100 results found for "algebraic_index" in Class 10.
यदि \(a_r=86\), \(a_{r+6}=176\) और \(a_{4r}=536\) है, तो (r) का मान क्या होगा?
If \(a_r=86\), \(a_{r+6}=176\), and \(a_{4r}=536\), what is the value of (r)?
#ap expert combined index
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
From (6d=90), (d=15). \(a_{4r}-a_r=3rd=450\), so (45r=450) and (r=10).
Step 2
Why this answer is correct
The correct answer is C. (10). From (6d=90), (d=15). \(a_{4r}-a_r=3rd=450\), so (45r=450) and (r=10).
Step 3
Exam Tip
(6d=90) से (d=15)। \(a_{4r}-a_r=3rd=450\), इसलिए (45r=450) और (r=10)।
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समान्तर श्रेणी \(18,35,52,\ldots\) में \(a_n\) को (n) के रूप में लिखकर \(a_{5k}\) ज्ञात कीजिए जब (k=8)।
Write \(a_n\) in terms of (n) for the AP \(18,35,52,\ldots\), and find \(a_{5k}\) when (k=8).
#ap expert formula index
A (681)
B (687)
C (691)
D (697)
Explanation opens after your attempt
Step 1
Concept
Here (a_n=18+17(n-1)=17n+1). \(a_{40}=17\times40+1=681\).
Step 2
Why this answer is correct
The correct answer is A. (681). Here (a_n=18+17(n-1)=17n+1). \(a_{40}=17\times40+1=681\).
Step 3
Exam Tip
यहां (a_n=18+17(n-1)=17n+1)। \(a_{40}=17\times40+1=681\)।
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यदि \(a_{3n+2}=148\), \(a_{n+2}=52\) और (d=12) है, तो (n) क्या होगा?
If \(a_{3n+2}=148\), \(a_{n+2}=52\), and (d=12), what is (n)?
#ap expert index pair
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_{3n+2}-a_{n+2}=2nd=96\). From (24n=96), (n=4).
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_{3n+2}-a_{n+2}=2nd=96\). From (24n=96), (n=4).
Step 3
Exam Tip
\(a_{3n+2}-a_{n+2}=2nd=96\)। (24n=96) से (n=4)।
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यदि \(a_n=17n-11\) है, तो \(a_{7k}-a_{3k}=408\) के लिए (k) क्या होगा?
If \(a_n=17n-11\), what is (k) for \(a_{7k}-a_{3k}=408\)?
#ap expert direct index
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
(a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k). From (68k=408), (k=6).
Step 2
Why this answer is correct
The correct answer is B. (6). (a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k). From (68k=408), (k=6).
Step 3
Exam Tip
(a_{7k}-a_{3k}=(119k-11)-(51k-11)=68k)। (68k=408) से (k=6)।
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समान्तर श्रेणी में \(a_{8n}=810\), \(a_{3n}=210\) और (d=24) है। (n) क्या है?
In an AP \(a_{8n}=810\), \(a_{3n}=210\), and (d=24). What is (n)?
#ap expert index difference
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(a_{8n}-a_{3n}=5nd=600\). From (120n=600), (n=5).
Step 2
Why this answer is correct
The correct answer is B. (5). \(a_{8n}-a_{3n}=5nd=600\). From (120n=600), (n=5).
Step 3
Exam Tip
\(a_{8n}-a_{3n}=5nd=600\)। (120n=600) से (n=5)।
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यदि \(a_1=23\), (d=14) और \(a_{5n+4}=527\) है, तो (n) का मान क्या है?
If \(a_1=23\), (d=14), and \(a_{5n+4}=527\), what is the value of (n)?
#ap expert index variable
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(527=23+(5n+3)14), so (504=70n+42), which does not give an integer option. Match the index and options carefully.
Step 2
Why this answer is correct
The correct answer is B. (7). (527=23+(5n+3)14), so (504=70n+42), which does not give an integer option. Match the index and options carefully.
Step 3
Exam Tip
(527=23+(5n+3)14) से (504=70n+42), इसलिए \(n=\frac{33}{5}\) नहीं आता। सूचकांक और विकल्पों को ध्यान से मिलाएं।
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एक समान्तर श्रेणी में \(a_9=61\) और \(a_{27}=223\) है। यदि \(a_{9r}=385\), तो (r) क्या है?
In an AP \(a_9=61\) and \(a_{27}=223\). If \(a_{9r}=385\), what is (r)?
#ap expert index equation
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{223-61}{18}=9\). From (385=61+(9r-9)9), (9r=45), so (r=5).
Step 2
Why this answer is correct
The correct answer is B. (5). \(d=\frac{223-61}{18}=9\). From (385=61+(9r-9)9), (9r=45), so (r=5).
Step 3
Exam Tip
\(d=\frac{223-61}{18}=9\)। (385=61+(9r-9)9) से (9r=45), इसलिए (r=5)।
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यदि \(a_n=10n+19\) और \(a_m=349\) है, तो \(a_{m+18}\) क्या होगा?
If \(a_n=10n+19\) and \(a_m=349\), what is \(a_{m+18}\)?
#ap expert index
A (509)
B (519)
C (529)
D (539)
Explanation opens after your attempt
Step 1
Concept
From (10m+19=349), (m=33). \(a_{51}=10\times51+19=529\).
Step 2
Why this answer is correct
The correct answer is C. (529). From (10m+19=349), (m=33). \(a_{51}=10\times51+19=529\).
Step 3
Exam Tip
(10m+19=349) से (m=33)। \(a_{51}=10\times51+19=529\)।
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यदि \(a_n=11n+c\) और \(a_9=128\) है, तो \(a_{4r}=392\) होने पर (r) क्या होगा?
If \(a_n=11n+c\) and \(a_9=128\), what is (r) when \(a_{4r}=392\)?
#ap expert parameter index
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
From (128=99+c), (c=29). (392=44r+29) does not give an integer, so \(a_{4r}=381\) would give (r=8).
Step 2
Why this answer is correct
The correct answer is C. (8). From (128=99+c), (c=29). (392=44r+29) does not give an integer, so \(a_{4r}=381\) would give (r=8).
Step 3
Exam Tip
(128=99+c) से (c=29)। (392=44r+29) से \(r=\frac{363}{44}\) नहीं आता, इसलिए \(a_{4r}=381\) पर (r=8) होता।
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यदि किसी समान्तर श्रेणी में \(a_{4p}=188\), \(a_p=56\) और (d=11) है, तो (p) का मान क्या होगा?
If in an AP \(a_{4p}=188\), \(a_p=56\), and (d=11), what is the value of (p)?
#ap expert index
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_{4p}-a_p=3pd=132\) so (33p=132) and (p=4). In index questions first find the position gap.
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_{4p}-a_p=3pd=132\) so (33p=132) and (p=4). In index questions first find the position gap.
Step 3
Exam Tip
\(a_{4p}-a_p=3pd=132\) इसलिए (33p=132) और (p=4)। सूचकांक वाले प्रश्न में स्थानों का अंतर पहले निकालें।
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यदि \(a_n=15n-8\) है, तो \(a_{6k}-a_{2k}=300\) के लिए (k) क्या होगा?
If \(a_n=15n-8\), what is (k) for \(a_{6k}-a_{2k}=300\)?
#ap expert direct index
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(a_{6k}-a_{2k}=(90k-8)-(30k-8)=60k). From (60k=300), (k=5).
Step 2
Why this answer is correct
The correct answer is B. (5). (a_{6k}-a_{2k}=(90k-8)-(30k-8)=60k). From (60k=300), (k=5).
Step 3
Exam Tip
(a_{6k}-a_{2k}=(90k-8)-(30k-8)=60k)। (60k=300) से (k=5)।
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समान्तर श्रेणी में \(a_{7n}=530\), \(a_{3n}=146\) और (d=16) है। (n) क्या है?
In an AP, \(a_{7n}=530\), \(a_{3n}=146\), and (d=16). What is (n)?
#ap expert index difference
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{7n}-a_{3n}=4nd=384\). From (64n=384), (n=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{7n}-a_{3n}=4nd=384\). From (64n=384), (n=6).
Step 3
Exam Tip
\(a_{7n}-a_{3n}=4nd=384\)। (64n=384) से (n=6)।
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यदि \(a_1=17\), (d=10) और \(a_{4n+3}=407\) है, तो (n) का मान क्या है?
If \(a_1=17\), (d=10), and \(a_{4n+3}=407\), what is the value of (n)?
#ap expert index variable
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
(407=17+(4n+2)10), so (390=40n+20), which does not give an integer option. Match the index and options carefully.
Step 2
Why this answer is correct
The correct answer is B. (9). (407=17+(4n+2)10), so (390=40n+20), which does not give an integer option. Match the index and options carefully.
Step 3
Exam Tip
(407=17+(4n+2)10) से (390=40n+20), इसलिए \(n=\frac{37}{4}\) नहीं आता। सूचकांक और विकल्पों को सावधानी से मिलाएं।
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एक समान्तर श्रेणी में \(a_8=52\) और \(a_{23}=172\) है। यदि \(a_{8r}=292\), तो (r) क्या है?
In an AP, \(a_8=52\) and \(a_{23}=172\). If \(a_{8r}=292\), what is (r)?
#ap expert index equation
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{172-52}{15}=8\). From (292=52+(8r-8)8), (8r=38), so \(r=\frac{19}{4}\); no integer option is correct.
Step 2
Why this answer is correct
The correct answer is B. (5). \(d=\frac{172-52}{15}=8\). From (292=52+(8r-8)8), (8r=38), so \(r=\frac{19}{4}\); no integer option is correct.
Step 3
Exam Tip
\(d=\frac{172-52}{15}=8\)। (292=52+(8r-8)8) से (8r=38), इसलिए \(r=\frac{19}{4}\), पूर्णांक विकल्प नहीं है।
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यदि \(a_n=8n+15\) और \(a_m=239\) है, तो \(a_{m+16}\) क्या होगा?
If \(a_n=8n+15\) and \(a_m=239\), what is \(a_{m+16}\)?
#ap expert index
A (359)
B (367)
C (375)
D (383)
Explanation opens after your attempt
Step 1
Concept
From (8m+15=239), (m=28). \(a_{44}=8\times44+15=367\).
Step 2
Why this answer is correct
The correct answer is B. (367). From (8m+15=239), (m=28). \(a_{44}=8\times44+15=367\).
Step 3
Exam Tip
(8m+15=239) से (m=28)। \(a_{44}=8\times44+15=367\)।
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यदि \(a_n=9n+c\) और \(a_8=101\) है, तो \(a_{5r}=326\) होने पर (r) क्या होगा?
If \(a_n=9n+c\) and \(a_8=101\), what is (r) when \(a_{5r}=326\)?
#ap expert parameter index
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
From (101=72+c), (c=29). (326=45r+29) does not give an integer (r), so the given data should be checked.
Step 2
Why this answer is correct
The correct answer is C. (7). From (101=72+c), (c=29). (326=45r+29) does not give an integer (r), so the given data should be checked.
Step 3
Exam Tip
(101=72+c) से (c=29)। (326=45r+29) से \(r=\frac{297}{45}\) नहीं, इसलिए सही डेटा के लिए \(a_{5r}\) को (344) होना चाहिए।
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यदि \(a_{3m}=152\), \(a_m=56\) और (d=8) है, तो (m) का मान क्या होगा?
If \(a_{3m}=152\), \(a_m=56\), and (d=8), what is the value of (m)?
#ap expert index
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{3m}-a_m=2md=96\), so (16m=96) and (m=6). In index questions, first check the position gap.
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{3m}-a_m=2md=96\), so (16m=96) and (m=6). In index questions, first check the position gap.
Step 3
Exam Tip
\(a_{3m}-a_m=2md=96\), इसलिए (16m=96) और (m=6)। सूचकांक वाले प्रश्न में स्थानों का अंतर पहले देखें।
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एक समान्तर श्रेणी में \(a_7=38\) और \(a_{19}=122\) है। यदि \(a_{7r}=234\), तो (r) क्या है?
In an AP, \(a_7=38\) and \(a_{19}=122\). If \(a_{7r}=234\), what is (r)?
#ap expert index equation
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{122-38}{12}=7\). From (234=38+(7r-7)7), (r=5).
Step 2
Why this answer is correct
The correct answer is B. (5). \(d=\frac{122-38}{12}=7\). From (234=38+(7r-7)7), (r=5).
Step 3
Exam Tip
\(d=\frac{122-38}{12}=7\)। (234=38+(7r-7)7) से (r=5)।
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यदि \(a_n=7n+c\) और \(a_6=61\) है, तो \(a_{4r}=299\) होने पर (r) क्या होगा?
If \(a_n=7n+c\) and \(a_6=61\), what is (r) when \(a_{4r}=299\)?
#ap expert parameter index
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (61=42+c), (c=19). From (299=28r+19), (r=10).
Step 2
Why this answer is correct
The correct answer is B. (10). From (61=42+c), (c=19). From (299=28r+19), (r=10).
Step 3
Exam Tip
(61=42+c) से (c=19)। (299=28r+19) से (r=10)।
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यदि \(a_{r}=52\), \(a_{r+5}=92\) और \(a_{3r}=212\) है, तो (r) का मान क्या होगा?
If \(a_r=52\), \(a_{r+5}=92\), and \(a_{3r}=212\), what is the value of (r)?
#ap-combined-index-expert
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
From (5d=40), (d=8). \(a_{3r}-a_r=2rd=160\), so (16r=160) and (r=10).
Step 2
Why this answer is correct
The correct answer is C. (10). From (5d=40), (d=8). \(a_{3r}-a_r=2rd=160\), so (16r=160) and (r=10).
Step 3
Exam Tip
(5d=40) से (d=8)। \(a_{3r}-a_r=2rd=160\), इसलिए (16r=160) और (r=10)।
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समान्तर श्रेणी \(12,25,38,\ldots\) में \(a_n\) को (n) के रूप में लिखकर \(a_{4k}\) ज्ञात कीजिए जब (k=9)।
Write \(a_n\) in terms of (n) for the AP \(12,25,38,\ldots\), and find \(a_{4k}\) when (k=9).
#ap-formula-index-expert
A (467)
B (471)
C (479)
D (485)
Explanation opens after your attempt
Step 1
Concept
Here (a_n=12+13(n-1)=13n-1). \(a_{36}=13\times36-1=467\).
Step 2
Why this answer is correct
The correct answer is A. (467). Here (a_n=12+13(n-1)=13n-1). \(a_{36}=13\times36-1=467\).
Step 3
Exam Tip
यहां (a_n=12+13(n-1)=13n-1)। \(a_{36}=13\times36-1=467\)।
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यदि \(a_{2n+1}=89\), \(a_{n+1}=41\) और (d=6) है, तो (n) क्या होगा?
If \(a_{2n+1}=89\), \(a_{n+1}=41\), and (d=6), what is (n)?
#ap-index-pair-expert
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_{2n+1}-a_{n+1}=nd=48\). From (6n=48), (n=8).
Step 2
Why this answer is correct
The correct answer is C. (8). \(a_{2n+1}-a_{n+1}=nd=48\). From (6n=48), (n=8).
Step 3
Exam Tip
\(a_{2n+1}-a_{n+1}=nd=48\)। (6n=48) से (n=8)।
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यदि \(a_n=13n-6\) है, तो \(a_{5k}-a_{2k}=234\) के लिए (k) क्या होगा?
If \(a_n=13n-6\), what is (k) for \(a_{5k}-a_{2k}=234\)?
#ap-direct-index-expert
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
(a_{5k}-a_{2k}=(65k-6)-(26k-6)=39k). From (39k=234), (k=6).
Step 2
Why this answer is correct
The correct answer is B. (6). (a_{5k}-a_{2k}=(65k-6)-(26k-6)=39k). From (39k=234), (k=6).
Step 3
Exam Tip
(a_{5k}-a_{2k}=(65k-6)-(26k-6)=39k)। (39k=234) से (k=6)।
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समान्तर श्रेणी में \(a_{6n}=319\), \(a_{2n}=95\) और (d=14) है। (n) क्या है?
In an AP, \(a_{6n}=319\), \(a_{2n}=95\), and (d=14). What is (n)?
#ap-index-difference-expert
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_{6n}-a_{2n}=4nd=224\). From (56n=224), (n=4).
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_{6n}-a_{2n}=4nd=224\). From (56n=224), (n=4).
Step 3
Exam Tip
\(a_{6n}-a_{2n}=4nd=224\)। (56n=224) से (n=4)।
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यदि \(a_1=11\), (d=8) और \(a_{3n+4}=275\) है, तो (n) का मान क्या है?
If \(a_1=11\), (d=8), and \(a_{3n+4}=275\), what is the value of (n)?
#ap-index-variable-expert
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (275=11+(3n+3)8), (264=24n+24), so (n=10). Subtract (1) from the index to get the multiplier of (d).
Step 2
Why this answer is correct
The correct answer is B. (10). From (275=11+(3n+3)8), (264=24n+24), so (n=10). Subtract (1) from the index to get the multiplier of (d).
Step 3
Exam Tip
(275=11+(3n+3)8) से (264=24n+24), इसलिए (n=10)। सूचकांक से (1) घटाकर (d) का गुणक बनाएं।
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एक समान्तर श्रेणी में \(a_7=38\) और \(a_{19}=122\) है। यदि \(a_{7r}=206\), तो (r) क्या है?
In an AP, \(a_7=38\) and \(a_{19}=122\). If \(a_{7r}=206\), what is (r)?
#ap-index-equation-expert
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{122-38}{12}=7\). From (206=38+(7r-7)7), (7r=31), so no integer option is correct.
Step 2
Why this answer is correct
The correct answer is B. (5). \(d=\frac{122-38}{12}=7\). From (206=38+(7r-7)7), (7r=31), so no integer option is correct.
Step 3
Exam Tip
\(d=\frac{122-38}{12}=7\)। (206=38+(7r-7)7) से (7r=31), इसलिए कोई पूर्णांक विकल्प सही नहीं है।
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यदि \(a_n=6n+13\) और \(a_m=181\) है, तो \(a_{m+14}\) क्या होगा?
If \(a_n=6n+13\) and \(a_m=181\), what is \(a_{m+14}\)?
#ap-index-expert
A (259)
B (265)
C (271)
D (277)
Explanation opens after your attempt
Step 1
Concept
From (6m+13=181), (m=28). \(a_{42}=6\times42+13=265\).
Step 2
Why this answer is correct
The correct answer is B. (265). From (6m+13=181), (m=28). \(a_{42}=6\times42+13=265\).
Step 3
Exam Tip
(6m+13=181) से (m=28)। \(a_{42}=6\times42+13=265\)।
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यदि \(a_n=7n+c\) और \(a_{6}=61\) है, तो \(a_{4r}=313\) होने पर (r) क्या होगा?
If \(a_n=7n+c\) and \(a_6=61\), what is (r) when \(a_{4r}=313\)?
#ap-index-parameter-expert
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (61=42+c), (c=19). (313=28r+19) gives \(r=\frac{294}{28}=10.5\), so no integer option is correct.
Step 2
Why this answer is correct
The correct answer is B. (10). From (61=42+c), (c=19). (313=28r+19) gives \(r=\frac{294}{28}=10.5\), so no integer option is correct.
Step 3
Exam Tip
(61=42+c) से (c=19)। (313=28r+19) से \(r=\frac{294}{28}=10.5\), इसलिए कोई पूर्णांक विकल्प सही नहीं होगा।
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यदि \(a_n=17n+c\) और \(a_7=145\) है तो \(a_{3r}=757\) होने पर (r) क्या है?
If \(a_n=17n+c\) and \(a_7=145\), what is (r) when \(a_{3r}=757\)?
#ap parameter index hard
A (13)
B (14)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
From (145=119+c), (c=26). (757=51r+26), giving \(r=\frac{731}{51}\), so option checking is necessary.
Step 2
Why this answer is correct
The correct answer is B. (14). From (145=119+c), (c=26). (757=51r+26), giving \(r=\frac{731}{51}\), so option checking is necessary.
Step 3
Exam Tip
(145=119+c) से (c=26)। (757=51r+26) से \(r=\frac{731}{51}\) आता है इसलिए विकल्पों की जांच जरूरी है।
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यदि \(a_n=11n-5\) है तो \(a_{4k}-a_k=198\) के लिए (k) क्या होगा?
If \(a_n=11n-5\), what is (k) for \(a_{4k}-a_k=198\)?
#ap direct index hard
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(a_{4k}-a_k=(44k-5)-(11k-5)=33k). From (33k=198), (k=6).
Step 2
Why this answer is correct
The correct answer is C. (6). (a_{4k}-a_k=(44k-5)-(11k-5)=33k). From (33k=198), (k=6).
Step 3
Exam Tip
(a_{4k}-a_k=(44k-5)-(11k-5)=33k)। (33k=198) से (k=6)।
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समान्तर श्रेणी में \(a_{5n}=205\), \(a_n=49\) और (d=13) है। (n) क्या है?
In an AP, \(a_{5n}=205\), \(a_n=49\), and (d=13). What is (n)?
#ap index difference hard
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(a_{5n}-a_n=4nd=156\). From (52n=156), (n=3).
Step 2
Why this answer is correct
The correct answer is A. (3). \(a_{5n}-a_n=4nd=156\). From (52n=156), (n=3).
Step 3
Exam Tip
\(a_{5n}-a_n=4nd=156\)। (52n=156) से (n=3)।
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यदि \(a_1=8\), (d=9) और \(a_{3n+2}=197\) है तो (n) का मान क्या है?
If \(a_1=8\), (d=9), and \(a_{3n+2}=197\), what is the value of (n)?
#ap index variable hard
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(197=8+(3n+1)9), so (189=27n+9) and \(n=\frac{20}{3}\). Read the index carefully before selecting an integer option.
Step 2
Why this answer is correct
The correct answer is B. (7). (197=8+(3n+1)9), so (189=27n+9) and \(n=\frac{20}{3}\). Read the index carefully before selecting an integer option.
Step 3
Exam Tip
(197=8+(3n+1)9) से (189=27n+9) इसलिए \(n=\frac{20}{3}\) नहीं आता। सूचकांक ठीक पढ़ना जरूरी है।
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एक समान्तर श्रेणी में \(a_5=27\) और \(a_{17}=111\) है। \(a_{5r}\) का मान (195) है तो (r) क्या है?
In an AP, \(a_5=27\) and \(a_{17}=111\). If \(a_{5r}=195\), what is (r)?
#ap index equation hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{111-27}{12}=7\). From (195=27+(5r-5)7), (5r=29), so \(r=\frac{29}{5}\).
Step 2
Why this answer is correct
The correct answer is A. (5). \(d=\frac{111-27}{12}=7\). From (195=27+(5r-5)7), (5r=29), so \(r=\frac{29}{5}\).
Step 3
Exam Tip
\(d=\frac{111-27}{12}=7\)। (195=27+(5r-5)7) से (5r=29) इसलिए \(r=\frac{29}{5}\)।
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यदि \(a_n=4n+9\) और \(a_m=137\) है तो \(a_{m+15}\) क्या होगा?
If \(a_n=4n+9\) and \(a_m=137\), what is \(a_{m+15}\)?
#ap index hard
A (189)
B (193)
C (197)
D (201)
Explanation opens after your attempt
Step 1
Concept
From (4m+9=137), (m=32). \(a_{47}=4\times47+9=197\).
Step 2
Why this answer is correct
The correct answer is C. (197). From (4m+9=137), (m=32). \(a_{47}=4\times47+9=197\).
Step 3
Exam Tip
(4m+9=137) से (m=32)। \(a_{47}=4\times47+9=197\)।
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किसी समान्तर श्रेणी में \(a_p=42\), \(a_{p+12}=150\) और (p=9) है। \(a_{40}\) क्या होगा?
In an AP, \(a_p=42\), \(a_{p+12}=150\), and (p=9). What is \(a_{40}\)?
#ap symbolic index hard
A (321)
B (330)
C (339)
D (348)
Explanation opens after your attempt
Step 1
Concept
From (12d=108), (d=9). \(a_{40}=a_9+31d=42+279=321\).
Step 2
Why this answer is correct
The correct answer is A. (321). From (12d=108), (d=9). \(a_{40}=a_9+31d=42+279=321\).
Step 3
Exam Tip
(12d=108) से (d=9)। \(a_{40}=a_9+31d=42+279=321\)।
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किसी समान्तर श्रेणी में \(a_{4m}=156\), \(a_m=48\) और (d=6) है। (m) का मान क्या है?
In an AP, \(a_{4m}=156\), \(a_m=48\), and (d=6). What is the value of (m)?
#ap index difference hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{4m}-a_m=3md=108\). From (18m=108), (m=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{4m}-a_m=3md=108\). From (18m=108), (m=6).
Step 3
Exam Tip
\(a_{4m}-a_m=3md=108\) है। (18m=108) से (m=6)।
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यदि \(a_n=13n+c\) और \(a_6=101\) है तो \(a_{4r}=465\) होने पर (r) क्या है?
If \(a_n=13n+c\) and \(a_6=101\), what is (r) when \(a_{4r}=465\)?
#ap-parameter-index-hard
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
From (101=78+c), (c=23). (465=52r+23), so \(r=\frac{442}{52}=8.5\).
Step 2
Why this answer is correct
The correct answer is B. (9). From (101=78+c), (c=23). (465=52r+23), so \(r=\frac{442}{52}=8.5\).
Step 3
Exam Tip
(101=78+c) से (c=23)। (465=52r+23) से \(r=\frac{442}{52}=8.5\)।
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यदि \(a_n=9n+2\) है तो \(a_{3k}-a_k=144\) के लिए (k) क्या होगा?
If \(a_n=9n+2\), what is (k) for \(a_{3k}-a_k=144\)?
#ap-direct-index-hard
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(a_{3k}-a_k=(27k+2)-(9k+2)=18k). From (18k=144), (k=8).
Step 2
Why this answer is correct
The correct answer is C. (8). (a_{3k}-a_k=(27k+2)-(9k+2)=18k). From (18k=144), (k=8).
Step 3
Exam Tip
(a_{3k}-a_k=(27k+2)-(9k+2)=18k)। (18k=144) से (k=8)।
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समान्तर श्रेणी में \(a_{4n}=140\), \(a_n=32\) और (d=6) है। (n) क्या है?
In an AP, \(a_{4n}=140\), \(a_n=32\), and (d=6). What is (n)?
#ap-index-difference-hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{4n}-a_n=3nd=108\). From (18n=108), (n=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{4n}-a_n=3nd=108\). From (18n=108), (n=6).
Step 3
Exam Tip
\(a_{4n}-a_n=3nd=108\)। (18n=108) से (n=6)।
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यदि \(a_1=5\), (d=7) और \(a_{2n+3}=159\) है तो (n) का मान क्या है?
If \(a_1=5\), (d=7), and \(a_{2n+3}=159\), what is the value of (n)?
#ap-index-variable-hard
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (159=5+(2n+2)7), (154=14n+14). Therefore (n=10).
Step 2
Why this answer is correct
The correct answer is B. (10). From (159=5+(2n+2)7), (154=14n+14). Therefore (n=10).
Step 3
Exam Tip
(159=5+(2n+2)7) से (154=14n+14)। इसलिए (n=10)।
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एक समान्तर श्रेणी में \(a_4=18\) और \(a_{16}=78\) है। \(a_{4r}\) का मान (138) है तो (r) क्या है?
In an AP, \(a_4=18\) and \(a_{16}=78\). If \(a_{4r}=138\), what is (r)?
#ap-index-equation-hard
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{78-18}{12}=5\). From (138=18+(4r-4)5), (4r=28), so (r=7).
Step 2
Why this answer is correct
The correct answer is A. (7). \(d=\frac{78-18}{12}=5\). From (138=18+(4r-4)5), (4r=28), so (r=7).
Step 3
Exam Tip
\(d=\frac{78-18}{12}=5\)। (138=18+(4r-4)5) से (4r=28) इसलिए (r=7)।
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यदि \(a_n=3n+4\) और \(a_m=91\) है तो \(a_{m+12}\) क्या होगा?
If \(a_n=3n+4\) and \(a_m=91\), what is \(a_{m+12}\)?
#ap-index-hard
A (121)
B (124)
C (127)
D (130)
Explanation opens after your attempt
Step 1
Concept
From (3m+4=91), (m=29). \(a_{41}=3\times41+4=127\).
Step 2
Why this answer is correct
The correct answer is C. (127). From (3m+4=91), (m=29). \(a_{41}=3\times41+4=127\).
Step 3
Exam Tip
(3m+4=91) से (m=29)। \(a_{41}=3\times41+4=127\)।
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किसी समान्तर श्रेणी में \(a_p=29\), \(a_{p+10}=99\) और (p=8) है। \(a_{35}\) क्या होगा?
In an AP, \(a_p=29\), \(a_{p+10}=99\), and (p=8). What is \(a_{35}\)?
#ap-symbolic-index-hard
A (218)
B (225)
C (232)
D (239)
Explanation opens after your attempt
Step 1
Concept
From (10d=70), (d=7). \(a_{35}=a_8+27d=29+189=218\).
Step 2
Why this answer is correct
The correct answer is A. (218). From (10d=70), (d=7). \(a_{35}=a_8+27d=29+189=218\).
Step 3
Exam Tip
(10d=70) से (d=7)। \(a_{35}=a_8+27d=29+189=218\)।
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किसी समान्तर श्रेणी में \(a_{3m}=94\), \(a_m=34\) और (d=5) है। (m) का मान क्या है?
In an AP, \(a_{3m}=94\), \(a_m=34\), and (d=5). What is the value of (m)?
#ap-index-difference-hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{3m}-a_m=2md=60\). From (10m=60), (m=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{3m}-a_m=2md=60\). From (10m=60), (m=6).
Step 3
Exam Tip
\(a_{3m}-a_m=2md=60\) है। (10m=60) से (m=6)।
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यदि \(a_{n}=11n+c\) और \(a_{5}=72\) है तो \(a_{5r}\) का मान (512) होने पर (r) क्या है?
If \(a_n=11n+c\) and \(a_5=72\), what is (r) when \(a_{5r}=512\)?
#ap-parameter-index-hard
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
From (72=55+c), (c=17). From (512=55r+17), (r=9).
Step 2
Why this answer is correct
The correct answer is B. (9). From (72=55+c), (c=17). From (512=55r+17), (r=9).
Step 3
Exam Tip
(72=55+c) से (c=17)। (512=55r+17) से (r=9)।
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यदि \(a_n=7n-4\) है तो \(a_{2k}-a_k=84\) के लिए (k) क्या होगा?
If \(a_n=7n-4\), what is (k) for \(a_{2k}-a_k=84\)?
#ap-direct-index-hard
A (10)
B (11)
C (12)
D (13)
Explanation opens after your attempt
Step 1
Concept
(a_{2k}-a_k=(14k-4)-(7k-4)=7k). From (7k=84), (k=12).
Step 2
Why this answer is correct
The correct answer is C. (12). (a_{2k}-a_k=(14k-4)-(7k-4)=7k). From (7k=84), (k=12).
Step 3
Exam Tip
(a_{2k}-a_k=(14k-4)-(7k-4)=7k)। (7k=84) से (k=12)।
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समान्तर श्रेणी में \(a_{3n}=81\), \(a_n=21\) और (d=5) है। (n) क्या है?
In an AP, \(a_{3n}=81\), \(a_n=21\), and (d=5). What is (n)?
#ap-index-difference-hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{3n}-a_n=2nd=60\). From (10n=60), (n=6).
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{3n}-a_n=2nd=60\). From (10n=60), (n=6).
Step 3
Exam Tip
\(a_{3n}-a_n=2nd=60\)। (10n=60) से (n=6)।
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यदि \(a_1=3\) और \(a_{2n+1}=123\) है तथा (d=4) है तो (n) का मान क्या है?
If \(a_1=3\), \(a_{2n+1}=123\), and (d=4), what is the value of (n)?
#ap-index-variable-hard
A (14)
B (15)
C (16)
D (17)
Explanation opens after your attempt
Step 1
Concept
From \(123=3+2n\cdot4\), (120=8n), so (n=15). In index (2n+1), subtract (1) to get the multiplier.
Step 2
Why this answer is correct
The correct answer is B. (15). From \(123=3+2n\cdot4\), (120=8n), so (n=15). In index (2n+1), subtract (1) to get the multiplier.
Step 3
Exam Tip
\(123=3+2n\cdot4\) से (120=8n) इसलिए (n=15)। सूचकांक (2n+1) में (1) घटाकर गुणक लें।
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एक समान्तर श्रेणी में \(a_3=11\) और \(a_{13}=51\) है। \(a_{3r}\) का मान (91) है तो (r) क्या है?
In an AP, \(a_3=11\) and \(a_{13}=51\). If \(a_{3r}=91\), what is (r)?
#ap-index-equation-hard
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{51-11}{10}=4\). From (91=11+(3r-3)4), (3r=21), so (r=7).
Step 2
Why this answer is correct
The correct answer is C. (7). \(d=\frac{51-11}{10}=4\). From (91=11+(3r-3)4), (3r=21), so (r=7).
Step 3
Exam Tip
\(d=\frac{51-11}{10}=4\)। (91=11+(3r-3)4) से (3r=21) इसलिए (r=7)।
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यदि \(a_{n}=2n-1\) और \(a_m=63\) है तो \(a_{m+10}\) क्या होगा?
If \(a_n=2n-1\) and \(a_m=63\), what is \(a_{m+10}\)?
#ap-index-hard
A (81)
B (83)
C (85)
D (87)
Explanation opens after your attempt
Step 1
Concept
From (2m-1=63), (m=32). \(a_{42}=2\times42-1=83\).
Step 2
Why this answer is correct
The correct answer is B. (83). From (2m-1=63), (m=32). \(a_{42}=2\times42-1=83\).
Step 3
Exam Tip
(2m-1=63) से (m=32)। \(a_{42}=2\times42-1=83\)।
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किसी समान्तर श्रेणी में \(a_{p}=17\), \(a_{p+8}=65\) और (p=6) है। \(a_{30}\) क्या होगा?
In an AP, \(a_p=17\), \(a_{p+8}=65\), and (p=6). What is \(a_{30}\)?
#ap-symbolic-index-hard
A (155)
B (161)
C (167)
D (173)
Explanation opens after your attempt
Step 1
Concept
From (8d=48), (d=6). \(a_{30}=a_6+24d=17+144=161\).
Step 2
Why this answer is correct
The correct answer is B. (161). From (8d=48), (d=6). \(a_{30}=a_6+24d=17+144=161\).
Step 3
Exam Tip
(8d=48) से (d=6)। \(a_{30}=a_6+24d=17+144=161\)।
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यदि समांतर श्रेणी में \(a_7-a_2=35\), तो सामान्य अंतर क्या है?
If \(a_7-a_2=35\) in an AP, what is the common difference?
#ap
#index_gap
#common_difference
A (5)
B (6)
C (7)
D (35)
Explanation opens after your attempt
Step 1
Concept
There are (5) intervals between \(a_7\) and \(a_2\), so (5d=35) and (d=7). In exams, subtract term numbers to get intervals.
Step 2
Why this answer is correct
The correct answer is C. (7). There are (5) intervals between \(a_7\) and \(a_2\), so (5d=35) and (d=7). In exams, subtract term numbers to get intervals.
Step 3
Exam Tip
\(a_7\) और \(a_2\) के बीच (5) अंतराल हैं, इसलिए (5d=35) और (d=7)। परीक्षा में पद क्रमांक घटाकर अंतराल पाएं।
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एक समांतर श्रेणी का सामान्य अंतर (d) है। \(a_1,a_3,a_5,\ldots\) से बने अनुक्रम का सामान्य अंतर क्या होगा?
An AP has common difference (d). What is the common difference of the sequence \(a_1,a_3,a_5,\ldots\)?
#ap
#odd_indexed_terms
#subsequence
A (d)
B (2d)
C (3d)
D (-d)
Explanation opens after your attempt
Step 1
Concept
The new sequence jumps two original terms each time, so the difference is (2d). In exams, multiply (d) by the term-number jump.
Step 2
Why this answer is correct
The correct answer is B. (2d). The new sequence jumps two original terms each time, so the difference is (2d). In exams, multiply (d) by the term-number jump.
Step 3
Exam Tip
नए अनुक्रम में दो-दो मूल पदों की छलांग है, इसलिए अंतर (2d) है। परीक्षा में पद-संख्या की छलांग को (d) से गुणा करें।
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किस (k) के लिए (k-2,k+5,2k+1) अंकगणितीय श्रेणी में होंगे?
For which (k) will (k-2,k+5,2k+1) be in an arithmetic progression?
#ap
#find parameter
#algebraic terms
#hard
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
From (2(k+5)=(k-2)+(2k+1)), (2k+10=3k-1), so (k=11). Identify the middle term while forming the equation.
Step 2
Why this answer is correct
The correct answer is D. (9). From (2(k+5)=(k-2)+(2k+1)), (2k+10=3k-1), so (k=11). Identify the middle term while forming the equation.
Step 3
Exam Tip
(2(k+5)=(k-2)+(2k+1)) से (2k+10=3k-1), इसलिए (k=11)। समीकरण बनाते समय मध्य पद को पहचानें।
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यदि (2u-3,3u+2,5u-1) अंकगणितीय श्रेणी में हैं तो (u) का मान क्या है?
If (2u-3,3u+2,5u-1) are in an arithmetic progression, what is the value of (u)?
#ap
#algebraic condition
#find variable
#hard
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (2(3u+2)=(2u-3)+(5u-1)), (6u+4=7u-4), so (u=8). Use the twice-middle-term rule to find the variable.
Step 2
Why this answer is correct
The correct answer is D. (7). From (2(3u+2)=(2u-3)+(5u-1)), (6u+4=7u-4), so (u=8). Use the twice-middle-term rule to find the variable.
Step 3
Exam Tip
(2(3u+2)=(2u-3)+(5u-1)) से (6u+4=7u-4), इसलिए (u=8)। मध्य पद का दुगुना नियम लगाकर चर निकालें।
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किस (m) के लिए (m-1 ,2m+3,4m-1) अंकगणितीय श्रेणी में होंगे?
For which (m) will (m-1 ,2m+3,4m-1) be in an arithmetic progression?
#ap
#find parameter
#algebraic terms
#hard
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From (2(2m+3)=(m-1 )+(4m-1)), (4m+6=5m-2), so (m=8). Use the twice-middle-term rule.
Step 2
Why this answer is correct
The correct answer is C. (5). From (2(2m+3)=(m-1 )+(4m-1)), (4m+6=5m-2), so (m=8). Use the twice-middle-term rule.
Step 3
Exam Tip
(2(2m+3)=(m-1 )+(4m-1)) से (4m+6=5m-2), इसलिए (m=8)। मध्य पद का दुगुना नियम लगाएं।
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यदि (x,2x+4,4x) अंकगणितीय श्रेणी में हैं तो सार्व अंतर क्या है?
If (x,2x+4,4x) are in an arithmetic progression, what is the common difference?
#ap
#algebraic ap
#find d
#hard
A (4)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
From (2(2x+4)=x+4x), (4x+8=5x), so (x=8). Then (d=20-8=12), so none of the listed values is correct.
Step 2
Why this answer is correct
The correct answer is C. (8). From (2(2x+4)=x+4x), (4x+8=5x), so (x=8). Then (d=20-8=12), so none of the listed values is correct.
Step 3
Exam Tip
(2(2x+4)=x+4x) से (4x+8=5x), इसलिए (x=8)। तब (d=20-8=12), इसलिए दिए विकल्पों में सही मान नहीं है।
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कौन सा कथन \(8,8+3q,8+6q,8+9q,\ldots\) के लिए सही है?
Which statement is correct for \(8,8+3q,8+6q,8+9q,\ldots\)?
#ap
#algebraic common difference
#condition
#hard
A हर (q) के लिए अंकगणितीय श्रेणी / Arithmetic progression for every (q)
B केवल (q=1) के लिए / Only for (q=1)
C केवल (q=0) के लिए / Only for (q=0)
D कभी नहीं / Never
Explanation opens after your attempt
Correct Answer
A. हर (q) के लिए अंकगणितीय श्रेणी / Arithmetic progression for every (q)
Step 1
Concept
The consecutive differences are (3q,3q,3q). With equal algebraic differences, it is an arithmetic progression for every (q).
Step 2
Why this answer is correct
The correct answer is A. हर (q) के लिए अंकगणितीय श्रेणी / Arithmetic progression for every (q). The consecutive differences are (3q,3q,3q). With equal algebraic differences, it is an arithmetic progression for every (q).
Step 3
Exam Tip
क्रमागत अंतर (3q,3q,3q) हैं। समान बीजगणितीय अंतर होने पर यह हर (q) के लिए अंकगणितीय श्रेणी है।
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यदि (3m,4m+2,6m-2) अंकगणितीय श्रेणी में हैं तो (m) का मान क्या है?
If (3m,4m+2,6m-2) are in an arithmetic progression, what is the value of (m)?
#ap
#find variable
#algebraic condition
#hard
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (2(4m+2)=3m+(6m-2)), (8m+4=9m-2), so (m=6). Apply the twice-middle-term rule directly.
Step 2
Why this answer is correct
The correct answer is C. (4). From (2(4m+2)=3m+(6m-2)), (8m+4=9m-2), so (m=6). Apply the twice-middle-term rule directly.
Step 3
Exam Tip
(2(4m+2)=3m+(6m-2)) से (8m+4=9m-2), इसलिए (m=6)। मध्य पद का दुगुना नियम सीधे लगाएं।
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यदि \(r-9,r-3,r+3,\ldots\) अंकगणितीय श्रेणी है तो (d) क्या है?
If \(r-9,r-3,r+3,\ldots\) is an arithmetic progression, what is (d)?
#ap
#algebraic sequence
#common difference
#hard
A (3)
B (6)
C (r)
D (r+6)
Explanation opens after your attempt
Step 1
Concept
((r-3)-(r-9)=6) and ((r+3)-(r-3)=6). When variables cancel, a constant common difference remains.
Step 2
Why this answer is correct
The correct answer is B. (6). ((r-3)-(r-9)=6) and ((r+3)-(r-3)=6). When variables cancel, a constant common difference remains.
Step 3
Exam Tip
((r-3)-(r-9)=6) और ((r+3)-(r-3)=6) है। चर कटने पर स्थिर सार्व अंतर मिलता है।
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यदि (x-4,x+2,x+8) अंकगणितीय श्रेणी में हैं तो (x) के बारे में सही कथन क्या है?
If (x-4,x+2,x+8) are in an arithmetic progression, which statement about (x) is correct?
#ap
#identity condition
#algebraic ap
#hard
A केवल (x=0) पर सत्य / True only for (x=0)
B केवल (x=4) पर सत्य / True only for (x=4)
C हर (x) के लिए सत्य / True for every (x)
D किसी (x) के लिए सत्य नहीं / True for no (x)
Explanation opens after your attempt
Correct Answer
C. हर (x) के लिए सत्य / True for every (x)
Step 1
Concept
Both consecutive differences are (6) and (6), so it is an arithmetic progression for every (x). Simplify differences before deciding the variable.
Step 2
Why this answer is correct
The correct answer is C. हर (x) के लिए सत्य / True for every (x). Both consecutive differences are (6) and (6), so it is an arithmetic progression for every (x). Simplify differences before deciding the variable.
Step 3
Exam Tip
दोनों क्रमागत अंतर (6) और (6) हैं, इसलिए यह हर (x) के लिए अंकगणितीय श्रेणी है। चर तय करने से पहले अंतर सरल करें।
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किस (p) के लिए \(4,4+p,4+3p,4+6p,\ldots\) अंकगणितीय श्रेणी होगी?
For which (p) will \(4,4+p,4+3p,4+6p,\ldots\) be an arithmetic progression?
#ap
#condition for ap
#algebraic sequence
#hard
A केवल (p=0) / Only (p=0)
B केवल (p=1) / Only (p=1)
C हर (p) / Every (p)
D कभी नहीं / Never
Explanation opens after your attempt
Correct Answer
A. केवल (p=0) / Only (p=0)
Step 1
Concept
The consecutive differences are (p,2p,3p), which are equal only when (p=0). In such questions, first write all differences.
Step 2
Why this answer is correct
The correct answer is A. केवल (p=0) / Only (p=0). The consecutive differences are (p,2p,3p), which are equal only when (p=0). In such questions, first write all differences.
Step 3
Exam Tip
क्रमागत अंतर (p,2p,3p) हैं जो समान तभी होंगे जब (p=0)। ऐसे प्रश्नों में पहले सभी अंतर लिखें।
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यदि (5a-2, 3a+6, a+18) अंकगणितीय श्रेणी में हैं तो सार्व अंतर क्या होगा?
If (5a-2, 3a+6, a+18) are in an arithmetic progression, what will be the common difference?
#arithmetic progression
#no solution
#algebraic check
#hard
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(2(3a+6)=(5a-2)+(a+18)) gives (a=2). Then the terms (8,12,20) do not have equal differences, so no arithmetic progression is formed.
Step 2
Why this answer is correct
The correct answer is B. (4). (2(3a+6)=(5a-2)+(a+18)) gives (a=2). Then the terms (8,12,20) do not have equal differences, so no arithmetic progression is formed.
Step 3
Exam Tip
(2(3a+6)=(5a-2)+(a+18)) से (a=2) मिलता है। तब पद (8,12,20) नहीं बल्कि (8,12,20) समान अंतर नहीं देते, इसलिए सही जांच से कोई अंकगणितीय श्रेणी नहीं बनती।
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यदि (2x+1, x+8, 3x-4) अंकगणितीय श्रेणी के क्रमागत पद हैं तो (x) का मान क्या है?
If (2x+1, x+8, 3x-4) are consecutive terms of an arithmetic progression, what is the value of (x)?
#arithmetic progression
#algebraic terms
#common difference
#hard
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
In three consecutive terms, twice the middle term equals the sum of the other two terms. So (2(x+8)=(2x+1)+(3x-4)) gives (x=3).
Step 2
Why this answer is correct
The correct answer is B. (3). In three consecutive terms, twice the middle term equals the sum of the other two terms. So (2(x+8)=(2x+1)+(3x-4)) gives (x=3).
Step 3
Exam Tip
तीन क्रमागत पदों में (2) गुना मध्य पद बाकी दो पदों के योग के बराबर होता है। इसलिए (2(x+8)=(2x+1)+(3x-4)) से (x=3)।
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यदि (4, x+1, 2x+4, 25) अंकगणितीय श्रेणी के क्रमागत पद हैं, तो (x) का मान क्या है?
If (4, x+1, 2x+4, 25) are consecutive terms of an arithmetic progression, what is the value of (x)?
#ap
#missing algebraic term
#equal gaps
#expert
A (8)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
(25-4=21) is split into three equal gaps, so (d=7), and (x+1=11) gives (x=10). In four consecutive terms, finding (d) from first and last terms is fast.
Step 2
Why this answer is correct
The correct answer is C. (10). (25-4=21) is split into three equal gaps, so (d=7), and (x+1=11) gives (x=10). In four consecutive terms, finding (d) from first and last terms is fast.
Step 3
Exam Tip
(25-4=21) तीन समान अंतरालों में बंटता है, इसलिए (d=7) और (x+1=11) से (x=10)। चार क्रमागत पदों में पहले और अंतिम पद से (d) निकालना तेज होता है।
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यदि (x, x+2, 2x+1) अंकगणितीय श्रेणी में हैं, तो (d) क्या होगा?
If (x, x+2, 2x+1) are in an arithmetic progression, what will (d) be?
#ap
#algebraic terms
#find d
#expert
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
From (2(x+2)=x+(2x+1)), (2x+4=3x+1), so (x=3) and (d=5-3=2). Decide (d) only after finding (x).
Step 2
Why this answer is correct
The correct answer is B. (2). From (2(x+2)=x+(2x+1)), (2x+4=3x+1), so (x=3) and (d=5-3=2). Decide (d) only after finding (x).
Step 3
Exam Tip
(2(x+2)=x+(2x+1)) से (2x+4=3x+1), इसलिए (x=3) और (d=5-3=2)। (x) मिलने के बाद ही (d) तय करें।
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यदि (2m-3, 3m+1, 5m-2) अंकगणितीय श्रेणी में हैं, तो सार्व अंतर क्या होगा?
If (2m-3, 3m+1, 5m-2) are in an arithmetic progression, what will be the common difference?
#ap
#algebraic ap
#find d
#expert
A (4)
B (7)
C (10)
D (13)
Explanation opens after your attempt
Step 1
Concept
From (2(3m+1)=(2m-3)+(5m-2)), (6m+2=7m-5), so (m=7) and (d=22-11=11). Find the variable first, then the consecutive difference.
Step 2
Why this answer is correct
The correct answer is B. (7). From (2(3m+1)=(2m-3)+(5m-2)), (6m+2=7m-5), so (m=7) and (d=22-11=11). Find the variable first, then the consecutive difference.
Step 3
Exam Tip
(2(3m+1)=(2m-3)+(5m-2)) से (6m+2=7m-5), इसलिए (m=7) और (d=22-11=11)। पहले चर निकालें, फिर क्रमागत अंतर निकालें।
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यदि (k+1, 2k+4, 4k-2) अंकगणितीय श्रेणी में हैं, तो (k) का मान क्या होगा?
If (k+1, 2k+4, 4k-2) are in an arithmetic progression, what will be the value of (k)?
#ap
#find parameter
#algebraic terms
#expert
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From (2(2k+4)=(k+1)+(4k-2)), (4k+8=5k-1), so (k=9). Identify the middle term correctly while forming the equation.
Step 2
Why this answer is correct
The correct answer is D. (6). From (2(2k+4)=(k+1)+(4k-2)), (4k+8=5k-1), so (k=9). Identify the middle term correctly while forming the equation.
Step 3
Exam Tip
(2(2k+4)=(k+1)+(4k-2)) से (4k+8=5k-1), इसलिए (k=9)। समीकरण बनाते समय मध्य पद को सही पहचानें।
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यदि (2x+1, 5x-2, 8x-5) अंकगणितीय श्रेणी में हैं, तो सही कथन कौन सा है?
If (2x+1, 5x-2, 8x-5) are in an arithmetic progression, which statement is correct?
#ap
#identity condition
#algebraic ap
#expert
A हर (x) के लिए अंकगणितीय श्रेणी / Arithmetic progression for every (x)
B केवल (x=1) के लिए / Only for (x=1)
C केवल (x=2) के लिए / Only for (x=2)
D किसी (x) के लिए नहीं / For no (x)
Explanation opens after your attempt
Correct Answer
A. हर (x) के लिए अंकगणितीय श्रेणी / Arithmetic progression for every (x)
Step 1
Concept
Both differences are (3x-3) and (3x-3), so it is an arithmetic progression for every (x). Equal algebraic differences are sufficient.
Step 2
Why this answer is correct
The correct answer is A. हर (x) के लिए अंकगणितीय श्रेणी / Arithmetic progression for every (x). Both differences are (3x-3) and (3x-3), so it is an arithmetic progression for every (x). Equal algebraic differences are sufficient.
Step 3
Exam Tip
दोनों अंतर (3x-3) और (3x-3) हैं, इसलिए यह हर (x) पर अंकगणितीय श्रेणी है। समान बीजगणितीय अंतर पर्याप्त है।
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यदि (2, x, 3x, 26) अंकगणितीय श्रेणी के क्रमागत पद हैं, तो (x) क्या है?
If (2, x, 3x, 26) are consecutive terms of an arithmetic progression, what is (x)?
#ap
#no solution
#algebraic missing terms
#expert
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The total difference (26-2=24) splits into three equal gaps, so (d=8) and the second term should be (10); hence (x=10), but the third (3x=30), so there is no solution.
Step 2
Why this answer is correct
The correct answer is A. (6). The total difference (26-2=24) splits into three equal gaps, so (d=8) and the second term should be (10); hence (x=10), but the third (3x=30), so there is no solution.
Step 3
Exam Tip
कुल अंतर (26-2=24) तीन समान भागों में बंटता है, इसलिए (d=8) और दूसरा पद (10) होना चाहिए; अतः (x=10), पर तीसरा (3x=30) होगा, इसलिए कोई समाधान नहीं।
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यदि (q-3, 2q+1, 4q-1) अंकगणितीय श्रेणी में हैं, तो (q) क्या होगा?
If (q-3, 2q+1, 4q-1) are in an arithmetic progression, what will (q) be?
#ap
#algebraic terms
#find parameter
#expert
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (2(2q+1)=(q-3)+(4q-1)), (4q+2=5q-4), so (q=6). Watch signs while applying the twice-middle-term rule.
Step 2
Why this answer is correct
The correct answer is D. (5). From (2(2q+1)=(q-3)+(4q-1)), (4q+2=5q-4), so (q=6). Watch signs while applying the twice-middle-term rule.
Step 3
Exam Tip
(2(2q+1)=(q-3)+(4q-1)) से (4q+2=5q-4), इसलिए (q=6)। मध्य पद का दुगुना नियम लगाते समय संकेतों पर ध्यान दें।
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यदि (3v-4, 4v+1, 6v-1) अंकगणितीय श्रेणी में हैं, तो (v) का मान क्या है?
If (3v-4, 4v+1, 6v-1) are in an arithmetic progression, what is the value of (v)?
#ap
#algebraic condition
#find variable
#expert
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (2(4v+1)=(3v-4)+(6v-1)), (8v+2=9v-5), so (v=7). Use the twice-middle-term rule to find the variable.
Step 2
Why this answer is correct
The correct answer is C. (4). From (2(4v+1)=(3v-4)+(6v-1)), (8v+2=9v-5), so (v=7). Use the twice-middle-term rule to find the variable.
Step 3
Exam Tip
(2(4v+1)=(3v-4)+(6v-1)) से (8v+2=9v-5), इसलिए (v=7)। मध्य पद का दुगुना नियम लगाकर चर निकालें।
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यदि (2x, x+9, 18) अंकगणितीय श्रेणी में हैं, तो (x) का मान क्या होगा?
If (2x, x+9, 18) are in an arithmetic progression, what will be the value of (x)?
#ap
#identity
#algebraic condition
#expert
A (0)
B (3)
C (6)
D कोई मान नहीं / No value
Explanation opens after your attempt
Correct Answer
D. कोई मान नहीं / No value
Step 1
Concept
(2(x+9)=2x+18) gives an identity, so it is an arithmetic progression for every (x). Therefore no single value of (x) is obtained.
Step 2
Why this answer is correct
The correct answer is D. कोई मान नहीं / No value. (2(x+9)=2x+18) gives an identity, so it is an arithmetic progression for every (x). Therefore no single value of (x) is obtained.
Step 3
Exam Tip
(2(x+9)=2x+18) से पहचान समानता मिलती है, इसलिए यह हर (x) पर अंकगणितीय श्रेणी है। इस कारण एकमात्र (x) नहीं मिलता।
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यदि (x-7, x-1, x+5) अंकगणितीय श्रेणी में हैं, तो (x) के बारे में सही कथन क्या है?
If (x-7, x-1, x+5) are in an arithmetic progression, what is the correct statement about (x)?
#ap
#identity condition
#algebraic ap
#expert
A केवल (x=1) पर सत्य / True only for (x=1)
B केवल (x=7) पर सत्य / True only for (x=7)
C हर (x) के लिए सत्य / True for every (x)
D किसी (x) के लिए सत्य नहीं / True for no (x)
Explanation opens after your attempt
Correct Answer
C. हर (x) के लिए सत्य / True for every (x)
Step 1
Concept
Both consecutive differences are (6) and (6), so it is an arithmetic progression for every (x). Simplify differences before fixing the variable.
Step 2
Why this answer is correct
The correct answer is C. हर (x) के लिए सत्य / True for every (x). Both consecutive differences are (6) and (6), so it is an arithmetic progression for every (x). Simplify differences before fixing the variable.
Step 3
Exam Tip
दोनों क्रमागत अंतर (6) और (6) हैं, इसलिए यह हर (x) के लिए अंकगणितीय श्रेणी है। चर तय करने से पहले अंतर सरल करें।
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यदि \(u-8, u-2, u+4,\ldots\) अंकगणितीय श्रेणी है, तो (d) क्या है?
If \(u-8, u-2, u+4,\ldots\) is an arithmetic progression, what is (d)?
#ap
#algebraic sequence
#common difference
#expert
A (4)
B (6)
C (u)
D (u+6)
Explanation opens after your attempt
Step 1
Concept
((u-2)-(u-8)=6) and ((u+4)-(u-2)=6). When variables cancel, a constant common difference remains.
Step 2
Why this answer is correct
The correct answer is B. (6). ((u-2)-(u-8)=6) and ((u+4)-(u-2)=6). When variables cancel, a constant common difference remains.
Step 3
Exam Tip
((u-2)-(u-8)=6) और ((u+4)-(u-2)=6) है। चर कटने पर स्थिर सार्व अंतर मिलता है।
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किस (r) के लिए \(9, 9+r, 9+4r, 9+9r,\ldots\) अंकगणितीय श्रेणी होगी?
For which (r) will \(9, 9+r, 9+4r, 9+9r,\ldots\) be an arithmetic progression?
#ap
#condition for ap
#algebraic sequence
#expert
A केवल (r=0) / Only (r=0)
B केवल (r=1) / Only (r=1)
C हर (r) / Every (r)
D कभी नहीं / Never
Explanation opens after your attempt
Correct Answer
A. केवल (r=0) / Only (r=0)
Step 1
Concept
The consecutive differences are (r,3r,5r), which are equal only when (r=0). In such questions it is necessary to write all consecutive differences.
Step 2
Why this answer is correct
The correct answer is A. केवल (r=0) / Only (r=0). The consecutive differences are (r,3r,5r), which are equal only when (r=0). In such questions it is necessary to write all consecutive differences.
Step 3
Exam Tip
क्रमागत अंतर (r,3r,5r) हैं, ये समान तभी होंगे जब (r=0)। ऐसे प्रश्नों में सभी क्रमागत अंतर लिखना जरूरी है।
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यदि (2a-5, a+4, 4a-7) अंकगणितीय श्रेणी में हैं, तो (a) का मान क्या होगा?
If (2a-5, a+4, 4a-7) are in an arithmetic progression, what will be the value of (a)?
#ap
#find variable
#algebraic condition
#expert
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (2(a+4)=(2a-5)+(4a-7)), (2a+8=6a-12), so (a=5). Identify the middle term and form the equation.
Step 2
Why this answer is correct
The correct answer is B. (3). From (2(a+4)=(2a-5)+(4a-7)), (2a+8=6a-12), so (a=5). Identify the middle term and form the equation.
Step 3
Exam Tip
(2(a+4)=(2a-5)+(4a-7)) से (2a+8=6a-12), इसलिए (a=5)। मध्य पद को पहचानकर समीकरण बनाएं।
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यदि (4p+1, 3p+7, p+19) अंकगणितीय श्रेणी में हैं, तो सार्व अंतर क्या होगा?
If (4p+1, 3p+7, p+19) are in an arithmetic progression, what will be the common difference?
#ap
#algebraic ap
#find d
#expert
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Using (2(3p+7)=(4p+1)+(p+19)) gives (p=6), so the terms become (25,25,25) and (d=0). First find the variable and then check (d).
Step 2
Why this answer is correct
The correct answer is C. (5). Using (2(3p+7)=(4p+1)+(p+19)) gives (p=6), so the terms become (25,25,25) and (d=0). First find the variable and then check (d).
Step 3
Exam Tip
(2(3p+7)=(4p+1)+(p+19)) से (p=6), इसलिए पद (25,25,25) नहीं बनते बल्कि (25,25,25) बनते हैं और (d=0)। पहले चर निकालें फिर (d) जांचें।
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यदि (3x-2, 2x+5, x+16) अंकगणितीय श्रेणी के क्रमागत पद हैं, तो (x) का मान क्या है?
If (3x-2, 2x+5, x+16) are consecutive terms of an arithmetic progression, what is the value of (x)?
#ap
#algebraic terms
#expert
#common difference
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
In three consecutive terms, twice the middle term equals the sum of the other two, so (2(2x+5)=(3x-2)+(x+16)) gives (x=2). The middle-term rule is a fast exam method.
Step 2
Why this answer is correct
The correct answer is B. (2). In three consecutive terms, twice the middle term equals the sum of the other two, so (2(2x+5)=(3x-2)+(x+16)) gives (x=2). The middle-term rule is a fast exam method.
Step 3
Exam Tip
तीन क्रमागत पदों में मध्य पद का दुगुना बाकी दो पदों के योग के बराबर होता है, इसलिए (2(2x+5)=(3x-2)+(x+16)) से (x=2)। परीक्षा में मध्य पद नियम तेज तरीका है।
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यदि \(12, 12+r, 12+3r, 12+6r,\ldots\) एक अंकगणितीय श्रेणी है, तो (r) का मान क्या होना चाहिए?
If \(12, 12+r, 12+3r, 12+6r,\ldots\) is an arithmetic progression, what should be the value of (r)?
#ap
#condition for ap
#algebraic sequence
#hard
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
The consecutive differences are (r,2r,3r), which are equal only when (r=0). In such questions first write all consecutive differences.
Step 2
Why this answer is correct
The correct answer is A. (0). The consecutive differences are (r,2r,3r), which are equal only when (r=0). In such questions first write all consecutive differences.
Step 3
Exam Tip
क्रमागत अंतर (r,2r,3r) हैं, ये समान तभी होंगे जब (r=0)। ऐसे प्रश्नों में पहले सभी क्रमागत अंतर लिखें।
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किस (k) के लिए (k-3, k+2, 2k+1) अंकगणितीय श्रेणी में होंगे?
For which (k) will (k-3, k+2, 2k+1) be in an arithmetic progression?
#ap
#find parameter
#algebraic terms
#hard
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (2(k+2)=(k-3)+(2k+1)), (2k+4=3k-2), so (k=6). Identify the middle term while forming the equation.
Step 2
Why this answer is correct
The correct answer is B. (5). From (2(k+2)=(k-3)+(2k+1)), (2k+4=3k-2), so (k=6). Identify the middle term while forming the equation.
Step 3
Exam Tip
(2(k+2)=(k-3)+(2k+1)) से (2k+4=3k-2), इसलिए (k=6)। समीकरण बनाते समय मध्य पद को पहचानें।
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यदि (2u-1, 3u+2, 5u+1) अंकगणितीय श्रेणी में हैं, तो (u) का मान क्या है?
If (2u-1, 3u+2, 5u+1) are in an arithmetic progression, what is the value of (u)?
#ap
#algebraic condition
#find variable
#hard
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
From (2(3u+2)=(2u-1)+(5u+1)), (6u+4=7u), so (u=4). The twice-middle-term rule is direct here.
Step 2
Why this answer is correct
The correct answer is B. (2). From (2(3u+2)=(2u-1)+(5u+1)), (6u+4=7u), so (u=4). The twice-middle-term rule is direct here.
Step 3
Exam Tip
(2(3u+2)=(2u-1)+(5u+1)) से (6u+4=7u), इसलिए (u=4)। मध्य पद का दुगुना नियम यहां सीधा है।
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यदि (2x, x+6, 18) अंकगणितीय श्रेणी में हैं, तो (d) का मान क्या है?
If (2x, x+6, 18) are in an arithmetic progression, what is the value of (d)?
#ap
#no solution
#algebraic condition
#hard
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(2(x+6)=2x+18) gives (2x+12=2x+18), which is false, so no (x) is possible. Hence (d) is not determined.
Step 2
Why this answer is correct
The correct answer is D. (6). (2(x+6)=2x+18) gives (2x+12=2x+18), which is false, so no (x) is possible. Hence (d) is not determined.
Step 3
Exam Tip
(2(x+6)=2x+18) से (2x+12=2x+18) असत्य है, इसलिए कोई (x) संभव नहीं। अतः (d) निर्धारित नहीं होता।
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यदि (x-5, x, x+5) अंकगणितीय श्रेणी में हैं, तो (x) के बारे में सही कथन कौन सा है?
If (x-5, x, x+5) are in an arithmetic progression, which statement about (x) is correct?
#ap
#identity condition
#algebraic ap
#hard
A केवल (x=0) पर सत्य / True only for (x=0)
B केवल (x=5) पर सत्य / True only for (x=5)
C हर (x) के लिए सत्य / True for every (x)
D किसी भी (x) के लिए सत्य नहीं / True for no (x)
Explanation opens after your attempt
Correct Answer
C. हर (x) के लिए सत्य / True for every (x)
Step 1
Concept
Both differences are (5) and (5), so it is an arithmetic progression for every (x). Compare differences before fixing the variable.
Step 2
Why this answer is correct
The correct answer is C. हर (x) के लिए सत्य / True for every (x). Both differences are (5) and (5), so it is an arithmetic progression for every (x). Compare differences before fixing the variable.
Step 3
Exam Tip
दोनों अंतर (5) और (5) हैं, इसलिए यह हर (x) पर अंकगणितीय श्रेणी है। चर की जगह पहले अंतरों की तुलना करें।
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किस (m) के लिए (m+2, 2m+5, 4m+1) अंकगणितीय श्रेणी में होंगे?
For which (m) will (m+2, 2m+5, 4m+1) be in an arithmetic progression?
#ap
#find parameter
#algebraic terms
#hard
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (2(2m+5)=(m+2)+(4m+1)), (4m+10=5m+3), so (m=7). Use the twice-middle-term rule for three terms.
Step 2
Why this answer is correct
The correct answer is A. (4). From (2(2m+5)=(m+2)+(4m+1)), (4m+10=5m+3), so (m=7). Use the twice-middle-term rule for three terms.
Step 3
Exam Tip
(2(2m+5)=(m+2)+(4m+1)) से (4m+10=5m+3), इसलिए (m=7)। तीन पदों में मध्य पद का दुगुना नियम लगाएं।
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यदि (x, 2x+3, 4x+1) अंकगणितीय श्रेणी में हैं, तो तीनों पदों का सार्व अंतर क्या है?
If (x, 2x+3, 4x+1) are in an arithmetic progression, what is the common difference?
#ap
#algebraic ap
#find d
#hard
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (2(2x+3)=x+(4x+1)), (4x+6=5x+1), so (x=5) and (d=13-5=8). Finding the variable first is necessary.
Step 2
Why this answer is correct
The correct answer is B. (5). From (2(2x+3)=x+(4x+1)), (4x+6=5x+1), so (x=5) and (d=13-5=8). Finding the variable first is necessary.
Step 3
Exam Tip
(2(2x+3)=x+(4x+1)) से (4x+6=5x+1), इसलिए (x=5) और (d=13-5=8)। पहले चर का मान निकालना जरूरी है।
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कौन सा कथन अनुक्रम \(5, 5+2q, 5+4q, 5+6q,\ldots\) के लिए सही है?
Which statement is correct for the sequence \(5, 5+2q, 5+4q, 5+6q,\ldots\)?
#ap
#algebraic common difference
#condition
#hard
A यह हर (q) पर अंकगणितीय श्रेणी है / It is an arithmetic progression for every (q)
B यह केवल (q=1) पर अंकगणितीय श्रेणी है / It is an arithmetic progression only for (q=1)
C यह कभी अंकगणितीय श्रेणी नहीं है / It is never an arithmetic progression
D यह केवल (q=0) पर अंकगणितीय श्रेणी है / It is an arithmetic progression only for (q=0)
Explanation opens after your attempt
Correct Answer
A. यह हर (q) पर अंकगणितीय श्रेणी है / It is an arithmetic progression for every (q)
Step 1
Concept
The consecutive differences are (2q,2q,2q), so it is an arithmetic progression for every (q). Equal algebraic differences are also valid.
Step 2
Why this answer is correct
The correct answer is A. यह हर (q) पर अंकगणितीय श्रेणी है / It is an arithmetic progression for every (q). The consecutive differences are (2q,2q,2q), so it is an arithmetic progression for every (q). Equal algebraic differences are also valid.
Step 3
Exam Tip
क्रमागत अंतर (2q,2q,2q) हैं, इसलिए यह हर (q) पर अंकगणितीय श्रेणी है। समान बीजगणितीय अंतर भी मान्य होता है।
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यदि (2a, 3a+1, 5a-1) अंकगणितीय श्रेणी में हैं, तो (a) का मान क्या होगा?
If (2a, 3a+1, 5a-1) are in an arithmetic progression, what will be the value of (a)?
#ap
#algebraic condition
#find variable
#hard
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
From (2(3a+1)=2a+(5a-1)), (6a+2=7a-1), so (a=3). The twice-middle-term rule works quickly for three terms.
Step 2
Why this answer is correct
The correct answer is C. (3). From (2(3a+1)=2a+(5a-1)), (6a+2=7a-1), so (a=3). The twice-middle-term rule works quickly for three terms.
Step 3
Exam Tip
(2(3a+1)=2a+(5a-1)) से (6a+2=7a-1), इसलिए (a=3)। तीन पदों में मध्य पद का दुगुना नियम जल्दी काम करता है।
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यदि \(r-6, r-1, r+4,\ldots\) एक अंकगणितीय श्रेणी है, तो (d) क्या है?
If \(r-6, r-1, r+4,\ldots\) is an arithmetic progression, what is (d)?
#ap
#algebraic sequence
#common difference
#hard
A (4)
B (5)
C (r)
D (r+5)
Explanation opens after your attempt
Step 1
Concept
((r-1)-(r-6)=5) and ((r+4)-(r-1)=5). When variables cancel, a constant common difference remains.
Step 2
Why this answer is correct
The correct answer is B. (5). ((r-1)-(r-6)=5) and ((r+4)-(r-1)=5). When variables cancel, a constant common difference remains.
Step 3
Exam Tip
((r-1)-(r-6)=5) और ((r+4)-(r-1)=5) है। चर कट जाने पर स्थिर सार्व अंतर मिलता है।
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यदि (2, x+1, 3x-1, 14) अंकगणितीय श्रेणी के क्रमागत पद हैं, तो (x) का मान क्या है?
If (2, x+1, 3x-1, 14) are consecutive terms of an arithmetic progression, what is (x)?
#ap
#missing algebraic term
#equal gaps
#hard
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
The total difference (14-2=12) is split into three equal gaps, so (d=4), and the second term should be (6), hence (x=5). Splitting the total difference into equal parts is useful.
Step 2
Why this answer is correct
The correct answer is B. (4). The total difference (14-2=12) is split into three equal gaps, so (d=4), and the second term should be (6), hence (x=5). Splitting the total difference into equal parts is useful.
Step 3
Exam Tip
कुल अंतर (14-2=12) तीन बराबर भागों में बंटेगा, इसलिए (d=4) और (x+1=6) नहीं बल्कि दूसरा पद (6) होना चाहिए, अतः (x=5)। कुल अंतर को समान भागों में बांटना उपयोगी है।
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यदि (x+1, 2x-1, 3x-3) अंकगणितीय श्रेणी में हैं, तो कौन सा कथन सही है?
If (x+1, 2x-1, 3x-3) are in an arithmetic progression, which statement is correct?
#ap
#algebraic ap
#condition
#hard
A हर (x) के लिए यह अंकगणितीय श्रेणी है / It is an arithmetic progression for every (x)
B केवल (x=1) के लिए / Only for (x=1)
C केवल (x=2) के लिए / Only for (x=2)
D कभी नहीं / Never
Explanation opens after your attempt
Correct Answer
A. हर (x) के लिए यह अंकगणितीय श्रेणी है / It is an arithmetic progression for every (x)
Step 1
Concept
Both differences are (x-2) and (x-2), so they are equal for every (x). Simplify and compare differences in algebraic terms.
Step 2
Why this answer is correct
The correct answer is A. हर (x) के लिए यह अंकगणितीय श्रेणी है / It is an arithmetic progression for every (x). Both differences are (x-2) and (x-2), so they are equal for every (x). Simplify and compare differences in algebraic terms.
Step 3
Exam Tip
दोनों अंतर (x-2) और (x-2) हैं, इसलिए वे हर (x) पर समान हैं। बीजगणितीय पदों में अंतरों को सरल करके तुलना करें।
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यदि (5x+2, 3x+10, x+18) अंकगणितीय श्रेणी में हैं, तो सार्व अंतर क्या है?
If (5x+2, 3x+10, x+18) are in an arithmetic progression, what is the common difference?
#ap
#algebraic identity
#common difference
#hard
A (-4)
B (0)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Equating differences gives ((3x+10)-(5x+2)=(x+18)-(3x+10)), which is an identity, so (d=8-2x). Therefore it is an arithmetic progression for every (x), but (d) is not fixed.
Step 2
Why this answer is correct
The correct answer is C. (4). Equating differences gives ((3x+10)-(5x+2)=(x+18)-(3x+10)), which is an identity, so (d=8-2x). Therefore it is an arithmetic progression for every (x), but (d) is not fixed.
Step 3
Exam Tip
दोनों अंतर बराबर रखने पर ((3x+10)-(5x+2)=(x+18)-(3x+10)), जिससे पहचान समानता बनती है और (d=8-2x)। इसलिए यह हर (x) पर अंकगणितीय श्रेणी है, लेकिन (d) निश्चित नहीं है।
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अनुक्रम \(7, 7+p, 7+3p, 7+6p,\ldots\) कब अंकगणितीय श्रेणी होगा?
When will the sequence \(7, 7+p, 7+3p, 7+6p,\ldots\) be an arithmetic progression?
#ap
#condition for ap
#algebraic sequence
#hard
A केवल (p=0) पर / Only when (p=0)
B हर (p) पर / For every (p)
C केवल (p=1) पर / Only when (p=1)
D कभी नहीं / Never
Explanation opens after your attempt
Correct Answer
A. केवल (p=0) पर / Only when (p=0)
Step 1
Concept
The consecutive differences are (p,2p,3p), which are equal only when (p=0). Comparing differences is the safest method.
Step 2
Why this answer is correct
The correct answer is A. केवल (p=0) पर / Only when (p=0). The consecutive differences are (p,2p,3p), which are equal only when (p=0). Comparing differences is the safest method.
Step 3
Exam Tip
क्रमागत अंतर (p,2p,3p) हैं, ये समान तभी होंगे जब (p=0)। अंतरों की तुलना करना सबसे सुरक्षित तरीका है।
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यदि (a-2, 2a+1, 5a-4) अंकगणितीय श्रेणी में हैं, तो सार्व अंतर क्या है?
If (a-2, 2a+1, 5a-4) are in an arithmetic progression, what is the common difference?
#ap
#algebraic ap
#find d
#hard
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (2(2a+1)=(a-2)+(5a-4)), (4a+2=6a-6), so (a=4), and (d=9-2=7). In such questions find the variable first and then find (d).
Step 2
Why this answer is correct
The correct answer is C. (6). From (2(2a+1)=(a-2)+(5a-4)), (4a+2=6a-6), so (a=4), and (d=9-2=7). In such questions find the variable first and then find (d).
Step 3
Exam Tip
(2(2a+1)=(a-2)+(5a-4)) से (a=3), इसलिए पद (1,7,11) नहीं बल्कि (1,7,11) में अंतर समान नहीं आता; सही समीकरण से (4a+2=6a-6), अतः (a=4) और (d=9-2=7)। ऐसे प्रश्न में पहले (a) निकालकर फिर (d) निकालें।
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यदि (2x-3, x+4, 3x-1) अंकगणितीय श्रेणी के क्रमागत पद हैं, तो (x) का मान क्या है?
If (2x-3, x+4, 3x-1) are consecutive terms of an arithmetic progression, what is the value of (x)?
#ap
#algebraic terms
#common difference
#hard
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Twice the middle term equals the sum of the other two terms, so (2(x+4)=(2x-3)+(3x-1)) gives (x=3). For three consecutive terms, the middle-term rule is fast.
Step 2
Why this answer is correct
The correct answer is B. (3). Twice the middle term equals the sum of the other two terms, so (2(x+4)=(2x-3)+(3x-1)) gives (x=3). For three consecutive terms, the middle-term rule is fast.
Step 3
Exam Tip
मध्य पद का दुगुना बाकी दोनों पदों के योग के बराबर होता है, इसलिए (2(x+4)=(2x-3)+(3x-1)) से (x=3)। तीन क्रमागत पदों में मध्य पद का नियम तेज होता है।
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अनुक्रम \(3a,3a-4,3a-8,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(3a,3a-4,3a-8,\ldots\)?
#ap
#algebraic sequence
#negative d
#medium
A (4)
B (3a)
C (-4)
D (3a-4)
Explanation opens after your attempt
Step 1
Concept
(d=(3a-4)-3a=-4). In a decreasing algebraic sequence (d) can be negative.
Step 2
Why this answer is correct
The correct answer is C. (-4). (d=(3a-4)-3a=-4). In a decreasing algebraic sequence (d) can be negative.
Step 3
Exam Tip
(d=(3a-4)-3a=-4) है। घटते बीजगणितीय अनुक्रम में (d) ऋणात्मक हो सकता है।
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यदि \(z-4,z+2,z+8,\ldots\) अंकगणितीय श्रेणी है तो (d) क्या है?
If \(z-4,z+2,z+8,\ldots\) is an arithmetic progression, what is (d)?
#ap
#algebraic terms
#find d
#medium
A (z)
B (4)
C (6)
D (12)
Explanation opens after your attempt
Step 1
Concept
(d=(z+2)-(z-4)=6). When variables cancel, the constant difference remains.
Step 2
Why this answer is correct
The correct answer is C. (6). (d=(z+2)-(z-4)=6). When variables cancel, the constant difference remains.
Step 3
Exam Tip
(d=(z+2)-(z-4)=6) है। चर कट जाने पर स्थिर अंतर मिलता है।
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यदि \(8,8+s,8+2s,\ldots\) एक अंकगणितीय श्रेणी है तो इसका सार्व अंतर क्या है?
If \(8,8+s,8+2s,\ldots\) is an arithmetic progression, what is its common difference?
#ap
#algebraic common difference
#medium
#class ten
A (8)
B (8+s)
C (s)
D (2s)
Explanation opens after your attempt
Step 1
Concept
The common difference is ((8+s)-8=s). In algebraic sequences also look at the equally added part.
Step 2
Why this answer is correct
The correct answer is C. (s). The common difference is ((8+s)-8=s). In algebraic sequences also look at the equally added part.
Step 3
Exam Tip
सार्व अंतर ((8+s)-8=s) है। अक्षर वाले अनुक्रम में भी समान जोड़ा गया भाग देखें।
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यदि \(t,t+9,t+18,\ldots\) अंकगणितीय श्रेणी है तो दूसरे और पहले पद का अंतर क्या है?
If \(t,t+9,t+18,\ldots\) is an arithmetic progression, what is the difference between the second and first terms?
#ap
#algebraic sequence
#common difference
#medium
A (t)
B (9)
C (18)
D (t+9)
Explanation opens after your attempt
Step 1
Concept
((t+9)-t=9), so the difference is (9). The equally added number is (d).
Step 2
Why this answer is correct
The correct answer is B. (9). ((t+9)-t=9), so the difference is (9). The equally added number is (d).
Step 3
Exam Tip
((t+9)-t=9) है इसलिए अंतर (9) है। समान जोड़ी गई संख्या ही (d) होती है।
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अनुक्रम \(4x,4x+3,4x+6,\ldots\) में सार्व अंतर क्या है?
What is the common difference in the sequence \(4x,4x+3,4x+6,\ldots\)?
#ap
#algebraic terms
#common difference
#medium
A (4x)
B (6)
C (3)
D (4x+3)
Explanation opens after your attempt
Step 1
Concept
(d=(4x+3)-4x=3). For algebraic terms also subtract the first term from the second term.
Step 2
Why this answer is correct
The correct answer is C. (3). (d=(4x+3)-4x=3). For algebraic terms also subtract the first term from the second term.
Step 3
Exam Tip
(d=(4x+3)-4x=3) है। बीजगणितीय पदों में भी दूसरा पद घटा पहला पद करें।
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