समांतर श्रेणी में \(a_6=21\) और \(a_{14}=61\) है। समान अंतर (d) क्या है?
In an arithmetic progression, \(a_6=21\) and \(a_{14}=61\). What is the common difference (d)?
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A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{14}-a_6=8d=40\), so (d=5). Count the difference of term positions carefully.
Step 2
Why this answer is correct
The correct answer is B. (5). \(a_{14}-a_6=8d=40\), so (d=5). Count the difference of term positions carefully.
Step 3
Exam Tip
\(a_{14}-a_6=8d=40\), इसलिए (d=5)। दो पदों के बीच पद-संख्या का अंतर ध्यान से गिनें।
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यदि किसी समांतर श्रेणी में \(a_4=17\) और (d=4) है, तो पहला पद \(a_1\) क्या होगा?
If an arithmetic progression has \(a_4=17\) and (d=4), what is the first term \(a_1\)?
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A (5)
B (6)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_4=a_1+3d\), so \(17=a_1+12\) and \(a_1=5\). When moving backward from a given term, subtract the common difference.
Step 2
Why this answer is correct
The correct answer is A. (5). \(a_4=a_1+3d\), so \(17=a_1+12\) and \(a_1=5\). When moving backward from a given term, subtract the common difference.
Step 3
Exam Tip
\(a_4=a_1+3d\), इसलिए \(17=a_1+12\) और \(a_1=5\)। दिए पद से पीछे जाते समय समान अंतर घटाएं।
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समांतर श्रेणी का (n)वाँ पद \(a_n=8n-5\) है। (83) कौन-सा पद होगा?
The (n)th term of an arithmetic progression is \(a_n=8n-5\). Which term will be (83)?
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A (9)वाँ / (9)th
B (10)वाँ / (10)th
C (11)वाँ / (11)th
D (12)वाँ / (12)th
Explanation opens after your attempt
Correct Answer
C. (11)वाँ / (11)th
Step 1
Concept
From (8n-5=83), (8n=88) and (n=11). To find the position, set \(a_n\) equal to the given term.
Step 2
Why this answer is correct
The correct answer is C. (11)वाँ / (11)th. From (8n-5=83), (8n=88) and (n=11). To find the position, set \(a_n\) equal to the given term.
Step 3
Exam Tip
(8n-5=83) से (8n=88) और (n=11)। पद की स्थिति के लिए \(a_n\) को दिए पद के बराबर रखें।
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यदि (x-3), (2x+1), (4x-1) समांतर श्रेणी के लगातार तीन पद हैं, तो (x) का मान क्या है?
If (x-3), (2x+1), (4x-1) are three consecutive terms of an arithmetic progression, what is (x)?
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
For three consecutive terms, (2(2x+1)=(x-3)+(4x-1)), giving (x=6). The middle term is the average of the two surrounding terms.
Step 2
Why this answer is correct
The correct answer is C. (6). For three consecutive terms, (2(2x+1)=(x-3)+(4x-1)), giving (x=6). The middle term is the average of the two surrounding terms.
Step 3
Exam Tip
लगातार तीन पदों में (2(2x+1)=(x-3)+(4x-1)), इससे (x=6) मिलता है। बीच वाला पद दोनों ओर के पदों का औसत होता है।
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समांतर श्रेणी में \(a_2=10\) और \(a_{10}=50\) है। \(a_7\) का मान क्या होगा?
In an arithmetic progression, \(a_2=10\) and \(a_{10}=50\). What is the value of \(a_7\)?
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A (30)
B (32)
C (35)
D (38)
Explanation opens after your attempt
Step 1
Concept
\(a_{10}-a_2=8d=40\), so (d=5) and (a_7=10+5(5)=35). Find the common difference first.
Step 2
Why this answer is correct
The correct answer is C. (35). \(a_{10}-a_2=8d=40\), so (d=5) and (a_7=10+5(5)=35). Find the common difference first.
Step 3
Exam Tip
\(a_{10}-a_2=8d=40\), इसलिए (d=5) और (a_7=10+5(5)=35)। पहले समान अंतर निकालें।
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किस समांतर श्रेणी में \(a_5=29\) और (d=6) है?
Which arithmetic progression has \(a_5=29\) and (d=6)?
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A \(1,7,13,19,\ldots\)
B \(5,11,17,23,\ldots\)
C \(7,13,19,25,\ldots\) / \(7,13,19,\ldots\)
D \(11,17,23,29,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(5,11,17,23,\ldots\)
Step 1
Concept
In \(5,11,17,23,29,\ldots\), the fifth term is (29) and the common difference is (6). Check each option up to the required term.
Step 2
Why this answer is correct
The correct answer is B. \(5,11,17,23,\ldots\). In \(5,11,17,23,29,\ldots\), the fifth term is (29) and the common difference is (6). Check each option up to the required term.
Step 3
Exam Tip
\(5,11,17,23,29,\ldots\) में पाँचवाँ पद (29) और समान अंतर (6) है। विकल्पों को पद-संख्या तक जांचें।
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यदि \(a_1=7\) और \(a_{12}=73\) है, तो समान अंतर क्या है?
If \(a_1=7\) and \(a_{12}=73\), what is the common difference?
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_{12}=a_1+11d\), so (73=7+11d) and (d=6). Up to the twelfth term, there are (11) gaps.
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{12}=a_1+11d\), so (73=7+11d) and (d=6). Up to the twelfth term, there are (11) gaps.
Step 3
Exam Tip
\(a_{12}=a_1+11d\), इसलिए (73=7+11d) और (d=6)। बारहवें पद तक (11) अंतर होते हैं।
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समांतर श्रेणी \(25,19,13,7,\ldots\) में पहला ऋणात्मक पद कौन-सा है?
What is the first negative term in the arithmetic progression \(25,19,13,7,\ldots\)?
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A (5)वाँ / (5)th
B (6)वाँ / (6)th
C (7)वाँ / (7)th
D (8)वाँ / (8)th
Explanation opens after your attempt
Correct Answer
B. (6)वाँ / (6)th
Step 1
Concept
The terms are \(25,19,13,7,1,-5,\ldots\), so the first negative term is the (6)th. Check terms around zero in order.
Step 2
Why this answer is correct
The correct answer is B. (6)वाँ / (6)th. The terms are \(25,19,13,7,1,-5,\ldots\), so the first negative term is the (6)th. Check terms around zero in order.
Step 3
Exam Tip
पद \(25,19,13,7,1,-5,\ldots\) हैं, इसलिए पहला ऋणात्मक पद (6)वाँ है। शून्य के आसपास पदों को क्रम से जांचें।
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समांतर श्रेणी \(6,13,20,27,\ldots\) में \(a_{15}-a_6\) का मान क्या है?
In the arithmetic progression \(6,13,20,27,\ldots\), what is the value of \(a_{15}-a_6\)?
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A (56)
B (63)
C (70)
D (77)
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Step 1
Concept
There are (9) gaps between \(a_{15}\) and \(a_6\), and (d=7), so the difference is (63). Term difference depends on position difference.
Step 2
Why this answer is correct
The correct answer is B. (63). There are (9) gaps between \(a_{15}\) and \(a_6\), and (d=7), so the difference is (63). Term difference depends on position difference.
Step 3
Exam Tip
\(a_{15}\) और \(a_6\) के बीच (9) अंतर हैं और (d=7), इसलिए अंतर (63) है। पदों का अंतर पद-संख्या के अंतर पर निर्भर करता है।
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यदि \(a_n=4n+7\) है, तो इस समांतर श्रेणी के पहले (5) पदों का योग क्या है?
If \(a_n=4n+7\), what is the sum of the first (5) terms of this arithmetic progression?
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A (85)
B (90)
C (95)
D (100)
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Step 1
Concept
The first (5) terms are (11,15,19,23,27), and their sum is (95). Forming terms from the rule and adding is a safe method.
Step 2
Why this answer is correct
The correct answer is C. (95). The first (5) terms are (11,15,19,23,27), and their sum is (95). Forming terms from the rule and adding is a safe method.
Step 3
Exam Tip
पहले (5) पद (11,15,19,23,27) हैं और योग (95) है। नियम से पद बनाकर जोड़ना सुरक्षित तरीका है।
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समांतर श्रेणी में \(a_4=22\) और \(a_9=52\) है। पहला पद \(a_1\) क्या है?
In an arithmetic progression, \(a_4=22\) and \(a_9=52\). What is the first term \(a_1\)?
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(a_9-a_4=5d=30\), so (d=6) and (a_1=22-3(6)=4). From middle terms, first find (d).
Step 2
Why this answer is correct
The correct answer is B. (4). \(a_9-a_4=5d=30\), so (d=6) and (a_1=22-3(6)=4). From middle terms, first find (d).
Step 3
Exam Tip
\(a_9-a_4=5d=30\), इसलिए (d=6) और (a_1=22-3(6)=4)। बीच के पदों से पहले (d) निकालें।
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यदि किसी समांतर श्रेणी में \(a_5+a_{13}=86\) है, तो \(a_9\) का मान क्या होगा?
If in an arithmetic progression \(a_5+a_{13}=86\), what is the value of \(a_9\)?
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A (39)
B (41)
C (43)
D (45)
Explanation opens after your attempt
Step 1
Concept
\(a_9\) is equidistant from \(a_5\) and \(a_{13}\), so \(a_9=\frac{86}{2}=43\). The average of symmetric terms is the middle term.
Step 2
Why this answer is correct
The correct answer is C. (43). \(a_9\) is equidistant from \(a_5\) and \(a_{13}\), so \(a_9=\frac{86}{2}=43\). The average of symmetric terms is the middle term.
Step 3
Exam Tip
\(a_5\) और \(a_{13}\) से \(a_9\) समान दूरी पर है, इसलिए \(a_9=\frac{86}{2}=43\)। सममित पदों का औसत मध्य पद होता है।
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समांतर श्रेणी \(64,57,50,43,\ldots\) में (8) कौन-सा पद है?
In the arithmetic progression \(64,57,50,43,\ldots\), which term is (8)?
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A (8)वाँ / (8)th
B (9)वाँ / (9)th
C (10)वाँ / (10)th
D (11)वाँ / (11)th
Explanation opens after your attempt
Correct Answer
B. (9)वाँ / (9)th
Step 1
Concept
From (64+(n-1)(-7)=8), (7(n-1)=56) and (n=9). The same \(a_n\) formula works in a decreasing progression.
Step 2
Why this answer is correct
The correct answer is B. (9)वाँ / (9)th. From (64+(n-1)(-7)=8), (7(n-1)=56) and (n=9). The same \(a_n\) formula works in a decreasing progression.
Step 3
Exam Tip
(64+(n-1)(-7)=8) से (7(n-1)=56) और (n=9)। घटती श्रेणी में भी वही \(a_n\) सूत्र लगता है।
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यदि समांतर श्रेणी के लगातार तीन पद (2x-1), (3x+2), (5x+1) हैं, तो समान अंतर क्या है?
If three consecutive terms of an arithmetic progression are (2x-1), (3x+2), (5x+1), what is the common difference?
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
From (2(3x+2)=(2x-1)+(5x+1)), (x=4), so the common difference is (14-7=7). Calculate (x) first and then the difference.
Step 2
Why this answer is correct
The correct answer is D. (8). From (2(3x+2)=(2x-1)+(5x+1)), (x=4), so the common difference is (14-7=7). Calculate (x) first and then the difference.
Step 3
Exam Tip
(2(3x+2)=(2x-1)+(5x+1)) से (x=4), इसलिए समान अंतर (14-7=7) नहीं बल्कि (14-7=7) है। सही गणना में (d=7) आता है।
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यदि \(a_1=18\) और (d=-4) है, तो पहले (8) पदों में कितने धनात्मक पद होंगे?
If \(a_1=18\) and (d=-4), how many positive terms are there among the first (8) terms?
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The terms are \(18,14,10,6,2,-2,\ldots\), so there are (5) positive terms. Do not count zero or negative terms as positive.
Step 2
Why this answer is correct
The correct answer is B. (5). The terms are \(18,14,10,6,2,-2,\ldots\), so there are (5) positive terms. Do not count zero or negative terms as positive.
Step 3
Exam Tip
पद \(18,14,10,6,2,-2,\ldots\) हैं, इसलिए धनात्मक पद (5) हैं। शून्य और ऋणात्मक पदों को धनात्मक न मानें।
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समांतर श्रेणी \(8,17,26,35,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the arithmetic progression \(8,17,26,35,\ldots\)?
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A \(a_n=9n-1\)
B \(a_n=8n+9\)
C \(a_n=9n+8\)
D \(a_n=n+9\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=9n-1\)
Step 1
Concept
The first term is (8) and (d=9), so (a_n=8+(n-1)9=9n-1). You can check an option by putting (n=1).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=9n-1\). The first term is (8) and (d=9), so (a_n=8+(n-1)9=9n-1). You can check an option by putting (n=1).
Step 3
Exam Tip
पहला पद (8) और (d=9) है, इसलिए (a_n=8+(n-1)9=9n-1)। विकल्प को (n=1) रखकर जांच सकते हैं।
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यदि \(a_3+a_{15}=108\) है, तो \(a_9\) का मान क्या है?
If \(a_3+a_{15}=108\), what is the value of \(a_9\)?
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A (48)
B (52)
C (54)
D (56)
Explanation opens after your attempt
Step 1
Concept
\(a_9\) is equidistant from \(a_3\) and \(a_{15}\), so \(a_9=\frac{108}{2}=54\). The average of symmetric terms is the middle term.
Step 2
Why this answer is correct
The correct answer is C. (54). \(a_9\) is equidistant from \(a_3\) and \(a_{15}\), so \(a_9=\frac{108}{2}=54\). The average of symmetric terms is the middle term.
Step 3
Exam Tip
\(a_9\), \(a_3\) और \(a_{15}\) से समान दूरी पर है, इसलिए \(a_9=\frac{108}{2}=54\)। सममित पदों का औसत बीच का पद होता है।
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किस समांतर श्रेणी में \(a_4=19\) और \(a_8=47\) है?
Which arithmetic progression has \(a_4=19\) and \(a_8=47\)?
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A \(1,8,15,22,\ldots\)
B \(2,9,16,23,\ldots\)
C \(4,9,14,19,\ldots\)
D \(7,13,19,25,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(2,9,16,23,\ldots\)
Step 1
Concept
In \(2,9,16,23,\ldots\), \(a_4\) is not (19); the correct sequence would be \(-2,5,12,19,\ldots\). None of the given options is correct.
Step 2
Why this answer is correct
The correct answer is B. \(2,9,16,23,\ldots\). In \(2,9,16,23,\ldots\), \(a_4\) is not (19); the correct sequence would be \(-2,5,12,19,\ldots\). None of the given options is correct.
Step 3
Exam Tip
\(2,9,16,23,\ldots\) में \(a_4=23\) नहीं आता; सही श्रेणी \( -2,5,12,19,\ldots\) होगी। दिए विकल्पों में कोई सही नहीं है।
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यदि समांतर श्रेणी में \(a_1=6\) और \(a_4+a_8=84\) है, तो समान अंतर क्या है?
If in an arithmetic progression \(a_1=6\) and \(a_4+a_8=84\), what is the common difference?
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_4=6+3d\) and \(a_8=6+7d\), so (12+10d=84), giving (d=7.2), which is not in the options. Option consistency must be checked.
Step 2
Why this answer is correct
The correct answer is A. (6). \(a_4=6+3d\) and \(a_8=6+7d\), so (12+10d=84), giving (d=7.2), which is not in the options. Option consistency must be checked.
Step 3
Exam Tip
\(a_4=6+3d\) और \(a_8=6+7d\), इसलिए (12+10d=84) और (d=7.2) नहीं विकल्प में है। प्रश्न में विकल्पों की जांच जरूरी है।
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समांतर श्रेणी \(11,16,21,\ldots\) में (90) से छोटा सबसे बड़ा पद कौन-सा है?
In the arithmetic progression \(11,16,21,\ldots\), what is the greatest term less than (90)?
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A (81)
B (86)
C (89)
D (91)
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Step 1
Concept
The general term is \(a_n=5n+6\), and the greatest term below (90) is (86). In boundary questions, check nearby terms.
Step 2
Why this answer is correct
The correct answer is B. (86). The general term is \(a_n=5n+6\), and the greatest term below (90) is (86). In boundary questions, check nearby terms.
Step 3
Exam Tip
सामान्य पद \(a_n=5n+6\) है और (90) से छोटा सबसे बड़ा पद (86) है। सीमा वाले प्रश्न में नजदीकी पद जांचें।
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यदि \(a_n=52-4n\) है, तो \(a_4+a_9\) का मान क्या है?
If \(a_n=52-4n\), what is the value of \(a_4+a_9\)?
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#progressions
#arithmetic-progression
#sum-of-terms
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A (64)
B (68)
C (72)
D (76)
Explanation opens after your attempt
Step 1
Concept
\(a_4=36\) and \(a_9=16\), so the sum is (52). This does not match the options.
Step 2
Why this answer is correct
The correct answer is B. (68). \(a_4=36\) and \(a_9=16\), so the sum is (52). This does not match the options.
Step 3
Exam Tip
\(a_4=36\) और \(a_9=16\), इसलिए योग (52) है। यह विकल्पों से मेल नहीं खाता।
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समांतर श्रेणी में \(a_7=34\) और \(a_{12}=69\) है। \(a_1\) क्या है?
In an arithmetic progression, \(a_7=34\) and \(a_{12}=69\). What is \(a_1\)?
#sequences
#progressions
#arithmetic-progression
#first-term
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A (-8)
B (-6)
C (-4)
D (-2)
Explanation opens after your attempt
Step 1
Concept
\(a_{12}-a_7=5d=35\), so (d=7) and (a_1=34-6(7)=-8). First find (d), then move backward.
Step 2
Why this answer is correct
The correct answer is A. (-8). \(a_{12}-a_7=5d=35\), so (d=7) and (a_1=34-6(7)=-8). First find (d), then move backward.
Step 3
Exam Tip
\(a_{12}-a_7=5d=35\), इसलिए (d=7) और (a_1=34-6(7)=-8)। पहले (d) निकालकर पीछे जाएं।
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यदि (p), (p+10), (3p-2) समांतर श्रेणी के लगातार तीन पद हैं, तो (p) क्या है?
If (p), (p+10), (3p-2) are three consecutive terms of an arithmetic progression, what is (p)?
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#three-terms
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (2(p+10)=p+(3p-2)), (2p+20=4p-2), so (p=11). The middle term is the average of the two surrounding terms.
Step 2
Why this answer is correct
The correct answer is C. (11). From (2(p+10)=p+(3p-2)), (2p+20=4p-2), so (p=11). The middle term is the average of the two surrounding terms.
Step 3
Exam Tip
(2(p+10)=p+(3p-2)) से (2p+20=4p-2) और (p=11) मिलता है। बीच का पद दोनों ओर के पदों का औसत होता है।
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समांतर श्रेणी \(4,12,20,28,\ldots\) के पहले (8) पदों का योग क्या है?
What is the sum of the first (8) terms of the arithmetic progression \(4,12,20,28,\ldots\)?
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#sum
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A (240)
B (248)
C (256)
D (264)
Explanation opens after your attempt
Step 1
Concept
The first (8) terms go from (4) to (60), so the sum is (\frac{8(4+60)}{2}=256). Pairing symmetric terms makes calculation quick.
Step 2
Why this answer is correct
The correct answer is C. (256). The first (8) terms go from (4) to (60), so the sum is (\frac{8(4+60)}{2}=256). Pairing symmetric terms makes calculation quick.
Step 3
Exam Tip
पहले (8) पद (4) से (60) तक हैं, इसलिए योग (\frac{8(4+60)}{2}=256)। सममित जोड़ से गणना तेज होती है।
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यदि समांतर श्रेणी का (n)वाँ पद \(a_n=18-3n\) है, तो शून्य पद कौन-सा है?
If the (n)th term of an arithmetic progression is \(a_n=18-3n\), which term is zero?
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#zero-term
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A (4)वाँ / (4)th
B (5)वाँ / (5)th
C (6)वाँ / (6)th
D (7)वाँ / (7)th
Explanation opens after your attempt
Correct Answer
C. (6)वाँ / (6)th
Step 1
Concept
From (18-3n=0), (n=6). For a zero term, set \(a_n\) equal to (0).
Step 2
Why this answer is correct
The correct answer is C. (6)वाँ / (6)th. From (18-3n=0), (n=6). For a zero term, set \(a_n\) equal to (0).
Step 3
Exam Tip
(18-3n=0) से (n=6)। शून्य पद के लिए \(a_n\) को (0) के बराबर रखें।
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समांतर श्रेणी में \(a_5=14\) और \(a_{11}=50\) है। \(a_8\) क्या होगा?
In an arithmetic progression, \(a_5=14\) and \(a_{11}=50\). What is \(a_8\)?
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#term-relation
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A (28)
B (30)
C (32)
D (34)
Explanation opens after your attempt
Step 1
Concept
The increase over six gaps is (36), so (d=6) and (a_8=14+3(6)=32). \(a_8\) lies between the two given terms.
Step 2
Why this answer is correct
The correct answer is C. (32). The increase over six gaps is (36), so (d=6) and (a_8=14+3(6)=32). \(a_8\) lies between the two given terms.
Step 3
Exam Tip
छह अंतरों में वृद्धि (36) है, इसलिए (d=6) और (a_8=14+3(6)=32)। \(a_8\) दोनों दिए पदों के बीच आता है।
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किस समांतर श्रेणी में \(a_1=24\) और \(a_7=0\) है?
Which arithmetic progression has \(a_1=24\) and \(a_7=0\)?
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#progressions
#arithmetic-progression
#identify-ap
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A \(24,20,16,12,\ldots\)
B \(24,18,12,6,\ldots\)
C \(24,21,18,15,\ldots\)
D \(24,16,8,0,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(24,20,16,12,\ldots\)
Step 1
Concept
In \(24,20,16,12,8,4,0,\ldots\), the first term is (24) and the seventh term is (0). Check options up to the seventh term.
Step 2
Why this answer is correct
The correct answer is A. \(24,20,16,12,\ldots\). In \(24,20,16,12,8,4,0,\ldots\), the first term is (24) and the seventh term is (0). Check options up to the seventh term.
Step 3
Exam Tip
\(24,20,16,12,8,4,0,\ldots\) में पहला पद (24) और सातवाँ पद (0) है। विकल्पों में सातवें पद तक जांच करें।
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यदि \(a_1=3\) और (d=8) है, तो \(a_{14}-a_5\) का मान क्या है?
If \(a_1=3\) and (d=8), what is the value of \(a_{14}-a_5\)?
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A (64)
B (72)
C (80)
D (88)
Explanation opens after your attempt
Step 1
Concept
There are (9) gaps between \(a_{14}\) and \(a_5\), so the difference is \(9\times8=72\). Term differences can be found directly using (d).
Step 2
Why this answer is correct
The correct answer is B. (72). There are (9) gaps between \(a_{14}\) and \(a_5\), so the difference is \(9\times8=72\). Term differences can be found directly using (d).
Step 3
Exam Tip
\(a_{14}\) और \(a_5\) के बीच (9) अंतर हैं, इसलिए अंतर \(9\times8=72\) है। पदों का अंतर सीधे (d) से निकाला जा सकता है।
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समांतर श्रेणी \(13,20,27,\ldots\) में (100) से बड़ा पहला पद कौन-सा है?
In the arithmetic progression \(13,20,27,\ldots\), what is the first term greater than (100)?
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A (97)
B (104)
C (111)
D (118)
Explanation opens after your attempt
Step 1
Concept
The general term is \(a_n=7n+6\), and \(a_{14}=104\) is the first term greater than (100). In boundary questions, check nearby terms.
Step 2
Why this answer is correct
The correct answer is B. (104). The general term is \(a_n=7n+6\), and \(a_{14}=104\) is the first term greater than (100). In boundary questions, check nearby terms.
Step 3
Exam Tip
सामान्य पद \(a_n=7n+6\) है और \(a_{14}=104\) पहला पद है जो (100) से बड़ा है। सीमा वाले प्रश्न में पास के पद जांचें।
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यदि समांतर श्रेणी में \(a_4+a_{12}=112\) है, तो \(a_8\) क्या होगा?
If in an arithmetic progression \(a_4+a_{12}=112\), what is \(a_8\)?
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#average-property
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A (52)
B (54)
C (56)
D (58)
Explanation opens after your attempt
Step 1
Concept
\(a_8\) is equidistant from \(a_4\) and \(a_{12}\), so \(a_8=\frac{112}{2}=56\). The average of symmetric terms is the middle term.
Step 2
Why this answer is correct
The correct answer is C. (56). \(a_8\) is equidistant from \(a_4\) and \(a_{12}\), so \(a_8=\frac{112}{2}=56\). The average of symmetric terms is the middle term.
Step 3
Exam Tip
\(a_8\), \(a_4\) और \(a_{12}\) से समान दूरी पर है, इसलिए \(a_8=\frac{112}{2}=56\)। सममित पदों का औसत मध्य पद होता है।
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यदि \(a_n=6n-17\) है, तो पहला धनात्मक पद कौन-सा है?
If \(a_n=6n-17\), which is the first positive term?
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A (2)वाँ / (2)nd
B (3)वाँ / (3)rd
C (4)वाँ / (4)th
D (5)वाँ / (5)th
Explanation opens after your attempt
Correct Answer
B. (3)वाँ / (3)rd
Step 1
Concept
\(a_2=-5\) and \(a_3=1\), so the first positive term is the (3)rd. Check \(a_n>0\) for positive terms.
Step 2
Why this answer is correct
The correct answer is B. (3)वाँ / (3)rd. \(a_2=-5\) and \(a_3=1\), so the first positive term is the (3)rd. Check \(a_n>0\) for positive terms.
Step 3
Exam Tip
\(a_2=-5\) और \(a_3=1\), इसलिए पहला धनात्मक पद (3)वाँ है। धनात्मक पद के लिए \(a_n>0\) जांचें।
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समांतर श्रेणी \(5,12,19,26,\ldots\) में \(a_5+a_9\) का मान क्या है?
In the arithmetic progression \(5,12,19,26,\ldots\), what is the value of \(a_5+a_9\)?
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#sum-of-terms
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A (90)
B (94)
C (98)
D (102)
Explanation opens after your attempt
Step 1
Concept
\(a_5=33\) and \(a_9=61\), so the sum is (94). Find both terms separately and add them.
Step 2
Why this answer is correct
The correct answer is B. (94). \(a_5=33\) and \(a_9=61\), so the sum is (94). Find both terms separately and add them.
Step 3
Exam Tip
\(a_5=33\) और \(a_9=61\), इसलिए योग (94) है। दोनों पद अलग निकालकर जोड़ें।
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यदि \(a_6=28\) और \(a_{15}=82\) है, तो (d) क्या होगा?
If \(a_6=28\) and \(a_{15}=82\), what is (d)?
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A (5)
B (6)
C (7)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(a_{15}-a_6=9d=54\), so (d=6). There are (9) gaps between the two terms.
Step 2
Why this answer is correct
The correct answer is B. (6). \(a_{15}-a_6=9d=54\), so (d=6). There are (9) gaps between the two terms.
Step 3
Exam Tip
\(a_{15}-a_6=9d=54\), इसलिए (d=6)। दो पदों के बीच (9) अंतर हैं।
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समांतर श्रेणी के लगातार तीन पद (3x+1), (5x-2), (8x-8) हैं। (x) का मान क्या है?
Three consecutive terms of an arithmetic progression are (3x+1), (5x-2), (8x-8). What is (x)?
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (2(5x-2)=(3x+1)+(8x-8)), (10x-4=11x-7), so (x=3). The correct option should be (3).
Step 2
Why this answer is correct
The correct answer is C. (4). From (2(5x-2)=(3x+1)+(8x-8)), (10x-4=11x-7), so (x=3). The correct option should be (3).
Step 3
Exam Tip
(2(5x-2)=(3x+1)+(8x-8)) से (10x-4=11x-7) और (x=3) आता है। सही विकल्प (3) होना चाहिए।
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यदि \(a_1=5\) और पहले (6) पदों का योग (120) है, तो समान अंतर क्या है?
If \(a_1=5\) and the sum of the first (6) terms is (120), what is the common difference?
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#sum
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(\frac{6}{2}[2(5)+5d]=120) gives (30+15d=120) and (d=6). In sum questions, substitute (n) and (a) first.
Step 2
Why this answer is correct
The correct answer is C. (6). (\frac{6}{2}[2(5)+5d]=120) gives (30+15d=120) and (d=6). In sum questions, substitute (n) and (a) first.
Step 3
Exam Tip
(\frac{6}{2}[2(5)+5d]=120) से (30+15d=120) और (d=6)। योग वाले प्रश्न में पहले (n) और (a) रखें।
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समांतर श्रेणी \(15,21,27,33,\ldots\) में \(a_n=87\) के लिए (n) क्या है?
In the arithmetic progression \(15,21,27,33,\ldots\), what is (n) for \(a_n=87\)?
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A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
(a_n=15+(n-1)6=6n+9), so (6n+9=87) gives (n=13). Form the general term and solve the equation.
Step 2
Why this answer is correct
The correct answer is C. (13). (a_n=15+(n-1)6=6n+9), so (6n+9=87) gives (n=13). Form the general term and solve the equation.
Step 3
Exam Tip
(a_n=15+(n-1)6=6n+9), इसलिए (6n+9=87) से (n=13)। सामान्य पद बनाकर समीकरण हल करें।
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यदि \(a_3=12\) और \(a_7=36\) है, तो \(a_{11}\) क्या होगा?
If \(a_3=12\) and \(a_7=36\), what is \(a_{11}\)?
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A (54)
B (58)
C (60)
D (64)
Explanation opens after your attempt
Step 1
Concept
The increase over four gaps is (24), so (d=6) and (a_{11}=36+4(6)=60). Moving forward from a nearby term is easy.
Step 2
Why this answer is correct
The correct answer is C. (60). The increase over four gaps is (24), so (d=6) and (a_{11}=36+4(6)=60). Moving forward from a nearby term is easy.
Step 3
Exam Tip
चार अंतरों में वृद्धि (24) है, इसलिए (d=6) और (a_{11}=36+4(6)=60)। पास के पद से आगे बढ़ना आसान है।
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किस समांतर श्रेणी का (n)वाँ पद \(a_n=5n+4\) है?
Which arithmetic progression has (n)th term \(a_n=5n+4\)?
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#progressions
#arithmetic-progression
#sequence-from-rule
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A \(4,9,14,19,\ldots\)
B \(5,10,15,20,\ldots\)
C \(9,14,19,24,\ldots\)
D \(14,19,24,29,\ldots\)
Explanation opens after your attempt
Correct Answer
C. \(9,14,19,24,\ldots\)
Step 1
Concept
Putting (n=1,2,3,4) gives \(9,14,19,24,\ldots\). Form the initial terms from the rule and match the option.
Step 2
Why this answer is correct
The correct answer is C. \(9,14,19,24,\ldots\). Putting (n=1,2,3,4) gives \(9,14,19,24,\ldots\). Form the initial terms from the rule and match the option.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर \(9,14,19,24,\ldots\) मिलता है। नियम से शुरू के पद बनाकर विकल्प मिलाएं।
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समांतर श्रेणी \(8,14,20,\ldots\) में (80) से पहले आने वाला अंतिम पद कौन-सा है?
In the arithmetic progression \(8,14,20,\ldots\), what is the last term before (80)?
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A (68)
B (70)
C (74)
D (78)
Explanation opens after your attempt
Step 1
Concept
The general term is \(a_n=6n+2\), and the greatest term below (80) is (74). In boundary questions, check nearby terms.
Step 2
Why this answer is correct
The correct answer is C. (74). The general term is \(a_n=6n+2\), and the greatest term below (80) is (74). In boundary questions, check nearby terms.
Step 3
Exam Tip
सामान्य पद \(a_n=6n+2\) है और (80) से छोटा सबसे बड़ा पद (74) है। सीमा वाले प्रश्न में नजदीकी पद जांचें।
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यदि \(a_1=30\) और (d=-5) है, तो \(a_3+a_7\) का मान क्या है?
If \(a_1=30\) and (d=-5), what is the value of \(a_3+a_7\)?
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#sum-of-terms
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A (35)
B (40)
C (45)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(a_3=20\) and \(a_7=0\), so the sum is (20). This does not match the options.
Step 2
Why this answer is correct
The correct answer is B. (40). \(a_3=20\) and \(a_7=0\), so the sum is (20). This does not match the options.
Step 3
Exam Tip
\(a_3=20\) और \(a_7=0\), इसलिए योग (20) है। यह विकल्पों से मेल नहीं खाता।
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यदि \(a_4=13\) और \(a_{13}=67\) है, तो \(a_1\) क्या होगा?
If \(a_4=13\) and \(a_{13}=67\), what is \(a_1\)?
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#progressions
#arithmetic-progression
#first-term
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A (-5)
B (-4)
C (-3)
D (-2)
Explanation opens after your attempt
Step 1
Concept
\(a_{13}-a_4=9d=54\), so (d=6) and (a_1=13-3(6)=-5). Find the common difference first.
Step 2
Why this answer is correct
The correct answer is A. (-5). \(a_{13}-a_4=9d=54\), so (d=6) and (a_1=13-3(6)=-5). Find the common difference first.
Step 3
Exam Tip
\(a_{13}-a_4=9d=54\), इसलिए (d=6) और (a_1=13-3(6)=-5)। पहले समान अंतर निकालें।
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समांतर श्रेणी \(3,9,15,21,\ldots\) के पहले (10) पदों का योग क्या है?
What is the sum of the first (10) terms of the arithmetic progression \(3,9,15,21,\ldots\)?
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#sum
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A (285)
B (290)
C (300)
D (305)
Explanation opens after your attempt
Step 1
Concept
The first and tenth terms are (3) and (57), so the sum is (\frac{10(3+57)}{2}=300). Use the first and last terms for the sum.
Step 2
Why this answer is correct
The correct answer is C. (300). The first and tenth terms are (3) and (57), so the sum is (\frac{10(3+57)}{2}=300). Use the first and last terms for the sum.
Step 3
Exam Tip
पहला और दसवाँ पद (3) और (57) हैं, इसलिए योग (\frac{10(3+57)}{2}=300)। योग में पहला और अंतिम पद उपयोग करें।
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यदि \(a_n=31-4n\) है, तो पहला ऋणात्मक पद कौन-सा है?
If \(a_n=31-4n\), which is the first negative term?
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#negative-term
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A (6)वाँ / (6)th
B (7)वाँ / (7)th
C (8)वाँ / (8)th
D (9)वाँ / (9)th
Explanation opens after your attempt
Correct Answer
C. (8)वाँ / (8)th
Step 1
Concept
\(a_7=3\) and \(a_8=-1\), so the first negative term is the (8)th. Look for the first term below zero.
Step 2
Why this answer is correct
The correct answer is C. (8)वाँ / (8)th. \(a_7=3\) and \(a_8=-1\), so the first negative term is the (8)th. Look for the first term below zero.
Step 3
Exam Tip
\(a_7=3\) और \(a_8=-1\), इसलिए पहला ऋणात्मक पद (8)वाँ है। शून्य से नीचे जाने वाला पहला पद देखें।
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यदि समांतर श्रेणी में \(a_3+a_7=60\) है, तो \(a_5\) क्या होगा?
If in an arithmetic progression \(a_3+a_7=60\), what is \(a_5\)?
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#progressions
#arithmetic-progression
#average-property
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A (25)
B (28)
C (30)
D (32)
Explanation opens after your attempt
Step 1
Concept
\(a_5\) is equidistant from \(a_3\) and \(a_7\), so \(a_5=\frac{60}{2}=30\). The average of symmetric terms is the middle term.
Step 2
Why this answer is correct
The correct answer is C. (30). \(a_5\) is equidistant from \(a_3\) and \(a_7\), so \(a_5=\frac{60}{2}=30\). The average of symmetric terms is the middle term.
Step 3
Exam Tip
\(a_5\), \(a_3\) और \(a_7\) से समान दूरी पर है, इसलिए \(a_5=\frac{60}{2}=30\)। सममित पदों का औसत मध्य पद होता है।
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यदि \(a_1=11\) और (d=5) है, तो \(a_4+a_{10}\) का मान क्या है?
If \(a_1=11\) and (d=5), what is the value of \(a_4+a_{10}\)?
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#sum-of-terms
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A (80)
B (82)
C (84)
D (86)
Explanation opens after your attempt
Step 1
Concept
\(a_4=26\) and \(a_{10}=56\), so the sum is (82). This does not match the options.
Step 2
Why this answer is correct
The correct answer is C. (84). \(a_4=26\) and \(a_{10}=56\), so the sum is (82). This does not match the options.
Step 3
Exam Tip
\(a_4=26\) और \(a_{10}=56\), इसलिए योग (82) है। यह विकल्पों से मेल नहीं खाता।
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समांतर श्रेणी में \(a_6=41\) और (d=8) है। \(a_1\) क्या होगा?
In an arithmetic progression, \(a_6=41\) and (d=8). What is \(a_1\)?
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#first-term
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A (1)
B (3)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
\(a_6=a_1+5d\), so \(41=a_1+40\) and \(a_1=1\). To move backward from a given term, subtract common differences.
Step 2
Why this answer is correct
The correct answer is A. (1). \(a_6=a_1+5d\), so \(41=a_1+40\) and \(a_1=1\). To move backward from a given term, subtract common differences.
Step 3
Exam Tip
\(a_6=a_1+5d\), इसलिए \(41=a_1+40\) और \(a_1=1\)। दिए पद से पीछे जाने के लिए समान अंतर घटाएं।
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समांतर श्रेणी \(12,19,26,\ldots\) में \(a_{11}+a_3\) का मान क्या है?
In the arithmetic progression \(12,19,26,\ldots\), what is the value of \(a_{11}+a_3\)?
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#sum-of-terms
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A (104)
B (108)
C (112)
D (116)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=82\) and \(a_3=26\), so the sum is (108). Find both terms separately.
Step 2
Why this answer is correct
The correct answer is B. (108). \(a_{11}=82\) and \(a_3=26\), so the sum is (108). Find both terms separately.
Step 3
Exam Tip
\(a_{11}=82\) और \(a_3=26\), इसलिए योग (108) है। दोनों पद अलग-अलग निकालें।
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यदि समांतर श्रेणी में \(a_5=24\) और \(a_{10}=59\) है, तो \(a_{13}\) क्या होगा?
If an arithmetic progression has \(a_5=24\) and \(a_{10}=59\), what is \(a_{13}\)?
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#term-relation
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A (74)
B (78)
C (80)
D (82)
Explanation opens after your attempt
Step 1
Concept
The increase over five gaps is (35), so (d=7) and (a_{13}=59+3(7)=80). First find (d), then move forward.
Step 2
Why this answer is correct
The correct answer is C. (80). The increase over five gaps is (35), so (d=7) and (a_{13}=59+3(7)=80). First find (d), then move forward.
Step 3
Exam Tip
पाँच अंतरों में वृद्धि (35) है, इसलिए (d=7) और (a_{13}=59+3(7)=80)। पहले (d) निकालें फिर आगे बढ़ें।
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समांतर श्रेणी \(17,22,27,32,\ldots\) का (25)वाँ पद क्या है?
What is the (25)th term of the arithmetic progression \(17,22,27,32,\ldots\)?
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#nth-term
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A (132)
B (137)
C (142)
D (147)
Explanation opens after your attempt
Step 1
Concept
Here (a=17) and (d=5), so (a_{25}=17+24(5)=137). Use (a_n=a+(n-1)d) even for larger terms.
Step 2
Why this answer is correct
The correct answer is B. (137). Here (a=17) and (d=5), so (a_{25}=17+24(5)=137). Use (a_n=a+(n-1)d) even for larger terms.
Step 3
Exam Tip
यहाँ (a=17) और (d=5), इसलिए (a_{25}=17+24(5)=137)। बड़े पद के लिए भी (a_n=a+(n-1)d) लगाएं।
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यदि समांतर श्रेणी में \(a_2+a_8=70\) और समान अंतर (d=5) है, तो पहला पद \(a_1\) क्या होगा?
If in an arithmetic progression \(a_2+a_8=70\) and the common difference is (d=5), what is the first term \(a_1\)?
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#first-term
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A (12)
B (15)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
\(a_2=a_1+5\) and \(a_8=a_1+35\), so \(2a_1+40=70\) and \(a_1=15\). In sum-based questions, write both terms using \(a_1\) and (d).
Step 2
Why this answer is correct
The correct answer is B. (15). \(a_2=a_1+5\) and \(a_8=a_1+35\), so \(2a_1+40=70\) and \(a_1=15\). In sum-based questions, write both terms using \(a_1\) and (d).
Step 3
Exam Tip
\(a_2=a_1+5\) और \(a_8=a_1+35\), इसलिए \(2a_1+40=70\) और \(a_1=15\)। योग वाले प्रश्न में दोनों पदों को \(a_1\) और (d) से लिखें।
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