अनुक्रम \(6,14,28,48,\ldots\) का सामान्य पद \(a_n=3n^2-n+4\) है। (10)वाँ पद क्या होगा?
The sequence \(6,14,28,48,\ldots\) has general term \(a_n=3n^2-n+4\). What will be the (10)th term?
#sequences
#nth-term
#quadratic
#class-9
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A (284)
B (294)
C (304)
D (314)
Explanation opens after your attempt
Step 1
Concept
\(a_{10}=3\times10^2-10+4=294\). Exam tip: substitute the term position directly for (n).
Step 2
Why this answer is correct
The correct answer is B. (294). \(a_{10}=3\times10^2-10+4=294\). Exam tip: substitute the term position directly for (n).
Step 3
Exam Tip
\(a_{10}=3\times10^2-10+4=294\) है। परीक्षा में (n) की जगह पद संख्या सीधे रखें।
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यदि \(a_n=n^2+5n-2\) है तो कौन सा पद (148) के बराबर है?
If \(a_n=n^2+5n-2\), which term is equal to (148)?
#sequences
#term-position
#quadratic
#class-9
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A (8)वाँ / (8)th
B (9)वाँ / (9)th
C (11)वाँ / (11)th
D (10)वाँ / (10)th
Explanation opens after your attempt
Correct Answer
D. (10)वाँ / (10)th
Step 1
Concept
\(10^2+5\times10-2=148\), so it is the (10)th term. Exam tip: test options quickly in the formula.
Step 2
Why this answer is correct
The correct answer is D. (10)वाँ / (10)th. \(10^2+5\times10-2=148\), so it is the (10)th term. Exam tip: test options quickly in the formula.
Step 3
Exam Tip
\(10^2+5\times10-2=148\) इसलिए यह (10)वाँ पद है। विकल्पों को सूत्र में रखकर तेजी से जाँचें।
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अनुक्रम \(2,7,17,32,52,\ldots\) में क्रमागत अंतर \(5,10,15,20,\ldots\) हैं। अगला पद क्या होगा?
In the sequence \(2,7,17,32,52,\ldots\), the successive differences are \(5,10,15,20,\ldots\). What will be the next term?
#sequences
#difference-pattern
#next-term
#class-9
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A (72)
B (75)
C (77)
D (80)
Explanation opens after your attempt
Step 1
Concept
The next difference is (25), so (52+25=77). Exam tip: identifying the sequence of differences is the key step.
Step 2
Why this answer is correct
The correct answer is C. (77). The next difference is (25), so (52+25=77). Exam tip: identifying the sequence of differences is the key step.
Step 3
Exam Tip
अगला अंतर (25) होगा इसलिए (52+25=77) है। अंतर का अनुक्रम पहचानना सबसे जरूरी कदम है।
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अनुक्रम \(120,117,111,102,90,\ldots\) में अंतरों का क्रम \(-3,-6,-9,-12,\ldots\) है। अगला पद क्या होगा?
In the sequence \(120,117,111,102,90,\ldots\), the differences are \(-3,-6,-9,-12,\ldots\). What will be the next term?
#sequences
#decreasing
#differences
#class-9
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A (75)
B (78)
C (81)
D (84)
Explanation opens after your attempt
Step 1
Concept
The next difference is (-15), so (90-15=75). Exam tip: pay special attention to negative signs in decreasing sequences.
Step 2
Why this answer is correct
The correct answer is A. (75). The next difference is (-15), so (90-15=75). Exam tip: pay special attention to negative signs in decreasing sequences.
Step 3
Exam Tip
अगला अंतर (-15) होगा इसलिए (90-15=75) है। घटते अनुक्रम में ऋण चिह्न पर विशेष ध्यान दें।
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अनुक्रम \(4,9,8,18,16,36,\ldots\) में दो अलग-अलग पैटर्न छिपे हैं। अगला पद क्या होगा?
In the sequence \(4,9,8,18,16,36,\ldots\), two different patterns are hidden. What will be the next term?
#sequences
#alternating-pattern
#hidden-sequence
#class-9
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A (24)
B (28)
C (32)
D (72)
Explanation opens after your attempt
Step 1
Concept
Odd positions are \(4,8,16,\ldots\), so the next odd-position term is (32). Exam tip: separate odd and even positions in alternating sequences.
Step 2
Why this answer is correct
The correct answer is C. (32). Odd positions are \(4,8,16,\ldots\), so the next odd-position term is (32). Exam tip: separate odd and even positions in alternating sequences.
Step 3
Exam Tip
विषम स्थानों पर \(4,8,16,\ldots\) हैं इसलिए अगला विषम पद (32) होगा। वैकल्पिक अनुक्रमों में विषम और सम स्थान अलग देखें।
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यदि \(a_1=2\) और \(a_{n+1}=3a_n-1\) है तो \(a_5\) का मान क्या होगा?
If \(a_1=2\) and \(a_{n+1}=3a_n-1\), what will be the value of \(a_5\)?
#sequences
#recurrence
#nth-term
#class-9
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A (116)
B (122)
C (126)
D (128)
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,14,41,122). Exam tip: apply every recursive step carefully.
Step 2
Why this answer is correct
The correct answer is B. (122). The terms are (2,5,14,41,122). Exam tip: apply every recursive step carefully.
Step 3
Exam Tip
पद (2,5,14,41,122) मिलते हैं। पुनरावर्ती नियम में हर चरण सावधानी से करें।
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यदि \(a_1=1\) और (a_{n+1}=a_n+n(n+1)) है तो \(a_5\) क्या होगा?
If \(a_1=1\) and (a_{n+1}=a_n+n(n+1)), what will \(a_5\) be?
#sequences
#recursive-product
#class-9
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A (31)
B (36)
C (39)
D (41)
Explanation opens after your attempt
Step 1
Concept
The terms are (1,3,9,21,41), so \(a_5=41\). Exam tip: write positions along with values to avoid recursive mistakes.
Step 2
Why this answer is correct
The correct answer is D. (41). The terms are (1,3,9,21,41), so \(a_5=41\). Exam tip: write positions along with values to avoid recursive mistakes.
Step 3
Exam Tip
पद (1,3,9,21,41) मिलते हैं इसलिए \(a_5=41\) है। क्रमांक साथ लिखने से पुनरावर्ती गलती कम होती है।
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अनुक्रम \(\frac{2}{3},\frac{3}{5},\frac{4}{7},\ldots\) में (12)वाँ पद क्या होगा?
What will be the (12)th term in the sequence \(\frac{2}{3},\frac{3}{5},\frac{4}{7},\ldots\)?
#sequences
#fraction-sequence
#nth-term
#class-9
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A \(\frac{13}{25}\)
B \(\frac{12}{25}\)
C \(\frac{13}{23}\)
D \(\frac{14}{25}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{13}{25}\)
Step 1
Concept
The general term is \(\frac{n+1}{2n+1}\), so the (12)th term is \(\frac{13}{25}\). Exam tip: observe numerator and denominator patterns separately.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{13}{25}\). The general term is \(\frac{n+1}{2n+1}\), so the (12)th term is \(\frac{13}{25}\). Exam tip: observe numerator and denominator patterns separately.
Step 3
Exam Tip
सामान्य पद \(\frac{n+1}{2n+1}\) है इसलिए (12)वाँ पद \(\frac{13}{25}\) है। भिन्नों में अंश और हर का पैटर्न अलग देखें।
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यदि (a_n=(-1)^n(n+1)) है तो \(a_7+a_8\) का मान क्या होगा?
If (a_n=(-1)^n(n+1)), what will be the value of \(a_7+a_8\)?
#sequences
#alternating-sign
#sum
#class-9
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A (-1)
B (1)
C (17)
D (-17)
Explanation opens after your attempt
Step 1
Concept
\(a_7=-8\) and \(a_8=9\), so the sum is (1). Exam tip: track even and odd powers in sign-changing sequences.
Step 2
Why this answer is correct
The correct answer is B. (1). \(a_7=-8\) and \(a_8=9\), so the sum is (1). Exam tip: track even and odd powers in sign-changing sequences.
Step 3
Exam Tip
\(a_7=-8\) और \(a_8=9\) इसलिए योग (1) है। चिह्न बदलने वाले अनुक्रम में सम-विषम घात ध्यान रखें।
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यदि \(a_n=2^n-n\) है तो \(a_8\) का मान क्या होगा?
If \(a_n=2^n-n\), what will be the value of \(a_8\)?
#sequences
#powers
#nth-term
#class-9
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A (240)
B (244)
C (248)
D (252)
Explanation opens after your attempt
Step 1
Concept
\(a_8=2^8-8=248\). Exam tip: calculate the power first and then subtract.
Step 2
Why this answer is correct
The correct answer is C. (248). \(a_8=2^8-8=248\). Exam tip: calculate the power first and then subtract.
Step 3
Exam Tip
\(a_8=2^8-8=248\) है। पहले घात निकालें फिर घटाएँ।
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अनुक्रम \(3,8,15,24,\ldots\) का सामान्य पद \(a_n=n^2+2n\) है। कौन सा पद (168) है?
The sequence \(3,8,15,24,\ldots\) has general term \(a_n=n^2+2n\). Which term is (168)?
#sequences
#term-position
#quadratic
#class-9
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A (10)वाँ / (10)th
B (11)वाँ / (11)th
C (12)वाँ / (12)th
D (13)वाँ / (13)th
Explanation opens after your attempt
Correct Answer
C. (12)वाँ / (12)th
Step 1
Concept
\(12^2+2\times12=168\), so it is the (12)th term. Exam tip: substitute options directly into the general term.
Step 2
Why this answer is correct
The correct answer is C. (12)वाँ / (12)th. \(12^2+2\times12=168\), so it is the (12)th term. Exam tip: substitute options directly into the general term.
Step 3
Exam Tip
\(12^2+2\times12=168\) इसलिए यह (12)वाँ पद है। विकल्पों को सीधे सामान्य पद में रखकर जाँचें।
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यदि \(a_n=2n^2+3n\) है तो (300) से छोटे कितने पद होंगे?
If \(a_n=2n^2+3n\), how many terms will be less than (300)?
#sequences
#inequality
#counting-terms
#class-9
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=275\) and \(a_{12}=324\), so (11) terms are less than (300). Exam tip: check the two terms near the boundary.
Step 2
Why this answer is correct
The correct answer is C. (11). \(a_{11}=275\) and \(a_{12}=324\), so (11) terms are less than (300). Exam tip: check the two terms near the boundary.
Step 3
Exam Tip
\(a_{11}=275\) और \(a_{12}=324\) है इसलिए (11) पद (300) से छोटे हैं। सीमा के पास वाले दो पद जरूर जाँचें।
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अनुक्रम (5,12,x,50,85) में क्रमागत अंतर (7,15,23,35) हैं। (x) का मान क्या है?
In the sequence (5,12,x,50,85), the successive differences are (7,15,23,35). What is the value of (x)?
#sequences
#missing-term
#difference-pattern
#class-9
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A (24)
B (27)
C (30)
D (32)
Explanation opens after your attempt
Step 1
Concept
(12+15=27) and (27+23=50). Exam tip: check both sides of a missing term.
Step 2
Why this answer is correct
The correct answer is B. (27). (12+15=27) and (27+23=50). Exam tip: check both sides of a missing term.
Step 3
Exam Tip
(12+15=27) और (27+23=50) है। missing पद के दोनों तरफ जाँच करना सुरक्षित है।
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अनुक्रम (200,188,171,x,122) में अंतरों का क्रम (-12,-17,-22,-27) है। (x) क्या होगा?
In the sequence (200,188,171,x,122), the differences are (-12,-17,-22,-27). What will (x) be?
#sequences
#missing-term
#negative-differences
#class-9
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A (149)
B (151)
C (154)
D (156)
Explanation opens after your attempt
Step 1
Concept
(171-22=149) and (149-27=122). Exam tip: apply negative differences carefully in decreasing sequences.
Step 2
Why this answer is correct
The correct answer is A. (149). (171-22=149) and (149-27=122). Exam tip: apply negative differences carefully in decreasing sequences.
Step 3
Exam Tip
(171-22=149) और (149-27=122) है। घटते अनुक्रम में ऋणात्मक अंतर ध्यान से लगाएँ।
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अनुक्रम \(3,-6,12,-24,\ldots\) में (9)वाँ पद क्या होगा?
What will be the (9)th term in the sequence \(3,-6,12,-24,\ldots\)?
#sequences
#geometric
#alternating-sign
#class-9
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A (384)
B (-384)
C (768)
D (-768)
Explanation opens after your attempt
Step 1
Concept
The general term is (3(-2)^{n-1}), so (a_9=3(-2)8 =768). Exam tip: an even power gives a positive sign.
Step 2
Why this answer is correct
The correct answer is C. (768). The general term is (3(-2)^{n-1}), so (a_9=3(-2)8 =768). Exam tip: an even power gives a positive sign.
Step 3
Exam Tip
सामान्य पद (3(-2)^{n-1}) है इसलिए (a_9=3(-2)8 =768) है। सम घात पर चिह्न धनात्मक होता है।
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अनुक्रम \(2,6,14,30,62,\ldots\) में हर अगला पद पिछले पद का दोगुना करके (2) जोड़ने से मिलता है। अगला पद क्या होगा?
In the sequence \(2,6,14,30,62,\ldots\), each next term is obtained by doubling the previous term and adding (2). What will be the next term?
#sequences
#recurrence
#double-add
#class-9
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A (124)
B (126)
C (128)
D (130)
Explanation opens after your attempt
Step 1
Concept
\(2\times62+2=126\). Exam tip: apply the recurrence rule directly to the last term.
Step 2
Why this answer is correct
The correct answer is B. (126). \(2\times62+2=126\). Exam tip: apply the recurrence rule directly to the last term.
Step 3
Exam Tip
\(2\times62+2=126\) है। पुनरावर्ती नियम को अंतिम पद पर सीधे लागू करें।
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अनुक्रम \(1,2,6,24,120,\ldots\) में अगला पद क्या होगा?
What will be the next term in the sequence \(1,2,6,24,120,\ldots\)?
#sequences
#factorial
#next-term
#class-9
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A (600)
B (720)
C (840)
D (960)
Explanation opens after your attempt
Step 1
Concept
This is the sequence \(1!,2!,3!,4!,5!,\ldots\), so the next term is (6!=720). Exam tip: recognize the multiplication pattern.
Step 2
Why this answer is correct
The correct answer is B. (720). This is the sequence \(1!,2!,3!,4!,5!,\ldots\), so the next term is (6!=720). Exam tip: recognize the multiplication pattern.
Step 3
Exam Tip
यह \(1!,2!,3!,4!,5!,\ldots\) का अनुक्रम है इसलिए अगला पद (6!=720) है। गुणा क्रम को पहचानें।
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अनुक्रम \(2,4,12,48,240,\ldots\) में गुणक क्रम \(2,3,4,5,\ldots\) है। अगला पद क्या होगा?
In the sequence \(2,4,12,48,240,\ldots\), the multiplier pattern is \(2,3,4,5,\ldots\). What will be the next term?
#sequences
#variable-multiplier
#next-term
#class-9
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A (1200)
B (1320)
C (1440)
D (1560)
Explanation opens after your attempt
Step 1
Concept
The next multiplier is (6), so \(240\times6=1440\). Exam tip: write changing multipliers separately.
Step 2
Why this answer is correct
The correct answer is C. (1440). The next multiplier is (6), so \(240\times6=1440\). Exam tip: write changing multipliers separately.
Step 3
Exam Tip
अगला गुणक (6) होगा इसलिए \(240\times6=1440\) है। बदलते गुणक को अलग से लिखें।
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यदि \(a_n=n^3+n^2\) है तो \(a_6-a_4\) का मान क्या होगा?
If \(a_n=n^3+n^2\), what will be the value of \(a_6-a_4\)?
#sequences
#cubic-plus-square
#difference
#class-9
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A (162)
B (168)
C (172)
D (176)
Explanation opens after your attempt
Step 1
Concept
\(a_6=252\) and \(a_4=80\), so the difference is (172). Exam tip: calculate the cube and square parts separately.
Step 2
Why this answer is correct
The correct answer is C. (172). \(a_6=252\) and \(a_4=80\), so the difference is (172). Exam tip: calculate the cube and square parts separately.
Step 3
Exam Tip
\(a_6=252\) और \(a_4=80\) इसलिए अंतर (172) है। घन और वर्ग दोनों अलग-अलग निकालें।
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यदि \(a_n=4n^2-1\) है तो (575) कौन सा पद है?
If \(a_n=4n^2-1\), which term is (575)?
#sequences
#term-position
#square-form
#class-9
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A (10)वाँ / (10)th
B (11)वाँ / (11)th
C (12)वाँ / (12)th
D (13)वाँ / (13)th
Explanation opens after your attempt
Correct Answer
C. (12)वाँ / (12)th
Step 1
Concept
\(4\times12^2-1=575\), so it is the (12)th term. Exam tip: substitute options in the formula to identify the term.
Step 2
Why this answer is correct
The correct answer is C. (12)वाँ / (12)th. \(4\times12^2-1=575\), so it is the (12)th term. Exam tip: substitute options in the formula to identify the term.
Step 3
Exam Tip
\(4\times12^2-1=575\) इसलिए यह (12)वाँ पद है। पद पहचानने के लिए विकल्पों को सूत्र में रखें।
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अनुक्रम \(2,5,10,17,26,\ldots\) के पहले (6) पदों का योग क्या है?
What is the sum of the first (6) terms of the sequence \(2,5,10,17,26,\ldots\)?
#sequences
#sum-of-terms
#squares
#class-9
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A (87)
B (92)
C (97)
D (102)
Explanation opens after your attempt
Step 1
Concept
The first (6) terms are (2,5,10,17,26,37), and their sum is (97). Exam tip: include all required terms in the sum.
Step 2
Why this answer is correct
The correct answer is C. (97). The first (6) terms are (2,5,10,17,26,37), and their sum is (97). Exam tip: include all required terms in the sum.
Step 3
Exam Tip
पहले (6) पद (2,5,10,17,26,37) हैं और उनका योग (97) है। योग में मांगे गए सभी पद शामिल करें।
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यदि \(a_n=pn+q\), \(a_3=17\) और \(a_8=42\) है तो \(a_{12}\) का मान क्या होगा?
If \(a_n=pn+q\), \(a_3=17\) and \(a_8=42\), what will be the value of \(a_{12}\)?
#sequences
#linear-form
#unknown-constants
#class-9
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A (58)
B (60)
C (62)
D (64)
Explanation opens after your attempt
Step 1
Concept
\(p=\frac{42-17}{8-3}=5\) and (q=2). Therefore \(a_{12}=5\times12+2=62\).
Step 2
Why this answer is correct
The correct answer is C. (62). \(p=\frac{42-17}{8-3}=5\) and (q=2). Therefore \(a_{12}=5\times12+2=62\).
Step 3
Exam Tip
\(p=\frac{42-17}{8-3}=5\) और (q=2) है। इसलिए \(a_{12}=5\times12+2=62\) होगा।
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यदि \(a_n=pn^2+q\), \(a_2=14\) और \(a_5=77\) है तो \(a_7\) क्या होगा?
If \(a_n=pn^2+q\), \(a_2=14\) and \(a_5=77\), what will \(a_7\) be?
#sequences
#quadratic-parameters
#nth-term
#class-9
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A (143)
B (147)
C (149)
D (151)
Explanation opens after your attempt
Step 1
Concept
The equations give (p=3) and (q=2). Hence \(a_7=3\times7^2+2=149\).
Step 2
Why this answer is correct
The correct answer is C. (149). The equations give (p=3) and (q=2). Hence \(a_7=3\times7^2+2=149\).
Step 3
Exam Tip
समीकरणों से (p=3) और (q=2) मिलता है। इसलिए \(a_7=3\times7^2+2=149\) है।
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अनुक्रम \(\frac{1}{3},\frac{1}{6},\frac{1}{9},\ldots\) में पहला पद जो \(\frac{1}{50}\) से छोटा है कौन सा है?
In the sequence \(\frac{1}{3},\frac{1}{6},\frac{1}{9},\ldots\), which is the first term less than \(\frac{1}{50}\)?
#sequences
#reciprocal-sequence
#inequality
#class-9
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A (16)वाँ / (16)th
B (17)वाँ / (17)th
C (18)वाँ / (18)th
D (19)वाँ / (19)th
Explanation opens after your attempt
Correct Answer
B. (17)वाँ / (17)th
Step 1
Concept
The general term is \(\frac{1}{3n}\), and \(\frac{1}{51}<\frac{1}{50}\). So the first such term is the (17)th.
Step 2
Why this answer is correct
The correct answer is B. (17)वाँ / (17)th. The general term is \(\frac{1}{3n}\), and \(\frac{1}{51}<\frac{1}{50}\). So the first such term is the (17)th.
Step 3
Exam Tip
सामान्य पद \(\frac{1}{3n}\) है और \(\frac{1}{51}<\frac{1}{50}\) होता है। इसलिए पहला पद (17)वाँ है।
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यदि \(a_n=\frac{2n-1}{3n+1}\) है तो \(a_8\) का सरल मान क्या होगा?
If \(a_n=\frac{2n-1}{3n+1}\), what will be the simplified value of \(a_8\)?
#sequences
#fraction-form
#simplification
#class-9
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A \(\frac{5}{9}\)
B \(\frac{3}{5}\)
C \(\frac{7}{12}\)
D \(\frac{4}{7}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3}{5}\)
Step 1
Concept
\(a_8=\frac{15}{25}=\frac{3}{5}\). Exam tip: simplify the fraction in the final answer.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{5}\). \(a_8=\frac{15}{25}=\frac{3}{5}\). Exam tip: simplify the fraction in the final answer.
Step 3
Exam Tip
\(a_8=\frac{15}{25}=\frac{3}{5}\) है। भिन्न को अंतिम उत्तर में सरल करना न भूलें।
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अनुक्रम \(5,8,13,20,29,\ldots\) का सामान्य पद \(a_n=n^2+4\) है। कौन सा पद (260) है?
The sequence \(5,8,13,20,29,\ldots\) has general term \(a_n=n^2+4\). Which term is (260)?
#sequences
#term-position
#perfect-square
#class-9
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A (14)वाँ / (14)th
B (15)वाँ / (15)th
C (16)वाँ / (16)th
D (17)वाँ / (17)th
Explanation opens after your attempt
Correct Answer
C. (16)वाँ / (16)th
Step 1
Concept
From \(n^2+4=260\), \(n^2=256\) and (n=16). Exam tip: recognizing perfect squares saves time.
Step 2
Why this answer is correct
The correct answer is C. (16)वाँ / (16)th. From \(n^2+4=260\), \(n^2=256\) and (n=16). Exam tip: recognizing perfect squares saves time.
Step 3
Exam Tip
\(n^2+4=260\) से \(n^2=256\) और (n=16) मिलता है। पूर्ण वर्ग पहचानना समय बचाता है।
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एक अनुक्रम \(4,6,9,14,21,32,\ldots\) में क्रमागत अंतर अभाज्य संख्याएँ \(2,3,5,7,11,\ldots\) हैं। अगला पद क्या होगा?
In the sequence \(4,6,9,14,21,32,\ldots\), the successive differences are prime numbers \(2,3,5,7,11,\ldots\). What will be the next term?
#sequences
#prime-differences
#next-term
#class-9
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A (41)
B (43)
C (45)
D (47)
Explanation opens after your attempt
Step 1
Concept
The next prime difference is (13), so (32+13=45). Exam tip: write the pattern of differences separately.
Step 2
Why this answer is correct
The correct answer is C. (45). The next prime difference is (13), so (32+13=45). Exam tip: write the pattern of differences separately.
Step 3
Exam Tip
अगला अभाज्य अंतर (13) है इसलिए (32+13=45) है। अंतर के रूप में दिए गए पैटर्न को अलग लिखें।
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अनुक्रम \(2,5,10,13,26,29,\ldots\) में क्रम है (3) जोड़ना फिर (2) से गुणा करना। अगला पद क्या होगा?
In the sequence \(2,5,10,13,26,29,\ldots\), the pattern is add (3) and then multiply by (2). What will be the next term?
#sequences
#alternating-operation
#next-term
#class-9
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A (32)
B (52)
C (55)
D (58)
Explanation opens after your attempt
Step 1
Concept
After (29), multiplication by (2) is applied, so \(29\times2=58\). Exam tip: identify the next operation in alternating-operation sequences.
Step 2
Why this answer is correct
The correct answer is D. (58). After (29), multiplication by (2) is applied, so \(29\times2=58\). Exam tip: identify the next operation in alternating-operation sequences.
Step 3
Exam Tip
(29) के बाद (2) से गुणा होगा इसलिए \(29\times2=58\) है। वैकल्पिक क्रिया में अगली क्रिया पहचानें।
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अनुक्रम \(3,8,18,38,78,\ldots\) में हर अगला पद पिछले पद का दोगुना करके (2) जोड़ने से मिलता है। अगला पद क्या होगा?
In the sequence \(3,8,18,38,78,\ldots\), each next term is obtained by doubling the previous term and adding (2). What will be the next term?
#sequences
#recurrence
#double-add
#class-9
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A (154)
B (156)
C (158)
D (160)
Explanation opens after your attempt
Step 1
Concept
\(2\times78+2=158\). Exam tip: apply the given recurrence rule to the last term.
Step 2
Why this answer is correct
The correct answer is C. (158). \(2\times78+2=158\). Exam tip: apply the given recurrence rule to the last term.
Step 3
Exam Tip
\(2\times78+2=158\) है। दिए गए पुनरावर्ती नियम को अंतिम पद पर लगाएँ।
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यदि (x+2,2x+1,4x-5) समान अंतर वाले अनुक्रम के लगातार तीन पद हैं तो (x) का मान क्या है?
If (x+2,2x+1,4x-5) are three consecutive terms of a sequence with equal differences, what is the value of (x)?
#sequences
#algebraic-sequence
#equal-difference
#class-9
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Equal differences give (2x+1-(x+2)=4x-5-(2x+1)), so (x=5). Exam tip: set the two consecutive differences equal.
Step 2
Why this answer is correct
The correct answer is C. (5). Equal differences give (2x+1-(x+2)=4x-5-(2x+1)), so (x=5). Exam tip: set the two consecutive differences equal.
Step 3
Exam Tip
बराबर अंतर से (2x+1-(x+2)=4x-5-(2x+1)) मिलता है इसलिए (x=5) है। लगातार तीन पदों में दोनों अंतर बराबर रखें।
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यदि \(a_n=n^2+kn\) और \(a_3=30\) है तो \(a_6\) का मान क्या होगा?
If \(a_n=n^2+kn\) and \(a_3=30\), what will be the value of \(a_6\)?
#sequences
#unknown-coefficient
#nth-term
#class-9
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A (72)
B (76)
C (78)
D (84)
Explanation opens after your attempt
Step 1
Concept
From (9+3k=30), we get (k=7). Therefore \(a_6=36+42=78\).
Step 2
Why this answer is correct
The correct answer is C. (78). From (9+3k=30), we get (k=7). Therefore \(a_6=36+42=78\).
Step 3
Exam Tip
(9+3k=30) से (k=7) मिलता है। इसलिए \(a_6=36+42=78\) है।
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यदि \(a_n=k2^n+1\) और \(a_3=33\) है तो \(a_5\) क्या होगा?
If \(a_n=k2^n+1\) and \(a_3=33\), what will \(a_5\) be?
#sequences
#power-form
#unknown-constant
#class-9
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A (121)
B (125)
C (129)
D (133)
Explanation opens after your attempt
Step 1
Concept
From (8k+1=33), (k=4). Then \(a_5=4\times32+1=129\).
Step 2
Why this answer is correct
The correct answer is C. (129). From (8k+1=33), (k=4). Then \(a_5=4\times32+1=129\).
Step 3
Exam Tip
(8k+1=33) से (k=4) है। फिर \(a_5=4\times32+1=129\) होगा।
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अनुक्रम \(1,4,2,8,4,16,8,32,\ldots\) में (9)वाँ पद क्या होगा?
What will be the (9)th term in the sequence \(1,4,2,8,4,16,8,32,\ldots\)?
#sequences
#alternating-pattern
#term-position
#class-9
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A (12)
B (16)
C (24)
D (64)
Explanation opens after your attempt
Step 1
Concept
Odd positions are \(1,2,4,8,16,\ldots\). Therefore the (9)th term is (16).
Step 2
Why this answer is correct
The correct answer is B. (16). Odd positions are \(1,2,4,8,16,\ldots\). Therefore the (9)th term is (16).
Step 3
Exam Tip
विषम स्थानों पर \(1,2,4,8,16,\ldots\) हैं। इसलिए (9)वाँ पद (16) है।
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अनुक्रम \(2,3,6,11,18,27,\ldots\) में क्रमागत अंतर \(1,3,5,7,9,\ldots\) हैं। अगला पद क्या होगा?
In the sequence \(2,3,6,11,18,27,\ldots\), the successive differences are \(1,3,5,7,9,\ldots\). What will be the next term?
#sequences
#odd-differences
#next-term
#class-9
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A (36)
B (38)
C (40)
D (42)
Explanation opens after your attempt
Step 1
Concept
The next difference is (11), so (27+11=38). Exam tip: recognize the pattern of odd differences.
Step 2
Why this answer is correct
The correct answer is B. (38). The next difference is (11), so (27+11=38). Exam tip: recognize the pattern of odd differences.
Step 3
Exam Tip
अगला अंतर (11) है इसलिए (27+11=38) है। विषम अंतरों के पैटर्न को पहचानें।
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यदि (a_n=n-2 +(-1)^n) है तो \(a_9\) का मान क्या होगा?
If (a_n=n-2 +(-1)^n), what will be the value of \(a_9\)?
#sequences
#alternating-formula
#nth-term
#class-9
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A (78)
B (79)
C (80)
D (82)
Explanation opens after your attempt
Step 1
Concept
((-1)9 =-1), so \(a_9=81-1=80\). Exam tip: check the sign of even and odd powers separately.
Step 2
Why this answer is correct
The correct answer is C. (80). ((-1)9 =-1), so \(a_9=81-1=80\). Exam tip: check the sign of even and odd powers separately.
Step 3
Exam Tip
((-1)9 =-1) है इसलिए \(a_9=81-1=80\) है। सम-विषम घात के चिह्न को अलग से जाँचें।
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अनुक्रम \(75,68,61,54,\ldots\) में कितने पद धनात्मक हैं?
In the sequence \(75,68,61,54,\ldots\), how many terms are positive?
#sequences
#decreasing-arithmetic
#counting-positive
#class-9
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A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
From (75-7(n-1)>0), \(n<\frac{82}{7}\). So (11) terms are positive.
Step 2
Why this answer is correct
The correct answer is B. (11). From (75-7(n-1)>0), \(n<\frac{82}{7}\). So (11) terms are positive.
Step 3
Exam Tip
(75-7(n-1)>0) से \(n<\frac{82}{7}\) मिलता है। इसलिए (11) पद धनात्मक हैं।
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अनुक्रम \(3,9,27,81,\ldots\) के पहले (4) पदों का योग क्या है?
What is the sum of the first (4) terms of the sequence \(3,9,27,81,\ldots\)?
#sequences
#geometric
#sum-of-terms
#class-9
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A (108)
B (114)
C (120)
D (126)
Explanation opens after your attempt
Step 1
Concept
The sum is (3+9+27+81=120). Exam tip: direct addition is safest for a small number of terms.
Step 2
Why this answer is correct
The correct answer is C. (120). The sum is (3+9+27+81=120). Exam tip: direct addition is safest for a small number of terms.
Step 3
Exam Tip
योग (3+9+27+81=120) है। छोटे पदों वाले योग में सीधे जोड़ना सबसे सुरक्षित है।
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अनुक्रम \(1,8,19,34,53,\ldots\) में अगला पद क्या होगा?
What will be the next term in the sequence \(1,8,19,34,53,\ldots\)?
#sequences
#difference-pattern
#next-term
#class-9
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A (72)
B (74)
C (76)
D (78)
Explanation opens after your attempt
Step 1
Concept
The differences are (7,11,15,19), so the next difference is (23). Thus (53+23=76).
Step 2
Why this answer is correct
The correct answer is C. (76). The differences are (7,11,15,19), so the next difference is (23). Thus (53+23=76).
Step 3
Exam Tip
अंतर (7,11,15,19) हैं इसलिए अगला अंतर (23) होगा। (53+23=76) है।
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यदि \(a_n=n^2+2^n\) है तो \(a_4+a_5\) का मान क्या होगा?
If \(a_n=n^2+2^n\), what will be the value of \(a_4+a_5\)?
#sequences
#power-plus-square
#sum
#class-9
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A (81)
B (85)
C (89)
D (93)
Explanation opens after your attempt
Step 1
Concept
\(a_4=32\) and \(a_5=57\), so the sum is (89). Exam tip: calculate the power and square parts separately.
Step 2
Why this answer is correct
The correct answer is C. (89). \(a_4=32\) and \(a_5=57\), so the sum is (89). Exam tip: calculate the power and square parts separately.
Step 3
Exam Tip
\(a_4=32\) और \(a_5=57\) हैं इसलिए योग (89) है। घात और वर्ग को अलग-अलग निकालें।
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यदि (a_n=n(n+3)) है तो कौन सा पद (130) है?
If (a_n=n(n+3)), which term is (130)?
#sequences
#product-form
#term-position
#class-9
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A (8)वाँ / (8)th
B (9)वाँ / (9)th
C (10)वाँ / (10)th
D (11)वाँ / (11)th
Explanation opens after your attempt
Correct Answer
C. (10)वाँ / (10)th
Step 1
Concept
(10(10+3)=130), so it is the (10)th term. Exam tip: test the given options directly in product-form formulas.
Step 2
Why this answer is correct
The correct answer is C. (10)वाँ / (10)th. (10(10+3)=130), so it is the (10)th term. Exam tip: test the given options directly in product-form formulas.
Step 3
Exam Tip
(10(10+3)=130) इसलिए यह (10)वाँ पद है। गुणनफल वाले सूत्र में दिए गए विकल्प सीधे जाँचें।
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अनुक्रम \(7,15,31,63,127,\ldots\) में हर अगला पद पिछले पद का दोगुना करके (1) जोड़ने से मिलता है। अगला पद क्या होगा?
In the sequence \(7,15,31,63,127,\ldots\), each next term is obtained by doubling the previous term and adding (1). What will be the next term?
#sequences
#recurrence
#double-plus-one
#class-9
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A (253)
B (254)
C (255)
D (256)
Explanation opens after your attempt
Step 1
Concept
\(2\times127+1=255\). Exam tip: do not change the order of multiplication and addition in recurrence rules.
Step 2
Why this answer is correct
The correct answer is C. (255). \(2\times127+1=255\). Exam tip: do not change the order of multiplication and addition in recurrence rules.
Step 3
Exam Tip
\(2\times127+1=255\) है। पुनरावर्ती नियम में गुणा और जोड़ का क्रम न बदलें।
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अनुक्रम \(2,4,8,16,32,64,\ldots\) के पहले (6) पदों का औसत क्या है?
What is the average of the first (6) terms of the sequence \(2,4,8,16,32,64,\ldots\)?
#sequences
#average
#geometric
#class-9
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A (19)
B (20)
C (21)
D (22)
Explanation opens after your attempt
Step 1
Concept
The sum of the first (6) terms is (126), and the average is \(\frac{126}{6}=21\). Exam tip: divide the sum by the number of terms.
Step 2
Why this answer is correct
The correct answer is C. (21). The sum of the first (6) terms is (126), and the average is \(\frac{126}{6}=21\). Exam tip: divide the sum by the number of terms.
Step 3
Exam Tip
पहले (6) पदों का योग (126) है और औसत \(\frac{126}{6}=21\) है। औसत में योग को पदों की संख्या से भाग दें।
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अनुक्रम \(1,4,9,16,\ldots\) में \(a_{11}+a_{12}\) का मान क्या होगा?
In the sequence \(1,4,9,16,\ldots\), what will be the value of \(a_{11}+a_{12}\)?
#sequences
#squares
#sum
#class-9
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A (245)
B (255)
C (265)
D (275)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=121\) and \(a_{12}=144\), so the sum is (265). Exam tip: square the term position in a square sequence.
Step 2
Why this answer is correct
The correct answer is C. (265). \(a_{11}=121\) and \(a_{12}=144\), so the sum is (265). Exam tip: square the term position in a square sequence.
Step 3
Exam Tip
\(a_{11}=121\) और \(a_{12}=144\) इसलिए योग (265) है। वर्ग अनुक्रम में पद संख्या का वर्ग लें।
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यदि \(a_n=n!+n\) है तो \(a_5\) का मान क्या होगा?
If \(a_n=n!+n\), what will be the value of \(a_5\)?
#sequences
#factorial-form
#nth-term
#class-9
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A (120)
B (123)
C (125)
D (130)
Explanation opens after your attempt
Step 1
Concept
\(a_5=5!+5=120+5=125\). Exam tip: calculate the factorial first and then add (n).
Step 2
Why this answer is correct
The correct answer is C. (125). \(a_5=5!+5=120+5=125\). Exam tip: calculate the factorial first and then add (n).
Step 3
Exam Tip
\(a_5=5!+5=120+5=125\) है। फैक्टोरियल निकालकर अंत में (n) जोड़ें।
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यदि \(a_n=\frac{n^2+1}{n}\) है तो \(a_5\) का मान क्या होगा?
If \(a_n=\frac{n^2+1}{n}\), what will be the value of \(a_5\)?
#sequences
#fractional-form
#nth-term
#class-9
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A \(\frac{24}{5}\)
B \(\frac{25}{5}\)
C \(\frac{26}{5}\)
D \(\frac{27}{5}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{26}{5}\)
Step 1
Concept
\(a_5=\frac{25+1}{5}=\frac{26}{5}\). Exam tip: complete the numerator first in fractional formulas.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{26}{5}\). \(a_5=\frac{25+1}{5}=\frac{26}{5}\). Exam tip: complete the numerator first in fractional formulas.
Step 3
Exam Tip
\(a_5=\frac{25+1}{5}=\frac{26}{5}\) है। भिन्न वाले सूत्र में अंश पहले पूरा करें।
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यदि \(a_n=n^2+2n\) है तो पहला पद जो (100) से बड़ा है कौन सा होगा?
If \(a_n=n^2+2n\), which is the first term greater than (100)?
#sequences
#inequality
#first-term
#class-9
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A (9)वाँ / (9)th
B (10)वाँ / (10)th
C (11)वाँ / (11)th
D (12)वाँ / (12)th
Explanation opens after your attempt
Correct Answer
B. (10)वाँ / (10)th
Step 1
Concept
\(a_9=99\) and \(a_{10}=120\), so the first greater term is the (10)th. Exam tip: check terms on both sides of the boundary.
Step 2
Why this answer is correct
The correct answer is B. (10)वाँ / (10)th. \(a_9=99\) and \(a_{10}=120\), so the first greater term is the (10)th. Exam tip: check terms on both sides of the boundary.
Step 3
Exam Tip
\(a_9=99\) और \(a_{10}=120\) है इसलिए पहला बड़ा पद (10)वाँ है। सीमा के दोनों तरफ के पद जाँचें।
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यदि (a_n=5n+(-1)^n) है तो \(a_{10}-a_9\) का मान क्या होगा?
If (a_n=5n+(-1)^n), what will be the value of \(a_{10}-a_9\)?
#sequences
#alternating-formula
#difference
#class-9
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A (5)
B (6)
C (7)
D (9)
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Step 1
Concept
\(a_{10}=51\) and \(a_9=44\), so the difference is (7). Exam tip: check the sign-changing part separately.
Step 2
Why this answer is correct
The correct answer is C. (7). \(a_{10}=51\) and \(a_9=44\), so the difference is (7). Exam tip: check the sign-changing part separately.
Step 3
Exam Tip
\(a_{10}=51\) और \(a_9=44\) है इसलिए अंतर (7) है। चिह्न बदलने वाले भाग को अलग से जाँचें।
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यदि \(a_1=2\) और \(a_{n+1}=2a_n+n^2\) है तो \(a_4\) क्या होगा?
If \(a_1=2\) and \(a_{n+1}=2a_n+n^2\), what will \(a_4\) be?
#sequences
#recursive-square
#nth-term
#class-9
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A (33)
B (35)
C (37)
D (39)
Explanation opens after your attempt
Step 1
Concept
The terms are (2,5,14,37). Exam tip: the value of \(n^2\) changes at every recursive step.
Step 2
Why this answer is correct
The correct answer is C. (37). The terms are (2,5,14,37). Exam tip: the value of \(n^2\) changes at every recursive step.
Step 3
Exam Tip
पद (2,5,14,37) मिलते हैं। पुनरावर्ती नियम में \(n^2\) का मान हर चरण बदलता है।
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एक समान अंतर वाले अनुक्रम में \(a_4=29\) और \(a_{10}=65\) है। \(a_1\) का मान क्या होगा?
In a sequence with equal differences, \(a_4=29\) and \(a_{10}=65\). What is the value of \(a_1\)?
#sequences
#equal-difference
#first-term
#class-9
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
The sum of six differences is (65-29=36), so one difference is (6). Thus \(a_1=29-3\times6=11\).
Step 2
Why this answer is correct
The correct answer is C. (11). The sum of six differences is (65-29=36), so one difference is (6). Thus \(a_1=29-3\times6=11\).
Step 3
Exam Tip
छह अंतरों का योग (65-29=36) है इसलिए एक अंतर (6) है। \(a_1=29-3\times6=11\) होगा।
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अनुक्रम \(1,3,6,10,15,\ldots\) में पहला पद जो (200) से बड़ा है कौन सा है?
In the sequence \(1,3,6,10,15,\ldots\), which is the first term greater than (200)?
#sequences
#triangular-numbers
#inequality
#class-9
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A (18)वाँ / (18)th
B (19)वाँ / (19)th
C (20)वाँ / (20)th
D (21)वाँ / (21)th
Explanation opens after your attempt
Correct Answer
C. (20)वाँ / (20)th
Step 1
Concept
\(T_{19}=190\) and \(T_{20}=210\), so the first greater term is the (20)th. Exam tip: strict inequality does not include equality.
Step 2
Why this answer is correct
The correct answer is C. (20)वाँ / (20)th. \(T_{19}=190\) and \(T_{20}=210\), so the first greater term is the (20)th. Exam tip: strict inequality does not include equality.
Step 3
Exam Tip
\(T_{19}=190\) और \(T_{20}=210\) है इसलिए पहला बड़ा पद (20)वाँ है। सख्त असमानता में बराबरी शामिल नहीं होती।
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