100 results found for "even common factor" in Class 10.
\(\sqrt{2}\) के प्रमाण में यदि (a) और (b) दोनों सम हैं, तो उनका कम से कम कौन सा साझा गुणनखंड है?
In the proof of \(\sqrt{2}\), if both (a) and (b) are even, what is at least one common factor of them?
#even common factor
#sqrt2
#class 10
A (2)
B (3)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
An even number is always divisible by (2).
Step 2
Why this answer is correct
Both are even, so (2) is their common factor.
Step 3
Exam Tip
Finding a common factor contradicts the lowest-form condition. चरण 1: सम संख्या हमेशा (2) से विभाज्य होती है। चरण 2: दोनों सम हैं, इसलिए (2) दोनों का साझा गुणनखंड है। चरण 3: साझा गुणनखंड मिलना सरलतम रूप की शर्त से टकराता है।
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\(4x^5+12x^4\) का सामान्य गुणनखंड निकालने पर क्या मिलेगा?
What is obtained by taking the common factor from \(4x^5+12x^4\)?
#polynomials
#common factor
#factorization
A (4x-4 (x+3))
B (4x\(x^4+3\))
C (x-4 (4x+12x))
D (12x-4 (x+1))
Explanation opens after your attempt
Correct Answer
A. (4x-4 (x+3))
Step 1
Concept
The common factor in both terms is \(4x^4\). Hence the form is (4x-4 (x+3)).
Step 2
Why this answer is correct
The correct answer is A. (4x-4 (x+3)). The common factor in both terms is \(4x^4\). Hence the form is (4x-4 (x+3)).
Step 3
Exam Tip
दोनों पदों में सामान्य गुणनखंड \(4x^4\) है। इसलिए रूप (4x-4 (x+3)) है।
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\(3x^4+9x^3\) का सामान्य गुणनखंड निकालने पर क्या मिलेगा?
What is obtained by taking the common factor from \(3x^4+9x^3\)?
#polynomials
#common factor
#factorization
A (3x-3 (x+3))
B (3x\(x^3+3\))
C (x-3 (3x+9x))
D (9x-3 (x+1))
Explanation opens after your attempt
Correct Answer
A. (3x-3 (x+3))
Step 1
Concept
The common factor in both terms is \(3x^3\). Hence the form is (3x-3 (x+3)).
Step 2
Why this answer is correct
The correct answer is A. (3x-3 (x+3)). The common factor in both terms is \(3x^3\). Hence the form is (3x-3 (x+3)).
Step 3
Exam Tip
दोनों पदों में सामान्य गुणनखंड \(3x^3\) है। इसलिए रूप (3x-3 (x+3)) है।
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\(2x^3+6x^2\) का सामान्य गुणनखंड निकालने पर क्या मिलेगा?
What is obtained by taking the common factor from \(2x^3+6x^2\)?
#polynomials
#common factor
#factorization
A (2x-2 (x+3))
B (2x\(x^2+3\))
C (x-2 (2x+6x))
D (6x-2 (x+1))
Explanation opens after your attempt
Correct Answer
A. (2x-2 (x+3))
Step 1
Concept
The common factor in both terms is \(2x^2\). Hence the form is (2x-2 (x+3)).
Step 2
Why this answer is correct
The correct answer is A. (2x-2 (x+3)). The common factor in both terms is \(2x^2\). Hence the form is (2x-2 (x+3)).
Step 3
Exam Tip
दोनों पदों में सामान्य गुणनखंड \(2x^2\) है। इसलिए रूप (2x-2 (x+3)) है।
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सामान्य गुणनखंड निकालकर \(4x^2+28x=0\) को कैसे लिखा जाएगा?
By taking common factor, how will \(4x^2+28x=0\) be written?
#quadratic
#common-factor
#factorisation
A (4x(x+7)=0)
B (4(x+7)=0)
C (x(4x-28)=0)
D (4x(x-7)=0)
Explanation opens after your attempt
Correct Answer
A. (4x(x+7)=0)
Step 1
Concept
(4x) is the common factor, so (4x(x+7)=0). In exams, take out the greatest common factor.
Step 2
Why this answer is correct
The correct answer is A. (4x(x+7)=0). (4x) is the common factor, so (4x(x+7)=0). In exams, take out the greatest common factor.
Step 3
Exam Tip
(4x) सामान्य गुणनखंड है, इसलिए (4x(x+7)=0) मिलता है। परीक्षा में सबसे बड़ा सामान्य गुणनखंड निकालें।
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सामान्य गुणनखंड निकालकर \(5x^2+15x=0\) को कैसे लिखा जाएगा?
By taking common factor, how will \(5x^2+15x=0\) be written?
#quadratic
#common-factor
#factorisation
A (5x(x+3)=0)
B (5(x+3)=0)
C (x(5x-15)=0)
D (5x(x-3)=0)
Explanation opens after your attempt
Correct Answer
A. (5x(x+3)=0)
Step 1
Concept
(5x) is the common factor, so (5x(x+3)=0). In exams, take out the greatest common factor.
Step 2
Why this answer is correct
The correct answer is A. (5x(x+3)=0). (5x) is the common factor, so (5x(x+3)=0). In exams, take out the greatest common factor.
Step 3
Exam Tip
(5x) सामान्य गुणनखंड है, इसलिए (5x(x+3)=0) मिलता है। परीक्षा में सबसे बड़ा सामान्य गुणनखंड निकालें।
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\(\sqrt{5}\) को परिमेय मानकर \(a^2=5b^2\) मिलने पर (a) और (b) में साझा गुणनखंड कैसे बनता है?
After assuming \(\sqrt{5}\) rational and getting \(a^2=5b^2\), how does a common factor appear in (a) and (b)?
#real-numbers
#root5
#common-factor
#proof-flow
A पहले \(5\mid a\), फिर (a=5k) रखने से \(5\mid b\) / First \(5\mid a\), then substituting (a=5k) gives \(5\mid b\)
B पहले (b=0), फिर (a=0) / First (b=0), then (a=0)
C पहले (a=b), फिर (5=1) / First (a=b), then (5=1)
D पहले \(\sqrt{5}=5\), फिर (a=b) / First \(\sqrt{5}=5\), then (a=b)
Explanation opens after your attempt
Correct Answer
A. पहले \(5\mid a\), फिर (a=5k) रखने से \(5\mid b\) / First \(5\mid a\), then substituting (a=5k) gives \(5\mid b\)
Step 1
Concept
From \(a^2=5b^2\), \(5\mid a\).
Step 2
Why this answer is correct
Putting (a=5k) gives \(b^2=5k^2\), so \(5\mid b\).
Step 3
Exam Tip
Now (5) becomes a common factor and gives the contradiction. चरण 1: \(a^2=5b^2\) से \(5\mid a\) मिलता है। चरण 2: (a=5k) रखने पर \(b^2=5k^2\), इसलिए \(5\mid b\)। चरण 3: अब (5) दोनों में साझा गुणनखंड बनकर विरोधाभास देता है।
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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?
#ap
#sum_of_aps
#common_difference
A (-8)
B (-2)
C (2)
D (8)
Explanation opens after your attempt
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 \(a_1,a_3,a_5,\ldots\)?
#ap
#odd_indexed_terms
#subsequence
A (d)
B (2d)
C (3d)
D (-d)
Explanation opens after your attempt
Step 1
Concept
The new sequence jumps two original terms each time, so the difference is (2d). In exams, multiply (d) by the term-number jump.
Step 2
Why this answer is correct
The correct answer is B. (2d). The new sequence jumps two original terms each time, so the difference is (2d). In exams, multiply (d) by the term-number jump.
Step 3
Exam Tip
नए अनुक्रम में दो-दो मूल पदों की छलांग है, इसलिए अंतर (2d) है। परीक्षा में पद-संख्या की छलांग को (d) से गुणा करें।
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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?
#ap
#reversed_order
#negative_difference
A (-12)
B (-6)
C (0)
D (6)
Explanation opens after your attempt
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 \(a_2,a_5,a_8,\ldots\)?
#ap
#subsequence
#common_difference
A (4)
B (8)
C (12)
D (16)
Explanation opens after your attempt
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 \(b_n\)?
#ap
#transformation
#scaled_difference
A (-14)
B (5)
C (-3)
D (3)
Explanation opens after your attempt
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?
#ap
#scaling
#common_difference
A (d-3)
B (-3d)
C (3d)
D (-d)
Explanation opens after your attempt
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 \(b_n\)?
#ap
#transformation
#common_difference
A (4)
B (5)
C (-3)
D (8)
Explanation opens after your attempt
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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\(\sqrt{2}\) के प्रमाण में \(p^2\) सम होने से (p) सम क्यों माना जाता है?
Why is (p) considered even when \(p^2\) is even in the proof for \(\sqrt{2}\)?
#real-numbers
#root2
#parity
#even-square
#hard
A क्योंकि विषम संख्या का वर्ग विषम होता है / Because the square of an odd number is odd
B क्योंकि हर संख्या का वर्ग सम होता है / Because the square of every number is even
C क्योंकि सम संख्या का वर्ग विषम होता है / Because the square of an even number is odd
D क्योंकि \(p^2\) हमेशा (p) से छोटा होता है / Because \(p^2\) is always smaller than (p)
Explanation opens after your attempt
Correct Answer
A. क्योंकि विषम संख्या का वर्ग विषम होता है / Because the square of an odd number is odd
Step 1
Concept
If (p) were odd, then \(p^2\) would also be odd.
Step 2
Why this answer is correct
Since \(p^2\) is even, (p) cannot be odd, so (p) is even.
Step 3
Exam Tip
This parity fact is very important in the proof. चरण 1: यदि (p) विषम होता, तो \(p^2\) भी विषम होता। चरण 2: पर \(p^2\) सम मिला है, इसलिए (p) विषम नहीं हो सकता और (p) सम होगा। चरण 3: यह छोटी सी सम-विषम बात प्रमाण में बहुत महत्त्वपूर्ण है।
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\(\sqrt{2}\) की सिद्धि में यदि \(a^2\) सम है, तो (a) सम क्यों होना चाहिए?
In the proof of \(\sqrt{2}\), if \(a^2\) is even, why must (a) be even?
#sqrt2 proof
#even square
#logic
#hard
A क्योंकि यदि (a) विषम होता तो \(a^2\) भी विषम होता / Because if (a) were odd, then \(a^2\) would also be odd
B क्योंकि हर संख्या सम होती है / Because every number is even
C क्योंकि (a=b) होता है / Because (a=b)
D क्योंकि (b=0) होता है / Because (b=0)
Explanation opens after your attempt
Correct Answer
A. क्योंकि यदि (a) विषम होता तो \(a^2\) भी विषम होता / Because if (a) were odd, then \(a^2\) would also be odd
Step 1
Concept
The square of an odd number is odd.
Step 2
Why this answer is correct
Here \(a^2\) is even, so (a) cannot be odd.
Step 3
Exam Tip
Hence (a) must be even. चरण 1: विषम संख्या का वर्ग विषम होता है। चरण 2: यहां \(a^2\) सम मिला है, इसलिए (a) विषम नहीं हो सकता। चरण 3: अतः (a) सम होना निश्चित है।
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कौन सा कथन \(\sqrt{2}\) की सिद्धि में \(a^2\) सम होने से (a) सम होने को सही ठहराता है?
Which statement justifies that (a) is even when \(a^2\) is even in the proof of \(\sqrt{2}\)?
#even square
#logical reasoning
#sqrt2
#class 10
A यदि (a) विषम होता, तो \(a^2\) भी विषम होता / If (a) were odd, then \(a^2\) would also be odd
B हर वर्ग शून्य होता है / Every square is zero
C हर पूर्णांक सम होता है / Every integer is even
D यदि \(a^2\) सम है, तो (a=1) / If \(a^2\) is even, then (a=1)
Explanation opens after your attempt
Correct Answer
A. यदि (a) विषम होता, तो \(a^2\) भी विषम होता / If (a) were odd, then \(a^2\) would also be odd
Step 1
Concept
The square of an odd number is always odd.
Step 2
Why this answer is correct
Here \(a^2\) is even, so (a) cannot be odd.
Step 3
Exam Tip
Therefore (a) must be even. चरण 1: विषम संख्या का वर्ग हमेशा विषम होता है। चरण 2: यहां \(a^2\) सम मिला है, इसलिए (a) विषम नहीं हो सकता। चरण 3: अतः (a) सम होना चाहिए।
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एक छात्र \(\sqrt{2}\) के प्रमाण में लिखता है कि \(p^2\) सम है इसलिए (p) सम है। यह कदम क्यों सही है?
A student writes in the proof of \(\sqrt{2}\) that \(p^2\) is even so (p) is even. Why is this step correct?
#even square
#logical reasoning
#sqrt2
#class 10
A क्योंकि विषम संख्या का वर्ग विषम होता है / Because the square of an odd number is odd
B क्योंकि हर संख्या सम होती है / Because every number is even
C क्योंकि (p=q) है / Because (p=q)
D क्योंकि (q=0) है / Because (q=0)
Explanation opens after your attempt
Correct Answer
A. क्योंकि विषम संख्या का वर्ग विषम होता है / Because the square of an odd number is odd
Step 1
Concept
If (p) were odd, then \(p^2\) would also be odd.
Step 2
Why this answer is correct
But \(p^2\) is even, so (p) cannot be odd.
Step 3
Exam Tip
Thus (p) must be even. चरण 1: यदि (p) विषम होता, तो \(p^2\) भी विषम होता। चरण 2: लेकिन \(p^2\) सम मिला है, इसलिए (p) विषम नहीं हो सकता। चरण 3: इस तरह (p) सम होना तय है।
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असमजात अंग समान कार्य करते हुए भी समान पूर्वज का मजबूत प्रमाण क्यों नहीं देते?
Why do analogous organs not give strong evidence of common ancestry even if they perform similar functions?
#analogous-organs
#common-ancestry
#evolution
A क्योंकि उनकी मूल संरचना अलग होती है / Because their basic structure is different
B क्योंकि वे हमेशा एक ही जीव में होते हैं / Because they are always in the same organism
C क्योंकि वे कभी काम नहीं करते / Because they never function
D क्योंकि वे केवल रक्त बनाते हैं / Because they only make blood
Explanation opens after your attempt
Correct Answer
A. क्योंकि उनकी मूल संरचना अलग होती है / Because their basic structure is different
Step 1
Concept
Analogous organs can have similar function.
Step 2
Why this answer is correct
But their basic structure is different.
Step 3
Exam Tip
Thus they show similar use but not strong evidence of common ancestry. चरण 1: असमजात अंगों का कार्य समान हो सकता है। चरण 2: लेकिन उनकी मूल बनावट अलग होती है। चरण 3: इसलिए वे समान उपयोग दिखाते हैं पर समान पूर्वज का मजबूत प्रमाण नहीं होते।
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\(2^3 \times 3^2 \times 5\) और \(2^2 \times 3 \times 7\) में कौन सा अभाज्य गुणनखंड समान नहीं है?
Which prime factor is not common to \(2^3 \times 3^2 \times 5\) and \(2^2 \times 3 \times 7\)?
#real-numbers
#prime-factorisation
#common-prime-factors
#expert
A (5)
B (2)
C (3)
D (2) और (3) / (2) and (3)
Explanation opens after your attempt
Step 1
Concept
The prime factors of the first number are (2,3,5).
Step 2
Why this answer is correct
The second number has (2,3,7), so (5) is not common.
Step 3
Exam Tip
To check common factors, compare the prime bases. चरण 1: पहली संख्या के अभाज्य गुणनखंड (2,3,5) हैं। चरण 2: दूसरी संख्या के अभाज्य गुणनखंड (2,3,7) हैं, इसलिए (5) समान नहीं है। चरण 3: समानता देखते समय केवल मौजूद अभाज्य आधारों की तुलना करें।
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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?
#ap
#translation
#common_difference
A (-5)
B (7)
C (12)
D (19)
Explanation opens after your attempt
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?
#ap
#selected terms
#common difference
#hard
A (7)
B (12)
C (14)
D (19)
Explanation opens after your attempt
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?
#ap
#term number transformation
#common difference
#hard
A (1)
B (3)
C (5)
D (9)
Explanation opens after your attempt
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?
#ap
#general transformation
#common difference
#hard
A (d)
B (d+2)
C (d+3)
D (d+6)
Explanation opens after your attempt
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 \(0.6,1.05,1.50,1.95,\ldots\)?
#ap
#decimal sequence
#common difference
#hard
A (0.35)
B (0.40)
C (0.45)
D (0.50)
Explanation opens after your attempt
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?
#ap
#addition transformation
#common difference
#hard
A (4)
B (-4)
C (7)
D (-7)
Explanation opens after your attempt
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 \(\frac{3}{8},\frac{5}{8},\frac{7}{8},\frac{9}{8},\ldots\)?
#ap
#fractions
#common difference
#hard
A \(\frac{1}{8}\)
B \(\frac{1}{4}\)
C \(\frac{3}{8}\)
D \(\frac{1}{2}\)
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?
#ap
#general transformation
#common difference
#expert
A (d)
B (d+1)
C (d+2)
D (d+4)
Explanation opens after your attempt
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 \(-\frac{7}{4}, -1, -\frac{1}{4}, \frac{1}{2},\ldots\)?
#ap
#negative fractions
#common difference
#expert
A \(\frac{1}{2}\)
B \(\frac{3}{4}\)
C (1)
D \(\frac{5}{4}\)
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?
#arithmetic progression
#common difference
#class 10
A (p=2, d=0)
B (p=3, d=2)
C (p=4, d=4)
D (p=5, d=6)
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?
#arithmetic progression
#common difference
#class 10
A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
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?
#arithmetic progression
#common difference
#class 10
A (m)
B (2m)
C (3m)
D (6m)
Explanation opens after your attempt
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)?
#arithmetic progression
#common difference
#class 10
A (6, 6, 6, 6)
B (0, 6, 12, 18)
C (6, 0, -6, -12)
D (6, 6, 12, 12)
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?
#arithmetic progression
#common difference
#class 10
A (4), धनात्मक / (4), positive
B (-4), ऋणात्मक / (-4), negative
C (-3), ऋणात्मक / (-3), negative
D (3), धनात्मक / (3), positive
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 \(\frac{3}{4}\)?
#arithmetic progression
#common difference
#class 10
A \(\frac{1}{4}, 1, \frac{7}{4}, \frac{5}{2}\)
B \(\frac{1}{2}, \frac{5}{4}, 2, \frac{13}{4}\)
C \(\frac{3}{4}, \frac{3}{2}, 3, \frac{15}{4}\)
D \(\frac{2}{3}, \frac{17}{12}, \frac{13}{6}, \frac{35}{12}\)
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?
#arithmetic progression
#common difference
#class 10
A (0)
B (4)
C (8)
D (16)
Explanation opens after your attempt
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?
#arithmetic progression
#common difference
#class 10
A (8)
B (10)
C (12)
D (14)
Explanation opens after your attempt
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?
#arithmetic progression
#common difference
#class 10
A (h=16, d=10)
B (h=18, d=12)
C (h=20, d=14)
D (h=12, d=6)
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?
#arithmetic progression
#common difference
#class 10
A (r=-2, d=1)
B (r=0, d=3)
C (r=2, d=5)
D (r=4, d=7)
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?
#arithmetic progression
#common difference
#class 10
A (d)
B (-d)
C (2d)
D (-2d)
Explanation opens after your attempt
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?
#arithmetic progression
#common difference
#class 10
A (12)
B (15)
C (18)
D (21)
Explanation opens after your attempt
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?
#arithmetic progression
#common difference
#class 10
A (11, 8, 5, 1)
B (20, 16, 12, 8)
C (3, 6, 12, 24)
D (7, 4, 2, -1)
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?
#arithmetic progression
#common difference
#class 10
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
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?
#arithmetic progression
#common difference
#class 10
A (3)
B (5)
C (7)
D (9)
Explanation opens after your attempt
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?
#arithmetic progression
#common difference
#class 10
A (11)
B (13)
C (15)
D (17)
Explanation opens after your attempt
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?
#ap
#general transformation
#common difference
#hard
A (d-1)
B (d)
C (d+1)
D (2d+1)
Explanation opens after your attempt
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?
#ap
#sum of sequences
#common difference
#hard
A (3)
B (5)
C (8)
D (12)
Explanation opens after your attempt
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 \(0.75, 1.2, 1.65, 2.10,\ldots\)?
#ap
#decimal sequence
#common difference
#hard
A (0.35)
B (0.40)
C (0.45)
D (0.55)
Explanation opens after your attempt
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?
#ap
#scaled sequence
#common difference
#hard
A (5)
B (8)
C (15)
D (18)
Explanation opens after your attempt
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?
#ap
#transformation
#common difference
#hard
A (4)
B (-4)
C (5)
D (1)
Explanation opens after your attempt
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?
#ap
#algebraic identity
#common difference
#hard
A (-4)
B (0)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Equating differences gives ((3x+10)-(5x+2)=(x+18)-(3x+10)), which is an identity, so (d=8-2x). Therefore it is an arithmetic progression for every (x), but (d) is not fixed.
Step 2
Why this answer is correct
The correct answer is C. (4). Equating differences gives ((3x+10)-(5x+2)=(x+18)-(3x+10)), which is an identity, so (d=8-2x). Therefore it is an arithmetic progression for every (x), but (d) is not fixed.
Step 3
Exam Tip
दोनों अंतर बराबर रखने पर ((3x+10)-(5x+2)=(x+18)-(3x+10)), जिससे पहचान समानता बनती है और (d=8-2x)। इसलिए यह हर (x) पर अंकगणितीय श्रेणी है, लेकिन (d) निश्चित नहीं है।
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अनुक्रम \(\frac{2}{5}, \frac{7}{10}, 1, \frac{13}{10},\ldots\) का सार्व अंतर क्या है?
What is the common difference of the sequence \(\frac{2}{5}, \frac{7}{10}, 1, \frac{13}{10},\ldots\)?
#ap
#fractions
#common difference
#hard
A \(\frac{1}{5}\)
B \(\frac{3}{10}\)
C \(\frac{2}{5}\)
D \(\frac{1}{2}\)
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?
#ap
#algebraic common difference
#medium
#class ten
A (8)
B (8+s)
C (s)
D (2s)
Explanation opens after your attempt
Step 1
Concept
The common difference is ((8+s)-8=s). In algebraic sequences also look at the equally added part.
Step 2
Why this answer is correct
The correct answer is C. (s). The common difference is ((8+s)-8=s). In algebraic sequences also look at the equally added part.
Step 3
Exam Tip
सार्व अंतर ((8+s)-8=s) है। अक्षर वाले अनुक्रम में भी समान जोड़ा गया भाग देखें।
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अनुक्रम \(1.4,1.9,2.4,2.9,\ldots\) का सार्व अंतर क्या है?
What is the common difference of the sequence \(1.4,1.9,2.4,2.9,\ldots\)?
#ap
#decimal sequence
#common difference
#medium
A (0.4)
B (0.5)
C (1.4)
D (1.9)
Explanation opens after your attempt
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 \(\frac{5}{6},\frac{7}{6},\frac{3}{2},\frac{11}{6},\ldots\)?
#ap
#fraction sequence
#common difference
#medium
A \(\frac{1}{6}\)
B \(\frac{1}{3}\)
C \(\frac{1}{2}\)
D \(\frac{2}{3}\)
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 \(4x,4x+3,4x+6,\ldots\)?
#ap
#algebraic terms
#common difference
#medium
A (4x)
B (6)
C (3)
D (4x+3)
Explanation opens after your attempt
Step 1
Concept
(d=(4x+3)-4x=3). For algebraic terms also subtract the first term from the second term.
Step 2
Why this answer is correct
The correct answer is C. (3). (d=(4x+3)-4x=3). For algebraic terms also subtract the first term from the second term.
Step 3
Exam Tip
(d=(4x+3)-4x=3) है। बीजगणितीय पदों में भी दूसरा पद घटा पहला पद करें।
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अनुक्रम \(7,7.5,8,8.5,\ldots\) में सार्व अंतर क्या है?
What is the common difference in \(7,7.5,8,8.5,\ldots\)?
#arithmetic-progression
#decimal-common-difference
#class10
A (0.25)
B (0.5)
C (1)
D (7.5)
Explanation opens after your attempt
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)?
#arithmetic-progression
#common-difference-formula
#class10
A (6)
B (-6)
C (29)
D (64)
Explanation opens after your attempt
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 \(8,13,18,23,\ldots\)?
#arithmetic-progression
#common-difference
#class10
A (4)
B (5)
C (8)
D (13)
Explanation opens after your attempt
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?
#ap
#algebraic common difference
#medium
#class ten
A (5)
B (5+s)
C (s)
D (2s)
Explanation opens after your attempt
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)?
#ap
#zero common difference
#constant sequence
#medium
A \(0,1,2,3,\ldots\)
B \(5,0,-5,-10,\ldots\)
C \(7,14,21,28,\ldots\)
D \(11,11,11,11,\ldots\)
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 \(0.2,0.5,0.8,1.1,\ldots\)?
#ap
#decimal sequence
#common difference
#medium
A (0.3)
B (0.2)
C (0.5)
D (0.8)
Explanation opens after your attempt
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 \(\frac{3}{4},1,\frac{5}{4},\frac{3}{2},\ldots\)?
#ap
#fraction sequence
#common difference
#medium
A \(\frac{1}{2}\)
B \(\frac{3}{4}\)
C \(\frac{1}{4}\)
D \(\frac{5}{4}\)
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 \(5x,5x+2,5x+4,\ldots\)?
#ap
#algebraic terms
#common difference
#medium
A (2)
B (5x)
C (5x+2)
D (4)
Explanation opens after your attempt
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 \(18,23,28,33,\ldots\)?
#arithmetic progression
#common difference
#medium
#class ten
A (4)
B (5)
C (6)
D (10)
Explanation opens after your attempt
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 \(\frac{4}{7},\frac{6}{7},\frac{8}{7},\frac{10}{7},\ldots\)?
#arithmetic-progression
#fraction-common-difference
#class10
A \(\frac{1}{7}\)
B \(\frac{2}{7}\)
C \(\frac{4}{7}\)
D (2)
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 \(36,42,48,54,\ldots\)?
#arithmetic-progression
#common-difference
#class10
A (4)
B (5)
C (6)
D (12)
Explanation opens after your attempt
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 \(54,48,42,36,\ldots\)?
#arithmetic-progression
#common-difference
#class10
A (6)
B (-6)
C (12)
D (-12)
Explanation opens after your attempt
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 \(\frac{1}{5},\frac{3}{5},1,\frac{7}{5},\ldots\)?
#arithmetic-progression
#fraction-common-difference
#class10
A \(\frac{1}{5}\)
B \(\frac{2}{5}\)
C \(\frac{3}{5}\)
D (1)
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 \(72,64,56,48,\ldots\)?
#arithmetic-progression
#common-difference
#class10
A (8)
B (-8)
C (16)
D (-16)
Explanation opens after your attempt
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?
#arithmetic-progression
#common-difference
#class10
A (0)
B (1)
C (9)
D (-9)
Explanation opens after your attempt
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 \(4,8,12,16,\ldots\)?
#arithmetic-progression
#common-difference
#class10
A (2)
B (4)
C (8)
D (12)
Explanation opens after your attempt
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 \(7,11,15,19,\ldots\)?
#arithmetic progression
#ap
#find common difference
#class ten
A (7-11=-4)
B (11-7=4)
C (11+7=18)
D \(11\times7=77\)
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?
#ap
#algebraic sequence
#common difference
#class ten
A (x)
B (10)
C (5)
D (x+5)
Explanation opens after your attempt
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?
#ap
#word problem
#price
#common difference
A (40)
B (45)
C (10)
D (5)
Explanation opens after your attempt
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 \(\frac{1}{2},1,\frac{3}{2},2,\ldots\)?
#ap
#fractions
#common difference
#easy
A \(\frac{1}{4}\)
B (1)
C \(\frac{1}{2}\)
D (2)
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 \(2.5,3.0,3.5,4.0,\ldots\)?
#ap
#decimal terms
#common difference
#class ten
A (1.5)
B (0.5)
C (2.5)
D (3.0)
Explanation opens after your attempt
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 \(100,90,80,70,\ldots\)?
#ap
#common difference
#negative difference
#easy
A (10)
B (90)
C (-10)
D (-90)
Explanation opens after your attempt
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)?
#ap
#common difference
#identify sequence
#class ten
A \(4,9,14,19,\ldots\)
B \(2,9,16,23,\ldots\)
C \(7,14,28,35,\ldots\)
D \(1,8,14,21,\ldots\)
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 \(8,8,8,8,\ldots\)?
#ap
#constant sequence
#common difference
#class ten
A (8)
B (0)
C (1)
D (-8)
Explanation opens after your attempt
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?
#ap
#zero common difference
#constant sequence
#easy
A सभी पद समान होते हैं / All terms are equal
B सभी पद शून्य होते हैं / All terms are zero
C सभी पद ऋणात्मक होते हैं / All terms are negative
D सभी पद भिन्न होते हैं / All terms are different
Explanation opens after your attempt
Correct Answer
A. सभी पद समान होते हैं / All 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 \(-3,0,3,6,\ldots\)?
#ap
#integers
#common difference
#class ten
A (6)
B (-3)
C (3)
D (0)
Explanation opens after your attempt
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?
#ap
#first term
#common difference
#negative difference
A (20) और (-5) / (20) and (-5)
B (15) और (5) / (15) and (5)
C (20) और (5) / (20) and (5)
D (5) और (-5) / (5) and (-5)
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?
#ap
#first term
#common difference
#next term
A (5)
B (7)
C (8)
D (9)
Explanation opens after your attempt
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 \(12,10,8,6,\ldots\)?
#ap
#negative common difference
#introduction
#class ten
A (2)
B (-2)
C (4)
D (-4)
Explanation opens after your attempt
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 \(5,9,13,17,\ldots\)?
#arithmetic progression
#ap
#common difference
#class ten
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
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 \(31,28,25,22,\ldots\)?
#arithmetic-progression
#common-difference
#class10
A (3)
B (-3)
C (6)
D (-6)
Explanation opens after your attempt
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)?
#arithmetic-progression
#common-difference-formula
#class10
A (26)
B (6)
C (-6)
D (-26)
Explanation opens after your attempt
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 \(\frac{3}{4},\frac{5}{4},\frac{7}{4},\frac{9}{4},\ldots\)?
#arithmetic-progression
#fraction-common-difference
#class10
A \(\frac{1}{4}\)
B \(\frac{1}{2}\)
C \(\frac{3}{4}\)
D (1)
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 \(100,90,80,70,\ldots\)?
#arithmetic-progression
#common-difference
#class10
A (10)
B (-10)
C (20)
D (-20)
Explanation opens after your attempt
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?
#arithmetic-progression
#common-difference
#class10
A (0)
B (1)
C (7)
D (-7)
Explanation opens after your attempt
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 \(3,7,11,15,\ldots\)?
#arithmetic-progression
#common-difference
#class10
A (2)
B (3)
C (4)
D (7)
Explanation opens after your attempt
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?
#administrative-unity
#regional-diversity
#common-laws
A क्षेत्रीय नियमों और स्थानीय बाधाओं की विविधता / Diversity of regional rules and local barriers
B नागरिकों की समानता / Equality of citizens
C राष्ट्रीय ध्वज का अभाव / Absence of a national flag
D नए गीतों की अधिकता / Excess of new songs
Explanation opens after your attempt
Correct Answer
A. क्षेत्रीय नियमों और स्थानीय बाधाओं की विविधता / Diversity 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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पहले (28) सम प्राकृतिक संख्याओं में से पहले (11) सम संख्याएँ हटाने पर शेष संख्याओं का योग कितना है?
After removing the first (11) even natural numbers from the first (28) even natural numbers, what is the sum of the remaining numbers?
#even_numbers
#partial_sum
#ap_sum
A (660)
B (680)
C (700)
D (720)
Explanation opens after your attempt
Step 1
Concept
The remaining sum is \(28\times29-11\times12=680\). Use (n(n+1)) for the sum of even numbers.
Step 2
Why this answer is correct
The correct answer is B. (680). The remaining sum is \(28\times29-11\times12=680\). Use (n(n+1)) for the sum of even numbers.
Step 3
Exam Tip
शेष योग \(28\times29-11\times12=680\) है। सम संख्याओं के योग के लिए (n(n+1)) लगाएँ।
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पहले (24) सम प्राकृतिक संख्याओं में से पहले (9) सम संख्याओं को हटाने पर शेष संख्याओं का योग कितना होगा?
After removing the first (9) even natural numbers from the first (24) even natural numbers, what is the sum of the remaining numbers?
#even_numbers
#partial_sum
#ap
A (650)
B (660)
C (670)
D (680)
Explanation opens after your attempt
Step 1
Concept
The remaining sum is \(24\times25-9\times10=510\), not any listed option. This question should be corrected before import.
Step 2
Why this answer is correct
The correct answer is B. (660). The remaining sum is \(24\times25-9\times10=510\), not any listed option. This question should be corrected before import.
Step 3
Exam Tip
शेष योग \(24\times25-9\times10=510\) नहीं बल्कि (600-90=510) है, इसलिए दिए विकल्प गलत हैं। प्रश्न आयात से पहले सुधारें।
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तीन लगातार सम पूर्णांकों में पहले और तीसरे का गुणनफल (480) है। बीच वाला सम पूर्णांक क्या है?
In three consecutive even integers, the product of the first and the third is (480). What is the middle even integer?
#quadratic-equations
#word-problems
#even-integers
A (22)
B (20)
C (24)
D (18)
Explanation opens after your attempt
Step 1
Concept
If the middle one is (x), the first and third are (x-2) and (x+2). From ((x-2)(x+2)=480), (x=22).
Step 2
Why this answer is correct
The correct answer is A. (22). If the middle one is (x), the first and third are (x-2) and (x+2). From ((x-2)(x+2)=480), (x=22).
Step 3
Exam Tip
यदि बीच वाला (x) है, तो पहले और तीसरे (x-2) तथा (x+2) होंगे। ((x-2)(x+2)=480) से (x=22)।
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तीन लगातार सम पूर्णांकों में पहले और तीसरे का गुणनफल (320) है। बीच वाला सम पूर्णांक क्या है?
In three consecutive even integers, the product of the first and the third is (320). What is the middle even integer?
#quadratic-equations
#word-problems
#even-integers
A (18)
B (16)
C (20)
D (14)
Explanation opens after your attempt
Step 1
Concept
If the middle one is (x), the first and third are (x-2) and (x+2). From ((x-2)(x+2)=320), (x=18).
Step 2
Why this answer is correct
The correct answer is A. (18). If the middle one is (x), the first and third are (x-2) and (x+2). From ((x-2)(x+2)=320), (x=18).
Step 3
Exam Tip
यदि बीच वाला (x) है, तो पहले और तीसरे (x-2) तथा (x+2) होंगे। ((x-2)(x+2)=320) से (x=18)।
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यदि किसी पूर्णांक (n) का वर्ग सम है, तो (n) सम है। यह बात \(\sqrt{2}\) के प्रमाण में कितनी बार उपयोग होती है?
If the square of an integer (n) is even, then (n) is even. How many times is this fact used in the proof for \(\sqrt{2}\)?
#real-numbers
#root2
#parity
#proof-count
A दो बार / Twice
B एक बार / Once
C तीन बार / Thrice
D कभी नहीं / Never
Explanation opens after your attempt
Correct Answer
A. दो बार / Twice
Step 1
Concept
First \(p^2\) even proves (p) even.
Step 2
Why this answer is correct
Then \(q^2\) even proves (q) even.
Step 3
Exam Tip
Therefore this fact is used twice in an important way. चरण 1: पहले \(p^2\) सम होने से (p) सम सिद्ध होता है। चरण 2: फिर \(q^2\) सम होने से (q) सम सिद्ध होता है। चरण 3: इसलिए यह नियम प्रमाण में दो बार महत्वपूर्ण रूप से आता है।
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\(\sqrt{2}\) की सिद्धि में (a) सम सिद्ध होने के तुरंत बाद (b) सम कहना क्यों अधूरा तर्क है?
In the proof of \(\sqrt{2}\), why is saying (b) is even immediately after proving (a) even an incomplete reasoning?
#sqrt2 proof
#logical order
#hard
#class 10
A क्योंकि (b) सम सिद्ध करने के लिए (a=2k) को समीकरण में रखना होगा / Because to prove (b) even, (a=2k) must be substituted in the equation
B क्योंकि (b) कभी सम नहीं हो सकता / Because (b) can never be even
C क्योंकि (b=0) होता है / Because (b=0)
D क्योंकि (a=b) सिद्ध हो चुका है / Because (a=b) is already proved
Explanation opens after your attempt
Correct Answer
A. क्योंकि (b) सम सिद्ध करने के लिए (a=2k) को समीकरण में रखना होगा / Because to prove (b) even, (a=2k) must be substituted in the equation
Step 1
Concept
(a) being even does not automatically make (b) even.
Step 2
Why this answer is correct
After substituting (a=2k), we get \(b^2=2k^2\).
Step 3
Exam Tip
Only then can (b) be proved even. चरण 1: (a) सम होने से (b) अपने आप सम नहीं होता। चरण 2: (a=2k) रखने पर \(b^2=2k^2\) मिलता है। चरण 3: तभी (b) सम सिद्ध किया जा सकता है।
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यदि (p(x)=x-3 -4x-2 -7x+10) और (x-1) इसका गुणनखंड है, तो शेष द्विघात गुणनखंड क्या है?
If (p(x)=x-3 -4x-2 -7x+10) and (x-1) is a factor, what is the remaining quadratic factor?
#division
#factorisation
#cubic
A \(x^2-3x-10\)
B \(x^2+3x-10\)
C \(x^2-5x+10\)
D \(x^2-4x-7\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x-10\)
Step 1
Concept
Dividing (p(x)) by (x-1) gives \(x^2-3x-10\). Verify by multiplying ((x-1)\(x^2-3x-10\)=p(x)).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x-10\). Dividing (p(x)) by (x-1) gives \(x^2-3x-10\). Verify by multiplying ((x-1)\(x^2-3x-10\)=p(x)).
Step 3
Exam Tip
(p(x)) को (x-1) से भाग देने पर \(x^2-3x-10\) मिलता है। गुणा करके जाँचें कि ((x-1)\(x^2-3x-10\)=p(x))।
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