किस (k) के लिए (k-2,k+5,2k+1) अंकगणितीय श्रेणी में होंगे?
For which (k) will (k-2,k+5,2k+1) be in an arithmetic progression?
#ap
#find parameter
#algebraic terms
#hard
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
From (2(k+5)=(k-2)+(2k+1)), (2k+10=3k-1), so (k=11). Identify the middle term while forming the equation.
Step 2
Why this answer is correct
The correct answer is D. (9). From (2(k+5)=(k-2)+(2k+1)), (2k+10=3k-1), so (k=11). Identify the middle term while forming the equation.
Step 3
Exam Tip
(2(k+5)=(k-2)+(2k+1)) से (2k+10=3k-1), इसलिए (k=11)। समीकरण बनाते समय मध्य पद को पहचानें।
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किस (m) के लिए (m-1 ,2m+3,4m-1) अंकगणितीय श्रेणी में होंगे?
For which (m) will (m-1 ,2m+3,4m-1) be in an arithmetic progression?
#ap
#find parameter
#algebraic terms
#hard
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From (2(2m+3)=(m-1 )+(4m-1)), (4m+6=5m-2), so (m=8). Use the twice-middle-term rule.
Step 2
Why this answer is correct
The correct answer is C. (5). From (2(2m+3)=(m-1 )+(4m-1)), (4m+6=5m-2), so (m=8). Use the twice-middle-term rule.
Step 3
Exam Tip
(2(2m+3)=(m-1 )+(4m-1)) से (4m+6=5m-2), इसलिए (m=8)। मध्य पद का दुगुना नियम लगाएं।
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यदि (2x+1, x+8, 3x-4) अंकगणितीय श्रेणी के क्रमागत पद हैं तो (x) का मान क्या है?
If (2x+1, x+8, 3x-4) are consecutive terms of an arithmetic progression, what is the value of (x)?
#arithmetic progression
#algebraic terms
#common difference
#hard
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
In three consecutive terms, twice the middle term equals the sum of the other two terms. So (2(x+8)=(2x+1)+(3x-4)) gives (x=3).
Step 2
Why this answer is correct
The correct answer is B. (3). In three consecutive terms, twice the middle term equals the sum of the other two terms. So (2(x+8)=(2x+1)+(3x-4)) gives (x=3).
Step 3
Exam Tip
तीन क्रमागत पदों में (2) गुना मध्य पद बाकी दो पदों के योग के बराबर होता है। इसलिए (2(x+8)=(2x+1)+(3x-4)) से (x=3)।
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यदि (x, x+2, 2x+1) अंकगणितीय श्रेणी में हैं, तो (d) क्या होगा?
If (x, x+2, 2x+1) are in an arithmetic progression, what will (d) be?
#ap
#algebraic terms
#find d
#expert
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
From (2(x+2)=x+(2x+1)), (2x+4=3x+1), so (x=3) and (d=5-3=2). Decide (d) only after finding (x).
Step 2
Why this answer is correct
The correct answer is B. (2). From (2(x+2)=x+(2x+1)), (2x+4=3x+1), so (x=3) and (d=5-3=2). Decide (d) only after finding (x).
Step 3
Exam Tip
(2(x+2)=x+(2x+1)) से (2x+4=3x+1), इसलिए (x=3) और (d=5-3=2)। (x) मिलने के बाद ही (d) तय करें।
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यदि (k+1, 2k+4, 4k-2) अंकगणितीय श्रेणी में हैं, तो (k) का मान क्या होगा?
If (k+1, 2k+4, 4k-2) are in an arithmetic progression, what will be the value of (k)?
#ap
#find parameter
#algebraic terms
#expert
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
From (2(2k+4)=(k+1)+(4k-2)), (4k+8=5k-1), so (k=9). Identify the middle term correctly while forming the equation.
Step 2
Why this answer is correct
The correct answer is D. (6). From (2(2k+4)=(k+1)+(4k-2)), (4k+8=5k-1), so (k=9). Identify the middle term correctly while forming the equation.
Step 3
Exam Tip
(2(2k+4)=(k+1)+(4k-2)) से (4k+8=5k-1), इसलिए (k=9)। समीकरण बनाते समय मध्य पद को सही पहचानें।
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यदि (q-3, 2q+1, 4q-1) अंकगणितीय श्रेणी में हैं, तो (q) क्या होगा?
If (q-3, 2q+1, 4q-1) are in an arithmetic progression, what will (q) be?
#ap
#algebraic terms
#find parameter
#expert
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (2(2q+1)=(q-3)+(4q-1)), (4q+2=5q-4), so (q=6). Watch signs while applying the twice-middle-term rule.
Step 2
Why this answer is correct
The correct answer is D. (5). From (2(2q+1)=(q-3)+(4q-1)), (4q+2=5q-4), so (q=6). Watch signs while applying the twice-middle-term rule.
Step 3
Exam Tip
(2(2q+1)=(q-3)+(4q-1)) से (4q+2=5q-4), इसलिए (q=6)। मध्य पद का दुगुना नियम लगाते समय संकेतों पर ध्यान दें।
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यदि (3x-2, 2x+5, x+16) अंकगणितीय श्रेणी के क्रमागत पद हैं, तो (x) का मान क्या है?
If (3x-2, 2x+5, x+16) are consecutive terms of an arithmetic progression, what is the value of (x)?
#ap
#algebraic terms
#expert
#common difference
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
In three consecutive terms, twice the middle term equals the sum of the other two, so (2(2x+5)=(3x-2)+(x+16)) gives (x=2). The middle-term rule is a fast exam method.
Step 2
Why this answer is correct
The correct answer is B. (2). In three consecutive terms, twice the middle term equals the sum of the other two, so (2(2x+5)=(3x-2)+(x+16)) gives (x=2). The middle-term rule is a fast exam method.
Step 3
Exam Tip
तीन क्रमागत पदों में मध्य पद का दुगुना बाकी दो पदों के योग के बराबर होता है, इसलिए (2(2x+5)=(3x-2)+(x+16)) से (x=2)। परीक्षा में मध्य पद नियम तेज तरीका है।
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किस (k) के लिए (k-3, k+2, 2k+1) अंकगणितीय श्रेणी में होंगे?
For which (k) will (k-3, k+2, 2k+1) be in an arithmetic progression?
#ap
#find parameter
#algebraic terms
#hard
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (2(k+2)=(k-3)+(2k+1)), (2k+4=3k-2), so (k=6). Identify the middle term while forming the equation.
Step 2
Why this answer is correct
The correct answer is B. (5). From (2(k+2)=(k-3)+(2k+1)), (2k+4=3k-2), so (k=6). Identify the middle term while forming the equation.
Step 3
Exam Tip
(2(k+2)=(k-3)+(2k+1)) से (2k+4=3k-2), इसलिए (k=6)। समीकरण बनाते समय मध्य पद को पहचानें।
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किस (m) के लिए (m+2, 2m+5, 4m+1) अंकगणितीय श्रेणी में होंगे?
For which (m) will (m+2, 2m+5, 4m+1) be in an arithmetic progression?
#ap
#find parameter
#algebraic terms
#hard
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From (2(2m+5)=(m+2)+(4m+1)), (4m+10=5m+3), so (m=7). Use the twice-middle-term rule for three terms.
Step 2
Why this answer is correct
The correct answer is A. (4). From (2(2m+5)=(m+2)+(4m+1)), (4m+10=5m+3), so (m=7). Use the twice-middle-term rule for three terms.
Step 3
Exam Tip
(2(2m+5)=(m+2)+(4m+1)) से (4m+10=5m+3), इसलिए (m=7)। तीन पदों में मध्य पद का दुगुना नियम लगाएं।
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यदि (2x-3, x+4, 3x-1) अंकगणितीय श्रेणी के क्रमागत पद हैं, तो (x) का मान क्या है?
If (2x-3, x+4, 3x-1) are consecutive terms of an arithmetic progression, what is the value of (x)?
#ap
#algebraic terms
#common difference
#hard
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Twice the middle term equals the sum of the other two terms, so (2(x+4)=(2x-3)+(3x-1)) gives (x=3). For three consecutive terms, the middle-term rule is fast.
Step 2
Why this answer is correct
The correct answer is B. (3). Twice the middle term equals the sum of the other two terms, so (2(x+4)=(2x-3)+(3x-1)) gives (x=3). For three consecutive terms, the middle-term rule is fast.
Step 3
Exam Tip
मध्य पद का दुगुना बाकी दोनों पदों के योग के बराबर होता है, इसलिए (2(x+4)=(2x-3)+(3x-1)) से (x=3)। तीन क्रमागत पदों में मध्य पद का नियम तेज होता है।
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यदि \(z-4,z+2,z+8,\ldots\) अंकगणितीय श्रेणी है तो (d) क्या है?
If \(z-4,z+2,z+8,\ldots\) is an arithmetic progression, what is (d)?
#ap
#algebraic terms
#find d
#medium
A (z)
B (4)
C (6)
D (12)
Explanation opens after your attempt
Step 1
Concept
(d=(z+2)-(z-4)=6). When variables cancel, the constant difference remains.
Step 2
Why this answer is correct
The correct answer is C. (6). (d=(z+2)-(z-4)=6). When variables cancel, the constant difference remains.
Step 3
Exam Tip
(d=(z+2)-(z-4)=6) है। चर कट जाने पर स्थिर अंतर मिलता है।
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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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यदि \(y-2,y+1,y+4,\ldots\) अंकगणितीय श्रेणी है तो (d) क्या है?
If \(y-2,y+1,y+4,\ldots\) is an arithmetic progression, what is (d)?
#ap
#algebraic terms
#find d
#medium
A (y)
B (3)
C (y+1)
D (6)
Explanation opens after your attempt
Step 1
Concept
(d=(y+1)-(y-2)=3). When variables cancel, the constant difference remains.
Step 2
Why this answer is correct
The correct answer is B. (3). (d=(y+1)-(y-2)=3). When variables cancel, the constant difference remains.
Step 3
Exam Tip
(d=(y+1)-(y-2)=3) है। चर कट जाने पर स्थिर अंतर मिलता है।
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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 \(2p,2p+3,2p+6,\ldots\) में (d) क्या है?
What is (d) in the sequence \(2p,2p+3,2p+6,\ldots\)?
#ap
#algebraic terms
#common difference
#easy
A (2p)
B (3)
C (6)
D (p)
Explanation opens after your attempt
Step 1
Concept
(d=(2p+3)-2p=3). The equal number added is the common difference.
Step 2
Why this answer is correct
The correct answer is B. (3). (d=(2p+3)-2p=3). The equal number added is the common difference.
Step 3
Exam Tip
(d=(2p+3)-2p=3) है। समान जोड़ी गई संख्या ही सार्व अंतर है।
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\(v^4\cdot v^5\) का सरल रूप क्या है?
What is the simplified form of \(v^4\cdot v^5\)?
#polynomials
#algebraic terms
#exponents
A \(v^9\)
B \(v^{20}\)
C \(2v^9\)
D (v)
Explanation opens after your attempt
Correct Answer
A. \(v^9\)
Step 1
Concept
For the same base (v), exponents add as (4+5=9). Therefore \(v^4\cdot v^5=v^9\).
Step 2
Why this answer is correct
The correct answer is A. \(v^9\). For the same base (v), exponents add as (4+5=9). Therefore \(v^4\cdot v^5=v^9\).
Step 3
Exam Tip
समान आधार (v) में घातें (4+5=9) जुड़ती हैं। इसलिए \(v^4\cdot v^5=v^9\) है।
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\(t^3\cdot t^4\) का सरल रूप क्या है?
What is the simplified form of \(t^3\cdot t^4\)?
#polynomials
#algebraic terms
#exponents
A \(t^7\)
B \(t^{12}\)
C \(2t^7\)
D (t)
Explanation opens after your attempt
Correct Answer
A. \(t^7\)
Step 1
Concept
For the same base (t), exponents add as (3+4=7). Therefore \(t^3\cdot t^4=t^7\).
Step 2
Why this answer is correct
The correct answer is A. \(t^7\). For the same base (t), exponents add as (3+4=7). Therefore \(t^3\cdot t^4=t^7\).
Step 3
Exam Tip
समान आधार (t) में घातें (3+4=7) जुड़ती हैं। इसलिए \(t^3\cdot t^4=t^7\) है।
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\(x^2\cdot x^5\) का सरल रूप क्या है?
What is the simplified form of \(x^2\cdot x^5\)?
#polynomials
#algebraic terms
#exponents
A \(x^7\)
B \(x^{10}\)
C \(2x^5\)
D \(x^3\)
Explanation opens after your attempt
Correct Answer
A. \(x^7\)
Step 1
Concept
For the same base (x), exponents are added, so \(x^2\cdot x^5=x^7\). The same law works for algebraic terms.
Step 2
Why this answer is correct
The correct answer is A. \(x^7\). For the same base (x), exponents are added, so \(x^2\cdot x^5=x^7\). The same law works for algebraic terms.
Step 3
Exam Tip
समान आधार (x) में घातें जुड़ती हैं इसलिए \(x^2\cdot x^5=x^7\)। बीजगणितीय पदों में भी वही नियम लागू होता है।
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