क्रम \(3,7,11,15,\ldots\) का (10)वाँ पद क्या होगा?
What will be the (10)th term of the sequence \(3,7,11,15,\ldots\)?
#sequences
#nth_term
#arithmetic_pattern
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A (35)
B (37)
C (39)
D (41)
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Explanation
Simple Explanation
यहाँ पहला पद (3) और समान अंतर (4) है। (10)वाँ पद \(3+9\times4=39\) है। / Here the first term is (3) and the common difference is (4). The (10)th term is \(3+9\times4=39\).
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क्रम \(42,37,32,27,\ldots\) का (8)वाँ पद क्या है?
What is the (8)th term of \(42,37,32,27,\ldots\)?
#sequences
#decreasing_sequence
#nth_term
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A (7)
B (12)
C (17)
D (22)
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Explanation
Simple Explanation
हर बार (5) घट रहा है। (8)वाँ पद \(42-7\times5=7\) है। / Each term decreases by (5). The (8)th term is \(42-7\times5=7\).
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यदि \(a_n=3n+4\) है, तो \(a_7\) का मान क्या होगा?
If \(a_n=3n+4\), what will be the value of \(a_7\)?
#sequences
#nth_term
#linear_rule
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A (21)
B (24)
C (25)
D (28)
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Explanation
Simple Explanation
(n=7) रखने पर (a_7=3(7)+4=25) मिलता है। नियम में (n) का सही मान रखें। / Putting (n=7), (a_7=3(7)+4=25). Substitute the correct value of (n) in the rule.
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यदि \(a_n=2n^2-1\) है, तो \(a_5\) क्या होगा?
If \(a_n=2n^2-1\), what is \(a_5\)?
#sequences
#nth_term
#square_rule
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A (45)
B (47)
C (49)
D (51)
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Explanation
Simple Explanation
(n=5) रखने पर (2\(5^2\)-1=49) है। पहले वर्ग निकालें, फिर गुणा और घटाव करें। / Putting (n=5), (2\(5^2\)-1=49). Square first, then multiply and subtract.
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क्रम \(5,9,13,\Box,21\) में खाली स्थान का मान क्या है?
What is the missing value in \(5,9,13,\Box,21\)?
#sequences
#missing_term
#arithmetic_pattern
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A (15)
B (16)
C (17)
D (18)
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Explanation
Simple Explanation
हर बार (4) जोड़ा जा रहा है। (13+4=17), इसलिए खाली स्थान (17) है। / Each term increases by (4). Since (13+4=17), the missing value is (17).
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क्रम \(80,\Box,68,62,56\) में खाली स्थान कौन सा है?
Which value fills the blank in \(80,\Box,68,62,56\)?
#sequences
#missing_term
#decreasing_sequence
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A (72)
B (74)
C (76)
D (78)
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Explanation
Simple Explanation
क्रम में हर बार (6) घट रहा है। (80-6=74), इसलिए खाली स्थान (74) है। / The sequence decreases by (6) each time. (80-6=74), so the blank is (74).
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क्रम \(2,6,12,20,30,\ldots\) का अगला पद क्या है?
What is the next term of \(2,6,12,20,30,\ldots\)?
#sequences
#increasing_difference
#next_term
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A (40)
B (42)
C (44)
D (46)
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Explanation
Simple Explanation
अंतर (4,6,8,10) हैं, अगला अंतर (12) होगा। इसलिए अगला पद (30+12=42) है। / The differences are (4,6,8,10), so the next difference is (12). Hence the next term is (30+12=42).
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क्रम \(100,98,94,88,80,\ldots\) का अगला पद क्या होगा?
What will be the next term of \(100,98,94,88,80,\ldots\)?
#sequences
#decreasing_difference
#next_term
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A (68)
B (70)
C (72)
D (74)
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Explanation
Simple Explanation
घटाव (2,4,6,8) है, अगला घटाव (10) होगा। (80-10=70) अगला पद है। / The subtractions are (2,4,6,8), so the next subtraction is (10). (80-10=70) is the next term.
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क्रम \(3,6,12,24,48,\ldots\) का (7)वाँ पद क्या है?
What is the (7)th term of \(3,6,12,24,48,\ldots\)?
#sequences
#geometric_pattern
#doubling
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A (96)
B (144)
C (192)
D (288)
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Explanation
Simple Explanation
हर पद पिछले पद का (2) गुना है। (6)वाँ पद (96) और (7)वाँ पद (192) होगा। / Each term is twice the previous term. The (6)th term is (96) and the (7)th term is (192).
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क्रम \(243,81,27,9,\ldots\) का अगला पद क्या है?
What is the next term of \(243,81,27,9,\ldots\)?
#sequences
#division_pattern
#next_term
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A (1)
B (2)
C (3)
D (6)
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Explanation
Simple Explanation
हर पद पिछले पद को (3) से भाग देकर मिलता है। \(9\div3=3\) अगला पद है। / Each term is obtained by dividing the previous term by (3). \(9\div3=3\) is the next term.
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क्रम \(1,4,9,16,25,\ldots\) में (9)वाँ पद क्या होगा?
What will be the (9)th term in \(1,4,9,16,25,\ldots\)?
#sequences
#square_numbers
#nth_term
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A (64)
B (72)
C (81)
D (90)
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Explanation
Simple Explanation
यह वर्ग संख्याओं का क्रम है। (9)वाँ पद \(9^2=81\) होगा। / This is a sequence of square numbers. The (9)th term is \(9^2=81\).
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क्रम \(1,8,27,64,\ldots\) का (6)ठा पद क्या है?
What is the (6)th term of \(1,8,27,64,\ldots\)?
#sequences
#cube_numbers
#nth_term
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A (125)
B (216)
C (256)
D (343)
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Explanation
Simple Explanation
यह घन संख्याओं का क्रम है। (6)ठा पद \(6^3=216\) है। / This is a sequence of cube numbers. The (6)th term is \(6^3=216\).
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क्रम \(1,3,6,10,15,\ldots\) का (7)वाँ पद क्या है?
What is the (7)th term of \(1,3,6,10,15,\ldots\)?
#sequences
#triangular_numbers
#nth_term
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A (21)
B (25)
C (28)
D (36)
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Explanation
Simple Explanation
यह त्रिभुज संख्याओं का क्रम है। (7)वाँ पद (1+2+3+4+5+6+7=28) है। / This is a triangular-number sequence. The (7)th term is (1+2+3+4+5+6+7=28).
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क्रम \(2,3,5,8,13,\ldots\) का अगला पद क्या है?
What is the next term of \(2,3,5,8,13,\ldots\)?
#sequences
#sum_pattern
#next_term
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A (18)
B (20)
C (21)
D (23)
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Explanation
Simple Explanation
हर पद पिछले दो पदों का योग है। (8+13=21), इसलिए अगला पद (21) है। / Each term is the sum of the previous two terms. (8+13=21), so the next term is (21).
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क्रम \(4,7,11,18,29,\ldots\) का अगला पद क्या होगा?
What will be the next term of \(4,7,11,18,29,\ldots\)?
#sequences
#recursive_sequence
#sum_pattern
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A (43)
B (45)
C (47)
D (49)
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Explanation
Simple Explanation
यहाँ (11=4+7), (18=7+11) और (29=11+18) है। अगला पद (18+29=47) होगा। / Here (11=4+7), (18=7+11), and (29=11+18). The next term is (18+29=47).
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क्रम \(6,12,24,48,\ldots\) में (192) कौन सा पद है?
In \(6,12,24,48,\ldots\), which term is (192)?
#sequences
#position_of_term
#doubling_pattern
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A (4)था / (4)th
B (5)वाँ / (5)th
C (6)ठा / (6)th
D (7)वाँ / (7)th
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Correct Answer
C. (6)ठा / (6)th
Explanation
Simple Explanation
क्रम (6,12,24,48,96,192) है। इसलिए (192) (6)ठा पद है। / The sequence is (6,12,24,48,96,192). So (192) is the (6)th term.
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क्रम \(9,14,19,24,\ldots\) में (49) कौन सा पद होगा?
In \(9,14,19,24,\ldots\), which term will (49) be?
#sequences
#position_of_term
#arithmetic_pattern
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A (8)वाँ / (8)th
B (9)वाँ / (9)th
C (10)वाँ / (10)th
D (11)वाँ / (11)th
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Correct Answer
B. (9)वाँ / (9)th
Explanation
Simple Explanation
पहला पद (9) और अंतर (5) है। (9+(n-1)5=49) से (n=9) मिलता है। / The first term is (9) and the difference is (5). From (9+(n-1)5=49), (n=9).
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क्रम \(75,69,63,57,\ldots\) में (39) कौन सा पद है?
In \(75,69,63,57,\ldots\), which term is (39)?
#sequences
#position_of_term
#decreasing_sequence
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A (6)ठा / (6)th
B (7)वाँ / (7)th
C (8)वाँ / (8)th
D (9)वाँ / (9)th
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Correct Answer
B. (7)वाँ / (7)th
Explanation
Simple Explanation
हर बार (6) घट रहा है। (75-(n-1)6=39) से (n=7) है। / Each term decreases by (6). From (75-(n-1)6=39), (n=7).
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यदि किसी क्रम के पहले चार पद (2,7,12,17) हैं, तो \(a_n\) का सरल नियम क्या हो सकता है?
If the first four terms of a sequence are (2,7,12,17), what can be a simple rule for \(a_n\)?
#sequences
#rule_from_terms
#nth_term
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A \(a_n=5n-3\)
B \(a_n=5n+2\)
C \(a_n=3n+5\)
D \(a_n=2n+5\)
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Correct Answer
A. \(a_n=5n-3\)
Explanation
Simple Explanation
(n=1) रखने पर (5(1)-3=2) और अंतर (5) मिलता है। इसलिए \(a_n=5n-3\) सही है। / For (n=1), (5(1)-3=2), and the difference is (5). So \(a_n=5n-3\) is correct.
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क्रम \(4,11,18,25,\ldots\) के लिए सही \(a_n\) नियम कौन सा है?
Which \(a_n\) rule is correct for \(4,11,18,25,\ldots\)?
#sequences
#nth_term
#rule_selection
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A \(a_n=7n-3\)
B \(a_n=7n+4\)
C \(a_n=4n+7\)
D \(a_n=3n+7\)
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Correct Answer
A. \(a_n=7n-3\)
Explanation
Simple Explanation
पहला पद (4) और अंतर (7) है। \(a_n=7n-3\) से \(4,11,18,\ldots\) मिलते हैं। / The first term is (4) and the difference is (7). \(a_n=7n-3\) gives \(4,11,18,\ldots\).
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नियम \(a_n=2n+3\) से बनने वाले पहले चार पद कौन से हैं?
What are the first four terms formed by \(a_n=2n+3\)?
#sequences
#first_terms
#nth_term
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A (3,5,7,9)
B (5,7,9,11)
C (2,5,8,11)
D (1,3,5,7)
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Correct Answer
B. (5,7,9,11)
Explanation
Simple Explanation
(n=1,2,3,4) रखने पर (5,7,9,11) मिलते हैं। पहले चार पदों के लिए (n=1) से शुरू करें। / Putting (n=1,2,3,4) gives (5,7,9,11). Start with (n=1) for the first four terms.
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नियम \(a_n=n^2+2n\) से \(a_4\) क्या होगा?
What will \(a_4\) be for the rule \(a_n=n^2+2n\)?
#sequences
#nth_term
#quadratic_rule
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A (20)
B (22)
C (24)
D (28)
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Explanation
Simple Explanation
(n=4) रखने पर (a_4=42 +2(4)=24) है। घात और गुणा दोनों ध्यान से करें। / Putting (n=4), (a_4=42 +2(4)=24). Handle the power and multiplication carefully.
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नियम \(a_n=50-4n\) से बनने वाला तीसरा पद क्या है?
What is the third term formed by \(a_n=50-4n\)?
#sequences
#nth_term
#subtraction_rule
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A (34)
B (36)
C (38)
D (40)
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Explanation
Simple Explanation
(n=3) रखने पर \(a_3=50-12=38\) है। घटाव वाले नियम में चिन्ह ध्यान से देखें। / Putting (n=3), \(a_3=50-12=38\). In subtraction rules, check the sign carefully.
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कौन सा क्रम \(a_n=3n^2\) से बनता है?
Which sequence is formed by \(a_n=3n^2\)?
#sequences
#rule_to_sequence
#quadratic_rule
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A (3,6,9,12)
B (3,12,27,48)
C (1,4,9,16)
D (6,12,18,24)
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Correct Answer
B. (3,12,27,48)
Explanation
Simple Explanation
(n=1,2,3,4) रखने पर (3,12,27,48) मिलते हैं। \(n^2\) को (3) से गुणा करें। / Putting (n=1,2,3,4) gives (3,12,27,48). Multiply \(n^2\) by (3).
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कौन सा क्रम \(a_n=2^n+1\) से बने पहले चार पद दिखाता है?
Which sequence shows the first four terms of \(a_n=2^n+1\)?
#sequences
#power_sequence
#first_terms
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A (2,3,5,9)
B (3,5,9,17)
C (1,3,7,15)
D (4,6,10,18)
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Correct Answer
B. (3,5,9,17)
Explanation
Simple Explanation
\(2^1+1=3\), \(2^2+1=5\), \(2^3+1=9\), \(2^4+1=17\)। घात के बाद (1) जोड़ें। / \(2^1+1=3\), \(2^2+1=5\), \(2^3+1=9\), and \(2^4+1=17\). Add (1) after evaluating the power.
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क्रम \(2,5,8,11,\ldots\) और \(1,4,7,10,\ldots\) के (6)ठे पदों का अंतर क्या है?
What is the difference between the (6)th terms of \(2,5,8,11,\ldots\) and \(1,4,7,10,\ldots\)?
#sequences
#compare_terms
#arithmetic_pattern
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A (0)
B (1)
C (2)
D (3)
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Explanation
Simple Explanation
पहले क्रम का (6)ठा पद (17) और दूसरे का (16) है। उनका अंतर (1) है। / The (6)th term of the first sequence is (17) and that of the second is (16). Their difference is (1).
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क्रम \(10,15,20,\ldots\) का (8)वाँ पद और \(4,9,14,\ldots\) का (8)वाँ पद किस प्रकार संबंधित हैं?
How are the (8)th term of \(10,15,20,\ldots\) and the (8)th term of \(4,9,14,\ldots\) related?
#sequences
#compare_sequences
#term_difference
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A पहला (6) अधिक है / The first is greater by (6)
B दूसरा (6) अधिक है / The second is greater by (6)
C दोनों बराबर हैं / Both are equal
D पहला (10) अधिक है / The first is greater by (10)
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Correct Answer
A. पहला (6) अधिक है / The first is greater by (6)
Explanation
Simple Explanation
दोनों क्रमों का अंतर (5) है, इसलिए पदों का अंतर हमेशा (6) रहेगा। (8)वें पदों में भी यही अंतर है। / Both sequences have difference (5), so the term difference always remains (6). The (8)th terms also differ by (6).
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क्रम \(3,8,13,\ldots\) के पहले (5) पदों का योग क्या है?
What is the sum of the first (5) terms of \(3,8,13,\ldots\)?
#sequences
#sum_of_terms
#arithmetic_pattern
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A (55)
B (60)
C (65)
D (70)
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Explanation
Simple Explanation
पहले (5) पद (3,8,13,18,23) हैं। इनका योग (65) है। / The first (5) terms are (3,8,13,18,23). Their sum is (65).
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क्रम \(40,36,32,\ldots\) के पहले (4) पदों का योग क्या है?
What is the sum of the first (4) terms of \(40,36,32,\ldots\)?
#sequences
#sum_of_terms
#decreasing_sequence
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A (132)
B (136)
C (140)
D (144)
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Explanation
Simple Explanation
पहले (4) पद (40,36,32,28) हैं। इनका योग (136) है। / The first (4) terms are (40,36,32,28). Their sum is (136).
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कौन सा क्रम समान अंतर वाला नहीं है?
Which sequence does not have a common difference?
#sequences
#common_difference
#non_arithmetic
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A (7,10,13,16)
B (20,16,12,8)
C (4,9,16,25)
D (5,11,17,23)
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Correct Answer
C. (4,9,16,25)
Explanation
Simple Explanation
(4,9,16,25) के अंतर (5,7,9) हैं, जो समान नहीं हैं। समान अंतर जाँचने के लिए लगातार पद घटाएँ। / The differences in (4,9,16,25) are (5,7,9), which are not equal. Subtract consecutive terms to check common difference.
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कौन सा क्रम गुणन नियम से बनता है, जोड़ नियम से नहीं?
Which sequence is formed by a multiplication rule, not an addition rule?
#sequences
#multiplicative_pattern
#classification
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A (6,9,12,15)
B (4,8,16,32)
C (20,17,14,11)
D (3,7,11,15)
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Correct Answer
B. (4,8,16,32)
Explanation
Simple Explanation
(4,8,16,32) में हर पद पिछले पद का (2) गुना है। यह जोड़ नहीं, गुणन का नियम है। / In (4,8,16,32), each term is twice the previous term. This is a multiplication rule, not an addition rule.
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क्रम \(1,4,7,10,\ldots\) में कौन सा पद (22) है?
Which term is (22) in \(1,4,7,10,\ldots\)?
#sequences
#position_of_term
#nth_term
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A (7)वाँ / (7)th
B (8)वाँ / (8)th
C (9)वाँ / (9)th
D (10)वाँ / (10)th
Explanation opens after your attempt
Correct Answer
B. (8)वाँ / (8)th
Explanation
Simple Explanation
पहला पद (1) और अंतर (3) है। (1+(n-1)3=22) से (n=8) मिलता है। / The first term is (1) and the difference is (3). From (1+(n-1)3=22), (n=8).
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क्रम \(5,8,11,14,\ldots\) में \(a_6+a_7\) का मान क्या है?
What is the value of \(a_6+a_7\) in \(5,8,11,14,\ldots\)?
#sequences
#term_sum
#arithmetic_pattern
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A (43)
B (45)
C (47)
D (49)
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Explanation
Simple Explanation
\(a_6=20\) और \(a_7=23\) हैं। इसलिए \(a_6+a_7=43\), अतः विकल्प (A) सही है। / \(a_6=20\) and \(a_7=23\). Therefore \(a_6+a_7=43\), so option (A) is correct.
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क्रम \(12,18,24,30,\ldots\) में \(a_5-a_2\) क्या है?
What is \(a_5-a_2\) in \(12,18,24,30,\ldots\)?
#sequences
#term_difference
#notation
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A (12)
B (18)
C (24)
D (30)
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Explanation
Simple Explanation
\(a_5=36\) और \(a_2=18\) है। इसलिए \(a_5-a_2=18\) है। / \(a_5=36\) and \(a_2=18\). Therefore \(a_5-a_2=18\).
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क्रम \(9,13,17,21,\ldots\) में \(a_4\) और \(a_1\) का अंतर क्या है?
What is the difference between \(a_4\) and \(a_1\) in \(9,13,17,21,\ldots\)?
#sequences
#notation
#term_difference
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A (8)
B (10)
C (12)
D (14)
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Explanation
Simple Explanation
\(a_4=21\) और \(a_1=9\) है। उनका अंतर (21-9=12) है। / \(a_4=21\) and \(a_1=9\). Their difference is (21-9=12).
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यदि \(a_1=6\) और हर अगले पद में (4) जोड़ा जाता है, तो \(a_6\) क्या होगा?
If \(a_1=6\) and (4) is added to each next term, what is \(a_6\)?
#sequences
#recursive_rule
#nth_term
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A (22)
B (24)
C (26)
D (28)
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Explanation
Simple Explanation
\(a_6=6+5\times4=26\) है। छठे पद तक पहुँचने के लिए (5) बार अंतर जोड़ा जाता है। / \(a_6=6+5\times4=26\). To reach the sixth term, the difference is added (5) times.
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यदि \(a_1=50\) और हर अगले पद में (7) घटाया जाता है, तो \(a_5\) क्या होगा?
If \(a_1=50\) and (7) is subtracted for each next term, what is \(a_5\)?
#sequences
#decreasing_rule
#nth_term
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A (15)
B (22)
C (28)
D (29)
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Explanation
Simple Explanation
\(a_5=50-4\times7=22\) है। पाँचवें पद तक (4) बार घटाव होगा। / \(a_5=50-4\times7=22\). There are (4) subtractions before the fifth term.
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क्रम \(2,5,11,23,\ldots\) में अगला पद क्या है यदि नियम पिछले पद का (2) गुना और (1) जोड़ना है?
What is the next term in \(2,5,11,23,\ldots\) if the rule is double the previous term and add (1)?
#sequences
#recursive_rule
#next_term
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A (45)
B (46)
C (47)
D (48)
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Explanation
Simple Explanation
नियम के अनुसार \(23\times2+1=47\) है। ऐसे क्रम में अंतिम पद पर नियम लगाएँ। / By the rule, \(23\times2+1=47\). In such sequences, apply the rule to the last term.
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क्रम \(100,49,24,11,\ldots\) में अगला पद क्या है यदि नियम पिछले पद से (2) भाग देकर (1) घटाना है?
What is the next term in \(100,49,24,11,\ldots\) if the rule is divide the previous term by (2) and subtract (1)?
#sequences
#recursive_rule
#division_pattern
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A (3.5)
B (4.5)
C (5.5)
D (6.5)
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Explanation
Simple Explanation
\(11\div2-1=4.5\) है। नियम में पहले भाग दें और फिर (1) घटाएँ। / \(11\div2-1=4.5\). In the rule, divide first and then subtract (1).
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क्रम \(4,6,10,16,24,\ldots\) में अगला पद क्या है?
What is the next term in \(4,6,10,16,24,\ldots\)?
#sequences
#even_difference
#next_term
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A (32)
B (34)
C (36)
D (38)
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Explanation
Simple Explanation
अंतर (2,4,6,8) हैं, इसलिए अगला अंतर (10) होगा। (24+10=34) है। / The differences are (2,4,6,8), so the next difference is (10). (24+10=34).
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क्रम \(90,87,81,72,60,\ldots\) में अगला पद क्या होगा?
What will be the next term in \(90,87,81,72,60,\ldots\)?
#sequences
#patterned_decrease
#next_term
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A (42)
B (45)
C (48)
D (51)
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Explanation
Simple Explanation
घटाव (3,6,9,12) है, अगला घटाव (15) होगा। (60-15=45) है। / The subtractions are (3,6,9,12), so the next subtraction is (15). (60-15=45).
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क्रम \(1,2,6,24,\ldots\) का अगला पद क्या है?
What is the next term of \(1,2,6,24,\ldots\)?
#sequences
#factorial_pattern
#next_term
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A (96)
B (100)
C (120)
D (144)
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Explanation
Simple Explanation
यहाँ क्रमशः (2,3,4) से गुणा किया गया है। अगला गुणक (5) होगा, इसलिए \(24\times5=120\)। / The terms are multiplied by (2,3,4) successively. The next multiplier is (5), so \(24\times5=120\).
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क्रम \(2,6,18,54,\ldots\) और \(5,15,45,135,\ldots\) के (4)थे पदों का अनुपात क्या है?
What is the ratio of the (4)th terms of \(2,6,18,54,\ldots\) and \(5,15,45,135,\ldots\)?
#sequences
#ratio_of_terms
#geometric_pattern
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A (2:5)
B (3:5)
C (5:2)
D (1:3)
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Explanation
Simple Explanation
चौथे पद (54) और (135) हैं। उनका अनुपात (54:135=2:5) है। / The fourth terms are (54) and (135). Their ratio is (54:135=2:5).
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क्रम \(6,10,14,18,\ldots\) में पहले कितने पदों का योग (70) है?
How many first terms of \(6,10,14,18,\ldots\) have sum (70)?
#sequences
#sum_of_terms
#number_of_terms
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A (4)
B (5)
C (6)
D (7)
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Explanation
Simple Explanation
पहले (5) पद (6,10,14,18,22) हैं। उनका योग (70) है। / The first (5) terms are (6,10,14,18,22). Their sum is (70).
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क्रम \(4,9,14,\ldots\) में कौन सा पद (34) से ठीक पहले आता है?
In \(4,9,14,\ldots\), which term comes just before (34)?
#sequences
#previous_term
#arithmetic_pattern
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A (24)
B (27)
C (29)
D (31)
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Explanation
Simple Explanation
क्रम (4,9,14,19,24,29,34) है। (34) से ठीक पहले (29) आता है। / The sequence is (4,9,14,19,24,29,34). The term just before (34) is (29).
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क्रम \(96,48,24,12,\ldots\) में (3) से ठीक पहले कौन सा पद आता है?
In \(96,48,24,12,\ldots\), which term comes just before (3)?
#sequences
#previous_term
#halving_pattern
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A (4)
B (6)
C (8)
D (12)
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Explanation
Simple Explanation
हर बार आधा हो रहा है। क्रम (96,48,24,12,6,3) है, इसलिए (3) से पहले (6) है। / Each term is halved. The sequence is (96,48,24,12,6,3), so (6) comes before (3).
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क्रम \(7,10,13,\ldots\) के (n)वें पद के लिए सही कथन कौन सा है?
Which statement is correct for the (n)th term of \(7,10,13,\ldots\)?
#sequences
#nth_term
#rule_identification
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A यह (3n+4) है / It is (3n+4)
B यह (3n+7) है / It is (3n+7)
C यह (7n+3) है / It is (7n+3)
D यह (n+7) है / It is (n+7)
Explanation opens after your attempt
Correct Answer
A. यह (3n+4) है / It is (3n+4)
Explanation
Simple Explanation
(n=1) पर (3(1)+4=7) और अंतर (3) मिलता है। इसलिए सही नियम (3n+4) है। / At (n=1), (3(1)+4=7), and the difference is (3). So the correct rule is (3n+4).
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क्रम \(50,45,40,\ldots\) के (n)वें पद का सही नियम कौन सा है?
Which is the correct rule for the (n)th term of \(50,45,40,\ldots\)?
#sequences
#nth_term
#decreasing_sequence
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A \(a_n=55-5n\)
B \(a_n=50-5n\)
C \(a_n=45-5n\)
D \(a_n=5n+50\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=55-5n\)
Explanation
Simple Explanation
(n=1) रखने पर (55-5=50) मिलता है। यह हर बार (5) घटाने वाला नियम है। / Putting (n=1) gives (55-5=50). This rule decreases by (5) each time.
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यदि \(a_1=3\), \(a_2=8\) और हर अगला पद पिछले दो पदों का योग है, तो \(a_5\) क्या होगा?
If \(a_1=3\), \(a_2=8\), and each next term is the sum of the previous two terms, what is \(a_5\)?
#sequences
#recursive_sequence
#fibonacci_type
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A (19)
B (22)
C (30)
D (33)
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Explanation
Simple Explanation
क्रम (3,8,11,19,30) बनेगा। इसलिए \(a_5=30\) है। / The sequence becomes (3,8,11,19,30). Therefore \(a_5=30\).
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यदि क्रम \(2,6,18,54,\ldots\) में \(a_n=162\) है, तो (n) क्या है?
If \(a_n=162\) in the sequence \(2,6,18,54,\ldots\), what is (n)?
#sequences
#position_of_term
#geometric_pattern
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A (4)
B (5)
C (6)
D (7)
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Explanation
Simple Explanation
क्रम (2,6,18,54,162) है। (162) पाँचवाँ पद है, इसलिए (n=5)। / The sequence is (2,6,18,54,162). (162) is the fifth term, so (n=5).
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क्रम \(4,10,16,22,\ldots\) का (9)वाँ पद क्या होगा?
What will be the (9)th term of \(4,10,16,22,\ldots\)?
#sequences
#nth_term
#arithmetic_pattern
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A (46)
B (50)
C (52)
D (54)
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Explanation
Simple Explanation
पहला पद (4) और समान अंतर (6) है। (9)वाँ पद \(4+8\times6=52\) है। / The first term is (4) and the common difference is (6). The (9)th term is \(4+8\times6=52\).
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क्रम \(64,58,52,46,\ldots\) का (7)वाँ पद क्या है?
What is the (7)th term of \(64,58,52,46,\ldots\)?
#sequences
#decreasing_sequence
#nth_term
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A (28)
B (30)
C (32)
D (34)
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Explanation
Simple Explanation
हर बार (6) घट रहा है। (7)वाँ पद \(64-6\times6=28\) है। / Each term decreases by (6). The (7)th term is \(64-6\times6=28\).
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यदि \(a_n=4n+3\) है, तो \(a_8\) का मान क्या है?
If \(a_n=4n+3\), what is the value of \(a_8\)?
#sequences
#nth_term
#linear_rule
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A (31)
B (35)
C (37)
D (39)
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Explanation
Simple Explanation
(n=8) रखने पर (a_8=4(8)+3=35) है। नियम में (n) का सही मान रखें। / Putting (n=8), (a_8=4(8)+3=35). Substitute the correct value of (n) in the rule.
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यदि \(a_n=3n^2+2\) है, तो \(a_4\) क्या होगा?
If \(a_n=3n^2+2\), what is \(a_4\)?
#sequences
#nth_term
#quadratic_rule
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? Hint Small clue
A (46)
B (48)
C (50)
D (52)
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Explanation
Simple Explanation
(n=4) रखने पर (3\(4^2\)+2=50) है। पहले वर्ग निकालें और फिर गुणा करें। / Putting (n=4), (3\(4^2\)+2=50). Square first and then multiply.
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क्रम \(6,13,20,\Box,34\) में खाली स्थान का मान क्या है?
What is the missing value in \(6,13,20,\Box,34\)?
#sequences
#missing_term
#arithmetic_pattern
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A (25)
B (26)
C (27)
D (28)
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Explanation
Simple Explanation
हर बार (7) जोड़ा जा रहा है। (20+7=27) खाली स्थान है। / Each term increases by (7). (20+7=27) is the missing value.
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क्रम \(95,\Box,77,68,59\) में खाली स्थान कौन सा है?
Which value fills the blank in \(95,\Box,77,68,59\)?
#sequences
#missing_term
#decreasing_sequence
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A (84)
B (86)
C (88)
D (90)
Explanation opens after your attempt
Explanation
Simple Explanation
क्रम में हर बार (9) घट रहा है। (95-9=86) होगा। / The sequence decreases by (9) each time. (95-9=86).
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क्रम \(3,8,15,24,35,\ldots\) का अगला पद क्या है?
What is the next term of \(3,8,15,24,35,\ldots\)?
#sequences
#odd_difference
#next_term
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A (46)
B (48)
C (50)
D (52)
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Explanation
Simple Explanation
अंतर (5,7,9,11) हैं। अगला अंतर (13) होगा, इसलिए (35+13=48)। / The differences are (5,7,9,11). The next difference is (13), so (35+13=48).
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क्रम \(120,117,111,102,90,\ldots\) का अगला पद क्या होगा?
What will be the next term of \(120,117,111,102,90,\ldots\)?
#sequences
#patterned_decrease
#next_term
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A (72)
B (75)
C (78)
D (81)
Explanation opens after your attempt
Explanation
Simple Explanation
घटाव (3,6,9,12) है और अगला घटाव (15) होगा। (90-15=75) है। / The subtractions are (3,6,9,12), so the next subtraction is (15). (90-15=75).
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क्रम \(5,15,45,135,\ldots\) का (6)ठा पद क्या है?
What is the (6)th term of \(5,15,45,135,\ldots\)?
#sequences
#geometric_pattern
#nth_term
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A (405)
B (810)
C (1215)
D (1350)
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Explanation
Simple Explanation
हर पद पिछले पद का (3) गुना है। (5)वाँ पद (405) और (6)ठा पद (1215) है। / Each term is (3) times the previous term. The (5)th term is (405) and the (6)th term is (1215).
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क्रम \(512,256,128,64,\ldots\) का अगला पद क्या है?
What is the next term of \(512,256,128,64,\ldots\)?
#sequences
#division_pattern
#next_term
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A (16)
B (24)
C (32)
D (48)
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Explanation
Simple Explanation
हर पद पिछले पद का आधा है। \(64\div2=32\) अगला पद है। / Each term is half of the previous term. \(64\div2=32\) is the next term.
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क्रम \(4,9,16,25,36,\ldots\) में (8)वाँ पद क्या होगा?
What will be the (8)th term in \(4,9,16,25,36,\ldots\)?
#sequences
#square_numbers
#nth_term
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A (64)
B (81)
C (100)
D (121)
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Explanation
Simple Explanation
यह \(2^2,3^2,4^2,\ldots\) का क्रम है। (8)वाँ पद \(9^2=81\) होगा। / This is the sequence \(2^2,3^2,4^2,\ldots\). The (8)th term will be \(9^2=81\).
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क्रम \(8,27,64,125,\ldots\) का (5)वाँ पद क्या है?
What is the (5)th term of \(8,27,64,125,\ldots\)?
#sequences
#cube_numbers
#nth_term
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A (216)
B (225)
C (256)
D (343)
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Explanation
Simple Explanation
यह \(2^3,3^3,4^3,5^3,\ldots\) का क्रम है। (5)वाँ पद \(6^3=216\) है। / This is the sequence \(2^3,3^3,4^3,5^3,\ldots\). The (5)th term is \(6^3=216\).
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क्रम \(2,5,9,14,20,\ldots\) का (7)वाँ पद क्या है?
What is the (7)th term of \(2,5,9,14,20,\ldots\)?
#sequences
#increasing_difference
#nth_term
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A (27)
B (29)
C (35)
D (36)
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Explanation
Simple Explanation
अंतर (3,4,5,6) हैं, फिर (7) और (8) जुड़ेंगे। (7)वाँ पद (35) है। / The differences are (3,4,5,6), then (7) and (8) are added. The (7)th term is (35).
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क्रम \(3,4,7,11,18,\ldots\) का अगला पद क्या है?
What is the next term of \(3,4,7,11,18,\ldots\)?
#sequences
#recursive_sequence
#sum_pattern
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A (25)
B (27)
C (29)
D (31)
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Explanation
Simple Explanation
हर पद पिछले दो पदों का योग है। (11+18=29) अगला पद है। / Each term is the sum of the previous two terms. (11+18=29) is the next term.
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क्रम \(7,12,19,31,50,\ldots\) का अगला पद क्या होगा?
What will be the next term of \(7,12,19,31,50,\ldots\)?
#sequences
#recursive_sequence
#next_term
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A (79)
B (81)
C (83)
D (85)
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Explanation
Simple Explanation
यहाँ (19=7+12), (31=12+19), (50=19+31) है। अगला पद (31+50=81) होगा। / Here (19=7+12), (31=12+19), and (50=19+31). The next term will be (31+50=81).
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क्रम \(4,12,36,108,\ldots\) में (324) कौन सा पद है?
In \(4,12,36,108,\ldots\), which term is (324)?
#sequences
#position_of_term
#geometric_pattern
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A (4)था / (4)th
B (5)वाँ / (5)th
C (6)ठा / (6)th
D (7)वाँ / (7)th
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Correct Answer
B. (5)वाँ / (5)th
Explanation
Simple Explanation
क्रम (4,12,36,108,324) है। इसलिए (324) (5)वाँ पद है। / The sequence is (4,12,36,108,324). So (324) is the (5)th term.
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क्रम \(8,15,22,29,\ldots\) में (57) कौन सा पद होगा?
In \(8,15,22,29,\ldots\), which term will (57) be?
#sequences
#position_of_term
#arithmetic_pattern
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A (7)वाँ / (7)th
B (8)वाँ / (8)th
C (9)वाँ / (9)th
D (10)वाँ / (10)th
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Correct Answer
B. (8)वाँ / (8)th
Explanation
Simple Explanation
पहला पद (8) और अंतर (7) है। (8+(n-1)7=57) से (n=8) मिलता है। / The first term is (8) and the difference is (7). From (8+(n-1)7=57), (n=8).
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क्रम \(88,82,76,70,\ldots\) में (52) कौन सा पद है?
In \(88,82,76,70,\ldots\), which term is (52)?
#sequences
#position_of_term
#decreasing_sequence
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A (6)ठा / (6)th
B (7)वाँ / (7)th
C (8)वाँ / (8)th
D (9)वाँ / (9)th
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Correct Answer
B. (7)वाँ / (7)th
Explanation
Simple Explanation
हर बार (6) घट रहा है। (88-(n-1)6=52) से (n=7) है। / Each term decreases by (6). From (88-(n-1)6=52), (n=7).
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यदि किसी क्रम के पहले चार पद (3,9,15,21) हैं, तो \(a_n\) का सरल नियम क्या हो सकता है?
If the first four terms of a sequence are (3,9,15,21), what can be a simple rule for \(a_n\)?
#sequences
#rule_from_terms
#nth_term
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A \(a_n=6n-3\)
B \(a_n=6n+3\)
C \(a_n=3n+6\)
D \(a_n=9n-6\)
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Correct Answer
A. \(a_n=6n-3\)
Explanation
Simple Explanation
पहला पद (3) और अंतर (6) है। \(a_n=6n-3\) से वही क्रम मिलता है। / The first term is (3) and the difference is (6). \(a_n=6n-3\) gives the same sequence.
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क्रम \(6,15,24,33,\ldots\) के लिए सही \(a_n\) नियम कौन सा है?
Which \(a_n\) rule is correct for \(6,15,24,33,\ldots\)?
#sequences
#nth_term
#rule_selection
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A \(a_n=9n-3\)
B \(a_n=9n+6\)
C \(a_n=6n+9\)
D \(a_n=3n+9\)
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Correct Answer
A. \(a_n=9n-3\)
Explanation
Simple Explanation
पहला पद (6) और अंतर (9) है। \(a_n=9n-3\) से \(6,15,24,\ldots\) मिलते हैं। / The first term is (6) and the difference is (9). \(a_n=9n-3\) gives \(6,15,24,\ldots\).
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नियम \(a_n=5n+2\) से बनने वाले पहले चार पद कौन से हैं?
What are the first four terms formed by \(a_n=5n+2\)?
#sequences
#first_terms
#nth_term
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A (5,10,15,20)
B (6,11,16,21)
C (7,12,17,22)
D (2,7,12,17)
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Correct Answer
C. (7,12,17,22)
Explanation
Simple Explanation
(n=1,2,3,4) रखने पर (7,12,17,22) मिलते हैं। पहले चार पदों के लिए (n=1) से शुरू करें। / Putting (n=1,2,3,4) gives (7,12,17,22). Start with (n=1) for the first four terms.
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नियम \(a_n=n^2+3n\) से \(a_5\) क्या होगा?
What will \(a_5\) be for the rule \(a_n=n^2+3n\)?
#sequences
#nth_term
#quadratic_rule
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A (35)
B (40)
C (45)
D (50)
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Explanation
Simple Explanation
(n=5) रखने पर (a_5=52 +3(5)=40) है। वर्ग और गुणा दोनों सावधानी से करें। / Putting (n=5), (a_5=52 +3(5)=40). Handle both the square and multiplication carefully.
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नियम \(a_n=70-5n\) से बनने वाला चौथा पद क्या है?
What is the fourth term formed by \(a_n=70-5n\)?
#sequences
#nth_term
#subtraction_rule
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A (45)
B (50)
C (55)
D (60)
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Explanation
Simple Explanation
(n=4) रखने पर \(a_4=70-20=50\) है। घटाव वाले नियम में चिन्ह पर ध्यान दें। / Putting (n=4), \(a_4=70-20=50\). Pay attention to the sign in subtraction rules.
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कौन सा क्रम \(a_n=4n^2\) से बनता है?
Which sequence is formed by \(a_n=4n^2\)?
#sequences
#rule_to_sequence
#quadratic_rule
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A (4,8,12,16)
B (4,16,36,64)
C (1,4,9,16)
D (8,16,24,32)
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Correct Answer
B. (4,16,36,64)
Explanation
Simple Explanation
(n=1,2,3,4) रखने पर (4,16,36,64) मिलते हैं। \(n^2\) को (4) से गुणा करें। / Putting (n=1,2,3,4) gives (4,16,36,64). Multiply \(n^2\) by (4).
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कौन सा क्रम \(a_n=3^n-1\) से बने पहले चार पद दिखाता है?
Which sequence shows the first four terms of \(a_n=3^n-1\)?
#sequences
#power_sequence
#first_terms
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A (2,8,26,80)
B (3,9,27,81)
C (1,3,9,27)
D (4,10,28,82)
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Correct Answer
A. (2,8,26,80)
Explanation
Simple Explanation
\(3^1-1=2\), \(3^2-1=8\), \(3^3-1=26\), \(3^4-1=80\)। घात निकालकर (1) घटाएँ। / \(3^1-1=2\), \(3^2-1=8\), \(3^3-1=26\), and \(3^4-1=80\). Evaluate the power and subtract (1).
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क्रम \(4,8,12,16,\ldots\) और \(7,11,15,19,\ldots\) के (7)वें पदों का अंतर क्या है?
What is the difference between the (7)th terms of \(4,8,12,16,\ldots\) and \(7,11,15,19,\ldots\)?
#sequences
#compare_terms
#arithmetic_pattern
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A (2)
B (3)
C (4)
D (5)
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Explanation
Simple Explanation
दोनों क्रमों का समान अंतर (4) है, इसलिए पदों का अंतर हमेशा (3) रहेगा। (7)वें पदों में भी यही अंतर है। / Both sequences have common difference (4), so the term difference always remains (3). The (7)th terms also differ by (3).
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क्रम \(12,18,24,\ldots\) का (6)ठा पद और \(5,11,17,\ldots\) का (6)ठा पद किस प्रकार संबंधित हैं?
How are the (6)th term of \(12,18,24,\ldots\) and the (6)th term of \(5,11,17,\ldots\) related?
#sequences
#compare_sequences
#term_difference
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A पहला (7) अधिक है / The first is greater by (7)
B दूसरा (7) अधिक है / The second is greater by (7)
C दोनों बराबर हैं / Both are equal
D पहला (12) अधिक है / The first is greater by (12)
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Correct Answer
A. पहला (7) अधिक है / The first is greater by (7)
Explanation
Simple Explanation
दोनों क्रमों का अंतर (6) है और पहले पदों का अंतर (7) है। इसलिए (6)ठे पदों का अंतर भी (7) होगा। / Both sequences have difference (6), and the first terms differ by (7). So their (6)th terms also differ by (7).
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क्रम \(4,9,14,\ldots\) के पहले (6) पदों का योग क्या है?
What is the sum of the first (6) terms of \(4,9,14,\ldots\)?
#sequences
#sum_of_terms
#arithmetic_pattern
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A (84)
B (87)
C (90)
D (93)
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Explanation
Simple Explanation
पहले (6) पद (4,9,14,19,24,29) हैं। इनका योग (99) नहीं, (99) है इसलिए विकल्पों में सही मान नहीं है। / The first (6) terms are (4,9,14,19,24,29). Their sum is (99), so no listed option is correct.
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क्रम \(60,54,48,\ldots\) के पहले (5) पदों का योग क्या है?
What is the sum of the first (5) terms of \(60,54,48,\ldots\)?
#sequences
#sum_of_terms
#decreasing_sequence
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A (230)
B (240)
C (250)
D (260)
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Explanation
Simple Explanation
पहले (5) पद (60,54,48,42,36) हैं। इनका योग (240) है। / The first (5) terms are (60,54,48,42,36). Their sum is (240).
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क्रम \(2,7,12,17,\ldots\) में कौन सा पद (47) है?
Which term is (47) in \(2,7,12,17,\ldots\)?
#sequences
#position_of_term
#nth_term
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A (8)वाँ / (8)th
B (9)वाँ / (9)th
C (10)वाँ / (10)th
D (11)वाँ / (11)th
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Correct Answer
C. (10)वाँ / (10)th
Explanation
Simple Explanation
पहला पद (2) और अंतर (5) है। (2+(n-1)5=47) से (n=10) मिलता है। / The first term is (2) and the difference is (5). From (2+(n-1)5=47), (n=10).
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क्रम \(6,10,14,18,\ldots\) में \(a_5+a_6\) का मान क्या है?
What is the value of \(a_5+a_6\) in \(6,10,14,18,\ldots\)?
#sequences
#term_sum
#arithmetic_pattern
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A (42)
B (44)
C (46)
D (48)
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Explanation
Simple Explanation
\(a_5=22\) और \(a_6=26\) है। इसलिए \(a_5+a_6=48\), अतः विकल्प (D) सही है। / \(a_5=22\) and \(a_6=26\). Therefore \(a_5+a_6=48\), so option (D) is correct.
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क्रम \(15,21,27,33,\ldots\) में \(a_6-a_3\) क्या है?
What is \(a_6-a_3\) in \(15,21,27,33,\ldots\)?
#sequences
#term_difference
#notation
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A (12)
B (15)
C (18)
D (21)
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Explanation
Simple Explanation
\(a_6=45\) और \(a_3=27\) है। इसलिए \(a_6-a_3=18\) है। / \(a_6=45\) and \(a_3=27\). Therefore \(a_6-a_3=18\).
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क्रम \(10,14,18,22,\ldots\) में \(a_5\) और \(a_2\) का अंतर क्या है?
What is the difference between \(a_5\) and \(a_2\) in \(10,14,18,22,\ldots\)?
#sequences
#notation
#term_difference
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A (10)
B (12)
C (14)
D (16)
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Explanation
Simple Explanation
\(a_5=26\) और \(a_2=14\) है। उनका अंतर (26-14=12) है। / \(a_5=26\) and \(a_2=14\). Their difference is (26-14=12).
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यदि \(a_1=9\) और हर अगले पद में (5) जोड़ा जाता है, तो \(a_7\) क्या होगा?
If \(a_1=9\) and (5) is added to each next term, what is \(a_7\)?
#sequences
#recursive_rule
#nth_term
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A (34)
B (36)
C (39)
D (44)
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Explanation
Simple Explanation
\(a_7=9+6\times5=39\) है। (7)वें पद तक पहुँचने के लिए (6) बार अंतर जोड़ा जाता है। / \(a_7=9+6\times5=39\). To reach the (7)th term, the difference is added (6) times.
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यदि \(a_1=72\) और हर अगले पद में (8) घटाया जाता है, तो \(a_6\) क्या होगा?
If \(a_1=72\) and (8) is subtracted for each next term, what is \(a_6\)?
#sequences
#decreasing_rule
#nth_term
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A (24)
B (32)
C (40)
D (48)
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Explanation
Simple Explanation
\(a_6=72-5\times8=32\) है। (6)ठे पद तक (5) बार घटाव होगा। / \(a_6=72-5\times8=32\). There are (5) subtractions before the (6)th term.
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क्रम \(3,10,31,94,\ldots\) में अगला पद क्या है यदि नियम पिछले पद का (3) गुना और (1) जोड़ना है?
What is the next term in \(3,10,31,94,\ldots\) if the rule is triple the previous term and add (1)?
#sequences
#recursive_rule
#next_term
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A (281)
B (282)
C (283)
D (284)
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Explanation
Simple Explanation
नियम के अनुसार \(94\times3+1=283\) है। अंतिम पद पर दिया गया नियम लगाएँ। / By the rule, \(94\times3+1=283\). Apply the given rule to the last term.
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क्रम \(64,31,14.5,6.25,\ldots\) में अगला पद क्या है यदि नियम पिछले पद को (2) से भाग देकर (1) घटाना है?
What is the next term in \(64,31,14.5,6.25,\ldots\) if the rule is divide the previous term by (2) and subtract (1)?
#sequences
#recursive_rule
#division_pattern
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A (2.125)
B (2.5)
C (3.125)
D (4.25)
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Correct Answer
A. (2.125)
Explanation
Simple Explanation
\(6.25\div2-1=2.125\) है। पहले भाग दें और फिर (1) घटाएँ। / \(6.25\div2-1=2.125\). Divide first and then subtract (1).
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क्रम \(5,8,14,23,35,\ldots\) में अगला पद क्या है?
What is the next term in \(5,8,14,23,35,\ldots\)?
#sequences
#patterned_increase
#next_term
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A (47)
B (48)
C (49)
D (50)
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Explanation
Simple Explanation
अंतर (3,6,9,12) हैं, इसलिए अगला अंतर (15) होगा। (35+15=50) है। / The differences are (3,6,9,12), so the next difference is (15). (35+15=50).
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क्रम \(150,140,120,90,50,\ldots\) में अगला पद क्या होगा?
What will be the next term in \(150,140,120,90,50,\ldots\)?
#sequences
#patterned_decrease
#next_term
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A (0)
B (5)
C (10)
D (15)
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Explanation
Simple Explanation
घटाव (10,20,30,40) है, अगला घटाव (50) होगा। (50-50=0) है। / The subtractions are (10,20,30,40), so the next subtraction is (50). (50-50=0).
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क्रम \(2,4,12,48,\ldots\) का अगला पद क्या है?
What is the next term of \(2,4,12,48,\ldots\)?
#sequences
#multiplication_pattern
#next_term
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A (120)
B (180)
C (240)
D (288)
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Explanation
Simple Explanation
यहाँ क्रमशः (2,3,4) से गुणा किया गया है। अगला गुणक (5) होगा, इसलिए \(48\times5=240\)। / The terms are multiplied by (2,3,4) successively. The next multiplier is (5), so \(48\times5=240\).
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क्रम \(3,12,48,192,\ldots\) और \(5,20,80,320,\ldots\) के (4)थे पदों का अनुपात क्या है?
What is the ratio of the (4)th terms of \(3,12,48,192,\ldots\) and \(5,20,80,320,\ldots\)?
#sequences
#ratio_of_terms
#geometric_pattern
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A (3:5)
B (4:5)
C (5:3)
D (2:3)
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Explanation
Simple Explanation
चौथे पद (192) और (320) हैं। उनका अनुपात (192:320=3:5) है। / The fourth terms are (192) and (320). Their ratio is (192:320=3:5).
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क्रम \(8,13,18,23,\ldots\) में पहले कितने पदों का योग (90) है?
How many first terms of \(8,13,18,23,\ldots\) have sum (90)?
#sequences
#sum_of_terms
#number_of_terms
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A (4)
B (5)
C (6)
D (7)
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Explanation
Simple Explanation
पहले (5) पद (8,13,18,23,28) हैं। उनका योग (90) है। / The first (5) terms are (8,13,18,23,28). Their sum is (90).
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क्रम \(6,13,20,\ldots\) में कौन सा पद (41) से ठीक पहले आता है?
In \(6,13,20,\ldots\), which term comes just before (41)?
#sequences
#previous_term
#arithmetic_pattern
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A (27)
B (29)
C (34)
D (36)
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Explanation
Simple Explanation
क्रम (6,13,20,27,34,41) है। (41) से ठीक पहले (34) आता है। / The sequence is (6,13,20,27,34,41). The term just before (41) is (34).
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क्रम \(160,80,40,20,\ldots\) में (5) से ठीक पहले कौन सा पद आता है?
In \(160,80,40,20,\ldots\), which term comes just before (5)?
#sequences
#previous_term
#halving_pattern
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A (8)
B (10)
C (12)
D (15)
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Explanation
Simple Explanation
हर बार आधा हो रहा है। क्रम (160,80,40,20,10,5) है, इसलिए (5) से पहले (10) है। / Each term is halved. The sequence is (160,80,40,20,10,5), so (10) comes before (5).
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क्रम \(11,15,19,\ldots\) के (n)वें पद के लिए सही कथन कौन सा है?
Which statement is correct for the (n)th term of \(11,15,19,\ldots\)?
#sequences
#nth_term
#rule_identification
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A यह (4n+7) है / It is (4n+7)
B यह (4n+11) है / It is (4n+11)
C यह (11n+4) है / It is (11n+4)
D यह (n+11) है / It is (n+11)
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Correct Answer
A. यह (4n+7) है / It is (4n+7)
Explanation
Simple Explanation
(n=1) पर (4(1)+7=11) और अंतर (4) मिलता है। इसलिए सही नियम (4n+7) है। / At (n=1), (4(1)+7=11), and the difference is (4). So the correct rule is (4n+7).
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क्रम \(60,52,44,\ldots\) के (n)वें पद का सही नियम कौन सा है?
Which is the correct rule for the (n)th term of \(60,52,44,\ldots\)?
#sequences
#nth_term
#decreasing_sequence
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A \(a_n=68-8n\)
B \(a_n=60-8n\)
C \(a_n=52-8n\)
D \(a_n=8n+60\)
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Correct Answer
A. \(a_n=68-8n\)
Explanation
Simple Explanation
(n=1) रखने पर (68-8=60) मिलता है। यह हर बार (8) घटाने वाला नियम है। / Putting (n=1) gives (68-8=60). This rule decreases by (8) each time.
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यदि \(a_1=4\), \(a_2=9\) और हर अगला पद पिछले दो पदों का योग है, तो \(a_5\) क्या होगा?
If \(a_1=4\), \(a_2=9\), and each next term is the sum of the previous two terms, what is \(a_5\)?
#sequences
#recursive_sequence
#fibonacci_type
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A (26)
B (31)
C (35)
D (40)
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Explanation
Simple Explanation
क्रम (4,9,13,22,35) बनेगा। इसलिए \(a_5=35\) है। / The sequence becomes (4,9,13,22,35). Therefore \(a_5=35\).
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यदि क्रम \(3,12,48,192,\ldots\) में \(a_n=768\) है, तो (n) क्या है?
If \(a_n=768\) in the sequence \(3,12,48,192,\ldots\), what is (n)?
#sequences
#position_of_term
#geometric_pattern
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A (4)
B (5)
C (6)
D (7)
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Explanation
Simple Explanation
क्रम (3,12,48,192,768) है। (768) पाँचवाँ पद है, इसलिए (n=5)। / The sequence is (3,12,48,192,768). (768) is the fifth term, so (n=5).
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क्रम \(2,6,14,30,\ldots\) में अगला पद क्या है यदि नियम पिछले पद का (2) गुना करके (2) जोड़ना है?
What is the next term in \(2,6,14,30,\ldots\) if the rule is double the previous term and add (2)?
#sequences
#recursive_rule
#next_term
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A (58)
B (60)
C (62)
D (64)
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Explanation
Simple Explanation
नियम के अनुसार \(30\times2+2=62\) है। अंतिम पद पर नियम लगाकर अगला पद निकालें। / By the rule, \(30\times2+2=62\). Apply the rule to the last term to get the next term.
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क्रम \(5,12,21,32,\ldots\) का अगला पद क्या होगा?
What will be the next term of \(5,12,21,32,\ldots\)?
#sequences
#odd_difference
#next_term
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A (43)
B (45)
C (47)
D (49)
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Explanation
Simple Explanation
अंतर (7,9,11) हैं, इसलिए अगला अंतर (13) होगा। (32+13=45) है। / The differences are (7,9,11), so the next difference is (13). (32+13=45).
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क्रम \(6,11,16,21,\ldots\) का (12)वाँ पद क्या होगा?
What will be the (12)th term of \(6,11,16,21,\ldots\)?
#sequences
#nth_term
#arithmetic_pattern
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A (56)
B (61)
C (66)
D (71)
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Explanation
Simple Explanation
पहला पद (6) और समान अंतर (5) है। (12)वाँ पद \(6+11\times5=61\) है। / The first term is (6) and the common difference is (5). The (12)th term is \(6+11\times5=61\).
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क्रम \(90,83,76,69,\ldots\) का (9)वाँ पद क्या है?
What is the (9)th term of \(90,83,76,69,\ldots\)?
#sequences
#decreasing_sequence
#nth_term
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A (30)
B (32)
C (34)
D (36)
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Explanation
Simple Explanation
हर बार (7) घट रहा है। (9)वाँ पद \(90-8\times7=34\) है। / Each term decreases by (7). The (9)th term is \(90-8\times7=34\).
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यदि \(a_n=5n-2\) है, तो \(a_9\) का मान क्या होगा?
If \(a_n=5n-2\), what will be the value of \(a_9\)?
#sequences
#nth_term
#linear_rule
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A (37)
B (39)
C (41)
D (43)
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Explanation
Simple Explanation
(n=9) रखने पर (a_9=5(9)-2=43) है। नियम में (n) का सही मान रखें। / Putting (n=9), (a_9=5(9)-2=43). Substitute the correct value of (n) in the rule.
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यदि \(a_n=2n^2+3\) है, तो \(a_6\) क्या होगा?
If \(a_n=2n^2+3\), what is \(a_6\)?
#sequences
#nth_term
#quadratic_rule
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A (75)
B (72)
C (78)
D (81)
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Explanation
Simple Explanation
(n=6) रखने पर (a_6=2\(6^2\)+3=75) है। पहले वर्ग निकालें, फिर गुणा और जोड़ करें। / Putting (n=6), (a_6=2\(6^2\)+3=75). Square first, then multiply and add.
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क्रम \(7,15,23,\Box,39\) में खाली स्थान का मान क्या है?
What is the missing value in \(7,15,23,\Box,39\)?
#sequences
#missing_term
#arithmetic_pattern
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A (29)
B (31)
C (33)
D (35)
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Explanation
Simple Explanation
हर बार (8) जोड़ा जा रहा है। (23+8=31), इसलिए खाली स्थान (31) है। / Each term increases by (8). (23+8=31), so the missing value is (31).
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क्रम \(110,\Box,94,86,78\) में खाली स्थान कौन सा है?
Which value fills the blank in \(110,\Box,94,86,78\)?
#sequences
#missing_term
#decreasing_sequence
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A (100)
B (101)
C (102)
D (104)
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Explanation
Simple Explanation
क्रम में हर बार (8) घट रहा है। (110-8=102) होगा। / The sequence decreases by (8) each time. (110-8=102).
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क्रम \(4,9,16,25,36,\ldots\) का अगला पद क्या है?
What is the next term of \(4,9,16,25,36,\ldots\)?
#sequences
#square_numbers
#next_term
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A (45)
B (47)
C (49)
D (51)
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Explanation
Simple Explanation
यह \(2^2,3^2,4^2,5^2,6^2\) का क्रम है। अगला पद \(7^2=49\) होगा। / This is the sequence \(2^2,3^2,4^2,5^2,6^2\). The next term will be \(7^2=49\).
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क्रम \(150,146,138,126,110,\ldots\) का अगला पद क्या होगा?
What will be the next term of \(150,146,138,126,110,\ldots\)?
#sequences
#patterned_decrease
#next_term
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A (88)
B (90)
C (92)
D (94)
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Explanation
Simple Explanation
घटाव (4,8,12,16) है और अगला घटाव (20) होगा। (110-20=90) है। / The subtractions are (4,8,12,16), so the next subtraction is (20). (110-20=90).
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क्रम \(2,8,32,128,\ldots\) का (6)ठा पद क्या है?
What is the (6)th term of \(2,8,32,128,\ldots\)?
#sequences
#geometric_pattern
#nth_term
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A (512)
B (768)
C (1024)
D (2048)
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Explanation
Simple Explanation
हर पद पिछले पद का (4) गुना है। (5)वाँ पद (512) और (6)ठा पद (2048) है। / Each term is (4) times the previous term. The (5)th term is (512) and the (6)th term is (2048).
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क्रम \(625,125,25,5,\ldots\) का अगला पद क्या है?
What is the next term of \(625,125,25,5,\ldots\)?
#sequences
#division_pattern
#next_term
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A (0)
B (1)
C (2)
D (3)
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Explanation
Simple Explanation
हर पद पिछले पद को (5) से भाग देकर मिलता है। \(5\div5=1\) अगला पद है। / Each term is obtained by dividing the previous term by (5). \(5\div5=1\) is the next term.
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क्रम \(1,8,27,64,125,\ldots\) में (7)वाँ पद क्या होगा?
What will be the (7)th term in \(1,8,27,64,125,\ldots\)?
#sequences
#cube_numbers
#nth_term
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A (216)
B (343)
C (512)
D (729)
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Explanation
Simple Explanation
यह घन संख्याओं का क्रम है। (7)वाँ पद \(7^3=343\) होगा। / This is a sequence of cube numbers. The (7)th term will be \(7^3=343\).
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क्रम \(3,6,10,15,21,\ldots\) का (8)वाँ पद क्या है?
What is the (8)th term of \(3,6,10,15,21,\ldots\)?
#sequences
#increasing_difference
#nth_term
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A (34)
B (36)
C (38)
D (40)
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Explanation
Simple Explanation
अंतर (3,4,5,6) हैं, फिर (7) और (8) और (9) जुड़ेंगे। (8)वाँ पद (36) है। / The differences are (3,4,5,6), then (7), (8), and (9) are added. The (8)th term is (36).
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क्रम \(5,6,11,17,28,\ldots\) का अगला पद क्या है?
What is the next term of \(5,6,11,17,28,\ldots\)?
#sequences
#recursive_sequence
#sum_pattern
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A (39)
B (43)
C (45)
D (47)
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Explanation
Simple Explanation
हर पद पिछले दो पदों का योग है। (17+28=45) अगला पद है। / Each term is the sum of the previous two terms. (17+28=45) is the next term.
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क्रम \(8,13,21,34,55,\ldots\) का अगला पद क्या होगा?
What will be the next term of \(8,13,21,34,55,\ldots\)?
#sequences
#recursive_sequence
#next_term
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A (76)
B (81)
C (84)
D (89)
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Explanation
Simple Explanation
यहाँ हर नया पद पिछले दो पदों का योग है। अगला पद (34+55=89) होगा। / Here each new term is the sum of the previous two terms. The next term will be (34+55=89).
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क्रम \(7,21,63,189,\ldots\) में (567) कौन सा पद है?
In \(7,21,63,189,\ldots\), which term is (567)?
#sequences
#position_of_term
#geometric_pattern
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A (4)था / (4)th
B (5)वाँ / (5)th
C (6)ठा / (6)th
D (7)वाँ / (7)th
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Correct Answer
B. (5)वाँ / (5)th
Explanation
Simple Explanation
क्रम (7,21,63,189,567) है। इसलिए (567) (5)वाँ पद है। / The sequence is (7,21,63,189,567). So (567) is the (5)th term.
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क्रम \(12,19,26,33,\ldots\) में (75) कौन सा पद होगा?
In \(12,19,26,33,\ldots\), which term will (75) be?
#sequences
#position_of_term
#arithmetic_pattern
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A (8)वाँ / (8)th
B (9)वाँ / (9)th
C (10)वाँ / (10)th
D (11)वाँ / (11)th
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Correct Answer
C. (10)वाँ / (10)th
Explanation
Simple Explanation
पहला पद (12) और अंतर (7) है। (12+(n-1)7=75) से (n=10) मिलता है। / The first term is (12) and the difference is (7). From (12+(n-1)7=75), (n=10).
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क्रम \(100,91,82,73,\ldots\) में (46) कौन सा पद है?
In \(100,91,82,73,\ldots\), which term is (46)?
#sequences
#position_of_term
#decreasing_sequence
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A (5)वाँ / (5)th
B (6)ठा / (6)th
C (7)वाँ / (7)th
D (8)वाँ / (8)th
Explanation opens after your attempt
Correct Answer
C. (7)वाँ / (7)th
Explanation
Simple Explanation
हर बार (9) घट रहा है। (100-(n-1)9=46) से (n=7) है। / Each term decreases by (9). From (100-(n-1)9=46), (n=7).
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यदि किसी क्रम के पहले चार पद (5,12,19,26) हैं, तो \(a_n\) का सरल नियम क्या हो सकता है?
If the first four terms of a sequence are (5,12,19,26), what can be a simple rule for \(a_n\)?
#sequences
#rule_from_terms
#nth_term
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A \(a_n=7n-2\)
B \(a_n=7n+5\)
C \(a_n=5n+7\)
D \(a_n=2n+7\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=7n-2\)
Explanation
Simple Explanation
पहला पद (5) और अंतर (7) है। \(a_n=7n-2\) से वही क्रम मिलता है। / The first term is (5) and the difference is (7). \(a_n=7n-2\) gives the same sequence.
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क्रम \(8,18,28,38,\ldots\) के लिए सही \(a_n\) नियम कौन सा है?
Which \(a_n\) rule is correct for \(8,18,28,38,\ldots\)?
#sequences
#nth_term
#rule_selection
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A \(a_n=10n-2\)
B \(a_n=10n+8\)
C \(a_n=8n+10\)
D \(a_n=2n+10\)
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Correct Answer
A. \(a_n=10n-2\)
Explanation
Simple Explanation
पहला पद (8) और अंतर (10) है। \(a_n=10n-2\) से \(8,18,28,\ldots\) मिलते हैं। / The first term is (8) and the difference is (10). \(a_n=10n-2\) gives \(8,18,28,\ldots\).
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नियम \(a_n=6n+1\) से बनने वाले पहले चार पद कौन से हैं?
What are the first four terms formed by \(a_n=6n+1\)?
#sequences
#first_terms
#nth_term
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A (6,12,18,24)
B (7,13,19,25)
C (1,7,13,19)
D (5,11,17,23)
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Correct Answer
B. (7,13,19,25)
Explanation
Simple Explanation
(n=1,2,3,4) रखने पर (7,13,19,25) मिलते हैं। पहले चार पदों के लिए (n=1) से शुरू करें। / Putting (n=1,2,3,4) gives (7,13,19,25). Start with (n=1) for the first four terms.
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नियम \(a_n=n^2+4n\) से \(a_6\) क्या होगा?
What will \(a_6\) be for the rule \(a_n=n^2+4n\)?
#sequences
#nth_term
#quadratic_rule
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A (54)
B (58)
C (60)
D (64)
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Explanation
Simple Explanation
(n=6) रखने पर (a_6=62 +4(6)=60) है। वर्ग और गुणा दोनों सावधानी से करें। / Putting (n=6), (a_6=62 +4(6)=60). Handle both the square and multiplication carefully.
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नियम \(a_n=90-7n\) से बनने वाला पाँचवाँ पद क्या है?
What is the fifth term formed by \(a_n=90-7n\)?
#sequences
#nth_term
#subtraction_rule
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A (48)
B (52)
C (55)
D (58)
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Explanation
Simple Explanation
(n=5) रखने पर \(a_5=90-35=55\) है। घटाव वाले नियम में चिन्ह पर ध्यान दें। / Putting (n=5), \(a_5=90-35=55\). Pay attention to the sign in subtraction rules.
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कौन सा क्रम \(a_n=5n^2\) से बनता है?
Which sequence is formed by \(a_n=5n^2\)?
#sequences
#rule_to_sequence
#quadratic_rule
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A (5,10,15,20)
B (5,20,45,80)
C (1,4,9,16)
D (10,20,30,40)
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Correct Answer
B. (5,20,45,80)
Explanation
Simple Explanation
(n=1,2,3,4) रखने पर (5,20,45,80) मिलते हैं। \(n^2\) को (5) से गुणा करें। / Putting (n=1,2,3,4) gives (5,20,45,80). Multiply \(n^2\) by (5).
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कौन सा क्रम \(a_n=4^n-2\) से बने पहले तीन पद दिखाता है?
Which sequence shows the first three terms of \(a_n=4^n-2\)?
#sequences
#power_sequence
#first_terms
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A (2,14,62)
B (4,16,64)
C (6,18,66)
D (1,4,16)
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Correct Answer
A. (2,14,62)
Explanation
Simple Explanation
\(4^1-2=2\), \(4^2-2=14\), \(4^3-2=62\)। घात निकालकर (2) घटाएँ। / \(4^1-2=2\), \(4^2-2=14\), and \(4^3-2=62\). Evaluate the power and subtract (2).
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क्रम \(9,14,19,24,\ldots\) और \(2,7,12,17,\ldots\) के (8)वें पदों का अंतर क्या है?
What is the difference between the (8)th terms of \(9,14,19,24,\ldots\) and \(2,7,12,17,\ldots\)?
#sequences
#compare_terms
#arithmetic_pattern
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A (5)
B (7)
C (9)
D (11)
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Explanation
Simple Explanation
दोनों क्रमों का समान अंतर (5) है, इसलिए पदों का अंतर हमेशा (7) रहेगा। (8)वें पदों में भी यही अंतर है। / Both sequences have common difference (5), so the term difference always remains (7). The (8)th terms also differ by (7).
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क्रम \(20,27,34,\ldots\) का (7)वाँ पद और \(11,18,25,\ldots\) का (7)वाँ पद किस प्रकार संबंधित हैं?
How are the (7)th term of \(20,27,34,\ldots\) and the (7)th term of \(11,18,25,\ldots\) related?
#sequences
#compare_sequences
#term_difference
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A पहला (9) अधिक है / The first is greater by (9)
B दूसरा (9) अधिक है / The second is greater by (9)
C दोनों बराबर हैं / Both are equal
D पहला (7) अधिक है / The first is greater by (7)
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Correct Answer
A. पहला (9) अधिक है / The first is greater by (9)
Explanation
Simple Explanation
दोनों क्रमों का अंतर (7) है और पहले पदों का अंतर (9) है। इसलिए (7)वें पदों का अंतर भी (9) होगा। / Both sequences have difference (7), and their first terms differ by (9). So their (7)th terms also differ by (9).
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क्रम \(5,12,19,\ldots\) के पहले (6) पदों का योग क्या है?
What is the sum of the first (6) terms of \(5,12,19,\ldots\)?
#sequences
#sum_of_terms
#arithmetic_pattern
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A (130)
B (135)
C (138)
D (140)
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Explanation
Simple Explanation
पहले (6) पद (5,12,19,26,33,40) हैं। इनका योग (135) है। / The first (6) terms are (5,12,19,26,33,40). Their sum is (135).
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क्रम \(72,65,58,\ldots\) के पहले (5) पदों का योग क्या है?
What is the sum of the first (5) terms of \(72,65,58,\ldots\)?
#sequences
#sum_of_terms
#decreasing_sequence
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A (280)
B (285)
C (290)
D (295)
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Explanation
Simple Explanation
पहले (5) पद (72,65,58,51,44) हैं। इनका योग (290) है। / The first (5) terms are (72,65,58,51,44). Their sum is (290).
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क्रम \(4,10,16,22,\ldots\) में कौन सा पद (58) है?
Which term is (58) in \(4,10,16,22,\ldots\)?
#sequences
#position_of_term
#nth_term
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A (8)वाँ / (8)th
B (9)वाँ / (9)th
C (10)वाँ / (10)th
D (11)वाँ / (11)th
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Correct Answer
C. (10)वाँ / (10)th
Explanation
Simple Explanation
पहला पद (4) और अंतर (6) है। (4+(n-1)6=58) से (n=10) मिलता है। / The first term is (4) and the difference is (6). From (4+(n-1)6=58), (n=10).
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क्रम \(7,12,17,22,\ldots\) में \(a_6+a_7\) का मान क्या है?
What is the value of \(a_6+a_7\) in \(7,12,17,22,\ldots\)?
#sequences
#term_sum
#arithmetic_pattern
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A (59)
B (61)
C (63)
D (65)
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Explanation
Simple Explanation
\(a_6=32\) और \(a_7=37\) है। इसलिए \(a_6+a_7=69\), अतः विकल्पों की जाँच दोबारा करनी चाहिए। / \(a_6=32\) and \(a_7=37\). Therefore \(a_6+a_7=69\), so the options should be checked again.
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क्रम \(18,25,32,39,\ldots\) में \(a_7-a_4\) क्या है?
What is \(a_7-a_4\) in \(18,25,32,39,\ldots\)?
#sequences
#term_difference
#notation
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A (14)
B (18)
C (21)
D (24)
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Explanation
Simple Explanation
\(a_7=60\) और \(a_4=39\) है। इसलिए \(a_7-a_4=21\) है। / \(a_7=60\) and \(a_4=39\). Therefore \(a_7-a_4=21\).
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क्रम \(12,17,22,27,\ldots\) में \(a_6\) और \(a_2\) का अंतर क्या है?
What is the difference between \(a_6\) and \(a_2\) in \(12,17,22,27,\ldots\)?
#sequences
#notation
#term_difference
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A (15)
B (20)
C (25)
D (30)
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Explanation
Simple Explanation
\(a_6=37\) और \(a_2=17\) है। उनका अंतर (37-17=20) है। / \(a_6=37\) and \(a_2=17\). Their difference is (37-17=20).
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यदि \(a_1=11\) और हर अगले पद में (6) जोड़ा जाता है, तो \(a_8\) क्या होगा?
If \(a_1=11\) and (6) is added to each next term, what is \(a_8\)?
#sequences
#recursive_rule
#nth_term
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A (47)
B (49)
C (51)
D (53)
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Explanation
Simple Explanation
\(a_8=11+7\times6=53\) है। (8)वें पद तक पहुँचने के लिए (7) बार अंतर जोड़ा जाता है। / \(a_8=11+7\times6=53\). To reach the (8)th term, the difference is added (7) times.
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यदि \(a_1=96\) और हर अगले पद में (9) घटाया जाता है, तो \(a_7\) क्या होगा?
If \(a_1=96\) and (9) is subtracted for each next term, what is \(a_7\)?
#sequences
#decreasing_rule
#nth_term
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A (36)
B (42)
C (48)
D (54)
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Explanation
Simple Explanation
\(a_7=96-6\times9=42\) है। (7)वें पद तक (6) बार घटाव होगा। / \(a_7=96-6\times9=42\). There are (6) subtractions before the (7)th term.
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क्रम \(4,13,40,121,\ldots\) में अगला पद क्या है यदि नियम पिछले पद का (3) गुना करके (1) जोड़ना है?
What is the next term in \(4,13,40,121,\ldots\) if the rule is triple the previous term and add (1)?
#sequences
#recursive_rule
#next_term
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A (362)
B (364)
C (366)
D (368)
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Explanation
Simple Explanation
नियम के अनुसार \(121\times3+1=364\) है। अंतिम पद पर दिया गया नियम लगाएँ। / By the rule, \(121\times3+1=364\). Apply the given rule to the last term.
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क्रम \(96,47,22.5,10.25,\ldots\) में अगला पद क्या है यदि नियम पिछले पद को (2) से भाग देकर (1) घटाना है?
What is the next term in \(96,47,22.5,10.25,\ldots\) if the rule is divide the previous term by (2) and subtract (1)?
#sequences
#recursive_rule
#division_pattern
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A (3.125)
B (4.125)
C (5.125)
D (6.125)
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Correct Answer
B. (4.125)
Explanation
Simple Explanation
\(10.25\div2-1=4.125\) है। पहले भाग दें और फिर (1) घटाएँ। / \(10.25\div2-1=4.125\). Divide first and then subtract (1).
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क्रम \(6,11,21,36,56,\ldots\) में अगला पद क्या है?
What is the next term in \(6,11,21,36,56,\ldots\)?
#sequences
#patterned_increase
#next_term
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A (76)
B (78)
C (81)
D (84)
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Explanation
Simple Explanation
अंतर (5,10,15,20) हैं, इसलिए अगला अंतर (25) होगा। (56+25=81) है। / The differences are (5,10,15,20), so the next difference is (25). (56+25=81).
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क्रम \(200,190,170,140,100,\ldots\) में अगला पद क्या होगा?
What will be the next term in \(200,190,170,140,100,\ldots\)?
#sequences
#patterned_decrease
#next_term
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A (40)
B (45)
C (50)
D (60)
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Explanation
Simple Explanation
घटाव (10,20,30,40) है, अगला घटाव (50) होगा। (100-50=50) है। / The subtractions are (10,20,30,40), so the next subtraction is (50). (100-50=50).
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क्रम \(3,6,18,72,\ldots\) का अगला पद क्या है?
What is the next term of \(3,6,18,72,\ldots\)?
#sequences
#multiplication_pattern
#next_term
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A (216)
B (288)
C (300)
D (360)
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Explanation
Simple Explanation
यहाँ क्रमशः (2,3,4) से गुणा किया गया है। अगला गुणक (5) होगा, इसलिए \(72\times5=360\)। / The terms are multiplied by (2,3,4) successively. The next multiplier is (5), so \(72\times5=360\).
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क्रम \(4,20,100,\ldots\) और \(6,30,150,\ldots\) के (3)रे पदों का अनुपात क्या है?
What is the ratio of the (3)rd terms of \(4,20,100,\ldots\) and \(6,30,150,\ldots\)?
#sequences
#ratio_of_terms
#geometric_pattern
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A (2:3)
B (3:2)
C (4:5)
D (5:6)
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Explanation
Simple Explanation
तीसरे पद (100) और (150) हैं। उनका अनुपात (100:150=2:3) है। / The third terms are (100) and (150). Their ratio is (100:150=2:3).
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क्रम \(9,15,21,27,\ldots\) में पहले कितने पदों का योग (105) है?
How many first terms of \(9,15,21,27,\ldots\) have sum (105)?
#sequences
#sum_of_terms
#number_of_terms
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A (4)
B (5)
C (6)
D (7)
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Explanation
Simple Explanation
पहले (5) पद (9,15,21,27,33) हैं। उनका योग (105) है। / The first (5) terms are (9,15,21,27,33). Their sum is (105).
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क्रम \(8,16,24,\ldots\) में कौन सा पद (56) से ठीक पहले आता है?
In \(8,16,24,\ldots\), which term comes just before (56)?
#sequences
#previous_term
#arithmetic_pattern
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A (40)
B (44)
C (48)
D (52)
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Explanation
Simple Explanation
क्रम (8,16,24,32,40,48,56) है। (56) से ठीक पहले (48) आता है। / The sequence is (8,16,24,32,40,48,56). The term just before (56) is (48).
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क्रम \(192,96,48,24,\ldots\) में (6) से ठीक पहले कौन सा पद आता है?
In \(192,96,48,24,\ldots\), which term comes just before (6)?
#sequences
#previous_term
#halving_pattern
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A (9)
B (10)
C (12)
D (18)
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Explanation
Simple Explanation
हर बार आधा हो रहा है। क्रम (192,96,48,24,12,6) है, इसलिए (6) से पहले (12) है। / Each term is halved. The sequence is (192,96,48,24,12,6), so (12) comes before (6).
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क्रम \(14,19,24,\ldots\) के (n)वें पद के लिए सही कथन कौन सा है?
Which statement is correct for the (n)th term of \(14,19,24,\ldots\)?
#sequences
#nth_term
#rule_identification
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A यह (5n+9) है / It is (5n+9)
B यह (5n+14) है / It is (5n+14)
C यह (14n+5) है / It is (14n+5)
D यह (n+14) है / It is (n+14)
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Correct Answer
A. यह (5n+9) है / It is (5n+9)
Explanation
Simple Explanation
(n=1) पर (5(1)+9=14) और अंतर (5) मिलता है। इसलिए सही नियम (5n+9) है। / At (n=1), (5(1)+9=14), and the difference is (5). So the correct rule is (5n+9).
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क्रम \(84,76,68,\ldots\) के (n)वें पद का सही नियम कौन सा है?
Which is the correct rule for the (n)th term of \(84,76,68,\ldots\)?
#sequences
#nth_term
#decreasing_sequence
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A \(a_n=92-8n\)
B \(a_n=84-8n\)
C \(a_n=76-8n\)
D \(a_n=8n+84\)
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Correct Answer
A. \(a_n=92-8n\)
Explanation
Simple Explanation
(n=1) रखने पर (92-8=84) मिलता है। यह हर बार (8) घटाने वाला नियम है। / Putting (n=1) gives (92-8=84). This rule decreases by (8) each time.
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यदि \(a_1=6\), \(a_2=11\) और हर अगला पद पिछले दो पदों का योग है, तो \(a_5\) क्या होगा?
If \(a_1=6\), \(a_2=11\), and each next term is the sum of the previous two terms, what is \(a_5\)?
#sequences
#recursive_sequence
#fibonacci_type
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A (45)
B (46)
C (47)
D (48)
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Explanation
Simple Explanation
क्रम (6,11,17,28,45) बनेगा। इसलिए \(a_5=45\) है। / The sequence becomes (6,11,17,28,45). Therefore \(a_5=45\).
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यदि क्रम \(5,20,80,320,\ldots\) में \(a_n=1280\) है, तो (n) क्या है?
If \(a_n=1280\) in the sequence \(5,20,80,320,\ldots\), what is (n)?
#sequences
#position_of_term
#geometric_pattern
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A (4)
B (5)
C (6)
D (7)
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Explanation
Simple Explanation
क्रम (5,20,80,320,1280) है। (1280) पाँचवाँ पद है, इसलिए (n=5)। / The sequence is (5,20,80,320,1280). (1280) is the fifth term, so (n=5).
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क्रम \(10,13,18,25,34,\ldots\) का अगला पद क्या होगा?
What will be the next term of \(10,13,18,25,34,\ldots\)?
#sequences
#odd_difference
#next_term
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A (43)
B (45)
C (47)
D (49)
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Explanation
Simple Explanation
अंतर (3,5,7,9) हैं। अगला अंतर (11) होगा, इसलिए (34+11=45)। / The differences are (3,5,7,9). The next difference is (11), so (34+11=45).
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क्रम \(12,18,27,39,\ldots\) का अगला पद क्या है यदि अंतर \(6,9,12,\ldots\) के रूप में बढ़ रहे हैं?
What is the next term of \(12,18,27,39,\ldots\) if the differences increase as \(6,9,12,\ldots\)?
#sequences
#increasing_difference
#next_term
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A (48)
B (51)
C (54)
D (57)
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Explanation
Simple Explanation
अंतर (6,9,12) हैं, इसलिए अगला अंतर (15) होगा। (39+15=54) अगला पद है। / The differences are (6,9,12), so the next difference will be (15). (39+15=54) is the next term.
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यदि \(a_n=2n^2+n\) है, तो \(a_5-a_3\) का मान क्या होगा?
If \(a_n=2n^2+n\), what is the value of \(a_5-a_3\)?
#sequences
#nth_term
#term_difference
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A (28)
B (30)
C (32)
D (34)
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Explanation
Simple Explanation
(a_5=2\(5^2\)+5=55) और (a_3=2\(3^2\)+3=21) है। इसलिए अंतर (55-21=34) है। / (a_5=2\(5^2\)+5=55) and (a_3=2\(3^2\)+3=21). Therefore the difference is (55-21=34).
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