186).
Step 3
Exam Tip
\(\frac{192}{24}=r^3=8\) से (r=2) और (a=6) है। इसलिए (S_5=6\(2^5-1\)=186) होगा।
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गुणोत्तर श्रेणी \(5,15,45,\ldots\) में कितने पदों तक योग (1820) होगा?
How many terms of the geometric progression \(5,15,45,\ldots\) have sum (1820)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(S_n=\frac{5\(3^n-1\)}{3-1}), and (\frac{5\(3^n-1\)}{2}=1820) gives \(3^n=729\), so (n=6). In exams, simplify the sum and identify the power.
Step 2
Why this answer is correct
The correct answer is C. (6). (S_n=\frac{5\(3^n-1\)}{3-1}), and (\frac{5\(3^n-1\)}{2}=1820) gives \(3^n=729\), so (n=6). In exams, simplify the sum and identify the power.
Step 3
Exam Tip
(S_n=\frac{5\(3^n-1\)}{3-1}) और (\frac{5\(3^n-1\)}{2}=1820) से \(3^n=729\), इसलिए (n=6) है। परीक्षा में योग को सरल करके घात पहचानें।
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यदि (a=4) और (r=6) है, तो \(a_4+a_5\) का मान क्या होगा?
If (a=4) and (r=6), what is the value of \(a_4+a_5\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (6048)
B (6480)
C (7344)
D (7776)
Explanation opens after your attempt
Step 1
Concept
\(a_4=4\cdot6^3=864\) and \(a_5=5184\), so the sum is (6048). In exams, calculate large powers separately.
Step 2
Why this answer is correct
The correct answer is A. (6048). \(a_4=4\cdot6^3=864\) and \(a_5=5184\), so the sum is (6048). In exams, calculate large powers separately.
Step 3
Exam Tip
\(a_4=4\cdot6^3=864\) और \(a_5=5184\), इसलिए योग (6048) है। परीक्षा में बड़े घातों को अलग-अलग निकालें।
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गुणोत्तर श्रेणी \(120,40,\frac{40}{3},\frac{40}{9},\ldots\) में \(\frac{40}{81}\) कौन-सा पद है?
In the geometric progression \(120,40,\frac{40}{3},\frac{40}{9},\ldots\), which term is \(\frac{40}{81}\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A छठा पद / (6)th term
B सातवाँ पद / (7)th term
C आठवाँ पद / (8)th term
D नौवाँ पद / (9)th term
Explanation opens after your attempt
Correct Answer
A. छठा पद / (6)th term
Step 1
Concept
Each term is multiplied by \(\frac{1}{3}\), and the sixth term is \(\frac{40}{81}\). In exams, fractional terms can also be checked in order.
Step 2
Why this answer is correct
The correct answer is A. छठा पद / (6)th term. Each term is multiplied by \(\frac{1}{3}\), and the sixth term is \(\frac{40}{81}\). In exams, fractional terms can also be checked in order.
Step 3
Exam Tip
हर बार \(\frac{1}{3}\) से गुणा होता है और छठा पद \(\frac{40}{81}\) आता है। परीक्षा में भिन्न पदों को क्रम से भी जाँच सकते हैं।
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यदि \(a_8=1280\) और (a=10) है तथा (r) धनात्मक है, तो (r) क्या होगा?
If \(a_8=1280\) and (a=10), and (r) is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From \(1280=10r^7\), \(r^7=128=2^7\), so (r=2). In exams, identify \(r^7\) for the eighth term.
Step 2
Why this answer is correct
The correct answer is A. (2). From \(1280=10r^7\), \(r^7=128=2^7\), so (r=2). In exams, identify \(r^7\) for the eighth term.
Step 3
Exam Tip
\(1280=10r^7\) से \(r^7=128=2^7\), इसलिए (r=2) है। परीक्षा में आठवें पद के लिए \(r^7\) पहचानें।
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गुणोत्तर श्रेणी \(12,24,48,\ldots\) के पहले (10) पदों का योग क्या है?
What is the sum of the first (10) terms of the geometric progression \(12,24,48,\ldots\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (12276)
B (12288)
C (12300)
D (12312)
Explanation opens after your attempt
Correct Answer
A. (12276)
Step 1
Concept
(S_{10}=12\(2^{10}-1\)=12276). In exams, use \(2^{10}=1024\).
Step 2
Why this answer is correct
The correct answer is A. (12276). (S_{10}=12\(2^{10}-1\)=12276). In exams, use \(2^{10}=1024\).
Step 3
Exam Tip
(S_{10}=12\(2^{10}-1\)=12276) है। परीक्षा में \(2^{10}=1024\) का उपयोग करें।
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यदि \(a_1=10\) और \(a_4=270\) है तथा (r) धनात्मक है, तो \(a_5\) क्या होगा?
If \(a_1=10\) and \(a_4=270\), and (r) is positive, what is \(a_5\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (540)
B (810)
C (1080)
D (1350)
Explanation opens after your attempt
Step 1
Concept
From \(270=10r^3\), \(r^3=27\) and (r=3), so \(a_5=270\cdot3=810\). In exams, find the ratio first.
Step 2
Why this answer is correct
The correct answer is B. (810). From \(270=10r^3\), \(r^3=27\) and (r=3), so \(a_5=270\cdot3=810\). In exams, find the ratio first.
Step 3
Exam Tip
\(270=10r^3\) से \(r^3=27\) और (r=3), इसलिए \(a_5=270\cdot3=810\) है। परीक्षा में पहले अनुपात निकालें।
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गुणोत्तर श्रेणी \(15,30,60,\ldots\) में \(a_n=3840\) हो, तो (n) क्या है?
In the geometric progression \(15,30,60,\ldots\), if \(a_n=3840\), what is (n)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
From \(15\cdot2^{n-1}=3840\), \(2^{n-1}=256=2^8\), so (n=9). In exams, factor first and compare powers.
Step 2
Why this answer is correct
The correct answer is B. (9). From \(15\cdot2^{n-1}=3840\), \(2^{n-1}=256=2^8\), so (n=9). In exams, factor first and compare powers.
Step 3
Exam Tip
\(15\cdot2^{n-1}=3840\) से \(2^{n-1}=256=2^8\), इसलिए (n=9) है। परीक्षा में गुणनखंड निकालकर घात तुलना करें।
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यदि \(a_n=6\cdot5^{n-1}\) है, तो \(a_4+a_5\) का मान क्या है?
If \(a_n=6\cdot5^{n-1}\), what is the value of \(a_4+a_5\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (4500)
B (4680)
C (4800)
D (5000)
Explanation opens after your attempt
Step 1
Concept
\(a_4=750\) and \(a_5=3750\), so the sum is (4500). In exams, find both terms separately and add.
Step 2
Why this answer is correct
The correct answer is A. (4500). \(a_4=750\) and \(a_5=3750\), so the sum is (4500). In exams, find both terms separately and add.
Step 3
Exam Tip
\(a_4=750\) और \(a_5=3750\), इसलिए योग (4500) है। परीक्षा में दोनों पद अलग निकालकर जोड़ें।
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गुणोत्तर श्रेणी में \(a_2=20\) और \(a_5=2500\) है, तो \(a_1\) क्या है?
In a geometric progression, \(a_2=20\) and \(a_5=2500\). What is \(a_1\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (2)
B (4)
C (5)
D (10)
Explanation opens after your attempt
Step 1
Concept
From \(\frac{2500}{20}=125=r^3\), (r=5) and \(a_1=20\div5=4\). In exams, find (r) first and then \(a_1\).
Step 2
Why this answer is correct
The correct answer is B. (4). From \(\frac{2500}{20}=125=r^3\), (r=5) and \(a_1=20\div5=4\). In exams, find (r) first and then \(a_1\).
Step 3
Exam Tip
\(\frac{2500}{20}=125=r^3\) से (r=5) और \(a_1=20\div5=4\) है। परीक्षा में पहले (r) निकालें फिर \(a_1\)।
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यदि \(a=96\) और \(r=\frac{1}{2}\) है, तो पहले \(6\) पदों का योग क्या है?
If \(a=96\) and \(r=\frac{1}{2}\), what is the sum of the first \(6\) terms?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (186)
B (189)
C (192)
D (195)
Explanation opens after your attempt
Step 1
Concept
The terms are \(96,48,24,12,6,3\), and their sum is \(189\). In exams, direct addition is also easy for small decreasing terms.
Step 2
Why this answer is correct
The correct answer is B. (189). The terms are \(96,48,24,12,6,3\), and their sum is \(189\). In exams, direct addition is also easy for small decreasing terms.
Step 3
Exam Tip
पद \(96,48,24,12,6,3\) हैं और योग (189) है। परीक्षा में छोटे घटते पदों को सीधे जोड़ना भी आसान है।
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गुणोत्तर श्रेणी \(11,33,99,\ldots\) में \(a_7\) क्या है?
What is \(a_7\) in the geometric progression \(11,33,99,\ldots\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (8019)
B (24057)
C (7293)
D (2673)
Explanation opens after your attempt
Step 1
Concept
\(a_7=11\cdot3^6=8019\). In exams, use \(r^6\) for the seventh term.
Step 2
Why this answer is correct
The correct answer is A. (8019). \(a_7=11\cdot3^6=8019\). In exams, use \(r^6\) for the seventh term.
Step 3
Exam Tip
\(a_7=11\cdot3^6=8019\) है। परीक्षा में सातवें पद के लिए \(r^6\) लगाएँ।
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यदि किसी गुणोत्तर श्रेणी में \(a_5=80\) और \(a_9=1280\) है, तो (r) का धनात्मक मान क्या है?
If a geometric progression has \(a_5=80\) and \(a_9=1280\), what is the positive value of (r)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(\frac{1280}{80}=16=r^4\), so (r=2). In exams, a position gap of (4) gives \(r^4\).
Step 2
Why this answer is correct
The correct answer is A. (2). \(\frac{1280}{80}=16=r^4\), so (r=2). In exams, a position gap of (4) gives \(r^4\).
Step 3
Exam Tip
\(\frac{1280}{80}=16=r^4\), इसलिए (r=2) है। परीक्षा में पद-संख्या का अंतर (4) होने पर \(r^4\) मिलेगा।
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गुणोत्तर श्रेणी \(10,20,40,\ldots\) के पहले (9) पदों का योग क्या है?
What is the sum of the first (9) terms of the geometric progression \(10,20,40,\ldots\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (5110)
B (5120)
C (5130)
D (5140)
Explanation opens after your attempt
Step 1
Concept
(S_9=10\(2^9-1\)=5110). In exams, remembering \(2^9=512\) is useful.
Step 2
Why this answer is correct
The correct answer is A. (5110). (S_9=10\(2^9-1\)=5110). In exams, remembering \(2^9=512\) is useful.
Step 3
Exam Tip
(S_9=10\(2^9-1\)=5110) है। परीक्षा में \(2^9=512\) याद रखना उपयोगी है।
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यदि \(a_n=405\left(\frac{1}{3}\right)^{n-1}\) है, तो कौन-सा पद (5) के बराबर होगा?
If \(a_n=405\left(\frac{1}{3}\right)^{n-1}\), which term will be equal to (5)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A तीसरा पद / (3)rd term
B चौथा पद / (4)th term
C पाँचवाँ पद / (5)th term
D छठा पद / (6)th term
Explanation opens after your attempt
Correct Answer
C. पाँचवाँ पद / (5)th term
Step 1
Concept
From \(405\left(\frac{1}{3}\right)^{n-1}=5\), \(\left(\frac{1}{3}\right)^{n-1}=\frac{1}{81}\), so (n=5). In exams, simplify fractions first.
Step 2
Why this answer is correct
The correct answer is C. पाँचवाँ पद / (5)th term. From \(405\left(\frac{1}{3}\right)^{n-1}=5\), \(\left(\frac{1}{3}\right)^{n-1}=\frac{1}{81}\), so (n=5). In exams, simplify fractions first.
Step 3
Exam Tip
\(405\left(\frac{1}{3}\right)^{n-1}=5\) से \(\left(\frac{1}{3}\right)^{n-1}=\frac{1}{81}\), इसलिए (n=5) है। परीक्षा में भिन्नों को पहले सरल करें।
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गुणोत्तर श्रेणी \(3,12,48,\ldots\) के \(a_5+a_6\) का मान क्या है?
What is the value of \(a_5+a_6\) for the geometric progression \(3,12,48,\ldots\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (3072)
B (3840)
C (4608)
D (5120)
Explanation opens after your attempt
Step 1
Concept
\(a_5=768\) and \(a_6=3072\), so the sum is (3840). In exams, find both terms separately and add.
Step 2
Why this answer is correct
The correct answer is B. (3840). \(a_5=768\) and \(a_6=3072\), so the sum is (3840). In exams, find both terms separately and add.
Step 3
Exam Tip
\(a_5=768\) और \(a_6=3072\), इसलिए योग (3840) है। परीक्षा में दोनों पद अलग-अलग निकालकर जोड़ें।
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यदि (a=8), (r=4) और \(S_4=680\) है, तो कथन कैसा है?
If (a=8), (r=4), and \(S_4=680\), what is the statement?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A सही क्योंकि \(S_4=680\) / True because \(S_4=680\)
B गलत क्योंकि \(S_4=640\) / False because \(S_4=640\)
C गलत क्योंकि \(S_4=672\) / False because \(S_4=672\)
D गलत क्योंकि \(S_4=688\) / False because \(S_4=688\)
Explanation opens after your attempt
Correct Answer
A. सही क्योंकि \(S_4=680\) / True because \(S_4=680\)
Step 1
Concept
(S_4=\frac{8\(4^4-1\)}{4-1}=680). In exams, confirm statement-type questions with the formula.
Step 2
Why this answer is correct
The correct answer is A. सही क्योंकि \(S_4=680\) / True because \(S_4=680\). (S_4=\frac{8\(4^4-1\)}{4-1}=680). In exams, confirm statement-type questions with the formula.
Step 3
Exam Tip
(S_4=\frac{8\(4^4-1\)}{4-1}=680) है। परीक्षा में कथन-प्रकार प्रश्न में सूत्र से पुष्टि करें।
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गुणोत्तर श्रेणी \(486,162,54,\ldots\) में (2) कौन-सा पद है?
In the geometric progression \(486,162,54,\ldots\), which term is (2)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A पाँचवाँ पद / (5)th term
B छठा पद / (6)th term
C सातवाँ पद / (7)th term
D आठवाँ पद / (8)th term
Explanation opens after your attempt
Correct Answer
B. छठा पद / (6)th term
Step 1
Concept
Each term is multiplied by \(\frac{1}{3}\), so the terms are (486,162,54,18,6,2). In exams, you can also check a decreasing GP in order.
Step 2
Why this answer is correct
The correct answer is B. छठा पद / (6)th term. Each term is multiplied by \(\frac{1}{3}\), so the terms are (486,162,54,18,6,2). In exams, you can also check a decreasing GP in order.
Step 3
Exam Tip
हर बार \(\frac{1}{3}\) से गुणा होता है, इसलिए पद (486,162,54,18,6,2) हैं। परीक्षा में घटती GP को क्रम से भी जाँच सकते हैं।
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यदि \(a_4=162\) और (r=3) है, तो \(a_9\) का मान क्या होगा?
If \(a_4=162\) and (r=3), what is the value of \(a_9\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (26244)
B (39366)
C (52488)
D (78732)
Explanation opens after your attempt
Correct Answer
B. (39366)
Step 1
Concept
There are (5) steps from the fourth to the ninth term, so \(a_9=162\cdot3^5=39366\). In exams, count the position gap.
Step 2
Why this answer is correct
The correct answer is B. (39366). There are (5) steps from the fourth to the ninth term, so \(a_9=162\cdot3^5=39366\). In exams, count the position gap.
Step 3
Exam Tip
चौथे से नौवें पद तक (5) कदम हैं, इसलिए \(a_9=162\cdot3^5=39366\) है। परीक्षा में पद-संख्या का अंतर गिनें।
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गुणोत्तर श्रेणी \(5,30,180,1080,\ldots\) के पहले (4) पदों का योग क्या है?
What is the sum of the first (4) terms of the geometric progression \(5,30,180,1080,\ldots\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (1290)
B (1295)
C (1300)
D (1305)
Explanation opens after your attempt
Step 1
Concept
The sum of the first four terms is (5+30+180+1080=1295). In exams, direct addition is safe when the number of terms is small.
Step 2
Why this answer is correct
The correct answer is B. (1295). The sum of the first four terms is (5+30+180+1080=1295). In exams, direct addition is safe when the number of terms is small.
Step 3
Exam Tip
पहले चार पदों का योग (5+30+180+1080=1295) है। परीक्षा में पद कम हों तो सीधे जोड़ना सुरक्षित है।
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यदि \(a_1=9\) और (r=-2) है, तो \(a_8\) क्या होगा?
If \(a_1=9\) and (r=-2), what is \(a_8\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (-1152)
B (1152)
C (-2304)
D (2304)
Explanation opens after your attempt
Correct Answer
A. (-1152)
Step 1
Concept
(a_8=9(-2)7 =-1152). In exams, an odd power of a negative ratio is negative.
Step 2
Why this answer is correct
The correct answer is A. (-1152). (a_8=9(-2)7 =-1152). In exams, an odd power of a negative ratio is negative.
Step 3
Exam Tip
(a_8=9(-2)7 =-1152) है। परीक्षा में ऋणात्मक अनुपात की विषम घात ऋणात्मक होती है।
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गुणोत्तर श्रेणी \(2,8,32,\ldots\) का कौन-सा पद (8192) है?
Which term of the geometric progression \(2,8,32,\ldots\) is (8192)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A छठा पद / (6)th term
B सातवाँ पद / (7)th term
C आठवाँ पद / (8)th term
D नौवाँ पद / (9)th term
Explanation opens after your attempt
Correct Answer
B. सातवाँ पद / (7)th term
Step 1
Concept
From \(2\cdot4^{n-1}=8192\), \(4^{n-1}=4096=4^6\), so (n=7). In exams, equate powers to find the term number.
Step 2
Why this answer is correct
The correct answer is B. सातवाँ पद / (7)th term. From \(2\cdot4^{n-1}=8192\), \(4^{n-1}=4096=4^6\), so (n=7). In exams, equate powers to find the term number.
Step 3
Exam Tip
\(2\cdot4^{n-1}=8192\) से \(4^{n-1}=4096=4^6\), इसलिए (n=7) है। परीक्षा में घात बराबर करके पद संख्या निकालें।
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यदि किसी गुणोत्तर श्रेणी के पहले (4) पद (7,21,63,189) हैं, तो \(S_4\) क्या है?
If the first (4) terms of a geometric progression are (7,21,63,189), what is \(S_4\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (280)
B (285)
C (290)
D (294)
Explanation opens after your attempt
Step 1
Concept
The sum is (7+21+63+189=280). In exams, direct addition is also fast for small (n).
Step 2
Why this answer is correct
The correct answer is A. (280). The sum is (7+21+63+189=280). In exams, direct addition is also fast for small (n).
Step 3
Exam Tip
योग (7+21+63+189=280) है। परीक्षा में छोटे (n) के लिए सीधे जोड़ना भी तेज होता है।
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गुणोत्तर श्रेणी \(4,16,64,\ldots\) में (4096) तक कितने पद हैं?
How many terms are there up to (4096) in the geometric progression \(4,16,64,\ldots\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(4\cdot4^{n-1}=4096\) gives \(4^n=4096=4^6\), so (n=6). In exams, equate the last term to the general term.
Step 2
Why this answer is correct
The correct answer is B. (6). \(4\cdot4^{n-1}=4096\) gives \(4^n=4096=4^6\), so (n=6). In exams, equate the last term to the general term.
Step 3
Exam Tip
\(4\cdot4^{n-1}=4096\) से \(4^n=4096=4^6\), इसलिए (n=6) है। परीक्षा में अंतिम पद को सामान्य पद के बराबर रखें।
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यदि गुणोत्तर श्रेणी \(x,,5x,,25x,\ldots\) में पाँचवाँ पद (3125) है, तो (x) क्या है?
If the fifth term of the geometric progression \(x,,5x,,25x,\ldots\) is (3125), what is (x)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The fifth term is \(x\cdot5^4=625x=3125\), so (x=5). In exams, put the algebraic first term in \(ar^{n-1}\) too.
Step 2
Why this answer is correct
The correct answer is D. (5). The fifth term is \(x\cdot5^4=625x=3125\), so (x=5). In exams, put the algebraic first term in \(ar^{n-1}\) too.
Step 3
Exam Tip
पाँचवाँ पद \(x\cdot5^4=625x=3125\) है, इसलिए (x=5) है। परीक्षा में बीजीय पहले पद को भी \(ar^{n-1}\) में रखें।
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किस गुणोत्तर श्रेणी में \(a_3=50\) और \(a_6=6250\) है। यदि (r) धनात्मक है, तो \(a_1\) क्या है?
In a geometric progression \(a_3=50\) and \(a_6=6250\). If (r) is positive, what is \(a_1\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (1)
B (2)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(\frac{6250}{50}=125=r^3\), so (r=5) and \(a_1=\frac{50}{5^2}=2\). In exams, find (r) first and then the first term.
Step 2
Why this answer is correct
The correct answer is B. (2). \(\frac{6250}{50}=125=r^3\), so (r=5) and \(a_1=\frac{50}{5^2}=2\). In exams, find (r) first and then the first term.
Step 3
Exam Tip
\(\frac{6250}{50}=125=r^3\) से (r=5) और \(a_1=\frac{50}{5^2}=2\) है। परीक्षा में पहले (r) निकालें फिर पहला पद।
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गुणोत्तर श्रेणी \(6,18,54,\ldots\) के पहले (7) पदों का योग क्या है?
What is the sum of the first (7) terms of the geometric progression \(6,18,54,\ldots\)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (6558)
B (6560)
C (6564)
D (6570)
Explanation opens after your attempt
Step 1
Concept
(S_7=\frac{6\(3^7-1\)}{3-1}=6558). In exams, first calculate the value of \(3^7\).
Step 2
Why this answer is correct
The correct answer is A. (6558). (S_7=\frac{6\(3^7-1\)}{3-1}=6558). In exams, first calculate the value of \(3^7\).
Step 3
Exam Tip
(S_7=\frac{6\(3^7-1\)}{3-1}=6558) है। परीक्षा में पहले \(3^7\) का मान निकालें।
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यदि (a=6) और \(a_7=384\) है तथा (r) धनात्मक है, तो (r) क्या होगा?
If (a=6) and \(a_7=384\), and (r) is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
From \(384=6r^6\), \(r^6=64=2^6\), so (r=2). In exams, use \(r^6\) for the seventh term.
Step 2
Why this answer is correct
The correct answer is A. (2). From \(384=6r^6\), \(r^6=64=2^6\), so (r=2). In exams, use \(r^6\) for the seventh term.
Step 3
Exam Tip
\(384=6r^6\) से \(r^6=64=2^6\), इसलिए (r=2) है। परीक्षा में सातवें पद के लिए \(r^6\) लगाएँ।
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यदि \(a_2=18\) और \(a_6=1458\) है, तो (r) का धनात्मक मान क्या है?
If \(a_2=18\) and \(a_6=1458\), what is the positive value of (r)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(\frac{a_6}{a_2}=r^4=\frac{1458}{18}=81\), so (r=3). In exams, a gap of (4) positions gives \(r^4\).
Step 2
Why this answer is correct
The correct answer is B. (3). \(\frac{a_6}{a_2}=r^4=\frac{1458}{18}=81\), so (r=3). In exams, a gap of (4) positions gives \(r^4\).
Step 3
Exam Tip
\(\frac{a_6}{a_2}=r^4=\frac{1458}{18}=81\), इसलिए (r=3) है। परीक्षा में पद-अंतर (4) हो तो \(r^4\) बनेगा।
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गुणोत्तर श्रेणी \(3,15,75,\ldots\) का वह पद कौन-सा है जो (9375) है?
Which term of the geometric progression \(3,15,75,\ldots\) is (9375)?
#sequences
#progressions
#geometric-progression
#class-9
#expert
A पाँचवाँ पद / (5)th term
B छठा पद / (6)th term
C सातवाँ पद / (7)th term
D आठवाँ पद / (8)th term
Explanation opens after your attempt
Correct Answer
B. छठा पद / (6)th term
Step 1
Concept
From \(3\cdot5^{n-1}=9375\), \(5^{n-1}=3125=5^5\), so (n=6). In exams, compare powers to find the term number.
Step 2
Why this answer is correct
The correct answer is B. छठा पद / (6)th term. From \(3\cdot5^{n-1}=9375\), \(5^{n-1}=3125=5^5\), so (n=6). In exams, compare powers to find the term number.
Step 3
Exam Tip
\(3\cdot5^{n-1}=9375\) से \(5^{n-1}=3125=5^5\), इसलिए (n=6) है। परीक्षा में पद संख्या के लिए घात की तुलना करें।
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