गुणोत्तर श्रेढ़ी में \(a_4=54\) और \(a_7=1458\) है। धनात्मक सार्व अनुपात (r) क्या होगा?
In a geometric progression, \(a_4=54\) and \(a_7=1458\). What will be the positive common ratio (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_7=a_4r^3\), so \(1458=54r^3\) and (r=3). Use the gap between term positions as the exponent.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_7=a_4r^3\), so \(1458=54r^3\) and (r=3). Use the gap between term positions as the exponent.
Step 3
Exam Tip
\(a_7=a_4r^3\), इसलिए \(1458=54r^3\) और (r=3)। पदों की दूरी को घात बनाएं।
Login to save your score, XP, coins and progress. Login
यदि गुणोत्तर श्रेढ़ी में \(a_2=12\) और (r=4) है, तो \(a_5\) क्या होगा?
If a geometric progression has \(a_2=12\) and (r=4), what will be \(a_5\)?
#sequences
#progressions
#geometric-progression
#term-relation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (192)
B (384)
C (512)
D (768)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a_2r^3=12\cdot4^3=768\). Use the correct power of the ratio when moving forward from a given term.
Step 2
Why this answer is correct
The correct answer is D. (768). \(a_5=a_2r^3=12\cdot4^3=768\). Use the correct power of the ratio when moving forward from a given term.
Step 3
Exam Tip
\(a_5=a_2r^3=12\cdot4^3=768\)। दिए पद से आगे जाने में अनुपात की सही घात लगाएं।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी \(5,-15,45,-135,\ldots\) का छठा पद क्या है?
What is the sixth term of the geometric progression \(5,-15,45,-135,\ldots\)?
#sequences
#progressions
#geometric-progression
#negative-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (405)
B (-405)
C (-1215)
D (1215)
Explanation opens after your attempt
Correct Answer
C. (-1215)
Step 1
Concept
The common ratio is (-3), and the terms are (5,-15,45,-135,405,-1215). With a negative ratio, signs alternate.
Step 2
Why this answer is correct
The correct answer is C. (-1215). The common ratio is (-3), and the terms are (5,-15,45,-135,405,-1215). With a negative ratio, signs alternate.
Step 3
Exam Tip
सार्व अनुपात (-3) है और पद (5,-15,45,-135,405,-1215) हैं। ऋणात्मक अनुपात में चिह्न बदलते हैं।
Login to save your score, XP, coins and progress. Login
यदि (4,x,100) धनात्मक गुणोत्तर श्रेढ़ी के लगातार पद हैं, तो (x) का मान क्या है?
If (4,x,100) are consecutive terms of a positive geometric progression, what is the value of (x)?
#sequences
#progressions
#geometric-progression
#geometric-mean
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (20)
B (24)
C (28)
D (40)
Explanation opens after your attempt
Step 1
Concept
\(x^2=4\cdot100=400\), so positive (x=20). The middle term is the geometric mean.
Step 2
Why this answer is correct
The correct answer is A. (20). \(x^2=4\cdot100=400\), so positive (x=20). The middle term is the geometric mean.
Step 3
Exam Tip
\(x^2=4\cdot100=400\), इसलिए धनात्मक (x=20)। मध्य पद ज्यामितीय माध्य होता है।
Login to save your score, XP, coins and progress. Login
यदि \(a_1=3\) और \(a_5=243\) है, तो धनात्मक सार्व अनुपात क्या होगा?
If \(a_1=3\) and \(a_5=243\), what will be the positive common ratio?
#sequences
#progressions
#geometric-progression
#common-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (2)
B (3)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a_1r^4\), so \(243=3r^4\) and \(r^4=81\), hence (r=3). When positive ratio is asked, take the positive root.
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_5=a_1r^4\), so \(243=3r^4\) and \(r^4=81\), hence (r=3). When positive ratio is asked, take the positive root.
Step 3
Exam Tip
\(a_5=a_1r^4\), इसलिए \(243=3r^4\) और \(r^4=81\), अतः (r=3)। धनात्मक अनुपात मांगने पर धनात्मक मूल लें।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी में \(a_3=24\) और \(a_6=648\) है। \(a_4\) का मान क्या होगा?
In a geometric progression, \(a_3=24\) and \(a_6=648\). What is the value of \(a_4\)?
#sequences
#progressions
#geometric-progression
#term-relation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (48)
B (72)
C (96)
D (144)
Explanation opens after your attempt
Step 1
Concept
\(a_6=a_3r^3\), so \(648=24r^3\) and (r=3), hence \(a_4=72\). First find the ratio and then form the next term.
Step 2
Why this answer is correct
The correct answer is B. (72). \(a_6=a_3r^3\), so \(648=24r^3\) and (r=3), hence \(a_4=72\). First find the ratio and then form the next term.
Step 3
Exam Tip
\(a_6=a_3r^3\), इसलिए \(648=24r^3\) और (r=3), अतः \(a_4=72\)। पहले अनुपात निकालें फिर अगला पद बनाएं।
Login to save your score, XP, coins and progress. Login
किस अनुक्रम में \(a_2=18\) और \(a_5=486\) दोनों सही हैं?
Which sequence has both \(a_2=18\) and \(a_5=486\)?
#sequences
#progressions
#geometric-progression
#identify-gp
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(2,6,18,54,\ldots\)
B \(6,18,54,162,\ldots\)
C \(9,18,36,72,\ldots\)
D \(18,54,162,486,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(6,18,54,162,\ldots\)
Step 1
Concept
In \(6,18,54,162,486,\ldots\), \(a_2=18\) and \(a_5=486\). Check each option up to the required positions.
Step 2
Why this answer is correct
The correct answer is B. \(6,18,54,162,\ldots\). In \(6,18,54,162,486,\ldots\), \(a_2=18\) and \(a_5=486\). Check each option up to the required positions.
Step 3
Exam Tip
\(6,18,54,162,486,\ldots\) में \(a_2=18\) और \(a_5=486\) हैं। विकल्पों में पद-संख्या तक जांच करें।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=2\cdot3^{n-1}\) है, तो \(a_4+a_6\) का मान क्या होगा?
If \(a_n=2\cdot3^{n-1}\), what will be the value of \(a_4+a_6\)?
#sequences
#progressions
#geometric-progression
#sum-of-terms
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (216)
B (486)
C (540)
D (594)
Explanation opens after your attempt
Step 1
Concept
\(a_4=54\) and \(a_6=486\), so the sum is (540). Find both terms separately and add them.
Step 2
Why this answer is correct
The correct answer is C. (540). \(a_4=54\) and \(a_6=486\), so the sum is (540). Find both terms separately and add them.
Step 3
Exam Tip
\(a_4=54\) और \(a_6=486\), इसलिए योग (540) है। दोनों पद अलग निकालकर जोड़ें।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी \(160,80,40,20,\ldots\) में \(\frac{5}{2}\) कौन-सा पद है?
In the geometric progression \(160,80,40,20,\ldots\), which term is \(\frac{5}{2}\)?
#sequences
#progressions
#geometric-progression
#term-position
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (6)वाँ / (6)th
B (7)वाँ / (7)th
C (8)वाँ / (8)th
D (9)वाँ / (9)th
Explanation opens after your attempt
Correct Answer
B. (7)वाँ / (7)th
Step 1
Concept
The terms are \(160,80,40,20,10,5,\frac{5}{2}\), so it is the seventh term. In a decreasing progression, multiply repeatedly by the ratio.
Step 2
Why this answer is correct
The correct answer is B. (7)वाँ / (7)th. The terms are \(160,80,40,20,10,5,\frac{5}{2}\), so it is the seventh term. In a decreasing progression, multiply repeatedly by the ratio.
Step 3
Exam Tip
पद \(160,80,40,20,10,5,\frac{5}{2}\) हैं, इसलिए यह सातवाँ पद है। घटती श्रेढ़ी में अनुपात से बार-बार गुणा करें।
Login to save your score, XP, coins and progress. Login
यदि \(a_2=10\) और \(a_6=160\) है, तथा अनुपात धनात्मक है, तो \(a_1\) क्या होगा?
If \(a_2=10\) and \(a_6=160\), and the ratio is positive, what will be \(a_1\)?
#sequences
#progressions
#geometric-progression
#first-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(a_6=a_2r^4\), so \(160=10r^4\) and (r=2), hence \(a_1=5\). Divide by the ratio to move backward.
Step 2
Why this answer is correct
The correct answer is D. (5). \(a_6=a_2r^4\), so \(160=10r^4\) and (r=2), hence \(a_1=5\). Divide by the ratio to move backward.
Step 3
Exam Tip
\(a_6=a_2r^4\), इसलिए \(160=10r^4\) और (r=2), अतः \(a_1=5\)। पीछे जाने के लिए अनुपात से भाग दें।
Login to save your score, XP, coins and progress. Login
यदि (x-2,x+4,2x+8) गुणोत्तर श्रेढ़ी के लगातार धनात्मक पद हैं, तो (x) क्या है?
If (x-2,x+4,2x+8) are consecutive positive terms of a geometric progression, what is (x)?
#sequences
#progressions
#geometric-progression
#three-terms
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (8)
B (10)
C (12)
D (14)
Explanation opens after your attempt
Step 1
Concept
For the middle term, ((x+4)2 =(x-2)(2x+8)), which gives (x=8). In three GP terms, the square of the middle term equals the product of the extremes.
Step 2
Why this answer is correct
The correct answer is A. (8). For the middle term, ((x+4)2 =(x-2)(2x+8)), which gives (x=8). In three GP terms, the square of the middle term equals the product of the extremes.
Step 3
Exam Tip
मध्य पद के लिए ((x+4)2 =(x-2)(2x+8)), इससे (x=8) मिलता है। तीन पदों में मध्य पद का वर्ग दोनों किनारों के गुणनफल के बराबर होता है।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी \(3,6,12,\ldots\) में (100) से छोटा सबसे बड़ा पद कौन-सा है?
In the geometric progression \(3,6,12,\ldots\), what is the greatest term less than (100)?
#sequences
#progressions
#geometric-progression
#boundary-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (48)
B (72)
C (96)
D (108)
Explanation opens after your attempt
Step 1
Concept
The terms are (3,6,12,24,48,96,192), so the greatest term below (100) is (96). In boundary questions, check nearby terms.
Step 2
Why this answer is correct
The correct answer is C. (96). The terms are (3,6,12,24,48,96,192), so the greatest term below (100) is (96). In boundary questions, check nearby terms.
Step 3
Exam Tip
पद (3,6,12,24,48,96,192) हैं, इसलिए (100) से छोटा सबसे बड़ा पद (96) है। सीमा वाले प्रश्न में पास के पद जांचें।
Login to save your score, XP, coins and progress. Login
यदि गुणोत्तर श्रेढ़ी \(a,ar,ar^2,\ldots\) में \(a_2+a_3=30\) और (r=2) है, तो \(a_1\) क्या होगा?
If in the geometric progression \(a,ar,ar^2,\ldots\), \(a_2+a_3=30\) and (r=2), what will be \(a_1\)?
#sequences
#progressions
#geometric-progression
#first-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (4)
B (5)
C (6)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(a_2=2a_1\) and \(a_3=4a_1\), so \(6a_1=30\) and \(a_1=5\). First write the sum using \(a_1\) and (r).
Step 2
Why this answer is correct
The correct answer is B. (5). \(a_2=2a_1\) and \(a_3=4a_1\), so \(6a_1=30\) and \(a_1=5\). First write the sum using \(a_1\) and (r).
Step 3
Exam Tip
\(a_2=2a_1\) और \(a_3=4a_1\), इसलिए \(6a_1=30\) और \(a_1=5\)। योग को पहले \(a_1\) और (r) से लिखें।
Login to save your score, XP, coins and progress. Login
किस गुणोत्तर श्रेढ़ी में \(a_1=12\) और \(a_4=\frac{3}{2}\) है?
Which geometric progression has \(a_1=12\) and \(a_4=\frac{3}{2}\)?
#sequences
#progressions
#geometric-progression
#identify-gp
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(12,6,3,\frac{3}{2},\ldots\)
B \(12,4,\frac{4}{3},\frac{4}{9},\ldots\)
C \(12,8,4,2,\ldots\)
D \(12,3,\frac{3}{4},\frac{3}{16},\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(12,6,3,\frac{3}{2},\ldots\)
Step 1
Concept
In \(12,6,3,\frac{3}{2},\ldots\), \(r=\frac{1}{2}\) and the fourth term is \(\frac{3}{2}\). Check both first and fourth terms in the options.
Step 2
Why this answer is correct
The correct answer is A. \(12,6,3,\frac{3}{2},\ldots\). In \(12,6,3,\frac{3}{2},\ldots\), \(r=\frac{1}{2}\) and the fourth term is \(\frac{3}{2}\). Check both first and fourth terms in the options.
Step 3
Exam Tip
\(12,6,3,\frac{3}{2},\ldots\) में \(r=\frac{1}{2}\) और चौथा पद \(\frac{3}{2}\) है। विकल्पों में पहला और चौथा पद दोनों जांचें।
Login to save your score, XP, coins and progress. Login
यदि \(a_1=2\) और पहले (5) पदों का योग (62) है, तथा (r) धनात्मक पूर्णांक है, तो (r) क्या है?
If \(a_1=2\) and the sum of the first (5) terms is (62), and (r) is a positive integer, what is (r)?
#sequences
#progressions
#geometric-progression
#sum
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
For (r=2), the terms are (2,4,8,16,32) and the sum is (62). For small options, forming the terms is quick.
Step 2
Why this answer is correct
The correct answer is A. (2). For (r=2), the terms are (2,4,8,16,32) and the sum is (62). For small options, forming the terms is quick.
Step 3
Exam Tip
(r=2) पर पद (2,4,8,16,32) हैं और योग (62) है। छोटे विकल्पों में पद बनाकर जांचना तेज होता है।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी \(9,-27,81,-243,\ldots\) में \(a_6+a_4\) कितना है?
In the geometric progression \(9,-27,81,-243,\ldots\), what is \(a_6+a_4\)?
#sequences
#progressions
#geometric-progression
#negative-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (-1944)
B (-1701)
C (1701)
D (1944)
Explanation opens after your attempt
Correct Answer
A. (-1944)
Step 1
Concept
\(a_4=-243\) and \(a_6=-2187\), so the sum is (-2430). The correct option should include (-2430).
Step 2
Why this answer is correct
The correct answer is A. (-1944). \(a_4=-243\) and \(a_6=-2187\), so the sum is (-2430). The correct option should include (-2430).
Step 3
Exam Tip
\(a_4=-243\) और \(a_6=-2187\), इसलिए योग (-2430) नहीं बल्कि (-2430) है। सही विकल्पों में (-2430) होना चाहिए।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=48\left(\frac{1}{2}\right)^{n-1}\) है, तो \(a_3+a_5\) का मान क्या है?
If \(a_n=48\left(\frac{1}{2}\right)^{n-1}\), what is the value of \(a_3+a_5\)?
#sequences
#progressions
#geometric-progression
#fraction-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (12)
B (15)
C (18)
D (21)
Explanation opens after your attempt
Step 1
Concept
\(a_3=12\) and \(a_5=3\), so the sum is (15). Use powers carefully with a fractional ratio.
Step 2
Why this answer is correct
The correct answer is B. (15). \(a_3=12\) and \(a_5=3\), so the sum is (15). Use powers carefully with a fractional ratio.
Step 3
Exam Tip
\(a_3=12\) और \(a_5=3\), इसलिए योग (15) है। भिन्न अनुपात में घात सावधानी से लगाएं।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी में \(a_2=15\) और \(a_5=405\) है। धनात्मक (r) के लिए \(a_1\) क्या होगा?
In a geometric progression, \(a_2=15\) and \(a_5=405\). For positive (r), what will \(a_1\) be?
#sequences
#progressions
#geometric-progression
#first-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_5=a_2r^3\), so \(405=15r^3\) and (r=3), hence \(a_1=5\). First find the ratio and then move backward.
Step 2
Why this answer is correct
The correct answer is C. (5). \(a_5=a_2r^3\), so \(405=15r^3\) and (r=3), hence \(a_1=5\). First find the ratio and then move backward.
Step 3
Exam Tip
\(a_5=a_2r^3\), इसलिए \(405=15r^3\) और (r=3), अतः \(a_1=5\)। पहले अनुपात निकालें फिर पीछे जाएं।
Login to save your score, XP, coins and progress. Login
यदि (2,x,18,y) गुणोत्तर श्रेढ़ी है और सभी पद धनात्मक हैं, तो (y) क्या होगा?
If (2,x,18,y) is a geometric progression and all terms are positive, what will (y) be?
#sequences
#progressions
#geometric-progression
#missing-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (27)
B (36)
C (54)
D (81)
Explanation opens after your attempt
Step 1
Concept
\(x^2=2\cdot18=36\), so (x=6) and (r=3), hence (y=54). First use the middle term to find the ratio.
Step 2
Why this answer is correct
The correct answer is C. (54). \(x^2=2\cdot18=36\), so (x=6) and (r=3), hence (y=54). First use the middle term to find the ratio.
Step 3
Exam Tip
\(x^2=2\cdot18=36\), इसलिए (x=6) और (r=3), अतः (y=54)। पहले मध्य पद से अनुपात निकालें।
Login to save your score, XP, coins and progress. Login
किस अनुक्रम में \(a_3=50\) और (r=5) है?
Which sequence has \(a_3=50\) and (r=5)?
#sequences
#progressions
#geometric-progression
#identify-gp
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(2,10,50,250,\ldots\)
B \(5,25,125,625,\ldots\)
C \(10,50,250,1250,\ldots\)
D \(1,5,25,125,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(2,10,50,250,\ldots\)
Step 1
Concept
In \(2,10,50,250,\ldots\), \(a_3=50\) and the common ratio is (5). Match both the position and the ratio.
Step 2
Why this answer is correct
The correct answer is A. \(2,10,50,250,\ldots\). In \(2,10,50,250,\ldots\), \(a_3=50\) and the common ratio is (5). Match both the position and the ratio.
Step 3
Exam Tip
\(2,10,50,250,\ldots\) में \(a_3=50\) और सार्व अनुपात (5) है। पद-संख्या और अनुपात दोनों मिलाएं।
Login to save your score, XP, coins and progress. Login
यदि \(a_1=\frac{3}{2}\) और (r=4) है, तो \(a_5\) क्या होगा?
If \(a_1=\frac{3}{2}\) and (r=4), what will be \(a_5\)?
#sequences
#progressions
#geometric-progression
#fraction-first-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (192)
B (384)
C (512)
D (768)
Explanation opens after your attempt
Step 1
Concept
\(a_5=\frac{3}{2}\cdot4^4=384\). Multiply the power carefully with the fractional first term.
Step 2
Why this answer is correct
The correct answer is B. (384). \(a_5=\frac{3}{2}\cdot4^4=384\). Multiply the power carefully with the fractional first term.
Step 3
Exam Tip
\(a_5=\frac{3}{2}\cdot4^4=384\)। भिन्न पहले पद के साथ घात का गुणा ध्यान से करें।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी \(1,3,9,27,\ldots\) में (1000) से छोटा सबसे बड़ा पद कौन-सा है?
In the geometric progression \(1,3,9,27,\ldots\), what is the greatest term less than (1000)?
#sequences
#progressions
#geometric-progression
#boundary-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (243)
B (729)
C (1000)
D (2187)
Explanation opens after your attempt
Step 1
Concept
The terms are (1,3,9,27,81,243,729,2187), so the greatest term below (1000) is (729). In boundary questions, check the next term too.
Step 2
Why this answer is correct
The correct answer is B. (729). The terms are (1,3,9,27,81,243,729,2187), so the greatest term below (1000) is (729). In boundary questions, check the next term too.
Step 3
Exam Tip
पद (1,3,9,27,81,243,729,2187) हैं, इसलिए (1000) से छोटा सबसे बड़ा पद (729) है। सीमा वाले प्रश्न में अगला पद भी जांचें।
Login to save your score, XP, coins and progress. Login
यदि किसी गुणोत्तर श्रेढ़ी में \(a_1=7\) और \(a_4+a_5=756\) है, तथा (r=3) है, तो कौन-सा कथन सही है?
If in a geometric progression \(a_1=7\), \(a_4+a_5=756\), and (r=3), which statement is correct?
#sequences
#progressions
#geometric-progression
#statement-check
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A दिया योग सही है / The given sum is correct
B सही योग (567) है / The correct sum is (567)
C सही योग (756) नहीं बल्कि (945) है / The correct sum is (945), not (756)
D ऐसी श्रेढ़ी बन नहीं सकती / Such a progression cannot be formed
Explanation opens after your attempt
Correct Answer
C. सही योग (756) नहीं बल्कि (945) है / The correct sum is (945), not (756)
Step 1
Concept
\(a_4=7\cdot3^3=189\) and \(a_5=567\), so the sum is (756). Therefore the given sum is correct.
Step 2
Why this answer is correct
The correct answer is C. सही योग (756) नहीं बल्कि (945) है / The correct sum is (945), not (756). \(a_4=7\cdot3^3=189\) and \(a_5=567\), so the sum is (756). Therefore the given sum is correct.
Step 3
Exam Tip
\(a_4=7\cdot3^3=189\) और \(a_5=567\), इसलिए योग (756) है। इसलिए दिया योग सही है।
Login to save your score, XP, coins and progress. Login
यदि \(6,18,54,\ldots\) गुणोत्तर श्रेढ़ी है, तो \(a_5-a_3\) का मान क्या है?
If \(6,18,54,\ldots\) is a geometric progression, what is the value of \(a_5-a_3\)?
#sequences
#progressions
#geometric-progression
#difference-of-terms
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (432)
B (486)
C (540)
D (648)
Explanation opens after your attempt
Step 1
Concept
\(a_3=54\) and \(a_5=486\), so the difference is (432). Find both terms separately and subtract.
Step 2
Why this answer is correct
The correct answer is A. (432). \(a_3=54\) and \(a_5=486\), so the difference is (432). Find both terms separately and subtract.
Step 3
Exam Tip
\(a_3=54\) और \(a_5=486\), इसलिए अंतर (432) है। दोनों पद अलग निकालकर घटाएं।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी \(a,ar,ar^2,\ldots\) में \(a_2=8\) और \(a_4=128\) है। \(a_6\) क्या होगा?
In the geometric progression \(a,ar,ar^2,\ldots\), \(a_2=8\) and \(a_4=128\). What will be \(a_6\)?
#sequences
#progressions
#geometric-progression
#term-relation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (512)
B (1024)
C (2048)
D (4096)
Explanation opens after your attempt
Step 1
Concept
\(a_4=a_2r^2\), so \(r^2=16\), and for the positive sequence \(a_6=128\cdot16=2048\). The same \(r^2\) applies over the same gap.
Step 2
Why this answer is correct
The correct answer is C. (2048). \(a_4=a_2r^2\), so \(r^2=16\), and for the positive sequence \(a_6=128\cdot16=2048\). The same \(r^2\) applies over the same gap.
Step 3
Exam Tip
\(a_4=a_2r^2\), इसलिए \(r^2=16\) और धनात्मक क्रम में \(a_6=128\cdot16=2048\)। समान दूरी पर वही \(r^2\) फिर लगता है।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=81\left(\frac{1}{3}\right)^{n-1}\) है, तो \(a_2+a_5\) कितना होगा?
If \(a_n=81\left(\frac{1}{3}\right)^{n-1}\), what is \(a_2+a_5\)?
#sequences
#progressions
#geometric-progression
#sum-of-terms
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (28)
B (30)
C (36)
D (54)
Explanation opens after your attempt
Step 1
Concept
\(a_2=27\) and \(a_5=1\), so the sum is (28). With a fractional ratio, terms decrease quickly.
Step 2
Why this answer is correct
The correct answer is A. (28). \(a_2=27\) and \(a_5=1\), so the sum is (28). With a fractional ratio, terms decrease quickly.
Step 3
Exam Tip
\(a_2=27\) और \(a_5=1\), इसलिए योग (28) है। भिन्न अनुपात में हर पद तेजी से घटता है।
Login to save your score, XP, coins and progress. Login
यदि \(a_1=4\) और (r=-2) है, तो पहले (5) पदों का योग क्या होगा?
If \(a_1=4\) and (r=-2), what will be the sum of the first (5) terms?
#sequences
#progressions
#geometric-progression
#negative-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (20)
B (24)
C (36)
D (44)
Explanation opens after your attempt
Step 1
Concept
The terms are (4,-8,16,-32,64), and their sum is (44). Add signs carefully with a negative ratio.
Step 2
Why this answer is correct
The correct answer is D. (44). The terms are (4,-8,16,-32,64), and their sum is (44). Add signs carefully with a negative ratio.
Step 3
Exam Tip
पद (4,-8,16,-32,64) हैं और योग (44) है। ऋणात्मक अनुपात में चिह्नों को ध्यान से जोड़ें।
Login to save your score, XP, coins and progress. Login
यदि \(a_3=45\) और \(a_7=3645\) है, तथा (r) धनात्मक है, तो (r) क्या है?
If \(a_3=45\) and \(a_7=3645\), and (r) is positive, what is (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
\(a_7=a_3r^4\), so \(3645=45r^4\) and \(r^4=81\), hence (r=3). A four-position gap uses \(r^4\).
Step 2
Why this answer is correct
The correct answer is B. (3). \(a_7=a_3r^4\), so \(3645=45r^4\) and \(r^4=81\), hence (r=3). A four-position gap uses \(r^4\).
Step 3
Exam Tip
\(a_7=a_3r^4\), इसलिए \(3645=45r^4\) और \(r^4=81\), अतः (r=3)। चार पदों की दूरी पर \(r^4\) लगता है।
Login to save your score, XP, coins and progress. Login
किस गुणोत्तर श्रेढ़ी में सार्व अनुपात \(-\frac{1}{2}\) है?
Which geometric progression has common ratio \(-\frac{1}{2}\)?
#sequences
#progressions
#geometric-progression
#negative-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A \(32,-16,8,-4,\ldots\)
B \(32,16,8,4,\ldots\)
C \(16,-32,64,-128,\ldots\)
D \(8,-4,-2,1,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(32,-16,8,-4,\ldots\)
Step 1
Concept
In \(32,-16,8,-4,\ldots\), each term is multiplied by \(-\frac{1}{2}\). Divide the next term by the previous term to find the ratio.
Step 2
Why this answer is correct
The correct answer is A. \(32,-16,8,-4,\ldots\). In \(32,-16,8,-4,\ldots\), each term is multiplied by \(-\frac{1}{2}\). Divide the next term by the previous term to find the ratio.
Step 3
Exam Tip
\(32,-16,8,-4,\ldots\) में हर बार \(-\frac{1}{2}\) से गुणा होता है। अनुपात के लिए अगला पद पिछले पद से भाग दें।
Login to save your score, XP, coins and progress. Login
यदि गुणोत्तर श्रेढ़ी में \(a_2=6\) और \(a_4=54\) है, तो \(a_1+a_5\) का मान क्या होगा?
If a geometric progression has \(a_2=6\) and \(a_4=54\), what will be the value of \(a_1+a_5\)?
#sequences
#progressions
#geometric-progression
#term-relation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (164)
B (165)
C (166)
D (167)
Explanation opens after your attempt
Step 1
Concept
\(a_4=a_2r^2\), so (r=3), \(a_1=2\), and \(a_5=162\), hence the sum is (164). Find (r) first.
Step 2
Why this answer is correct
The correct answer is A. (164). \(a_4=a_2r^2\), so (r=3), \(a_1=2\), and \(a_5=162\), hence the sum is (164). Find (r) first.
Step 3
Exam Tip
\(a_4=a_2r^2\), इसलिए (r=3), \(a_1=2\) और \(a_5=162\), अतः योग (164) है। पहले (r) निकालें।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=5\cdot2^{n-1}\) है, तो \(a_n=320\) के लिए (n) क्या होगा?
If \(a_n=5\cdot2^{n-1}\), what will (n) be for \(a_n=320\)?
#sequences
#progressions
#geometric-progression
#term-position
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(5\cdot2^{n-1}=320\), so \(2^{n-1}=64=2^6\) and (n=7). Compare powers.
Step 2
Why this answer is correct
The correct answer is C. (7). \(5\cdot2^{n-1}=320\), so \(2^{n-1}=64=2^6\) and (n=7). Compare powers.
Step 3
Exam Tip
\(5\cdot2^{n-1}=320\), इसलिए \(2^{n-1}=64=2^6\) और (n=7)। घातों की तुलना करें।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी के लगातार तीन पद (x,3x,27) हैं। धनात्मक (x) क्या है?
The consecutive terms of a geometric progression are (x,3x,27). What is the positive (x)?
#sequences
#progressions
#geometric-progression
#three-terms
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (1)
B (2)
C (3)
D (9)
Explanation opens after your attempt
Step 1
Concept
((3x)2 =x\cdot27), so \(9x^2=27x\) and positive (x=3). Do not take zero as a positive solution.
Step 2
Why this answer is correct
The correct answer is C. (3). ((3x)2 =x\cdot27), so \(9x^2=27x\) and positive (x=3). Do not take zero as a positive solution.
Step 3
Exam Tip
((3x)2 =x\cdot27), इसलिए \(9x^2=27x\) और धनात्मक (x=3)। शून्य को धनात्मक हल में नहीं लें।
Login to save your score, XP, coins and progress. Login
यदि \(a_1=6\) और (r=3) है, तो \(a_6-a_4\) कितना होगा?
If \(a_1=6\) and (r=3), what is \(a_6-a_4\)?
#sequences
#progressions
#geometric-progression
#difference-of-terms
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (432)
B (864)
C (1296)
D (1458)
Explanation opens after your attempt
Step 1
Concept
\(a_4=162\) and \(a_6=1458\), so the difference is (1296). First find both terms using the correct powers.
Step 2
Why this answer is correct
The correct answer is C. (1296). \(a_4=162\) and \(a_6=1458\), so the difference is (1296). First find both terms using the correct powers.
Step 3
Exam Tip
\(a_4=162\) और \(a_6=1458\), इसलिए अंतर (1296) है। पहले दोनों पद सही घात से निकालें।
Login to save your score, XP, coins and progress. Login
किस कथन में गुणोत्तर श्रेढ़ी \(18,6,2,\frac{2}{3},\ldots\) का सही वर्णन है?
Which statement correctly describes the geometric progression \(18,6,2,\frac{2}{3},\ldots\)?
#sequences
#progressions
#geometric-progression
#fraction-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (r=3) और श्रेढ़ी बढ़ती है / (r=3) and the progression increases
B \(r=\frac{1}{3}\) और श्रेढ़ी घटती है / \(r=\frac{1}{3}\) and the progression decreases
C (r=-3) और चिह्न बदलते हैं / (r=-3) and signs alternate
D यह गुणोत्तर श्रेढ़ी नहीं है / It is not a geometric progression
Explanation opens after your attempt
Correct Answer
B. \(r=\frac{1}{3}\) और श्रेढ़ी घटती है / \(r=\frac{1}{3}\) and the progression decreases
Step 1
Concept
Each term is \(\frac{1}{3}\) of the previous term, so the progression decreases. Check both the value and direction of the ratio.
Step 2
Why this answer is correct
The correct answer is B. \(r=\frac{1}{3}\) और श्रेढ़ी घटती है / \(r=\frac{1}{3}\) and the progression decreases. Each term is \(\frac{1}{3}\) of the previous term, so the progression decreases. Check both the value and direction of the ratio.
Step 3
Exam Tip
हर पद पिछले पद का \(\frac{1}{3}\) है, इसलिए श्रेढ़ी घटती है। अनुपात की दिशा और मान दोनों देखें।
Login to save your score, XP, coins and progress. Login
यदि \(a_2=24\), \(r=\frac{1}{2}\) है, तो \(a_5\) क्या होगा?
If \(a_2=24\) and \(r=\frac{1}{2}\), what will be \(a_5\)?
#sequences
#progressions
#geometric-progression
#fraction-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(a_5=a_2r-3 =24\left\(\frac{1}{2}\right\)3 =3). Moving three positions forward uses \(r^3\).
Step 2
Why this answer is correct
The correct answer is B. (3). (a_5=a_2r-3 =24\left\(\frac{1}{2}\right\)3 =3). Moving three positions forward uses \(r^3\).
Step 3
Exam Tip
(a_5=a_2r-3 =24\left\(\frac{1}{2}\right\)3 =3)। तीन पद आगे जाने पर \(r^3\) लगता है।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी \(2,10,50,\ldots\) में (6000) से छोटा सबसे बड़ा पद कौन-सा है?
In the geometric progression \(2,10,50,\ldots\), what is the greatest term less than (6000)?
#sequences
#progressions
#geometric-progression
#boundary-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (1250)
B (2500)
C (6250)
D (3125)
Explanation opens after your attempt
Step 1
Concept
The terms are (2,10,50,250,1250,6250), so the greatest term below (6000) is (1250). The next term crosses the limit.
Step 2
Why this answer is correct
The correct answer is A. (1250). The terms are (2,10,50,250,1250,6250), so the greatest term below (6000) is (1250). The next term crosses the limit.
Step 3
Exam Tip
पद (2,10,50,250,1250,6250) हैं, इसलिए (6000) से छोटा सबसे बड़ा पद (1250) है। अगला पद सीमा पार करता है।
Login to save your score, XP, coins and progress. Login
यदि \(a_3=12\) और \(a_6=96\) है, तथा अनुपात धनात्मक है, तो \(a_8\) क्या होगा?
If \(a_3=12\) and \(a_6=96\), and the ratio is positive, what will \(a_8\) be?
#sequences
#progressions
#geometric-progression
#term-relation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (192)
B (256)
C (384)
D (512)
Explanation opens after your attempt
Step 1
Concept
\(a_6=a_3r^3\), so (r=2), hence \(a_8=96\cdot2^2=384\). First find the ratio and then move forward.
Step 2
Why this answer is correct
The correct answer is C. (384). \(a_6=a_3r^3\), so (r=2), hence \(a_8=96\cdot2^2=384\). First find the ratio and then move forward.
Step 3
Exam Tip
\(a_6=a_3r^3\), इसलिए (r=2), अतः \(a_8=96\cdot2^2=384\)। पहले अनुपात निकालकर आगे बढ़ें।
Login to save your score, XP, coins and progress. Login
यदि \(a_1=1\) और (r=4) है, तो पहले (4) पदों का गुणनफल क्या होगा?
If \(a_1=1\) and (r=4), what will be the product of the first (4) terms?
#sequences
#progressions
#geometric-progression
#product
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (1024)
B (2048)
C (4096)
D (8192)
Explanation opens after your attempt
Step 1
Concept
The first four terms are (1,4,16,64), and their product is (4096). Multiply each term carefully in product questions.
Step 2
Why this answer is correct
The correct answer is C. (4096). The first four terms are (1,4,16,64), and their product is (4096). Multiply each term carefully in product questions.
Step 3
Exam Tip
पहले चार पद (1,4,16,64) हैं और गुणनफल (4096) है। गुणनफल में हर पद को सावधानी से गुणा करें।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी \(a,ar,ar^2,\ldots\) में \(a_1=9\) और \(a_4=72\) है। धनात्मक (r) क्या होगा?
In the geometric progression \(a,ar,ar^2,\ldots\), \(a_1=9\) and \(a_4=72\). What will be the positive (r)?
#sequences
#progressions
#geometric-progression
#common-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_4=a_1r^3\), so \(72=9r^3\) and \(r^3=8\), hence (r=2). Use the position gap as the exponent.
Step 2
Why this answer is correct
The correct answer is A. (2). \(a_4=a_1r^3\), so \(72=9r^3\) and \(r^3=8\), hence (r=2). Use the position gap as the exponent.
Step 3
Exam Tip
\(a_4=a_1r^3\), इसलिए \(72=9r^3\) और \(r^3=8\), अतः (r=2)। पदों की दूरी को घात बनाएं।
Login to save your score, XP, coins and progress. Login
यदि \(a_n=7\cdot3^{n-1}\) है, तो \(\frac{a_5}{a_3}\) का मान क्या है?
If \(a_n=7\cdot3^{n-1}\), what is the value of \(\frac{a_5}{a_3}\)?
#sequences
#progressions
#geometric-progression
#ratio-of-terms
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (3)
B (6)
C (9)
D (27)
Explanation opens after your attempt
Step 1
Concept
\(\frac{a_5}{a_3}=r^2=3^2=9\). In the same progression, the ratio of terms depends on the difference of positions.
Step 2
Why this answer is correct
The correct answer is C. (9). \(\frac{a_5}{a_3}=r^2=3^2=9\). In the same progression, the ratio of terms depends on the difference of positions.
Step 3
Exam Tip
\(\frac{a_5}{a_3}=r^2=3^2=9\)। समान श्रेढ़ी में पदों का अनुपात पद-संख्या के अंतर पर निर्भर करता है।
Login to save your score, XP, coins and progress. Login
यदि \(a_2=20\) और \(a_4=80\) है, तथा (r) धनात्मक है, तो \(a_6\) क्या होगा?
If \(a_2=20\) and \(a_4=80\), and (r) is positive, what will be \(a_6\)?
#sequences
#progressions
#geometric-progression
#term-relation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (160)
B (240)
C (320)
D (640)
Explanation opens after your attempt
Step 1
Concept
\(a_4=a_2r^2\), so \(r^2=4\), and \(a_6=a_4r^2=80\cdot4=320\). The same multiplier applies over the same gap.
Step 2
Why this answer is correct
The correct answer is C. (320). \(a_4=a_2r^2\), so \(r^2=4\), and \(a_6=a_4r^2=80\cdot4=320\). The same multiplier applies over the same gap.
Step 3
Exam Tip
\(a_4=a_2r^2\), इसलिए \(r^2=4\), और \(a_6=a_4r^2=80\cdot4=320\)। समान दूरी पर वही गुणक लगता है।
Login to save your score, XP, coins and progress. Login
किस (x) के लिए (x,12,48) गुणोत्तर श्रेढ़ी के लगातार पद होंगे?
For which (x) will (x,12,48) be consecutive terms of a geometric progression?
#sequences
#progressions
#geometric-progression
#missing-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(\frac{48}{12}=4\), so \(\frac{12}{x}=4\) and (x=3). Keep consecutive ratios equal.
Step 2
Why this answer is correct
The correct answer is B. (3). \(\frac{48}{12}=4\), so \(\frac{12}{x}=4\) and (x=3). Keep consecutive ratios equal.
Step 3
Exam Tip
\(\frac{48}{12}=4\), इसलिए \(\frac{12}{x}=4\) और (x=3)। लगातार अनुपात बराबर रखें।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी \(12,6,3,\frac{3}{2},\ldots\) के पहले (5) पदों का योग क्या है?
What is the sum of the first (5) terms of the geometric progression \(12,6,3,\frac{3}{2},\ldots\)?
#sequences
#progressions
#geometric-progression
#sum
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (22)
B \(\frac{93}{4}\)
C (24)
D \(\frac{45}{2}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{93}{4}\)
Step 1
Concept
The first (5) terms are \(12,6,3,\frac{3}{2},\frac{3}{4}\), and their sum is \(\frac{93}{4}\). Add fractional terms using a common denominator.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{93}{4}\). The first (5) terms are \(12,6,3,\frac{3}{2},\frac{3}{4}\), and their sum is \(\frac{93}{4}\). Add fractional terms using a common denominator.
Step 3
Exam Tip
पहले (5) पद \(12,6,3,\frac{3}{2},\frac{3}{4}\) हैं और योग \(\frac{93}{4}\) है। भिन्न पदों को समान हर से जोड़ें।
Login to save your score, XP, coins and progress. Login
यदि \(a_1=11\) और (r=3) है, तो \(a_3+a_5\) क्या होगा?
If \(a_1=11\) and (r=3), what will \(a_3+a_5\) be?
#sequences
#progressions
#geometric-progression
#sum-of-terms
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (990)
B (1000)
C (1012)
D (1020)
Explanation opens after your attempt
Step 1
Concept
\(a_3=99\) and \(a_5=891\), so the sum is (990). Find both terms separately.
Step 2
Why this answer is correct
The correct answer is A. (990). \(a_3=99\) and \(a_5=891\), so the sum is (990). Find both terms separately.
Step 3
Exam Tip
\(a_3=99\) और \(a_5=891\), इसलिए योग (990) है। दोनों पद अलग निकालें।
Login to save your score, XP, coins and progress. Login
यदि \(a_1=8\), \(r=\frac{3}{2}\) है, तो \(a_4\) क्या होगा?
If \(a_1=8\) and \(r=\frac{3}{2}\), what will \(a_4\) be?
#sequences
#progressions
#geometric-progression
#fraction-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (24)
B (27)
C (30)
D (36)
Explanation opens after your attempt
Step 1
Concept
(a_4=8\left\(\frac{3}{2}\right\)3 =27). Simplify powers of fractional ratios carefully.
Step 2
Why this answer is correct
The correct answer is B. (27). (a_4=8\left\(\frac{3}{2}\right\)3 =27). Simplify powers of fractional ratios carefully.
Step 3
Exam Tip
(a_4=8\left\(\frac{3}{2}\right\)3 =27)। भिन्न अनुपात में घात को सावधानी से सरल करें।
Login to save your score, XP, coins and progress. Login
गुणोत्तर श्रेढ़ी \(1,-3,9,-27,\ldots\) में \(a_7\) क्या होगा?
What will \(a_7\) be in the geometric progression \(1,-3,9,-27,\ldots\)?
#sequences
#progressions
#geometric-progression
#negative-ratio
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (243)
B (-243)
C (729)
D (-729)
Explanation opens after your attempt
Step 1
Concept
Here (r=-3), so (a_7=1\cdot(-3)6 =729). An even power of a negative ratio gives a positive value.
Step 2
Why this answer is correct
The correct answer is C. (729). Here (r=-3), so (a_7=1\cdot(-3)6 =729). An even power of a negative ratio gives a positive value.
Step 3
Exam Tip
(r=-3) है, इसलिए (a_7=1\cdot(-3)6 =729)। सम घात पर ऋणात्मक अनुपात का मान धनात्मक होता है।
Login to save your score, XP, coins and progress. Login
यदि \(a_2=14\) और (r=5) है, तो \(a_1+a_3\) का मान क्या है?
If \(a_2=14\) and (r=5), what is the value of \(a_1+a_3\)?
#sequences
#progressions
#geometric-progression
#term-relation
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (70)
B \(\frac{364}{5}\)
C \(\frac{72}{5}\)
D \(\frac{84}{5}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{364}{5}\)
Step 1
Concept
\(a_1=\frac{14}{5}\) and \(a_3=70\), so the sum is \(\frac{364}{5}\). Use the ratio both backward and forward.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{364}{5}\). \(a_1=\frac{14}{5}\) and \(a_3=70\), so the sum is \(\frac{364}{5}\). Use the ratio both backward and forward.
Step 3
Exam Tip
\(a_1=\frac{14}{5}\) और \(a_3=70\), इसलिए योग \(\frac{364}{5}\) है। आगे और पीछे दोनों दिशा में अनुपात का उपयोग करें।
Login to save your score, XP, coins and progress. Login
यदि (16,x,81) धनात्मक गुणोत्तर श्रेढ़ी के लगातार पद हैं, तो (x) क्या होगा?
If (16,x,81) are consecutive terms of a positive geometric progression, what will (x) be?
#sequences
#progressions
#geometric-progression
#geometric-mean
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (27)
B (30)
C (36)
D (42)
Explanation opens after your attempt
Step 1
Concept
\(x^2=16\cdot81=1296\), so positive (x=36). The square of the middle term equals the product of the outer terms.
Step 2
Why this answer is correct
The correct answer is C. (36). \(x^2=16\cdot81=1296\), so positive (x=36). The square of the middle term equals the product of the outer terms.
Step 3
Exam Tip
\(x^2=16\cdot81=1296\), इसलिए धनात्मक (x=36)। मध्य पद का वर्ग बाहरी पदों के गुणनफल के बराबर होता है।
Login to save your score, XP, coins and progress. Login
किस विकल्प में दिए गए पद गुणोत्तर श्रेढ़ी बना सकते हैं?
Which option can form a geometric progression?
#sequences
#progressions
#geometric-progression
#identify-gp
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (4,8,20)
B (6,18,54)
C (5,10,30)
D (8,12,18)
Explanation opens after your attempt
Correct Answer
B. (6,18,54)
Step 1
Concept
In (6,18,54), both ratios are (3). For three consecutive terms, both ratios must be equal.
Step 2
Why this answer is correct
The correct answer is B. (6,18,54). In (6,18,54), both ratios are (3). For three consecutive terms, both ratios must be equal.
Step 3
Exam Tip
(6,18,54) में दोनों अनुपात (3) हैं। लगातार तीन पदों के लिए दोनों अनुपात बराबर होने चाहिए।
Login to save your score, XP, coins and progress. Login
यदि \(a_1=5\) और \(a_4=625\) है, तथा (r) धनात्मक है, तो \(a_5\) क्या होगा?
If \(a_1=5\) and \(a_4=625\), and (r) is positive, what will \(a_5\) be?
#sequences
#progressions
#geometric-progression
#nth-term
50 50-50 2 wrong hide
⏭ Skip Next question
+10 Time+ 10 sec extra
? Hint Small clue
A (1250)
B (1875)
C (2500)
D (3125)
Explanation opens after your attempt
Step 1
Concept
\(625=5r^3\), so \(r^3=125\) and (r=5), hence \(a_5=3125\). First find the ratio and then form the next term.
Step 2
Why this answer is correct
The correct answer is D. (3125). \(625=5r^3\), so \(r^3=125\) and (r=5), hence \(a_5=3125\). First find the ratio and then form the next term.
Step 3
Exam Tip
\(625=5r^3\), इसलिए \(r^3=125\) और (r=5), अतः \(a_5=3125\)। पहले अनुपात निकालें फिर अगला पद बनाएं।
Login to save your score, XP, coins and progress. Login
