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100 results found for "common-premises" in Class 10.

दो समांतर श्रेणियों के सामान्य अंतर क्रमशः (3) और (-5) हैं। उनके समान क्रमांक वाले पदों को जोड़ने से बने अनुक्रम का सामान्य अंतर क्या होगा?

Two APs have common differences (3) and (-5). What is the common difference of the sequence formed by adding corresponding terms?

Explanation opens after your attempt
Correct Answer

B. (-2)

Step 1

Concept

The sum sequence has difference (3+(-5)=-2). In exams, for sums of corresponding terms, add the differences too.

Step 2

Why this answer is correct

The correct answer is B. (-2). The sum sequence has difference (3+(-5)=-2). In exams, for sums of corresponding terms, add the differences too.

Step 3

Exam Tip

योग अनुक्रम का अंतर (3+(-5)=-2) होगा। परीक्षा में समान क्रमांक वाले पदों के योग में अंतरों का भी योग करें।

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एक समांतर श्रेणी का सामान्य अंतर (d) है। \(a_1,a_3,a_5,\ldots\) से बने अनुक्रम का सामान्य अंतर क्या होगा?

An AP has common difference (d). What is the common difference of the sequence \(a_1,a_3,a_5,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (2d)

Step 1

Concept

The new sequence jumps two original terms each time, so the difference is (2d). In exams, multiply (d) by the term-number jump.

Step 2

Why this answer is correct

The correct answer is B. (2d). The new sequence jumps two original terms each time, so the difference is (2d). In exams, multiply (d) by the term-number jump.

Step 3

Exam Tip

नए अनुक्रम में दो-दो मूल पदों की छलांग है, इसलिए अंतर (2d) है। परीक्षा में पद-संख्या की छलांग को (d) से गुणा करें।

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एक सीमित समांतर श्रेणी का सामान्य अंतर (-6) है। उसे उलटे क्रम में लिखने पर नया सामान्य अंतर क्या होगा?

A finite AP has common difference (-6). What will be the new common difference after writing it in reverse order?

Explanation opens after your attempt
Correct Answer

D. (6)

Step 1

Concept

Reversing changes each step to the opposite sign. In exams, reverse order changes (d) to (-d).

Step 2

Why this answer is correct

The correct answer is D. (6). Reversing changes each step to the opposite sign. In exams, reverse order changes (d) to (-d).

Step 3

Exam Tip

उलटने पर हर कदम का अंतर विपरीत चिन्ह वाला हो जाता है। परीक्षा में उलटा क्रम (d) को (-d) कर देता है।

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एक समांतर श्रेणी का सामान्य अंतर (4) है। पद \(a_2,a_5,a_8,\ldots\) से बने नए अनुक्रम का सामान्य अंतर क्या है?

An AP has common difference (4). What is the common difference of the new sequence \(a_2,a_5,a_8,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (12)

Step 1

Concept

The new sequence jumps three original terms each time, so its difference is (3d=12). In exams, count the gap between selected term numbers.

Step 2

Why this answer is correct

The correct answer is C. (12). The new sequence jumps three original terms each time, so its difference is (3d=12). In exams, count the gap between selected term numbers.

Step 3

Exam Tip

नए अनुक्रम में हर बार तीन पदों की छलांग है, इसलिए अंतर (3d=12) है। परीक्षा में चुने गए पदों के बीच की दूरी गिनें।

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यदि \(a_n\) का सामान्य अंतर (-9) है और \(b_n=\frac{a_n}{3}+5\), तो \(b_n\) का सामान्य अंतर क्या होगा?

If \(a_n\) has common difference (-9) and \(b_n=\frac{a_n}{3}+5\), what is the common difference of \(b_n\)?

Explanation opens after your attempt
Correct Answer

C. (-3)

Step 1

Concept

Multiplying by \(\frac{1}{3}\) changes the difference from (-9) to (-3), and adding (5) does not change it. In exams, separate the effects of addition and multiplication.

Step 2

Why this answer is correct

The correct answer is C. (-3). Multiplying by \(\frac{1}{3}\) changes the difference from (-9) to (-3), and adding (5) does not change it. In exams, separate the effects of addition and multiplication.

Step 3

Exam Tip

\(\frac{1}{3}\) से गुणा करने पर अंतर (-9) से (-3) हो जाता है, और (5) जोड़ने से अंतर नहीं बदलता। परीक्षा में जोड़ और गुणन के प्रभाव अलग करें।

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एक समांतर श्रेणी का सामान्य अंतर (d) है। हर पद को (-3) से गुणा करने पर नया सामान्य अंतर क्या होगा?

An AP has common difference (d). If every term is multiplied by (-3), what is the new common difference?

Explanation opens after your attempt
Correct Answer

B. (-3d)

Step 1

Concept

Multiplication scales all differences by the same factor, so the new difference is (-3d). In exams, apply the transformation to the difference.

Step 2

Why this answer is correct

The correct answer is B. (-3d). Multiplication scales all differences by the same factor, so the new difference is (-3d). In exams, apply the transformation to the difference.

Step 3

Exam Tip

गुणन से सभी अंतर उसी गुणक से गुणा होते हैं, इसलिए नया अंतर (-3d) है। परीक्षा में रूपांतरण का असर अंतर पर लगाएं।

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यदि \(a_n\) एक समांतर श्रेणी है जिसका सामान्य अंतर (4) है और \(b_n=2a_n-3\), तो \(b_n\) का सामान्य अंतर क्या है?

If \(a_n\) is an AP with common difference (4) and \(b_n=2a_n-3\), what is the common difference of \(b_n\)?

Explanation opens after your attempt
Correct Answer

D. (8)

Step 1

Concept

Multiplying terms by (2) multiplies the difference by (2), so it becomes (8). In exams, adding or subtracting a constant does not change the difference, but multiplication does.

Step 2

Why this answer is correct

The correct answer is D. (8). Multiplying terms by (2) multiplies the difference by (2), so it becomes (8). In exams, adding or subtracting a constant does not change the difference, but multiplication does.

Step 3

Exam Tip

पदों को (2) से गुणा करने पर अंतर भी (2) गुना हो जाता है, इसलिए (8)। परीक्षा में जोड़ना-घटाना अंतर नहीं बदलता, गुणा बदलता है।

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यदि किसी समांतर श्रेणी का सामान्य अंतर (7) है और प्रत्येक पद से (12) घटाया जाए, तो नया सामान्य अंतर क्या होगा?

If an AP has common difference (7) and (12) is subtracted from every term, what is the new common difference?

Explanation opens after your attempt
Correct Answer

B. (7)

Step 1

Concept

Subtracting the same number from every term does not change the difference. In exams, treat uniform subtraction as changing only the first term.

Step 2

Why this answer is correct

The correct answer is B. (7). Subtracting the same number from every term does not change the difference. In exams, treat uniform subtraction as changing only the first term.

Step 3

Exam Tip

हर पद से समान संख्या घटाने पर अंतर नहीं बदलता। परीक्षा में समान घटाव को केवल पहला पद बदलने वाला समझें।

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यदि \(5,12,19,26,\ldots\) में हर दूसरा पद चुना जाए तो बने अनुक्रम का सार्व अंतर क्या होगा?

If every second term is selected from \(5,12,19,26,\ldots\), what will be the common difference of the formed sequence?

Explanation opens after your attempt
Correct Answer

C. (14)

Step 1

Concept

The selected sequence is \(5,19,33,\ldots\), and its difference is (14). Selecting every second term makes the new (d) twice the original (d).

Step 2

Why this answer is correct

The correct answer is C. (14). The selected sequence is \(5,19,33,\ldots\), and its difference is (14). Selecting every second term makes the new (d) twice the original (d).

Step 3

Exam Tip

चुना गया अनुक्रम \(5,19,33,\ldots\) होगा और इसका अंतर (14) है। हर दूसरा पद लेने पर नया (d) मूल (d) का (2) गुना होता है।

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यदि \(3,8,13,\ldots\) में प्रत्येक पद से (4n) घटाया जाए तो नया सार्व अंतर क्या होगा?

If (4n) is subtracted from each term of \(3,8,13,\ldots\), what will be the new common difference?

Explanation opens after your attempt
Correct Answer

A. (1)

Step 1

Concept

The original (d=5), and (4n) has (d=4), so the new (d=1). In term-number changes, subtract its difference.

Step 2

Why this answer is correct

The correct answer is A. (1). The original (d=5), and (4n) has (d=4), so the new (d=1). In term-number changes, subtract its difference.

Step 3

Exam Tip

मूल (d=5) है और (4n) का (d=4) है, इसलिए नया (d=1)। पद संख्या से जुड़े परिवर्तन में उसके अंतर को घटाएं।

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यदि (a,a+d,a+2d) के तीनों पदों में क्रमशः (3,6,9) जोड़े जाएं तो नया सार्व अंतर क्या होगा?

If (3,6,9) are added respectively to (a,a+d,a+2d), what will be the new common difference?

Explanation opens after your attempt
Correct Answer

C. (d+3)

Step 1

Concept

The new terms are (a+3,a+d+6,a+2d+9), and both differences are (d+3). The difference of the added numbers is added to (d).

Step 2

Why this answer is correct

The correct answer is C. (d+3). The new terms are (a+3,a+d+6,a+2d+9), and both differences are (d+3). The difference of the added numbers is added to (d).

Step 3

Exam Tip

नए पद (a+3,a+d+6,a+2d+9) हैं और दोनों अंतर (d+3) हैं। क्रमशः बढ़ते जोड़ का अंतर (d) में जुड़ता है।

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अनुक्रम \(0.6,1.05,1.50,1.95,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(0.6,1.05,1.50,1.95,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (0.45)

Step 1

Concept

(1.05-0.60=0.45) and (1.50-1.05=0.45). Adding zeros makes decimal subtraction safer.

Step 2

Why this answer is correct

The correct answer is C. (0.45). (1.05-0.60=0.45) and (1.50-1.05=0.45). Adding zeros makes decimal subtraction safer.

Step 3

Exam Tip

(1.05-0.60=0.45) और (1.50-1.05=0.45) है। दशमलव में शून्य लगाकर घटाना सुरक्षित है।

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यदि \(24,20,16,12,\ldots\) के प्रत्येक पद में (7) जोड़ा जाए तो नए अनुक्रम का सार्व अंतर क्या होगा?

If (7) is added to each term of \(24,20,16,12,\ldots\), what will be the common difference of the new sequence?

Explanation opens after your attempt
Correct Answer

B. (-4)

Step 1

Concept

Adding the same number to all terms does not change the common difference. The original (d=20-24=-4), so the new (d) remains (-4).

Step 2

Why this answer is correct

The correct answer is B. (-4). Adding the same number to all terms does not change the common difference. The original (d=20-24=-4), so the new (d) remains (-4).

Step 3

Exam Tip

सभी पदों में समान संख्या जोड़ने से सार्व अंतर नहीं बदलता। मूल (d=20-24=-4) है, इसलिए नया (d=-4) ही रहेगा।

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अनुक्रम \(\frac{3}{8},\frac{5}{8},\frac{7}{8},\frac{9}{8},\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(\frac{3}{8},\frac{5}{8},\frac{7}{8},\frac{9}{8},\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{1}{4}\)

Step 1

Concept

\(\frac{5}{8}-\frac{3}{8}=\frac{2}{8}=\frac{1}{4}\). When denominators are equal, subtract the numerators.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{1}{4}\). \(\frac{5}{8}-\frac{3}{8}=\frac{2}{8}=\frac{1}{4}\). When denominators are equal, subtract the numerators.

Step 3

Exam Tip

\(\frac{5}{8}-\frac{3}{8}=\frac{2}{8}=\frac{1}{4}\) है। भिन्नों में समान हर होने पर अंशों का अंतर लें।

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यदि (a,a+d,a+2d) के तीनों पदों में क्रमशः (2,4,6) जोड़े जाएं, तो नया सार्व अंतर क्या होगा?

If (2,4,6) are added respectively to (a,a+d,a+2d), what will be the new common difference?

Explanation opens after your attempt
Correct Answer

C. (d+2)

Step 1

Concept

The new terms are (a+2, a+d+4, a+2d+6), and both differences are (d+2). The difference (2) of the added numbers is also added to (d).

Step 2

Why this answer is correct

The correct answer is C. (d+2). The new terms are (a+2, a+d+4, a+2d+6), and both differences are (d+2). The difference (2) of the added numbers is also added to (d).

Step 3

Exam Tip

नए पद (a+2, a+d+4, a+2d+6) हैं और दोनों अंतर (d+2) हैं। क्रमशः बढ़ते जोड़ का अंतर (2) भी (d) में जुड़ता है।

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अनुक्रम \(-\frac{7}{4}, -1, -\frac{1}{4}, \frac{1}{2},\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(-\frac{7}{4}, -1, -\frac{1}{4}, \frac{1}{2},\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{3}{4}\)

Step 1

Concept

(-1-\left\(-\frac{7}{4}\right\)=\frac{3}{4}), and the next difference is also \(\frac{3}{4}\). Be careful while subtracting negative fractions.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{3}{4}\). (-1-\left\(-\frac{7}{4}\right\)=\frac{3}{4}), and the next difference is also \(\frac{3}{4}\). Be careful while subtracting negative fractions.

Step 3

Exam Tip

(-1-\left\(-\frac{7}{4}\right\)=\frac{3}{4}) और अगला अंतर भी \(\frac{3}{4}\) है। ऋणात्मक भिन्नों में घटाव सावधानी से करें।

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यदि (4p+1, 6p-3, 9p-10) समांतर श्रेणी में हैं, तो (p) और सामान्य अंतर का सही युग्म कौन-सा है?

If (4p+1, 6p-3, 9p-10) are in an arithmetic progression, which pair of (p) and common difference is correct?

Explanation opens after your attempt
Correct Answer

B. (p=3, d=2)

Step 1

Concept

The differences are (2p-4) and (3p-7). Equating them gives (p=3), so (d=2).

Step 2

Why this answer is correct

The correct answer is B. (p=3, d=2). The differences are (2p-4) and (3p-7). Equating them gives (p=3), so (d=2).

Step 3

Exam Tip

अंतर (2p-4) और (3p-7) हैं। बराबर करने पर (p=3), इसलिए (d=2).

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यदि (13, 2x+1, 4x-5) समांतर श्रेणी में हैं, तो सामान्य अंतर क्या है?

If (13, 2x+1, 4x-5) are in an arithmetic progression, what is the common difference?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

From (2(2x+1)=13+(4x-5)), we get (2=8), which is impossible. Therefore no such common difference exists.

Step 2

Why this answer is correct

The correct answer is C. (7). From (2(2x+1)=13+(4x-5)), we get (2=8), which is impossible. Therefore no such common difference exists.

Step 3

Exam Tip

(2(2x+1)=13+(4x-5)) से (2=8) असंभव है। इसलिए ऐसा सामान्य अंतर नहीं होगा।

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यदि (3, 3+2m, 3+4m, 3+6m) समांतर श्रेणी है, तो सामान्य अंतर क्या है?

If (3, 3+2m, 3+4m, 3+6m) is an arithmetic progression, what is the common difference?

Explanation opens after your attempt
Correct Answer

B. (2m)

Step 1

Concept

Each time (2m) is added. Therefore the common difference is (2m).

Step 2

Why this answer is correct

The correct answer is B. (2m). Each time (2m) is added. Therefore the common difference is (2m).

Step 3

Exam Tip

हर बार (2m) जुड़ रहा है। इसलिए सामान्य अंतर (2m) है।

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किस विकल्प में दिए गए पद समांतर श्रेणी हैं लेकिन सामान्य अंतर (0) है?

In which option do the terms form an arithmetic progression with common difference (0)?

Explanation opens after your attempt
Correct Answer

A. (6, 6, 6, 6)

Step 1

Concept

When all terms are equal, every difference is (0). A constant sequence is also an arithmetic progression.

Step 2

Why this answer is correct

The correct answer is A. (6, 6, 6, 6). When all terms are equal, every difference is (0). A constant sequence is also an arithmetic progression.

Step 3

Exam Tip

सभी पद समान हों तो हर अंतर (0) होता है। स्थिर क्रम भी समांतर श्रेणी होता है।

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क्रम \(101, 97, 93, 89, \ldots\) में सामान्य अंतर क्या है और यह कैसा है?

In the sequence \(101, 97, 93, 89, \ldots\), what is the common difference and what is its nature?

Explanation opens after your attempt
Correct Answer

B. (-4), ऋणात्मक(-4), negative

Step 1

Concept

Each next term is (4) less than the previous one, so (d=-4). A decreasing arithmetic progression has a negative common difference.

Step 2

Why this answer is correct

The correct answer is B. (-4), ऋणात्मक / (-4), negative. Each next term is (4) less than the previous one, so (d=-4). A decreasing arithmetic progression has a negative common difference.

Step 3

Exam Tip

हर अगला पद पिछले से (4) कम है, इसलिए (d=-4). घटती समांतर श्रेणी में सामान्य अंतर ऋणात्मक होता है।

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किस क्रम में सामान्य अंतर \(\frac{3}{4}\) है?

Which sequence has common difference \(\frac{3}{4}\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{1}{4}, 1, \frac{7}{4}, \frac{5}{2}\)

Step 1

Concept

In the first option, every consecutive difference is \(\frac{3}{4}\). With fractions, using common denominators is the safer method.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{1}{4}, 1, \frac{7}{4}, \frac{5}{2}\). In the first option, every consecutive difference is \(\frac{3}{4}\). With fractions, using common denominators is the safer method.

Step 3

Exam Tip

पहले विकल्प में हर लगातार अंतर \(\frac{3}{4}\) है। भिन्नों में हर को समान बनाकर अंतर निकालना सुरक्षित तरीका है।

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क्रम (4x-3, 3x+5, x+21) समांतर श्रेणी में है। सही सामान्य अंतर कौन-सा है?

The sequence (4x-3, 3x+5, x+21) is in an arithmetic progression. Which is the correct common difference?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

For equal differences, (-x+8=-2x+16), which gives (x=8). Then both differences are (0).

Step 2

Why this answer is correct

The correct answer is A. (0). For equal differences, (-x+8=-2x+16), which gives (x=8). Then both differences are (0).

Step 3

Exam Tip

बराबर अंतर के लिए (-x+8=-2x+16), जिससे (x=8). तब दोनों अंतर (0) हैं।

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क्रम (4x-3, 3x+5, x+21) समांतर श्रेणी में है। सामान्य अंतर क्या है?

The sequence (4x-3, 3x+5, x+21) is in an arithmetic progression. What is the common difference?

Explanation opens after your attempt
Correct Answer

A. (8)

Step 1

Concept

The differences are (-x+8) and (-2x+16). Equating them gives (x=8), so (d=0), not (8).

Step 2

Why this answer is correct

The correct answer is A. (8). The differences are (-x+8) and (-2x+16). Equating them gives (x=8), so (d=0), not (8).

Step 3

Exam Tip

अंतर (-x+8) और (-2x+16) हैं। बराबर करने पर (x=8), इसलिए (d=0) नहीं बल्कि (d=0) आता है।

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यदि (6, h, 30) समांतर श्रेणी में हैं, तो (h) और सामान्य अंतर का सही युग्म कौन-सा है?

If (6, h, 30) are in an arithmetic progression, which pair of (h) and common difference is correct?

Explanation opens after your attempt
Correct Answer

B. (h=18, d=12)

Step 1

Concept

The middle term is \(\frac{6+30}{2}=18\). The common difference is (18-6=12).

Step 2

Why this answer is correct

The correct answer is B. (h=18, d=12). The middle term is \(\frac{6+30}{2}=18\). The common difference is (18-6=12).

Step 3

Exam Tip

बीच का पद \(\frac{6+30}{2}=18\) है। सामान्य अंतर (18-6=12) है।

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किस (r) के लिए (r-1, 2r+2, 4r+7) समांतर श्रेणी में होंगे और सामान्य अंतर क्या होगा?

For which (r) will (r-1, 2r+2, 4r+7) be in an arithmetic progression, and what will be the common difference?

Explanation opens after your attempt
Correct Answer

A. (r=-2, d=1)

Step 1

Concept

The differences are (r+3) and (2r+5). Equating them gives (r=-2) and (d=1).

Step 2

Why this answer is correct

The correct answer is A. (r=-2, d=1). The differences are (r+3) and (2r+5). Equating them gives (r=-2) and (d=1).

Step 3

Exam Tip

अंतर (r+3) और (2r+5) हैं। बराबर करने पर (r=-2) और (d=1) मिलता है।

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यदि (14, 14-d, 14-2d, 14-3d) समांतर श्रेणी है, तो सामान्य अंतर क्या है?

If (14, 14-d, 14-2d, 14-3d) is an arithmetic progression, what is the common difference?

Explanation opens after your attempt
Correct Answer

B. (-d)

Step 1

Concept

Each next term is (d) less than the previous term. Therefore the common difference is (-d).

Step 2

Why this answer is correct

The correct answer is B. (-d). Each next term is (d) less than the previous term. Therefore the common difference is (-d).

Step 3

Exam Tip

हर अगला पद पिछले पद से (d) कम है। इसलिए सामान्य अंतर (-d) है।

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यदि (9, y, 2y+6) समांतर श्रेणी में हैं, तो सामान्य अंतर क्या है?

If (9, y, 2y+6) are in an arithmetic progression, what is the common difference?

Explanation opens after your attempt
Correct Answer

B. (15)

Step 1

Concept

From (2y=9+(2y+6)), we get (0=15), so it never forms an arithmetic progression. None of the listed values can be its common difference.

Step 2

Why this answer is correct

The correct answer is B. (15). From (2y=9+(2y+6)), we get (0=15), so it never forms an arithmetic progression. None of the listed values can be its common difference.

Step 3

Exam Tip

(2y=9+(2y+6)) से (0=15) नहीं, इसलिए यह कभी समांतर श्रेणी नहीं बनती। सही विकल्पों में ऐसा कोई सामान्य अंतर नहीं है।

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किस क्रम का सामान्य अंतर ऋणात्मक है और सभी लगातार अंतर बराबर हैं?

Which sequence has a negative common difference and all consecutive differences equal?

Explanation opens after your attempt
Correct Answer

B. (20, 16, 12, 8)

Step 1

Concept

In (20,16,12,8), (4) is subtracted each time, so (d=-4). Do not just see decreasing order; check equal differences too.

Step 2

Why this answer is correct

The correct answer is B. (20, 16, 12, 8). In (20,16,12,8), (4) is subtracted each time, so (d=-4). Do not just see decreasing order; check equal differences too.

Step 3

Exam Tip

(20,16,12,8) में हर बार (4) घटता है, इसलिए (d=-4). केवल घटते क्रम को देखकर नहीं, बराबर अंतर भी जांचें।

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किस मान पर (2x+5, 4x+1, 7x-7) के सामान्य अंतर बराबर होंगे?

For what value will the common differences of (2x+5, 4x+1, 7x-7) be equal?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

The first difference is (2x-4), and the second is (3x-8). Equating them gives (x=4).

Step 2

Why this answer is correct

The correct answer is C. (4). The first difference is (2x-4), and the second is (3x-8). Equating them gives (x=4).

Step 3

Exam Tip

पहला अंतर (2x-4) और दूसरा अंतर (3x-8) है। दोनों बराबर करने पर (x=4).

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चार संख्याएँ (x-6, x+1, 2x-1, 3x-8) समांतर श्रेणी में हैं। सामान्य अंतर क्या है?

Four numbers (x-6, x+1, 2x-1, 3x-8) are in an arithmetic progression. What is the common difference?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

The first difference is always (7). From (x-2=7), (x=9), and the last difference also becomes (7).

Step 2

Why this answer is correct

The correct answer is C. (7). The first difference is always (7). From (x-2=7), (x=9), and the last difference also becomes (7).

Step 3

Exam Tip

पहला अंतर हमेशा (7) है। (x-2=7) से (x=9) और अंतिम अंतर भी (7) हो जाता है।

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यदि (p-4, 2p+1, 4p-2) समांतर श्रेणी में हैं, तो सामान्य अंतर क्या होगा?

If (p-4, 2p+1, 4p-2) are in an arithmetic progression, what will be the common difference?

Explanation opens after your attempt
Correct Answer

B. (13)

Step 1

Concept

First, (2(2p+1)=(p-4)+(4p-2)) gives (p=8). Then the common difference is ((2p+1)-(p-4)=13).

Step 2

Why this answer is correct

The correct answer is B. (13). First, (2(2p+1)=(p-4)+(4p-2)) gives (p=8). Then the common difference is ((2p+1)-(p-4)=13).

Step 3

Exam Tip

पहले (2(2p+1)=(p-4)+(4p-2)) से (p=8) मिलता है। तब सामान्य अंतर ((2p+1)-(p-4)=13) है।

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यदि (a, a+d, a+2d) के तीनों पदों में क्रमशः (1,2,3) जोड़े जाएं, तो नया सार्व अंतर क्या होगा?

If (1,2,3) are added respectively to (a, a+d, a+2d), what will be the new common difference?

Explanation opens after your attempt
Correct Answer

C. (d+1)

Step 1

Concept

The new terms are (a+1, a+d+2, a+2d+3), and both differences are (d+1). Adding increasing numbers respectively adds (1) to (d).

Step 2

Why this answer is correct

The correct answer is C. (d+1). The new terms are (a+1, a+d+2, a+2d+3), and both differences are (d+1). Adding increasing numbers respectively adds (1) to (d).

Step 3

Exam Tip

नए पद (a+1, a+d+2, a+2d+3) हैं और दोनों अंतर (d+1) हैं। क्रमशः बढ़ती हुई जोड़ से (d) में (1) जुड़ता है।

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यदि \(2, 5, 8,\ldots\) और \(7, 12, 17,\ldots\) को पद-दर-पद जोड़ा जाए, तो बने अनुक्रम का सार्व अंतर क्या होगा?

If \(2, 5, 8,\ldots\) and \(7, 12, 17,\ldots\) are added term by term, what will be the common difference of the formed sequence?

Explanation opens after your attempt
Correct Answer

C. (8)

Step 1

Concept

The two common differences are (3) and (5), so the sum sequence has (d=3+5=8). In termwise addition, common differences add.

Step 2

Why this answer is correct

The correct answer is C. (8). The two common differences are (3) and (5), so the sum sequence has (d=3+5=8). In termwise addition, common differences add.

Step 3

Exam Tip

दोनों सार्व अंतर (3) और (5) हैं, इसलिए योग अनुक्रम का (d=3+5=8)। पद-दर-पद योग में सार्व अंतरों का योग होता है।

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अनुक्रम \(0.75, 1.2, 1.65, 2.10,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(0.75, 1.2, 1.65, 2.10,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (0.45)

Step 1

Concept

(1.20-0.75=0.45) and (1.65-1.20=0.45). In decimals, adding zeros helps subtraction.

Step 2

Why this answer is correct

The correct answer is C. (0.45). (1.20-0.75=0.45) and (1.65-1.20=0.45). In decimals, adding zeros helps subtraction.

Step 3

Exam Tip

(1.20-0.75=0.45) और (1.65-1.20=0.45) है। दशमलव में शून्य लगाकर घटाना बेहतर होता है।

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यदि \(6, 11, 16, 21,\ldots\) के प्रत्येक पद को (3) से गुणा किया जाए, तो नया सार्व अंतर क्या होगा?

If each term of \(6, 11, 16, 21,\ldots\) is multiplied by (3), what will be the new common difference?

Explanation opens after your attempt
Correct Answer

C. (15)

Step 1

Concept

The original common difference is (5), so after multiplying by (3), the new (d=15). When all terms are multiplied by the same factor, (d) is multiplied by that factor too.

Step 2

Why this answer is correct

The correct answer is C. (15). The original common difference is (5), so after multiplying by (3), the new (d=15). When all terms are multiplied by the same factor, (d) is multiplied by that factor too.

Step 3

Exam Tip

मूल सार्व अंतर (5) है, इसलिए (3) से गुणा करने पर नया (d=15) होगा। सभी पदों को समान गुणक से गुणा करने पर (d) भी उसी गुणक से गुणा होता है।

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यदि \(10, 6, 2, -2,\ldots\) के प्रत्येक पद में (5) जोड़ दिया जाए, तो नए अनुक्रम का सार्व अंतर क्या होगा?

If (5) is added to each term of \(10, 6, 2, -2,\ldots\), what will be the common difference of the new sequence?

Explanation opens after your attempt
Correct Answer

B. (-4)

Step 1

Concept

Adding the same (5) to all terms does not change (d), so (d=-4) remains. Equal addition or subtraction keeps the common difference unchanged.

Step 2

Why this answer is correct

The correct answer is B. (-4). Adding the same (5) to all terms does not change (d), so (d=-4) remains. Equal addition or subtraction keeps the common difference unchanged.

Step 3

Exam Tip

सभी पदों में समान (5) जोड़ने से (d) नहीं बदलता, इसलिए (d=-4) रहेगा। समान जोड़ या घटाव से सार्व अंतर अपरिवर्तित रहता है।

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यदि (5x+2, 3x+10, x+18) अंकगणितीय श्रेणी में हैं, तो सार्व अंतर क्या है?

If (5x+2, 3x+10, x+18) are in an arithmetic progression, what is the common difference?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

Equating differences gives ((3x+10)-(5x+2)=(x+18)-(3x+10)), which is an identity, so (d=8-2x). Therefore it is an arithmetic progression for every (x), but (d) is not fixed.

Step 2

Why this answer is correct

The correct answer is C. (4). Equating differences gives ((3x+10)-(5x+2)=(x+18)-(3x+10)), which is an identity, so (d=8-2x). Therefore it is an arithmetic progression for every (x), but (d) is not fixed.

Step 3

Exam Tip

दोनों अंतर बराबर रखने पर ((3x+10)-(5x+2)=(x+18)-(3x+10)), जिससे पहचान समानता बनती है और (d=8-2x)। इसलिए यह हर (x) पर अंकगणितीय श्रेणी है, लेकिन (d) निश्चित नहीं है।

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अनुक्रम \(\frac{2}{5}, \frac{7}{10}, 1, \frac{13}{10},\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(\frac{2}{5}, \frac{7}{10}, 1, \frac{13}{10},\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{3}{10}\)

Step 1

Concept

\(\frac{7}{10}-\frac{2}{5}=\frac{3}{10}\) and \(1-\frac{7}{10}=\frac{3}{10}\). Do not forget to use common denominators in fractions.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{3}{10}\). \(\frac{7}{10}-\frac{2}{5}=\frac{3}{10}\) and \(1-\frac{7}{10}=\frac{3}{10}\). Do not forget to use common denominators in fractions.

Step 3

Exam Tip

\(\frac{7}{10}-\frac{2}{5}=\frac{3}{10}\) और \(1-\frac{7}{10}=\frac{3}{10}\) है। भिन्नों में हर समान करना न भूलें।

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यदि \(8,8+s,8+2s,\ldots\) एक अंकगणितीय श्रेणी है तो इसका सार्व अंतर क्या है?

If \(8,8+s,8+2s,\ldots\) is an arithmetic progression, what is its common difference?

Explanation opens after your attempt
Correct Answer

C. (s)

Step 1

Concept

The common difference is ((8+s)-8=s). In algebraic sequences also look at the equally added part.

Step 2

Why this answer is correct

The correct answer is C. (s). The common difference is ((8+s)-8=s). In algebraic sequences also look at the equally added part.

Step 3

Exam Tip

सार्व अंतर ((8+s)-8=s) है। अक्षर वाले अनुक्रम में भी समान जोड़ा गया भाग देखें।

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अनुक्रम \(1.4,1.9,2.4,2.9,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(1.4,1.9,2.4,2.9,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (0.5)

Step 1

Concept

The common difference is (1.9-1.4=0.5). In decimal subtraction pay attention to place value.

Step 2

Why this answer is correct

The correct answer is B. (0.5). The common difference is (1.9-1.4=0.5). In decimal subtraction pay attention to place value.

Step 3

Exam Tip

सार्व अंतर (1.9-1.4=0.5) है। दशमलव घटाते समय स्थान मान का ध्यान रखें।

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अनुक्रम \(\frac{5}{6},\frac{7}{6},\frac{3}{2},\frac{11}{6},\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(\frac{5}{6},\frac{7}{6},\frac{3}{2},\frac{11}{6},\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{1}{3}\)

Step 1

Concept

\(\frac{7}{6}-\frac{5}{6}=\frac{1}{3}\) and \(\frac{3}{2}-\frac{7}{6}=\frac{1}{3}\). For fractions subtract using common denominators.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{1}{3}\). \(\frac{7}{6}-\frac{5}{6}=\frac{1}{3}\) and \(\frac{3}{2}-\frac{7}{6}=\frac{1}{3}\). For fractions subtract using common denominators.

Step 3

Exam Tip

\(\frac{7}{6}-\frac{5}{6}=\frac{1}{3}\) और \(\frac{3}{2}-\frac{7}{6}=\frac{1}{3}\) है। भिन्नों में हर समान करके घटाएं।

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अनुक्रम \(4x,4x+3,4x+6,\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(4x,4x+3,4x+6,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

(d=(4x+3)-4x=3). For algebraic terms also subtract the first term from the second term.

Step 2

Why this answer is correct

The correct answer is C. (3). (d=(4x+3)-4x=3). For algebraic terms also subtract the first term from the second term.

Step 3

Exam Tip

(d=(4x+3)-4x=3) है। बीजगणितीय पदों में भी दूसरा पद घटा पहला पद करें।

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अनुक्रम \(7,7.5,8,8.5,\ldots\) में सार्व अंतर क्या है?

What is the common difference in \(7,7.5,8,8.5,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (0.5)

Step 1

Concept

The common difference is (7.5-7=0.5). For decimal terms also, check the regular difference.

Step 2

Why this answer is correct

The correct answer is B. (0.5). The common difference is (7.5-7=0.5). For decimal terms also, check the regular difference.

Step 3

Exam Tip

सार्व अंतर (7.5-7=0.5) है। दशमलव पदों में भी नियमित अंतर देखें।

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यदि \(a_1=35\) और \(a_2=29\) हैं, तो सार्व अंतर (d) क्या है?

If \(a_1=35\) and \(a_2=29\), what is the common difference (d)?

Explanation opens after your attempt
Correct Answer

B. (-6)

Step 1

Concept

\(d=a_2-a_1=29-35=-6\). Subtract the first term from the second term.

Step 2

Why this answer is correct

The correct answer is B. (-6). \(d=a_2-a_1=29-35=-6\). Subtract the first term from the second term.

Step 3

Exam Tip

\(d=a_2-a_1=29-35=-6\) है। दूसरे पद से पहले पद को घटाएँ।

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अनुक्रम \(8,13,18,23,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(8,13,18,23,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (5)

Step 1

Concept

The common difference is (13-8=5). Always check the difference of two consecutive terms.

Step 2

Why this answer is correct

The correct answer is B. (5). The common difference is (13-8=5). Always check the difference of two consecutive terms.

Step 3

Exam Tip

सार्व अंतर (13-8=5) है। हमेशा लगातार दो पदों का अंतर जाँचें।

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यदि \(5,5+s,5+2s,\ldots\) एक अंकगणितीय श्रेणी है तो इसका सार्व अंतर क्या है?

If \(5,5+s,5+2s,\ldots\) is an arithmetic progression, what is its common difference?

Explanation opens after your attempt
Correct Answer

C. (s)

Step 1

Concept

The common difference is ((5+s)-5=s). In algebraic sequences also look at the equal added part.

Step 2

Why this answer is correct

The correct answer is C. (s). The common difference is ((5+s)-5=s). In algebraic sequences also look at the equal added part.

Step 3

Exam Tip

सार्व अंतर ((5+s)-5=s) है। अक्षर वाले अनुक्रम में भी समान जोड़ा गया भाग देखें।

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किस अनुक्रम में सार्व अंतर (0) है?

Which sequence has common difference (0)?

Explanation opens after your attempt
Correct Answer

D. \(11,11,11,11,\ldots\)

Step 1

Concept

All terms are equal, so (d=0). A constant sequence is also considered an arithmetic progression.

Step 2

Why this answer is correct

The correct answer is D. \(11,11,11,11,\ldots\). All terms are equal, so (d=0). A constant sequence is also considered an arithmetic progression.

Step 3

Exam Tip

सभी पद समान हैं इसलिए (d=0) है। स्थिर अनुक्रम भी अंकगणितीय श्रेणी माना जाता है।

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अनुक्रम \(0.2,0.5,0.8,1.1,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(0.2,0.5,0.8,1.1,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (0.3)

Step 1

Concept

The common difference is (0.5-0.2=0.3). In decimal questions pay attention to place value.

Step 2

Why this answer is correct

The correct answer is A. (0.3). The common difference is (0.5-0.2=0.3). In decimal questions pay attention to place value.

Step 3

Exam Tip

सार्व अंतर (0.5-0.2=0.3) है। दशमलव वाले प्रश्नों में स्थान मान का ध्यान रखें।

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अनुक्रम \(\frac{3}{4},1,\frac{5}{4},\frac{3}{2},\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(\frac{3}{4},1,\frac{5}{4},\frac{3}{2},\ldots\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{1}{4}\)

Step 1

Concept

\(1-\frac{3}{4}=\frac{1}{4}\) and \(\frac{5}{4}-1=\frac{1}{4}\). For fractions subtract using common denominators.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{1}{4}\). \(1-\frac{3}{4}=\frac{1}{4}\) and \(\frac{5}{4}-1=\frac{1}{4}\). For fractions subtract using common denominators.

Step 3

Exam Tip

\(1-\frac{3}{4}=\frac{1}{4}\) और \(\frac{5}{4}-1=\frac{1}{4}\) है। भिन्नों में समान हर बनाकर घटाएं।

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अनुक्रम \(5x,5x+2,5x+4,\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(5x,5x+2,5x+4,\ldots\)?

Explanation opens after your attempt
Correct Answer

A. (2)

Step 1

Concept

The common difference is ((5x+2)-5x=2). For algebraic terms also subtract the first term from the second.

Step 2

Why this answer is correct

The correct answer is A. (2). The common difference is ((5x+2)-5x=2). For algebraic terms also subtract the first term from the second.

Step 3

Exam Tip

सार्व अंतर ((5x+2)-5x=2) है। बीजगणितीय पदों में भी दूसरे पद में से पहला पद घटाएं।

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अनुक्रम \(18,23,28,33,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(18,23,28,33,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (5)

Step 1

Concept

The common difference is (23-18=5), and the same difference continues. In exams always check the difference of consecutive terms.

Step 2

Why this answer is correct

The correct answer is B. (5). The common difference is (23-18=5), and the same difference continues. In exams always check the difference of consecutive terms.

Step 3

Exam Tip

सार्व अंतर (23-18=5) है और आगे भी यही अंतर है। परीक्षा में दो क्रमागत पदों का अंतर जरूर जांचें।

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अनुक्रम \(\frac{4}{7},\frac{6}{7},\frac{8}{7},\frac{10}{7},\ldots\) का सार्व अंतर क्या है?

What is the common difference of \(\frac{4}{7},\frac{6}{7},\frac{8}{7},\frac{10}{7},\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{2}{7}\)

Step 1

Concept

\(\frac{6}{7}-\frac{4}{7}=\frac{2}{7}\). For fractions with the same denominator, quickly check the difference of numerators.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{2}{7}\). \(\frac{6}{7}-\frac{4}{7}=\frac{2}{7}\). For fractions with the same denominator, quickly check the difference of numerators.

Step 3

Exam Tip

\(\frac{6}{7}-\frac{4}{7}=\frac{2}{7}\) है। समान हर वाले भिन्नों में अंशों का अंतर जल्दी जाँचें।

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अनुक्रम \(36,42,48,54,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(36,42,48,54,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (6)

Step 1

Concept

The difference of consecutive terms is (42-36=6). Always subtract the previous term from the next term to find the common difference.

Step 2

Why this answer is correct

The correct answer is C. (6). The difference of consecutive terms is (42-36=6). Always subtract the previous term from the next term to find the common difference.

Step 3

Exam Tip

लगातार पदों का अंतर (42-36=6) है। सार्व अंतर निकालते समय हमेशा अगले पद से पिछले पद को घटाएँ।

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समांतर श्रेढ़ी \(54,48,42,36,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the arithmetic progression \(54,48,42,36,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (-6)

Step 1

Concept

(48-54=-6). In a decreasing progression, always check the sign of the answer.

Step 2

Why this answer is correct

The correct answer is B. (-6). (48-54=-6). In a decreasing progression, always check the sign of the answer.

Step 3

Exam Tip

(48-54=-6) है। घटती श्रेढ़ी में उत्तर के चिन्ह की जाँच जरूर करें।

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समांतर श्रेढ़ी \(\frac{1}{5},\frac{3}{5},1,\frac{7}{5},\ldots\) का सार्व अंतर क्या है?

What is the common difference of \(\frac{1}{5},\frac{3}{5},1,\frac{7}{5},\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{2}{5}\)

Step 1

Concept

\(\frac{3}{5}-\frac{1}{5}=\frac{2}{5}\). (d) can be found easily from the first two terms.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{2}{5}\). \(\frac{3}{5}-\frac{1}{5}=\frac{2}{5}\). (d) can be found easily from the first two terms.

Step 3

Exam Tip

\(\frac{3}{5}-\frac{1}{5}=\frac{2}{5}\) है। पहले दो पदों से (d) आसानी से मिल जाता है।

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अनुक्रम \(72,64,56,48,\ldots\) का सार्व अंतर क्या है?

What is the common difference of \(72,64,56,48,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (-8)

Step 1

Concept

Here (64-72=-8). The common difference can be found from the first two terms.

Step 2

Why this answer is correct

The correct answer is B. (-8). Here (64-72=-8). The common difference can be found from the first two terms.

Step 3

Exam Tip

यहाँ (64-72=-8) है। पहले दो पदों से ही सार्व अंतर मिल जाता है।

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यदि हर अगला पद पिछले पद से (9) अधिक है, तो सार्व अंतर क्या है?

If every next term is (9) more than the previous term, what is the common difference?

Explanation opens after your attempt
Correct Answer

C. (9)

Step 1

Concept

Being (9) more each time means (d=9). This is the identity of an arithmetic progression.

Step 2

Why this answer is correct

The correct answer is C. (9). Being (9) more each time means (d=9). This is the identity of an arithmetic progression.

Step 3

Exam Tip

हर बार (9) अधिक होने का अर्थ (d=9) है। यही समांतर श्रेढ़ी की पहचान है।

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अनुक्रम \(4,8,12,16,\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(4,8,12,16,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

The difference of consecutive terms is (8-4=4). In exams, find (d) by subtracting the first term from the second term.

Step 2

Why this answer is correct

The correct answer is B. (4). The difference of consecutive terms is (8-4=4). In exams, find (d) by subtracting the first term from the second term.

Step 3

Exam Tip

लगातार पदों का अंतर (8-4=4) है। परीक्षा में (d) के लिए दूसरा पद घटा पहला पद करें।

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अनुक्रम \(7,11,15,19,\ldots\) में पहले दो पदों से सार्व अंतर कैसे मिलेगा?

How will the common difference be found from the first two terms of \(7,11,15,19,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (11-7=4)

Step 1

Concept

The common difference is second term minus first term, so (11-7=4). In exams do not reverse the order of subtraction.

Step 2

Why this answer is correct

The correct answer is B. (11-7=4). The common difference is second term minus first term, so (11-7=4). In exams do not reverse the order of subtraction.

Step 3

Exam Tip

सार्व अंतर दूसरा पद घटा पहला पद होता है इसलिए (11-7=4) है। परीक्षा में घटाव का क्रम न बदलें।

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यदि अनुक्रम \(x, x+5, x+10,\ldots\) है तो सार्व अंतर क्या है?

If the sequence is \(x, x+5, x+10,\ldots\), what is the common difference?

Explanation opens after your attempt
Correct Answer

C. (5)

Step 1

Concept

The common difference is ((x+5)-x=5). For algebraic terms also subtract the first term from the second.

Step 2

Why this answer is correct

The correct answer is C. (5). The common difference is ((x+5)-x=5). For algebraic terms also subtract the first term from the second.

Step 3

Exam Tip

सार्व अंतर ((x+5)-x=5) है। अक्षर वाले पदों में भी दूसरा पद घटा पहला पद करें।

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यदि टिकटों की कीमतें \(40,45,50,55,\ldots\) हैं तो कीमतों का सार्व अंतर क्या है?

If ticket prices are \(40,45,50,55,\ldots\), what is the common difference of the prices?

Explanation opens after your attempt
Correct Answer

D. (5)

Step 1

Concept

(45-40=5), and the same difference continues. The equal increase in prices is (d).

Step 2

Why this answer is correct

The correct answer is D. (5). (45-40=5), and the same difference continues. The equal increase in prices is (d).

Step 3

Exam Tip

(45-40=5) है और आगे भी यही अंतर है। कीमतों में समान वृद्धि (d) होती है।

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अनुक्रम \(\frac{1}{2},1,\frac{3}{2},2,\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(\frac{1}{2},1,\frac{3}{2},2,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{1}{2}\)

Step 1

Concept

The common difference is \(1-\frac{1}{2}=\frac{1}{2}\). For fractions also subtract consecutive terms.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{1}{2}\). The common difference is \(1-\frac{1}{2}=\frac{1}{2}\). For fractions also subtract consecutive terms.

Step 3

Exam Tip

सार्व अंतर \(1-\frac{1}{2}=\frac{1}{2}\) है। भिन्नों में भी क्रमागत पद घटाएं।

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अनुक्रम \(2.5,3.0,3.5,4.0,\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(2.5,3.0,3.5,4.0,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (0.5)

Step 1

Concept

The common difference is (3.0-2.5=0.5). The same rule applies to decimal terms.

Step 2

Why this answer is correct

The correct answer is B. (0.5). The common difference is (3.0-2.5=0.5). The same rule applies to decimal terms.

Step 3

Exam Tip

सार्व अंतर (3.0-2.5=0.5) है। दशमलव पदों में भी वही नियम लागू होता है।

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अनुक्रम \(100,90,80,70,\ldots\) में सार्व अंतर कितना है?

What is the common difference in the sequence \(100,90,80,70,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (-10)

Step 1

Concept

The common difference is (90-100=-10). In a decreasing sequence carefully check the sign.

Step 2

Why this answer is correct

The correct answer is C. (-10). The common difference is (90-100=-10). In a decreasing sequence carefully check the sign.

Step 3

Exam Tip

सार्व अंतर (90-100=-10) है। घटते अनुक्रम में उत्तर का चिह्न जरूर देखें।

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निम्न में से किस अनुक्रम का सार्व अंतर (7) है?

Which of the following sequences has common difference (7)?

Explanation opens after your attempt
Correct Answer

B. \(2,9,16,23,\ldots\)

Step 1

Concept

(9-2=7), (16-9=7), and (23-16=7). All consecutive differences must be equal.

Step 2

Why this answer is correct

The correct answer is B. \(2,9,16,23,\ldots\). (9-2=7), (16-9=7), and (23-16=7). All consecutive differences must be equal.

Step 3

Exam Tip

(9-2=7), (16-9=7) और (23-16=7) हैं। सभी क्रमागत अंतर समान होने चाहिए।

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अनुक्रम \(8,8,8,8,\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(8,8,8,8,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (0)

Step 1

Concept

The common difference is (8-8=0). A sequence with equal terms has difference (0).

Step 2

Why this answer is correct

The correct answer is B. (0). The common difference is (8-8=0). A sequence with equal terms has difference (0).

Step 3

Exam Tip

सार्व अंतर (8-8=0) है। समान पदों वाली श्रेणी में अंतर (0) होता है।

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यदि सार्व अंतर (0) हो तो अंकगणितीय श्रेणी कैसी होती है?

If the common difference is (0), what type of arithmetic progression is formed?

Explanation opens after your attempt
Correct Answer

A. सभी पद समान होते हैंAll terms are equal

Step 1

Concept

When (d=0), each next term remains the same. This can also be an arithmetic progression.

Step 2

Why this answer is correct

The correct answer is A. सभी पद समान होते हैं / All terms are equal. When (d=0), each next term remains the same. This can also be an arithmetic progression.

Step 3

Exam Tip

(d=0) होने पर प्रत्येक अगला पद पहले जैसा रहता है। यह भी अंकगणितीय श्रेणी हो सकती है।

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अनुक्रम \(-3,0,3,6,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(-3,0,3,6,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

The common difference is (0-(-3)=3). Be careful while subtracting negative terms.

Step 2

Why this answer is correct

The correct answer is C. (3). The common difference is (0-(-3)=3). Be careful while subtracting negative terms.

Step 3

Exam Tip

सार्व अंतर (0-(-3)=3) है। ऋणात्मक पदों में घटाव सावधानी से करें।

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अनुक्रम \(20,15,10,5,\ldots\) में पहला पद और सार्व अंतर क्रमशः क्या हैं?

In the sequence \(20,15,10,5,\ldots\), what are the first term and common difference respectively?

Explanation opens after your attempt
Correct Answer

A. (20) और (-5)(20) and (-5)

Step 1

Concept

The first term is (20) and (15-20=-5). When asked respectively keep the order in mind.

Step 2

Why this answer is correct

The correct answer is A. (20) और (-5) / (20) and (-5). The first term is (20) and (15-20=-5). When asked respectively keep the order in mind.

Step 3

Exam Tip

पहला पद (20) है और (15-20=-5) है। क्रमशः पूछे जाने पर क्रम का ध्यान रखें।

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यदि किसी अंकगणितीय श्रेणी का पहला पद (7) और सार्व अंतर (2) है तो दूसरा पद क्या होगा?

If the first term of an arithmetic progression is (7) and the common difference is (2), what is the second term?

Explanation opens after your attempt
Correct Answer

D. (9)

Step 1

Concept

The second term is (7+2=9). Add the common difference to get the next term.

Step 2

Why this answer is correct

The correct answer is D. (9). The second term is (7+2=9). Add the common difference to get the next term.

Step 3

Exam Tip

दूसरा पद (7+2=9) होगा। अगला पद पाने के लिए सार्व अंतर जोड़ें।

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अनुक्रम \(12,10,8,6,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the sequence \(12,10,8,6,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (-2)

Step 1

Concept

The common difference is (10-12=-2). A decreasing progression can have a negative difference.

Step 2

Why this answer is correct

The correct answer is B. (-2). The common difference is (10-12=-2). A decreasing progression can have a negative difference.

Step 3

Exam Tip

सार्व अंतर (10-12=-2) है। घटती श्रेणी में अंतर ऋणात्मक हो सकता है।

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अनुक्रम \(5,9,13,17,\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(5,9,13,17,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

Here (9-5=4) and (13-9=4). In exams subtract any two consecutive terms.

Step 2

Why this answer is correct

The correct answer is C. (4). Here (9-5=4) and (13-9=4). In exams subtract any two consecutive terms.

Step 3

Exam Tip

यहां (9-5=4) और (13-9=4) है। परीक्षा में किसी भी दो क्रमागत पदों को घटाएं।

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समांतर श्रेढ़ी \(31,28,25,22,\ldots\) का सार्व अंतर क्या है?

What is the common difference of the arithmetic progression \(31,28,25,22,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (-3)

Step 1

Concept

(28-31=-3). In a decreasing progression, the common difference is written as negative.

Step 2

Why this answer is correct

The correct answer is B. (-3). (28-31=-3). In a decreasing progression, the common difference is written as negative.

Step 3

Exam Tip

(28-31=-3) है। घटती श्रेढ़ी में सार्व अंतर ऋणात्मक लिखा जाता है।

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यदि \(a_1=16\) और \(a_2=10\) हैं, तो सार्व अंतर (d) क्या होगा?

If \(a_1=16\) and \(a_2=10\), what will be the common difference (d)?

Explanation opens after your attempt
Correct Answer

C. (-6)

Step 1

Concept

\(d=a_2-a_1=10-16=-6\). Always subtract the first term from the second term.

Step 2

Why this answer is correct

The correct answer is C. (-6). \(d=a_2-a_1=10-16=-6\). Always subtract the first term from the second term.

Step 3

Exam Tip

\(d=a_2-a_1=10-16=-6\) है। दूसरे पद से पहला पद ही घटाएँ।

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समांतर श्रेढ़ी \(\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4},\ldots\) का सार्व अंतर क्या है?

What is the common difference of the arithmetic progression \(\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4},\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{1}{2}\)

Step 1

Concept

\(\frac{5}{4}-\frac{3}{4}=\frac{2}{4}=\frac{1}{2}\). For fractions with the same denominator, subtract the numerators.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{1}{2}\). \(\frac{5}{4}-\frac{3}{4}=\frac{2}{4}=\frac{1}{2}\). For fractions with the same denominator, subtract the numerators.

Step 3

Exam Tip

\(\frac{5}{4}-\frac{3}{4}=\frac{2}{4}=\frac{1}{2}\) है। समान हर वाले भिन्नों में अंश घटाएँ।

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अनुक्रम \(100,90,80,70,\ldots\) का सार्व अंतर क्या है?

What is the common difference of \(100,90,80,70,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (-10)

Step 1

Concept

Here (90-100=-10). Do not take the answer as positive in a decreasing sequence.

Step 2

Why this answer is correct

The correct answer is B. (-10). Here (90-100=-10). Do not take the answer as positive in a decreasing sequence.

Step 3

Exam Tip

यहाँ (90-100=-10) है। घटते अनुक्रम में उत्तर को धनात्मक न मान लें।

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यदि किसी अनुक्रम में हर अगला पद पिछले पद से (7) अधिक है, तो उसका सार्व अंतर क्या है?

If each next term of a sequence is (7) more than the previous term, what is its common difference?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

Adding (7) each time means the common difference is (7). Such a sequence will be an arithmetic progression.

Step 2

Why this answer is correct

The correct answer is C. (7). Adding (7) each time means the common difference is (7). Such a sequence will be an arithmetic progression.

Step 3

Exam Tip

हर बार (7) जोड़ने का अर्थ सार्व अंतर (7) है। ऐसी श्रेढ़ी समांतर श्रेढ़ी होगी।

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अनुक्रम \(3,7,11,15,\ldots\) में सार्व अंतर क्या है?

What is the common difference in the sequence \(3,7,11,15,\ldots\)?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

The difference of consecutive terms is (7-3=4). In exams, find common difference by subtracting the first term from the second term.

Step 2

Why this answer is correct

The correct answer is C. (4). The difference of consecutive terms is (7-3=4). In exams, find common difference by subtracting the first term from the second term.

Step 3

Exam Tip

लगातार पदों का अंतर (7-3=4) है। परीक्षा में सार्व अंतर के लिए दूसरा पद घटा पहला पद करें।

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फ्रांस में समान प्रशासन और समान कानून किस पुरानी समस्या को कम करने के लिए थे?

Common administration and common laws in France were meant to reduce which old problem?

Explanation opens after your attempt
Correct Answer

A. क्षेत्रीय नियमों और स्थानीय बाधाओं की विविधताDiversity of regional rules and local barriers

Step 1

Concept

In old France, rules differed across regions.

Step 2

Why this answer is correct

Common administration reduced these differences and increased unity.

Step 3

Exam Tip

Understand it as political and administrative integration. चरण 1: पुराने फ्रांस में कई क्षेत्रों के नियम अलग थे। चरण 2: समान प्रशासन ने इन भेदों को कम करके एकता बढ़ाई। चरण 3: इसे राजनीतिक और प्रशासनिक एकीकरण के रूप में समझें।

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यदि (3,x,11,y,19) एक समांतर श्रेणी के लगातार पांच पद हैं, तो (x,y) और सामान्य अंतर क्या हैं?

If (3,x,11,y,19) are five consecutive terms of an AP, what are (x,y) and the common difference?

Explanation opens after your attempt
Correct Answer

B. (x=7,y=15,d=4)

Step 1

Concept

There are (4) equal gaps between the first and fifth terms, so \(d=\frac{19-3}{4}=4\). In exams, divide the total difference between distant terms by the number of gaps.

Step 2

Why this answer is correct

The correct answer is B. (x=7,y=15,d=4). There are (4) equal gaps between the first and fifth terms, so \(d=\frac{19-3}{4}=4\). In exams, divide the total difference between distant terms by the number of gaps.

Step 3

Exam Tip

पहले और पांचवें पद के बीच (4) बराबर अंतराल हैं, इसलिए \(d=\frac{19-3}{4}=4\)। परीक्षा में दूर दिए गए पदों के बीच कुल अंतर को अंतरालों की संख्या से भाग दें।

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यदि \(a_n=An+B\), \(a_2=11\) और \(a_5=26\), तो सामान्य अंतर क्या है?

If \(a_n=An+B\), \(a_2=11\) and \(a_5=26\), what is the common difference?

Explanation opens after your attempt
Correct Answer

C. (5)

Step 1

Concept

\(a_5-a_2=3d=15\), so (d=5). In exams, even for a linear form, (d) can be found from term differences.

Step 2

Why this answer is correct

The correct answer is C. (5). \(a_5-a_2=3d=15\), so (d=5). In exams, even for a linear form, (d) can be found from term differences.

Step 3

Exam Tip

\(a_5-a_2=3d=15\), इसलिए (d=5)। परीक्षा में रैखिक रूप में भी पदों के अंतर से (d) निकाला जा सकता है।

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अनुक्रम \(100,97.5,95,92.5,\ldots\) का सामान्य अंतर क्या है?

What is the common difference of \(100,97.5,95,92.5,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (-2.5)

Step 1

Concept

Each term is (2.5) less than the previous one, so (d=-2.5). In exams, do not forget the negative sign in decreasing decimal sequences.

Step 2

Why this answer is correct

The correct answer is B. (-2.5). Each term is (2.5) less than the previous one, so (d=-2.5). In exams, do not forget the negative sign in decreasing decimal sequences.

Step 3

Exam Tip

हर पद पिछले से (2.5) कम है, इसलिए (d=-2.5)। परीक्षा में घटते दशमलव अनुक्रम में ऋणात्मक चिन्ह न भूलें।

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किसी समांतर श्रेणी में \(a_3=4\) और \(a_6=25\) हैं। सामान्य अंतर क्या है?

In an AP, \(a_3=4\) and \(a_6=25\). What is the common difference?

Explanation opens after your attempt
Correct Answer

A. (7)

Step 1

Concept

\(a_6-a_3=3d=21\), so (d=7). In exams, the term-number gap is (3), not (6).

Step 2

Why this answer is correct

The correct answer is A. (7). \(a_6-a_3=3d=21\), so (d=7). In exams, the term-number gap is (3), not (6).

Step 3

Exam Tip

\(a_6-a_3=3d=21\), इसलिए (d=7)। परीक्षा में पद क्रमांक का अंतर (3) है, (6) नहीं।

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यदि (a,b,c) समांतर श्रेणी में हैं और प्रत्येक पद को (t) से गुणा किया जाता है, तो नया सामान्य अंतर क्या होगा?

If (a,b,c) are in AP and each term is multiplied by (t), what will be the new common difference?

Explanation opens after your attempt
Correct Answer

C. (t(b-a))

Step 1

Concept

Multiplication makes every difference (t) times as large. In exams, apply scaling directly to the common difference.

Step 2

Why this answer is correct

The correct answer is C. (t(b-a)). Multiplication makes every difference (t) times as large. In exams, apply scaling directly to the common difference.

Step 3

Exam Tip

गुणन से हर अंतर (t) गुना हो जाता है। परीक्षा में स्केलिंग सीधे सामान्य अंतर पर भी लागू करें।

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तीन पद (2a-3b,5a-b,8a+b) के लिए सामान्य अंतर क्या है?

What is the common difference for the three terms (2a-3b,5a-b,8a+b)?

Explanation opens after your attempt
Correct Answer

A. (3a+2b)

Step 1

Concept

Both consecutive differences are (3a+2b), so the terms are in AP. In exams, also check equality of the two differences.

Step 2

Why this answer is correct

The correct answer is A. (3a+2b). Both consecutive differences are (3a+2b), so the terms are in AP. In exams, also check equality of the two differences.

Step 3

Exam Tip

दोनों लगातार अंतर (3a+2b) हैं, इसलिए ये पद समांतर श्रेणी में हैं। परीक्षा में दोनों अंतरों की समानता भी साथ-साथ जांचें।

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यदि समांतर श्रेणी में \(a_7-a_2=35\), तो सामान्य अंतर क्या है?

If \(a_7-a_2=35\) in an AP, what is the common difference?

Explanation opens after your attempt
Correct Answer

C. (7)

Step 1

Concept

There are (5) intervals between \(a_7\) and \(a_2\), so (5d=35) and (d=7). In exams, subtract term numbers to get intervals.

Step 2

Why this answer is correct

The correct answer is C. (7). There are (5) intervals between \(a_7\) and \(a_2\), so (5d=35) and (d=7). In exams, subtract term numbers to get intervals.

Step 3

Exam Tip

\(a_7\) और \(a_2\) के बीच (5) अंतराल हैं, इसलिए (5d=35) और (d=7)। परीक्षा में पद क्रमांक घटाकर अंतराल पाएं।

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एक समांतर श्रेणी में \(a_{n+2}-a_n=18\) हर (n) के लिए है। सामान्य अंतर क्या है?

In an AP, \(a_{n+2}-a_n=18\) for every (n). What is the common difference?

Explanation opens after your attempt
Correct Answer

B. (9)

Step 1

Concept

Moving two terms ahead changes the value by (2d), so (2d=18) and (d=9). In exams, count the number of jumps.

Step 2

Why this answer is correct

The correct answer is B. (9). Moving two terms ahead changes the value by (2d), so (2d=18) and (d=9). In exams, count the number of jumps.

Step 3

Exam Tip

दो पद आगे जाने पर परिवर्तन (2d) होता है, इसलिए (2d=18) और (d=9)। परीक्षा में छलांगों की संख्या गिनें।

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कैलेंडर की तारीखें (3,10,17,24,31) एक अनुक्रम बनाती हैं। सामान्य अंतर क्या है?

The calendar dates (3,10,17,24,31) form a sequence. What is the common difference?

Explanation opens after your attempt
Correct Answer

A. (7) दिन(7) days

Step 1

Concept

Each next date is (7) days later. In exams, including the unit makes the answer clearer.

Step 2

Why this answer is correct

The correct answer is A. (7) दिन / (7) days. Each next date is (7) days later. In exams, including the unit makes the answer clearer.

Step 3

Exam Tip

हर अगली तारीख (7) दिन बाद है। परीक्षा में इकाई के साथ उत्तर देना अधिक स्पष्ट होता है।

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अनुक्रम \(81,72,63,54,\ldots\) का सामान्य अंतर क्या है?

What is the common difference of \(81,72,63,54,\ldots\)?

Explanation opens after your attempt
Correct Answer

B. (-9)

Step 1

Concept

Each step subtracts (9), so (d=-9). In exams, keep the difference negative for descending order.

Step 2

Why this answer is correct

The correct answer is B. (-9). Each step subtracts (9), so (d=-9). In exams, keep the difference negative for descending order.

Step 3

Exam Tip

हर कदम पर (9) घट रहा है, इसलिए (d=-9)। परीक्षा में अवरोही क्रम में अंतर ऋणात्मक रखें।

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यदि \(a_n=4n+7\) है और \(c_n=a_{n+1}-a_n\), तो \(c_n\) अनुक्रम का सामान्य अंतर क्या है?

If \(a_n=4n+7\) and \(c_n=a_{n+1}-a_n\), what is the common difference of the sequence \(c_n\)?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

Here \(c_n=4\) for every (n), so its common difference is (0). In exams, treat the sequence of differences as a separate sequence.

Step 2

Why this answer is correct

The correct answer is A. (0). Here \(c_n=4\) for every (n), so its common difference is (0). In exams, treat the sequence of differences as a separate sequence.

Step 3

Exam Tip

यहां \(c_n=4\) हर (n) के लिए स्थिर है, इसलिए उसका सामान्य अंतर (0) है। परीक्षा में अंतरों के अनुक्रम को अलग अनुक्रम मानकर देखें।

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एक वाहन समान समयांतरालों में (18,30,42,54) किलोमीटर चलता है। दूरी अनुक्रम का सामान्य अंतर क्या है?

A vehicle covers (18,30,42,54) kilometres in equal time intervals. What is the common difference of the distance sequence?

Explanation opens after your attempt
Correct Answer

B. (12) किलोमीटर(12) kilometres

Step 1

Concept

The distance increases by (12) kilometres each time. In word problems, still find the same consecutive difference.

Step 2

Why this answer is correct

The correct answer is B. (12) किलोमीटर / (12) kilometres. The distance increases by (12) kilometres each time. In word problems, still find the same consecutive difference.

Step 3

Exam Tip

हर बार दूरी (12) किलोमीटर बढ़ती है। परीक्षा में वास्तविक जीवन प्रश्न में भी वही लगातार अंतर निकालें।

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अनुक्रम \(x,x+\sqrt{5},x+2\sqrt{5},x+3\sqrt{5}\) का सामान्य अंतर क्या है?

What is the common difference of \(x,x+\sqrt{5},x+2\sqrt{5},x+3\sqrt{5}\)?

Explanation opens after your attempt
Correct Answer

B. \(\sqrt{5}\)

Step 1

Concept

Each next term adds \(\sqrt{5}\). In exams, the variable (x) is the fixed part, not the common difference.

Step 2

Why this answer is correct

The correct answer is B. \(\sqrt{5}\). Each next term adds \(\sqrt{5}\). In exams, the variable (x) is the fixed part, not the common difference.

Step 3

Exam Tip

हर अगले पद में \(\sqrt{5}\) जुड़ता है। परीक्षा में चर (x) स्थिर भाग है, सामान्य अंतर नहीं।

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किसी समांतर श्रेणी के पहले दो पद \(\lambda-4\) और \(3\lambda+2\) हैं। सामान्य अंतर क्या है?

The first two terms of an AP are \(\lambda-4\) and \(3\lambda+2\). What is the common difference?

Explanation opens after your attempt
Correct Answer

A. \(2\lambda+6\)

Step 1

Concept

The common difference is second term minus first term, so (3\lambda+2-\(\lambda-4\)=2\lambda+6). In exams, handle the minus sign before brackets carefully.

Step 2

Why this answer is correct

The correct answer is A. \(2\lambda+6\). The common difference is second term minus first term, so (3\lambda+2-\(\lambda-4\)=2\lambda+6). In exams, handle the minus sign before brackets carefully.

Step 3

Exam Tip

सामान्य अंतर दूसरा पद घटा पहला पद है, इसलिए (3\lambda+2-\(\lambda-4\)=2\lambda+6)। परीक्षा में कोष्ठक हटाते समय ऋण चिन्ह संभालें।

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अनुक्रम \(\frac{7}{8},\frac{5}{8},\frac{3}{8},\frac{1}{8},\ldots\) का सामान्य अंतर क्या है?

What is the common difference of \(\frac{7}{8},\frac{5}{8},\frac{3}{8},\frac{1}{8},\ldots\)?

Explanation opens after your attempt
Correct Answer

B. \(-\frac{1}{4}\)

Step 1

Concept

\(\frac{5}{8}-\frac{7}{8}=-\frac{2}{8}=-\frac{1}{4}\). In exams, with equal denominators, subtract numerators directly.

Step 2

Why this answer is correct

The correct answer is B. \(-\frac{1}{4}\). \(\frac{5}{8}-\frac{7}{8}=-\frac{2}{8}=-\frac{1}{4}\). In exams, with equal denominators, subtract numerators directly.

Step 3

Exam Tip

\(\frac{5}{8}-\frac{7}{8}=-\frac{2}{8}=-\frac{1}{4}\)। परीक्षा में समान हर हो तो अंशों का अंतर तुरंत लें।

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यदि \(a_n=mn+n\) है, तो अनुक्रम का सामान्य अंतर क्या है?

If \(a_n=mn+n\), what is the common difference of the sequence?

Explanation opens after your attempt
Correct Answer

D. (m+1)

Step 1

Concept

(a_n=(m+1)n), so the coefficient of (n) is (m+1). In exams, combine like terms before identifying the linear coefficient.

Step 2

Why this answer is correct

The correct answer is D. (m+1). (a_n=(m+1)n), so the coefficient of (n) is (m+1). In exams, combine like terms before identifying the linear coefficient.

Step 3

Exam Tip

(a_n=(m+1)n) है, इसलिए (n) का गुणांक (m+1) है। परीक्षा में पहले समान पदों को मिलाकर रैखिक रूप बनाएं।

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यदि (a_n=c-(n-1)r) है, तो पहला पद और सामान्य अंतर क्या हैं?

If (a_n=c-(n-1)r), what are the first term and common difference?

Explanation opens after your attempt
Correct Answer

D. \(a_1=c,d=-r\)

Step 1

Concept

Putting (n=1) gives \(a_1=c\), and each next term subtracts (r). In exams, compare with the form (a+d(n-1)).

Step 2

Why this answer is correct

The correct answer is D. \(a_1=c,d=-r\). Putting (n=1) gives \(a_1=c\), and each next term subtracts (r). In exams, compare with the form (a+d(n-1)).

Step 3

Exam Tip

(n=1) रखने पर \(a_1=c\) और हर अगले पद में (r) घटता है। परीक्षा में (a+d(n-1)) रूप से तुलना करें।

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तापमानों का अनुक्रम \(42^\circ,38.5^\circ,35^\circ,31.5^\circ\) है। सामान्य अंतर क्या है?

The temperatures form the sequence \(42^\circ,38.5^\circ,35^\circ,31.5^\circ\). What is the common difference?

Explanation opens after your attempt
Correct Answer

C. \(-3.5^\circ\)

Step 1

Concept

Each step decreases by \(3.5^\circ\), so \(d=-3.5^\circ\). In exams, use a negative sign for a decreasing sequence.

Step 2

Why this answer is correct

The correct answer is C. \(-3.5^\circ\). Each step decreases by \(3.5^\circ\), so \(d=-3.5^\circ\). In exams, use a negative sign for a decreasing sequence.

Step 3

Exam Tip

हर बार \(3.5^\circ\) की कमी है, इसलिए \(d=-3.5^\circ\)। परीक्षा में घटते अनुक्रम में ऋणात्मक चिन्ह लगाएं।

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कौन सा अनुक्रम सामान्य अंतर (0.75) वाली समांतर श्रेणी है?

Which sequence is an AP with common difference (0.75)?

Explanation opens after your attempt
Correct Answer

D. (2.5,3.25,4,4.75)

Step 1

Concept

In that option, each step increases by (0.75). In exams, use consecutive difference as the test even with decimals.

Step 2

Why this answer is correct

The correct answer is D. (2.5,3.25,4,4.75). In that option, each step increases by (0.75). In exams, use consecutive difference as the test even with decimals.

Step 3

Exam Tip

विकल्प में हर बार (0.75) की वृद्धि है। परीक्षा में दशमलवों में भी लगातार अंतर को ही कसौटी बनाएं।

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एक समांतर श्रेणी में \(a_4=12\) और \(a_{10}=-6\) हैं। सामान्य अंतर क्या है?

In an AP, \(a_4=12\) and \(a_{10}=-6\). What is the common difference?

Explanation opens after your attempt
Correct Answer

C. (-3)

Step 1

Concept

\(a_{10}-a_4=6d=-18\), so (d=-3). In exams, divide the total change by the gap in term numbers.

Step 2

Why this answer is correct

The correct answer is C. (-3). \(a_{10}-a_4=6d=-18\), so (d=-3). In exams, divide the total change by the gap in term numbers.

Step 3

Exam Tip

\(a_{10}-a_4=6d=-18\), इसलिए (d=-3)। परीक्षा में पद-संख्या के अंतर को कुल परिवर्तन से भाग दें।

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