100 results found for "short-term-profit" in Class 10.
फूट डालो और राज करो नीति को अल्पकालिक नियंत्रण और दीर्घकालिक संकट दोनों से कैसे जोड़ा जा सकता है?
How can divide and rule policy be linked with both short term control and long term crisis?
#divide-and-rule
#short-term-control
#long-term-crisis
A इससे तत्काल विरोध कमजोर हो सकता था लेकिन सामाजिक अविश्वास बचता था / It could weaken immediate resistance but leave social distrust
B इससे स्थायी समानता बनती थी / It created permanent equality
C इससे उपनिवेशवाद तुरंत समाप्त होता था / It immediately ended colonialism
D यह केवल वित्तीय नीति थी / It was only financial policy
Explanation opens after your attempt
Correct Answer
A. इससे तत्काल विरोध कमजोर हो सकता था लेकिन सामाजिक अविश्वास बचता था / It could weaken immediate resistance but leave social distrust
Step 1
Concept
This policy used division for control. For exams also write its legacy.
Step 2
Why this answer is correct
The correct answer is A. इससे तत्काल विरोध कमजोर हो सकता था लेकिन सामाजिक अविश्वास बचता था / It could weaken immediate resistance but leave social distrust. This policy used division for control. For exams also write its legacy.
Step 3
Exam Tip
यह नीति नियंत्रण के लिए विभाजन का उपयोग करती थी। परीक्षा में इसकी विरासत भी लिखें।
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मोलोटोव रिबेंट्रोप संधि को अल्पकालीन लाभ और दीर्घकालीन खतरे दोनों से कैसे समझा जा सकता है?
How can the Molotov-Ribbentrop Pact be understood through both short-term benefit and long-term risk?
#world history
#world wars
#molotov ribbentrop
#long term
A जर्मनी को पूर्व से राहत मिली लेकिन सोवियत जर्मन संघर्ष अंततः टला नहीं / Germany got relief from the east but Soviet-German conflict was not ultimately avoided
B इसने जर्मनी और सोवियत संघ को स्थायी मित्र बना दिया / It made Germany and the Soviet Union permanent friends
C इसने जापान को यूरोप दे दिया / It gave Europe to Japan
D इसने संयुक्त राष्ट्र बना दिया / It created the United Nations
Explanation opens after your attempt
Correct Answer
A. जर्मनी को पूर्व से राहत मिली लेकिन सोवियत जर्मन संघर्ष अंततः टला नहीं / Germany got relief from the east but Soviet-German conflict was not ultimately avoided
Step 1
Concept
The pact was immediate strategy but ideological and strategic conflict remained. For exams separate short-term and long-term results.
Step 2
Why this answer is correct
The correct answer is A. जर्मनी को पूर्व से राहत मिली लेकिन सोवियत जर्मन संघर्ष अंततः टला नहीं / Germany got relief from the east but Soviet-German conflict was not ultimately avoided. The pact was immediate strategy but ideological and strategic conflict remained. For exams separate short-term and long-term results.
Step 3
Exam Tip
संधि तत्काल रणनीतिक थी पर वैचारिक और सामरिक टकराव बना रहा। परीक्षा में अल्पकालीन और दीर्घकालीन परिणाम अलग करें।
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यदि समान्तर श्रेणी का (5)वां पद (x+7) और (12)वां पद (x+42) है तो (20)वां पद (x) के रूप में क्या होगा?
If the (5)th term of an AP is (x+7) and the (12)th term is (x+42), what is the (20)th term in terms of (x)?
#ap-algebra-hard
A (x+74)
B (x+77)
C (x+82)
D (x+89)
Explanation opens after your attempt
Step 1
Concept
From (7d=35), (d=5). \(a_{20}=a_{12}+8d=x+42+40=x+82\).
Step 2
Why this answer is correct
The correct answer is C. (x+82). From (7d=35), (d=5). \(a_{20}=a_{12}+8d=x+42+40=x+82\).
Step 3
Exam Tip
(7d=35) से (d=5)। \(a_{20}=a_{12}+8d=x+42+40=x+82\)।
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यदि AP का (5)वां पद (27) और (14)वां पद (90) है तो (20)वां पद क्या होगा?
If the (5)th term of an AP is (27) and the (14)th term is (90), what is the (20)th term?
#ap two-terms nth-term class10
A (126)
B (130)
C (132)
D (136)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{90-27}{14-5}=7\) and \(a_{20}=90+6\times7=132\). First find (d) then move forward.
Step 2
Why this answer is correct
The correct answer is C. (132). \(d=\frac{90-27}{14-5}=7\) and \(a_{20}=90+6\times7=132\). First find (d) then move forward.
Step 3
Exam Tip
\(d=\frac{90-27}{14-5}=7\) और \(a_{20}=90+6\times7=132\)। पहले (d) निकालें फिर आगे बढ़ें।
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यदि समान्तर श्रेणी का (4)वां पद (15) और (12)वां पद (55) है तो (16)वां पद क्या होगा?
If the (4)th term of an AP is (15) and the (12)th term is (55), what is the (16)th term?
#ap
#two-terms
#nth-term
#class10
A (70)
B (80)
C (75)
D (85)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.
Step 2
Why this answer is correct
The correct answer is C. (75). \(d=\frac{55-15}{12-4}=5\) and \(a_{16}=55+4\times5=75\). First find (d), then the required term.
Step 3
Exam Tip
\(d=\frac{55-15}{12-4}=5\) और \(a_{16}=55+4\times5=75\)। पहले (d) फिर वांछित पद निकालें।
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यदि AP का (3)वां पद (8) और (8)वां पद (3) है, तो (11)वां पद क्या होगा?
If the (3)rd term of an AP is (8) and the (8)th term is (3), what is the (11)th term?
#ap
#two-terms
#nth-term
#class10
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{3-8}{8-3}=-1\), so (a_{11}=3+3(-1)=0). Moving from the nearer known term is simple.
Step 2
Why this answer is correct
The correct answer is A. (0). \(d=\frac{3-8}{8-3}=-1\), so (a_{11}=3+3(-1)=0). Moving from the nearer known term is simple.
Step 3
Exam Tip
\(d=\frac{3-8}{8-3}=-1\), इसलिए (a_{11}=3+3(-1)=0)। ज्ञात पास वाले पद से आगे बढ़ना सरल है।
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यदि किसी AP का (p)वां पद (q) और (q)वां पद (p) है, तो उसका ((p+q))वां पद क्या होगा?
If the (p)th term of an AP is (q) and the (q)th term is (p), what is its ((p+q))th term?
#ap
#symbolic
#nth-term
#class10
A (0)
B (p+q)
C (p-q)
D (q-p)
Explanation opens after your attempt
Step 1
Concept
Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).
Step 2
Why this answer is correct
The correct answer is A. (0). Subtracting the relations gives (d=-1), and substitution gives \(a_{p+q}=0\). Even in symbolic APs, use (a_n=a+(n-1)d).
Step 3
Exam Tip
संबंधों को घटाने पर (d=-1) और आगे रखने पर \(a_{p+q}=0\) मिलता है। प्रतीकात्मक AP में भी (a_n=a+(n-1)d) ही लगाएं।
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यदि किसी समान्तर श्रेणी का (5)वां पद (16) और (9)वां पद (32) है, तो (13)वां पद क्या होगा?
If the (5)th term of an AP is (16) and the (9)th term is (32), what is the (13)th term?
#ap
#two-known-terms
#nth-term
#class10
A (44)
B (46)
C (48)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(d=\frac{32-16}{9-5}=4\), so \(a_{13}=32+4\times4=48\). Equal position gaps give equal term gaps in an AP.
Step 2
Why this answer is correct
The correct answer is C. (48). \(d=\frac{32-16}{9-5}=4\), so \(a_{13}=32+4\times4=48\). Equal position gaps give equal term gaps in an AP.
Step 3
Exam Tip
\(d=\frac{32-16}{9-5}=4\), इसलिए \(a_{13}=32+4\times4=48\)। समान स्थान अंतर होने पर पदों का अंतर भी समान होता है।
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कौन सा विकल्प \(\sqrt{3}\) की अपरिमेयता का सही संक्षिप्त प्रमाण विचार है?
Which option is the correct short proof idea for the irrationality of \(\sqrt{3}\)?
#sqrt3 proof
#short proof
#class 10
A परिमेय मानने पर अंश और हर दोनों (3) से विभाज्य मिलते हैं / Assuming rational makes both numerator and denominator divisible by (3)
B क्योंकि (3) पूर्ण वर्ग है / Because (3) is a perfect square
C क्योंकि \(\sqrt{3}=3\) / Because \(\sqrt{3}=3\)
D क्योंकि हर वर्गमूल परिमेय होता है / Because every square root is rational
Explanation opens after your attempt
Correct Answer
A. परिमेय मानने पर अंश और हर दोनों (3) से विभाज्य मिलते हैं / Assuming rational makes both numerator and denominator divisible by (3)
Step 1
Concept
Assume \(\sqrt{3}\) rational and write it in lowest form.
Step 2
Why this answer is correct
The proof shows both numerator and denominator divisible by (3).
Step 3
Exam Tip
This contradicts the condition of a lowest-form fraction. चरण 1: \(\sqrt{3}\) को परिमेय मानकर सरलतम भिन्न में लिखते हैं। चरण 2: प्रमाण से अंश और हर दोनों (3) से विभाज्य मिलते हैं। चरण 3: यह सरलतम भिन्न की शर्त से विरोधाभास है।
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कौन सा विकल्प \(\sqrt{2}\) की अपरिमेयता का सही छोटा कारण है?
Which option is the correct short reason for the irrationality of \(\sqrt{2}\)?
#sqrt2 short reason
#irrationality
#class 10
A परिमेय मानने पर सरलतम भिन्न के अंश और हर दोनों सम हो जाते हैं / Assuming rational makes numerator and denominator of a lowest-form fraction both even
B क्योंकि (2) ऋणात्मक है / Because (2) is negative
C क्योंकि \(\sqrt{2}=2\) है / Because \(\sqrt{2}=2\)
D क्योंकि हर वर्गमूल पूर्णांक होता है / Because every square root is an integer
Explanation opens after your attempt
Correct Answer
A. परिमेय मानने पर सरलतम भिन्न के अंश और हर दोनों सम हो जाते हैं / Assuming rational makes numerator and denominator of a lowest-form fraction both even
Step 1
Concept
Assume \(\sqrt{2}\) rational and write it in lowest form.
Step 2
Why this answer is correct
The proof gives both numerator and denominator even.
Step 3
Exam Tip
This contradicts lowest form, so \(\sqrt{2}\) is irrational. चरण 1: \(\sqrt{2}\) को परिमेय मानकर सरलतम भिन्न में लिखते हैं। चरण 2: प्रमाण से अंश और हर दोनों सम मिलते हैं। चरण 3: यह सरलतम रूप से विरोध करता है, इसलिए \(\sqrt{2}\) अपरिमेय है।
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यदि समान्तर श्रेणी का (8)वां पद (x+19) और (20)वां पद (x+91) है, तो (35)वां पद (x) के रूप में क्या होगा?
If the (8)th term of an AP is (x+19) and the (20)th term is (x+91), what is the (35)th term in terms of (x)?
#ap-algebra-expert
A (x+169)
B (x+175)
C (x+181)
D (x+187)
Explanation opens after your attempt
Correct Answer
C. (x+181)
Step 1
Concept
(12d=72), so (d=6). \(a_{35}=x+91+15\times6=x+181\).
Step 2
Why this answer is correct
The correct answer is C. (x+181). (12d=72), so (d=6). \(a_{35}=x+91+15\times6=x+181\).
Step 3
Exam Tip
(12d=72), इसलिए (d=6)। \(a_{35}=x+91+15\times6=x+181\)।
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यदि समान्तर श्रेणी का (7)वां पद (x+13) और (18)वां पद (x+90) है तो (32)वां पद (x) के रूप में क्या होगा?
If the (7)th term of an AP is (x+13) and the (18)th term is (x+90), what is the (32)nd term in terms of (x)?
#ap algebra hard
A (x+181)
B (x+188)
C (x+195)
D (x+202)
Explanation opens after your attempt
Correct Answer
B. (x+188)
Step 1
Concept
From (11d=77), (d=7). \(a_{32}=a_{18}+14d=x+90+98=x+188\).
Step 2
Why this answer is correct
The correct answer is B. (x+188). From (11d=77), (d=7). \(a_{32}=a_{18}+14d=x+90+98=x+188\).
Step 3
Exam Tip
(11d=77) से (d=7)। \(a_{32}=a_{18}+14d=x+90+98=x+188\)।
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यदि समान्तर श्रेणी का (6)वां पद (x+11) और (15)वां पद (x+65) है तो (27)वां पद (x) के रूप में क्या होगा?
If the (6)th term of an AP is (x+11) and the (15)th term is (x+65), what is the (27)th term in terms of (x)?
#ap-algebra-hard
A (x+131)
B (x+137)
C (x+143)
D (x+149)
Explanation opens after your attempt
Correct Answer
B. (x+137)
Step 1
Concept
From (9d=54), (d=6). \(a_{27}=a_{15}+12d=x+65+72=x+137\).
Step 2
Why this answer is correct
The correct answer is B. (x+137). From (9d=54), (d=6). \(a_{27}=a_{15}+12d=x+65+72=x+137\).
Step 3
Exam Tip
(9d=54) से (d=6)। \(a_{27}=a_{15}+12d=x+65+72=x+137\)।
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किसी समान्तर श्रेणी का (12)वां पद (71) और सार्व अंतर (5) है। पहला पद क्या होगा?
The (12)th term of an AP is (71) and the common difference is (5). What is the first term?
#ap first-term known-term class10
A (18)
B (14)
C (20)
D (16)
Explanation opens after your attempt
Step 1
Concept
From \(71=a+11\times5\), (a=16). To move from the known term to the first term subtract (11d).
Step 2
Why this answer is correct
The correct answer is D. (16). From \(71=a+11\times5\), (a=16). To move from the known term to the first term subtract (11d).
Step 3
Exam Tip
\(71=a+11\times5\) से (a=16)। ज्ञात पद से पहले पद तक जाने के लिए (11d) घटाएं।
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किसी समान्तर श्रेणी का (9)वां पद (47) और सार्व अंतर (4) है। पहला पद क्या है?
The (9)th term of an AP is (47) and the common difference is (4). What is the first term?
#ap
#first-term
#nth-term
#class10
A (11)
B (13)
C (17)
D (15)
Explanation opens after your attempt
Step 1
Concept
From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).
Step 2
Why this answer is correct
The correct answer is D. (15). From \(47=a+8\times4\), (a=15). To move from the known term to the first term, subtract (8d).
Step 3
Exam Tip
\(47=a+8\times4\) से (a=15)। ज्ञात पद से पहले पद तक जाने के लिए (8d) घटाएं।
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एक समान्तर श्रेणी का (6)वां पद (23) और सार्व अंतर (5) है। पहला पद क्या होगा?
The (6)th term of an AP is (23) and the common difference is (5). What is the first term?
#ap
#first-term
#nth-term
#class10
A (0)
B (3)
C (2)
D (-2)
Explanation opens after your attempt
Step 1
Concept
(23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).
Step 2
Why this answer is correct
The correct answer is D. (-2). (23=a+5d=a+25), so (a=-2). When moving backward from a given term, subtract (5d).
Step 3
Exam Tip
(23=a+5d=a+25), इसलिए (a=-2)। दिए गए पद से पीछे जाते समय (5d) घटाया जाता है।
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समांतर श्रेढ़ी का सामान्य पद \(a_n=7n+2\) है। (11)वाँ पद ज्ञात कीजिए।
The general term of an AP is \(a_n=7n+2\). Find the (11)th term.
#ap
#general term
#nth term
A (72)
B (84)
C (79)
D (77)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.
Step 2
Why this answer is correct
The correct answer is C. (79). \(a_{11}=7\times11+2=79\). The main step is substituting the correct term number in the general term.
Step 3
Exam Tip
\(a_{11}=7\times11+2=79\)। सामान्य पद में सही पद संख्या रखना ही मुख्य कदम है।
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अलेक्जेंडर की अल्पायु में विशाल विजय का दीर्घकालिक परिणाम क्या था?
What was the long term result of Alexander's vast conquests in a short life?
#world-leaders
#alexander
#hellenistic
A राजनीतिक साम्राज्य टूट गया पर सांस्कृतिक प्रभाव फैला / The political empire broke but cultural influence spread
B यूनानी संस्कृति समाप्त हो गई / Greek culture ended
C रोमन साम्राज्य तुरंत बना / Roman Empire formed immediately
D भारत यूरोप में मिल गया / India merged into Europe
Explanation opens after your attempt
Correct Answer
A. राजनीतिक साम्राज्य टूट गया पर सांस्कृतिक प्रभाव फैला / The political empire broke but cultural influence spread
Step 1
Concept
After Alexander's death the empire split but Hellenistic culture spread. For exams distinguish conquest and cultural diffusion.
Step 2
Why this answer is correct
The correct answer is A. राजनीतिक साम्राज्य टूट गया पर सांस्कृतिक प्रभाव फैला / The political empire broke but cultural influence spread. After Alexander's death the empire split but Hellenistic culture spread. For exams distinguish conquest and cultural diffusion.
Step 3
Exam Tip
अलेक्जेंडर की मृत्यु के बाद साम्राज्य बंटा पर हेल्लेनिस्टिक संस्कृति फैली। परीक्षा में विजय और सांस्कृतिक प्रसार अलग समझें।
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एक समांतर श्रेढ़ी का पहला पद (6) है और उसका (14)वाँ पद उसके (4)वें पद का (3) गुना है। पहले (30) पदों का योग क्या होगा?
The first term of an AP is (6), and its (14)th term is (3) times its (4)th term. What is the sum of the first (30) terms?
#term condition
#ap sum
#expert
A (1425)
B (1485)
C (1545)
D (1605)
Explanation opens after your attempt
Step 1
Concept
The condition gives (6+13d=3(6+3d)), so (d=3) and \(S_{30}=1485\). Convert the term condition into an equation first.
Step 2
Why this answer is correct
The correct answer is B. (1485). The condition gives (6+13d=3(6+3d)), so (d=3) and \(S_{30}=1485\). Convert the term condition into an equation first.
Step 3
Exam Tip
शर्त से (6+13d=3(6+3d)), इसलिए (d=3) और \(S_{30}=1485\) है। पदों की शर्त को पहले समीकरण में बदलें।
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एक समांतर श्रेढ़ी का पहला पद (5) है और उसका (12)वाँ पद उसके (3)वें पद का (4) गुना है। पहले (20) पदों का योग क्या होगा?
The first term of an AP is (5), and its (12)th term is (4) times its (3)rd term. What is the sum of the first (20) terms?
#term condition
#ap sum
#hard
A (1050)
B (1025)
C (1075)
D (1100)
Explanation opens after your attempt
Step 1
Concept
The condition gives (5+11d=4(5+2d)), so (d=5) and \(S_{20}=1050\). Convert the term condition into an equation first.
Step 2
Why this answer is correct
The correct answer is A. (1050). The condition gives (5+11d=4(5+2d)), so (d=5) and \(S_{20}=1050\). Convert the term condition into an equation first.
Step 3
Exam Tip
शर्त से (5+11d=4(5+2d)), इसलिए (d=5) और \(S_{20}=1050\) है। पदों की शर्त को पहले समीकरण में बदलें।
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एक समांतर श्रेढ़ी का पहला पद (6) है और उसका (9)वाँ पद उसके (4)वें पद का (2) गुना है। पहले (25) पदों का योग क्या होगा?
The first term of an AP is (6), and its (9)th term is (2) times its (4)th term. What is the sum of the first (25) terms?
#term condition
#ap sum
#hard
A (1000)
B (1025)
C (1050)
D (1075)
Explanation opens after your attempt
Step 1
Concept
The condition gives (6+8d=2(6+3d)), so (d=3) and \(S_{25}=1050\). Convert the term condition into an equation first.
Step 2
Why this answer is correct
The correct answer is C. (1050). The condition gives (6+8d=2(6+3d)), so (d=3) and \(S_{25}=1050\). Convert the term condition into an equation first.
Step 3
Exam Tip
शर्त से (6+8d=2(6+3d)), इसलिए (d=3) और \(S_{25}=1050\) है। पदों की शर्त को पहले समीकरण में बदलें।
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एक समांतर श्रेढ़ी का पहला पद (4) है और उसका (8)वाँ पद उसके (3)वें पद का (3) गुना है। पहले (12) पदों का योग क्या होगा?
The first term of an AP is (4), and its (8)th term is (3) times its (3)rd term. What is the sum of the first (12) terms?
#term condition
#ap sum
#hard
A (528)
B (552)
C (576)
D (600)
Explanation opens after your attempt
Step 1
Concept
The condition gives (4+7d=3(4+2d)), so (d=8) and \(S_{12}=576\). Convert the term condition into an equation first.
Step 2
Why this answer is correct
The correct answer is C. (576). The condition gives (4+7d=3(4+2d)), so (d=8) and \(S_{12}=576\). Convert the term condition into an equation first.
Step 3
Exam Tip
शर्त से (4+7d=3(4+2d)), इसलिए (d=8) और \(S_{12}=576\)। पदों की शर्त को पहले समीकरण में बदलें।
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समान्तर श्रेणी \(23,31,39,\ldots\) के (n)वें पद का सूत्र \(a_n=8n+15\) है। (36)वां पद क्या होगा?
The (n)th-term formula of the AP \(23,31,39,\ldots\) is \(a_n=8n+15\). What is the (36)th term?
#ap direct-formula nth-term class10
A (293)
B (301)
C (303)
D (311)
Explanation opens after your attempt
Step 1
Concept
\(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.
Step 2
Why this answer is correct
The correct answer is C. (303). \(a_{36}=8\times36+15=303\). Put (n=36) in the formed formula to get the answer directly.
Step 3
Exam Tip
\(a_{36}=8\times36+15=303\)। बने हुए सूत्र में (n=36) रखकर सीधे उत्तर पाएं।
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यदि किसी AP का (r)वां पद (3r-2) और (d=4) है तो ((r+6))वां पद क्या होगा?
If the (r)th term of an AP is (3r-2) and (d=4), what is the ((r+6))th term?
#ap symbolic nth-term class10
A (3r+18)
B (3r+20)
C (3r+22)
D (3r+24)
Explanation opens after your attempt
Correct Answer
C. (3r+22)
Step 1
Concept
The ((r+6))th term is (6d) ahead of the (r)th term so (3r-2+24=3r+22). In symbolic questions look at the position gap.
Step 2
Why this answer is correct
The correct answer is C. (3r+22). The ((r+6))th term is (6d) ahead of the (r)th term so (3r-2+24=3r+22). In symbolic questions look at the position gap.
Step 3
Exam Tip
((r+6))वां पद (r)वें पद से (6d) आगे है इसलिए (3r-2+24=3r+22)। प्रतीकात्मक प्रश्न में स्थान अंतर देखें।
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समान्तर श्रेणी \(19,26,33,\ldots\) के (n)वें पद का सूत्र \(a_n=7n+12\) है। (41)वां पद क्या होगा?
The (n)th-term formula of the AP \(19,26,33,\ldots\) is \(a_n=7n+12\). What is the (41)st term?
#ap
#direct-formula
#nth-term
#class10
A (294)
B (304)
C (309)
D (299)
Explanation opens after your attempt
Step 1
Concept
\(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
Step 2
Why this answer is correct
The correct answer is D. (299). \(a_{41}=7\times41+12=299\). Put only (n=41) in the formed formula.
Step 3
Exam Tip
\(a_{41}=7\times41+12=299\)। बने हुए सूत्र में केवल (n=41) रखें।
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यदि किसी समान्तर श्रेणी का (m)वां पद (2m+3) और (d=2) है तो ((m+5))वां पद क्या होगा?
If the (m)th term of an AP is (2m+3) and (d=2), what is the ((m+5))th term?
#ap
#symbolic
#nth-term
#class10
A (2m+8)
B (2m+10)
C (2m+11)
D (2m+13)
Explanation opens after your attempt
Correct Answer
D. (2m+13)
Step 1
Concept
The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.
Step 2
Why this answer is correct
The correct answer is D. (2m+13). The ((m+5))th term is (5d) ahead of the (m)th term, so (2m+3+10=2m+13). In symbolic terms, look at the position gap.
Step 3
Exam Tip
((m+5))वां पद (m)वें पद से (5d) आगे है इसलिए (2m+3+10=2m+13)। प्रतीकात्मक पदों में भी स्थान अंतर देखें।
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समान्तर श्रेणी का पहला पद (25) है और (18)वां पद (93) है। सार्व अंतर क्या है?
The first term of an AP is (25) and the (18)th term is (93). What is the common difference?
#ap
#common-difference
#nth-term
#class10
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).
Step 2
Why this answer is correct
The correct answer is C. (4). From (93=25+17d), (68=17d) so (d=4). For the (18)th term, the multiplier is (17).
Step 3
Exam Tip
(93=25+17d) से (68=17d) इसलिए (d=4)। (18)वें पद के लिए गुणक (17) होता है।
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समान्तर श्रेणी \(11,17,23,\ldots\) का (n)वां पद \(a_n=6n+5\) है। इसका (32)वां पद क्या होगा?
The (n)th term of the AP \(11,17,23,\ldots\) is \(a_n=6n+5\). What is its (32)nd term?
#ap
#direct-formula
#nth-term
#class10
A (191)
B (197)
C (203)
D (209)
Explanation opens after your attempt
Step 1
Concept
\(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.
Step 2
Why this answer is correct
The correct answer is B. (197). \(a_{32}=6\times32+5=197\). Substitute the correct value of (n) in the formed formula.
Step 3
Exam Tip
\(a_{32}=6\times32+5=197\)। बनाए गए सूत्र में (n) का सही मान रखें।
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एक समान्तर श्रेणी का पहला पद (18) और (16)वां पद (93) है। सार्व अंतर क्या है?
The first term of an AP is (18) and the (16)th term is (93). What is the common difference?
#ap
#common-difference
#nth-term
#class10
A (5)
B (4)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).
Step 2
Why this answer is correct
The correct answer is A. (5). (93=18+15d), so (75=15d) and (d=5). For the (16)th term, the multiplier is (15).
Step 3
Exam Tip
(93=18+15d), इसलिए (75=15d) और (d=5)। (16)वें पद के लिए गुणक (15) होगा।
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यदि किसी समान्तर श्रेणी का (10)वां पद (41) और (20)वां पद (81) है, तो उसका सार्व अंतर क्या है?
If the (10)th term of an AP is (41) and the (20)th term is (81), what is its common difference?
#ap
#common-difference
#nth-term
#class10
A (3)
B (5)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).
Step 2
Why this answer is correct
\(The correct answer is C. (4). The difference of terms is (81-41=40) and the difference of positions is (10), so (d=4). Use (d=\frac{\)difference of terms}{difference of positions}).
Step 3
Exam Tip
दो पदों का अंतर (81-41=40) है और पद संख्या का अंतर (10), इसलिए (d=4)। \(दो ज्ञात पदों में (d=\frac{\)पदों का अंतर}{स्थान का अंतर}) लगाएं।
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यदि किसी समान्तर श्रेणी का पहला पद (7) और सार्व अंतर (4) है, तो उसका (18)वां पद क्या होगा?
If the first term of an AP is (7) and the common difference is (4), what is its (18)th term?
#ap
#nth-term
#medium
#class10
A (75)
B (71)
C (79)
D (83)
Explanation opens after your attempt
Step 1
Concept
Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).
Step 2
Why this answer is correct
The correct answer is A. (75). Using (a_n=a+(n-1)d), \(7+17\times4=75\). Exam tip: do not forget (n-1).
Step 3
Exam Tip
सूत्र (a_n=a+(n-1)d) लगाने पर \(7+17\times4=75\)। परीक्षा में (n-1) को भूलना नहीं चाहिए।
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यदि एपी का (4)था पद (21) और (d=6) है तो (10)वाँ पद क्या होगा?
If the (4)th term of an AP is (21) and (d=6), what is the (10)th term?
#ap
#nth-term
#easy
#class10
A (53)
B (55)
C (57)
D (59)
Explanation opens after your attempt
Step 1
Concept
The (10)th term is (6d) after the (4)th term, so (21+36=57). Use the difference in term numbers directly.
Step 2
Why this answer is correct
The correct answer is C. (57). The (10)th term is (6d) after the (4)th term, so (21+36=57). Use the difference in term numbers directly.
Step 3
Exam Tip
(10)वाँ पद (4)थे पद से (6d) आगे है इसलिए (21+36=57)। पद संख्या का अंतर सीधे उपयोग करें।
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यदि एपी का प्रथम पद (-12) और सार्व अंतर (5) है तो (16)वाँ पद क्या होगा?
If the first term of an AP is (-12) and the common difference is (5), what is the (16)th term?
#ap
#nth-term
#easy
#class10
A (61)
B (63)
C (65)
D (67)
Explanation opens after your attempt
Step 1
Concept
\(a_{16}=-12+15\times5=63\). First calculate (15d), then add the first term.
Step 2
Why this answer is correct
The correct answer is B. (63). \(a_{16}=-12+15\times5=63\). First calculate (15d), then add the first term.
Step 3
Exam Tip
\(a_{16}=-12+15\times5=63\)। पहले (15d) निकालें फिर प्रथम पद जोड़ें।
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यदि किसी एपी का प्रथम पद (9) और सार्व अंतर (10) है तो (7)वाँ पद क्या होगा?
If the first term of an AP is (9) and the common difference is (10), what is the (7)th term?
#ap
#nth-term
#easy
#class10
A (59)
B (69)
C (79)
D (89)
Explanation opens after your attempt
Step 1
Concept
\(a_7=9+6\times10=69\). For the (7)th term, (6d) is added.
Step 2
Why this answer is correct
The correct answer is B. (69). \(a_7=9+6\times10=69\). For the (7)th term, (6d) is added.
Step 3
Exam Tip
\(a_7=9+6\times10=69\)। (7)वें पद के लिए (6d) जोड़ना होता है।
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यदि किसी एपी का (3)रा पद (14) और (d=5) है तो (7)वाँ पद क्या होगा?
If the (3)rd term of an AP is (14) and (d=5), what is the (7)th term?
#ap
#nth-term
#easy
#class10
A (29)
B (31)
C (34)
D (36)
Explanation opens after your attempt
Step 1
Concept
The (7)th term is (4d) after the (3)rd term, so (14+20=34). Count the gap between terms correctly.
Step 2
Why this answer is correct
The correct answer is C. (34). The (7)th term is (4d) after the (3)rd term, so (14+20=34). Count the gap between terms correctly.
Step 3
Exam Tip
(7)वाँ पद (3)रे पद से (4d) आगे है इसलिए (14+20=34)। बीच के पदों की संख्या सही गिनें।
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यदि एपी का प्रथम पद (-2) और सार्व अंतर (6) है तो (12)वाँ पद क्या होगा?
If the first term of an AP is (-2) and the common difference is (6), what is the (12)th term?
#ap
#nth-term
#easy
#class10
A (62)
B (64)
C (66)
D (68)
Explanation opens after your attempt
Step 1
Concept
\(a_{12}=-2+11\times6=64\). Multiply first and then add (-2).
Step 2
Why this answer is correct
The correct answer is B. (64). \(a_{12}=-2+11\times6=64\). Multiply first and then add (-2).
Step 3
Exam Tip
\(a_{12}=-2+11\times6=64\)। पहले गुणा करें फिर (-2) जोड़ें।
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यदि किसी एपी का (5)वाँ पद (22) और (d=6) है तो (8)वाँ पद क्या है?
If the (5)th term of an AP is (22) and (d=6), what is the (8)th term?
#ap
#nth-term
#easy
#class10
A (34)
B (36)
C (38)
D (40)
Explanation opens after your attempt
Step 1
Concept
The (8)th term is (3d) after the (5)th term, so (22+18=40). Counting the gap between terms is an easy method.
Step 2
Why this answer is correct
The correct answer is D. (40). The (8)th term is (3d) after the (5)th term, so (22+18=40). Counting the gap between terms is an easy method.
Step 3
Exam Tip
(8)वाँ पद (5)वें पद से (3d) आगे है इसलिए (22+18=40)। पदों का अंतर गिनना आसान तरीका है।
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यदि एपी का (7)वाँ पद (31) है और (d=4) है तो (10)वाँ पद क्या होगा?
If the (7)th term of an AP is (31) and (d=4), what is the (10)th term?
#ap
#nth-term
#easy
#class10
A (39)
B (41)
C (43)
D (45)
Explanation opens after your attempt
Step 1
Concept
The (10)th term is (3d) after the (7)th term, so \(31+3\times4=43\). The difference method is quick for nearby terms.
Step 2
Why this answer is correct
The correct answer is C. (43). The (10)th term is (3d) after the (7)th term, so \(31+3\times4=43\). The difference method is quick for nearby terms.
Step 3
Exam Tip
(10)वाँ पद (7)वें पद से (3d) आगे है इसलिए \(31+3\times4=43\)। पास के पदों के लिए अंतर विधि तेज होती है।
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यदि एपी का प्रथम पद (15) और सार्व अंतर (-4) है तो (8)वाँ पद क्या होगा?
If the first term of an AP is (15) and the common difference is (-4), what is the (8)th term?
#ap
#nth-term
#easy
#class10
A (-13)
B (-11)
C (-9)
D (-7)
Explanation opens after your attempt
Step 1
Concept
(a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.
Step 2
Why this answer is correct
The correct answer is A. (-13). (a_8=15+7(-4)=-13). Writing negative (d) in brackets is useful.
Step 3
Exam Tip
(a_8=15+7(-4)=-13)। ऋणात्मक (d) को कोष्ठक में लिखना उपयोगी है।
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यदि किसी एपी का प्रथम पद (5) और सार्व अंतर (3) है तो (8)वाँ पद क्या होगा?
If the first term of an AP is (5) and common difference is (3), what is the (8)th term?
#ap
#nth-term
#easy
#class10
A (23)
B (24)
C (26)
D (28)
Explanation opens after your attempt
Step 1
Concept
Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).
Step 2
Why this answer is correct
The correct answer is C. (26). Using (a_n=a+(n-1)d), \(5+7\times3=26\). In exams, do not forget (n-1).
Step 3
Exam Tip
सूत्र (a_n=a+(n-1)d) लगाएं तो \(5+7\times3=26\)। परीक्षा में (n-1) लेना न भूलें।
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किसी समांतर श्रेढ़ी का (n)वाँ पद \(a_n=2n+3\) है। (18)वाँ पद क्या होगा?
The (n)th term of an AP is \(a_n=2n+3\). What will be the (18)th term?
#nth term
#ap expression
#class 10
A (39)
B (41)
C (36)
D (38)
Explanation opens after your attempt
Step 1
Concept
Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).
Step 2
Why this answer is correct
The correct answer is A. (39). Putting (n=18), \(a_{18}=2\times18+3=39\). Substitute the term number directly in the given \(a_n\).
Step 3
Exam Tip
(n=18) रखने पर \(a_{18}=2\times18+3=39\)। दिए गए \(a_n\) में सीधे पद संख्या रखें।
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एक समांतर श्रेढ़ी का प्रथम पद (25) और सार्व अंतर (4) है। (21)वाँ पद क्या होगा?
The first term of an AP is (25) and the common difference is (4). What will be the (21)st term?
#ap formula
#nth term
#class 10
A (101)
B (105)
C (109)
D (96)
Explanation opens after your attempt
Step 1
Concept
\(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.
Step 2
Why this answer is correct
The correct answer is B. (105). \(a_{21}=25+20\times4=105\). Do not forget to subtract (1) from the term number.
Step 3
Exam Tip
\(a_{21}=25+20\times4=105\)। पद संख्या से (1) घटाना न भूलें।
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यदि समांतर श्रेढ़ी का प्रथम पद (6) और सार्व अंतर (7) है, तो (11)वाँ पद क्या है?
If the first term of an AP is (6) and the common difference is (7), what is the (11)th term?
#ap common difference
#nth term
#easy
A (83)
B (70)
C (79)
D (76)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=6+10\times7=76\). Up to the (11)th term, the difference is added (10) times.
Step 2
Why this answer is correct
The correct answer is D. (76). \(a_{11}=6+10\times7=76\). Up to the (11)th term, the difference is added (10) times.
Step 3
Exam Tip
\(a_{11}=6+10\times7=76\)। (11)वें पद तक (10) बार अंतर जुड़ता है।
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समांतर श्रेढ़ी में प्रथम पद (a=4) और सार्व अंतर (d=3) है। इसका (10)वाँ पद क्या होगा?
In an AP, first term (a=4) and common difference (d=3). What is the (10)th term?
#arithmetic progression
#nth term
#easy
#class 10
A (31)
B (30)
C (34)
D (27)
Explanation opens after your attempt
Step 1
Concept
Using (a_n=a+(n-1)d), \(a_{10}=4+9\times3=31\). Exam tip: write (n-1) carefully.
Step 2
Why this answer is correct
The correct answer is A. (31). Using (a_n=a+(n-1)d), \(a_{10}=4+9\times3=31\). Exam tip: write (n-1) carefully.
Step 3
Exam Tip
सूत्र (a_n=a+(n-1)d) लगाने पर \(a_{10}=4+9\times3=31\)। परीक्षा में (n-1) को ध्यान से लिखें।
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किसी समांतर श्रेढ़ी के पहले पद और (60)वें पद का योग (300) है। (21)वें पद से (40)वें पद तक का योग ज्ञात कीजिए।
The sum of the first term and the (60)th term of an AP is (300). Find the sum from the (21)st term to the (40)th term.
#symmetric terms
#range sum
#ap
A (2900)
B (2950)
C (3000)
D (3050)
Explanation opens after your attempt
Step 1
Concept
\(a_{21}+a_{40}=a_1+a_{60}=300\), so the sum of (20) terms is (3000). Sums of symmetric terms are equal in an AP.
Step 2
Why this answer is correct
The correct answer is C. (3000). \(a_{21}+a_{40}=a_1+a_{60}=300\), so the sum of (20) terms is (3000). Sums of symmetric terms are equal in an AP.
Step 3
Exam Tip
\(a_{21}+a_{40}=a_1+a_{60}=300\), इसलिए (20) पदों का योग (3000) है। सममित पदों का योग बराबर होता है।
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किसी समांतर श्रेढ़ी के पहले पद और (40)वें पद का योग (210) है। (11)वें पद से (30)वें पद तक का योग ज्ञात कीजिए।
The sum of the first term and the (40)th term of an AP is (210). Find the sum from the (11)th term to the (30)th term.
#symmetric terms
#range sum
#ap
A (2000)
B (2100)
C (2200)
D (2300)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}+a_{30}=a_1+a_{40}=210\), so the sum of (20) terms is (2100). Sums of symmetric terms are equal in an AP.
Step 2
Why this answer is correct
The correct answer is B. (2100). \(a_{11}+a_{30}=a_1+a_{40}=210\), so the sum of (20) terms is (2100). Sums of symmetric terms are equal in an AP.
Step 3
Exam Tip
\(a_{11}+a_{30}=a_1+a_{40}=210\), इसलिए (20) पदों का योग (2100) है। सममित पदों का योग बराबर होता है।
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किसी समांतर श्रेढ़ी में पहले (20) पदों का योग (740) है और (20)वाँ पद (60) है। पहला पद ज्ञात कीजिए।
In an AP, the sum of the first (20) terms is (740), and the (20)th term is (60). Find the first term.
#first term
#last term
#sum
#ap
A (10)
B (14)
C (18)
D (22)
Explanation opens after your attempt
Step 1
Concept
From (740=10(a+60)), (a=14). When the (n)th term is given, use it as the last term for the first (n) terms.
Step 2
Why this answer is correct
The correct answer is B. (14). From (740=10(a+60)), (a=14). When the (n)th term is given, use it as the last term for the first (n) terms.
Step 3
Exam Tip
(740=10(a+60)) से (a=14) मिलता है। जब (n)वाँ पद दिया हो तो उसे अंतिम पद की तरह इस्तेमाल करें।
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(600) से कम (13) के धनात्मक गुणजों में अंतिम पद क्या है?
What is the last term among the positive multiples of (13) less than (600)?
#ap multiples last-term nth-term
A (585)
B (598)
C (611)
D (624)
Explanation opens after your attempt
Step 1
Concept
In (13n<600), the greatest (n=46) so the term is \(13\times46=598\). Take the greatest integer below the limit.
Step 2
Why this answer is correct
The correct answer is B. (598). In (13n<600), the greatest (n=46) so the term is \(13\times46=598\). Take the greatest integer below the limit.
Step 3
Exam Tip
(13n<600) में सबसे बड़ा (n=46) है इसलिए पद \(13\times46=598\)। सीमा से कम सबसे बड़ा पूर्णांक लें।
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समान्तर श्रेणी \(73,68,63,\ldots\) का (n)वां पद (-12) है। (n) क्या है?
The (n)th term of the AP \(73,68,63,\ldots\) is (-12). What is (n)?
#ap negative-term term-number class10
A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
Step 1
Concept
From (-12=73+(n-1)(-5)), (85=5(n-1)) so (n=18). In a decreasing AP keep signs correct up to the negative target.
Step 2
Why this answer is correct
The correct answer is C. (18). From (-12=73+(n-1)(-5)), (85=5(n-1)) so (n=18). In a decreasing AP keep signs correct up to the negative target.
Step 3
Exam Tip
(-12=73+(n-1)(-5)) से (85=5(n-1)) इसलिए (n=18)। घटती AP में ऋणात्मक लक्ष्य तक चिन्ह सही रखें।
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यदि AP \(z,z+5,z+10,\ldots\) का (19)वां पद (112) है तो (z) क्या होगा?
If the (19)th term of the AP \(z,z+5,z+10,\ldots\) is (112), what is (z)?
#ap variable-first-term nth-term class10
A (18)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
From \(112=z+18\times5\), (z=22). Treat the variable first term as (a) and apply the formula.
Step 2
Why this answer is correct
The correct answer is C. (22). From \(112=z+18\times5\), (z=22). Treat the variable first term as (a) and apply the formula.
Step 3
Exam Tip
\(112=z+18\times5\) से (z=22)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं।
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समान्तर श्रेणी \(7,12,17,\ldots\) में (180) से कम अंतिम पद क्या है?
In the AP \(7,12,17,\ldots\), what is the last term less than (180)?
#ap last-term-less-than nth-term class10
A (172)
B (175)
C (177)
D (179)
Explanation opens after your attempt
Step 1
Concept
The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).
Step 2
Why this answer is correct
The correct answer is C. (177). The terms are (7+5(n-1)). The last term less than (180) is (177) because the next term will be (182).
Step 3
Exam Tip
पद (7+5(n-1)) हैं। (180) से कम अंतिम पद (177) है क्योंकि अगला पद (182) होगा।
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एक AP में (a=63) और (d=-4) है। कौन-सा पद (-1) होगा?
In an AP (a=63) and (d=-4). Which term will be (-1)?
#ap negative-term term-number class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
Explanation opens after your attempt
Correct Answer
C. (17)वां / (17)th
Step 1
Concept
From (-1=63+(n-1)(-4)), (64=4(n-1)) so (n=17). Handle signs carefully with a negative target term.
Step 2
Why this answer is correct
The correct answer is C. (17)वां / (17)th. From (-1=63+(n-1)(-4)), (64=4(n-1)) so (n=17). Handle signs carefully with a negative target term.
Step 3
Exam Tip
(-1=63+(n-1)(-4)) से (64=4(n-1)) इसलिए (n=17)। ऋणात्मक लक्ष्य पद में चिन्हों को ध्यान से संभालें।
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समान्तर श्रेणी \(105,98,91,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?
Which is the first negative term of the AP \(105,98,91,\ldots\)?
#ap first-negative-term nth-term class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
Explanation opens after your attempt
Correct Answer
C. (17)वां / (17)th
Step 1
Concept
(a_n=105+(n-1)(-7)=112-7n). From \(a_n<0\), (n>16) so the first negative term is the (17)th.
Step 2
Why this answer is correct
The correct answer is C. (17)वां / (17)th. (a_n=105+(n-1)(-7)=112-7n). From \(a_n<0\), (n>16) so the first negative term is the (17)th.
Step 3
Exam Tip
(a_n=105+(n-1)(-7)=112-7n)। \(a_n<0\) से (n>16) इसलिए पहला ऋणात्मक पद (17)वां है।
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समान्तर श्रेणी \(26,35,44,\ldots\) का कौन-सा पद (206) है?
Which term of the AP \(26,35,44,\ldots\) is (206)?
#ap term-number nth-term class10
A (19)वां / (19)th
B (20)वां / (20)th
C (21)वां / (21)st
D (22)वां / (22)nd
Explanation opens after your attempt
Correct Answer
C. (21)वां / (21)st
Step 1
Concept
From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).
Step 2
Why this answer is correct
The correct answer is C. (21)वां / (21)st. From (206=26+(n-1)9), (180=9(n-1)) so (n=21). Divide the difference between the term and first term by (d).
Step 3
Exam Tip
(206=26+(n-1)9) से (180=9(n-1)) इसलिए (n=21)। पद और पहले पद का अंतर (d) से भाग दें।
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किसी समान्तर श्रेणी का (14)वां पद (92) और (d=7) है। \(a_1\) क्या होगा?
The (14)th term of an AP is (92) and (d=7). What is \(a_1\)?
#ap first-term known-term class10
A (1)
B (3)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
From \(92=a+13\times7\), (a=1). From the (14)th term to the first term (13d) is subtracted.
Step 2
Why this answer is correct
The correct answer is A. (1). From \(92=a+13\times7\), (a=1). From the (14)th term to the first term (13d) is subtracted.
Step 3
Exam Tip
\(92=a+13\times7\) से (a=1)। (14)वें पद से पहले पद तक (13d) घटता है।
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समान्तर श्रेणी \(9,17,25,\ldots\) का कौन-सा पद (201) है?
Which term of the AP \(9,17,25,\ldots\) is (201)?
#ap term-position nth-term class10
A (23)वां / (23)rd
B (24)वां / (24)th
C (25)वां / (25)th
D (26)वां / (26)th
Explanation opens after your attempt
Correct Answer
C. (25)वां / (25)th
Step 1
Concept
From (201=9+(n-1)8), (192=8(n-1)) and (n=25). If the term number is an integer the answer is on the right track.
Step 2
Why this answer is correct
The correct answer is C. (25)वां / (25)th. From (201=9+(n-1)8), (192=8(n-1)) and (n=25). If the term number is an integer the answer is on the right track.
Step 3
Exam Tip
(201=9+(n-1)8) से (192=8(n-1)) और (n=25)। पद संख्या पूर्णांक आए तो उत्तर सही दिशा में है।
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(500) से कम (11) के धनात्मक गुणजों में अंतिम पद क्या है?
What is the last term among the positive multiples of (11) less than (500)?
#ap
#multiples
#last-term
#nth-term
A (484)
B (495)
C (506)
D (517)
Explanation opens after your attempt
Step 1
Concept
In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.
Step 2
Why this answer is correct
The correct answer is B. (495). In (11n<500), the greatest (n=45), so the term is \(11\times45=495\). Take the greatest integer below the limit.
Step 3
Exam Tip
(11n<500) में सबसे बड़ा (n=45) है इसलिए पद \(11\times45=495\)। सीमा से कम सबसे बड़ा पूर्णांक लें।
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समान्तर श्रेणी \(55,51,47,\ldots\) का (n)वां पद (-17) है। (n) क्या है?
The (n)th term of the AP \(55,51,47,\ldots\) is (-17). What is (n)?
#ap
#negative-term
#term-number
#class10
A (17)
B (18)
C (19)
D (20)
Explanation opens after your attempt
Step 1
Concept
From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.
Step 2
Why this answer is correct
The correct answer is C. (19). From (-17=55+(n-1)(-4)), (72=4(n-1)) so (n=19). Keep signs correct while reaching a negative term.
Step 3
Exam Tip
(-17=55+(n-1)(-4)) से (72=4(n-1)) इसलिए (n=19)। ऋणात्मक पद तक जाते समय चिन्ह सही रखें।
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यदि समान्तर श्रेणी \(y,y+6,y+12,\ldots\) का (12)वां पद (89) है तो (y) का मान क्या है?
If the (12)th term of the AP \(y,y+6,y+12,\ldots\) is (89), what is the value of (y)?
#ap
#variable-first-term
#nth-term
#class10
A (17)
B (19)
C (21)
D (23)
Explanation opens after your attempt
Step 1
Concept
From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).
Step 2
Why this answer is correct
The correct answer is D. (23). From \(89=y+11\times6\), (y=23). Treat the variable first term directly as (a).
Step 3
Exam Tip
\(89=y+11\times6\) से (y=23)। चर वाले पहले पद को सीधे (a) मानें।
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समान्तर श्रेणी \(2,6,10,\ldots\) में (75) से कम अंतिम पद क्या है?
In the AP \(2,6,10,\ldots\), what is the last term less than (75)?
#ap
#last-term-less-than
#nth-term
#class10
A (74)
B (70)
C (72)
D (76)
Explanation opens after your attempt
Step 1
Concept
The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
Step 2
Why this answer is correct
The correct answer is A. (74). The terms of this sequence are (2+4(n-1)). The last term less than (75) is (74).
Step 3
Exam Tip
इस श्रेणी के पद (2+4(n-1)) हैं। (75) से कम अंतिम पद (74) है।
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एक समान्तर श्रेणी में (a=48) और (d=-3) है। कौन-सा पद (0) होगा?
In an AP, (a=48) and (d=-3). Which term will be (0)?
#ap
#zero-term
#term-number
#class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
Explanation opens after your attempt
Correct Answer
C. (17)वां / (17)th
Step 1
Concept
From (0=48+(n-1)(-3)), (3(n-1)=48) so (n=17). Use the usual formula even for the zero term.
Step 2
Why this answer is correct
The correct answer is C. (17)वां / (17)th. From (0=48+(n-1)(-3)), (3(n-1)=48) so (n=17). Use the usual formula even for the zero term.
Step 3
Exam Tip
(0=48+(n-1)(-3)) से (3(n-1)=48) इसलिए (n=17)। शून्य पद के लिए भी सामान्य सूत्र लगाएं।
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समान्तर श्रेणी \(72,66,60,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?
Which is the first negative term of the AP \(72,66,60,\ldots\)?
#ap
#first-negative-term
#nth-term
#class10
A (13)वां / (13)th
B (14)वां / (14)th
C (15)वां / (15)th
D (16)वां / (16)th
Explanation opens after your attempt
Correct Answer
B. (14)वां / (14)th
Step 1
Concept
(a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.
Step 2
Why this answer is correct
The correct answer is B. (14)वां / (14)th. (a_n=72+(n-1)(-6)=78-6n). From \(a_n<0\), (n>13) so the first negative term is the (14)th.
Step 3
Exam Tip
(a_n=72+(n-1)(-6)=78-6n)। \(a_n<0\) से (n>13) इसलिए पहला ऋणात्मक पद (14)वां है।
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समान्तर श्रेणी \(14,23,32,\ldots\) का कौन-सा पद (185) है?
Which term of the AP \(14,23,32,\ldots\) is (185)?
#ap
#term-number
#nth-term
#class10
A (18)वां / (18)th
B (19)वां / (19)th
C (20)वां / (20)th
D (21)वां / (21)th
Explanation opens after your attempt
Correct Answer
C. (20)वां / (20)th
Step 1
Concept
From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.
Step 2
Why this answer is correct
The correct answer is C. (20)वां / (20)th. From (185=14+(n-1)9), (171=9(n-1)) and (n=20). Divide the difference by (d) to get the term number.
Step 3
Exam Tip
(185=14+(n-1)9) से (171=9(n-1)) और (n=20)। अंतर को (d) से भाग देकर पद संख्या पाएं।
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किसी समान्तर श्रेणी का (10)वां पद (62) और (d=5) है। \(a_1\) क्या होगा?
The (10)th term of an AP is (62) and (d=5). What is \(a_1\)?
#ap
#first-term
#known-term
#class10
A (12)
B (15)
C (20)
D (17)
Explanation opens after your attempt
Step 1
Concept
From \(62=a+9\times5\), (a=17). From the (10)th term to the first term, subtract (9d).
Step 2
Why this answer is correct
The correct answer is D. (17). From \(62=a+9\times5\), (a=17). From the (10)th term to the first term, subtract (9d).
Step 3
Exam Tip
\(62=a+9\times5\) से (a=17)। (10)वें पद से पहले पद तक (9d) घटता है।
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समान्तर श्रेणी \(21,29,37,\ldots\) का कौन-सा पद (149) है?
Which term of the AP \(21,29,37,\ldots\) is (149)?
#ap
#term-position
#nth-term
#class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
Explanation opens after your attempt
Correct Answer
C. (17)वां / (17)th
Step 1
Concept
From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).
Step 2
Why this answer is correct
The correct answer is C. (17)वां / (17)th. From (149=21+(n-1)8), (128=8(n-1)) so (n=17). When term number is asked, treat the given term as \(a_n\).
Step 3
Exam Tip
(149=21+(n-1)8) से (128=8(n-1)) इसलिए (n=17)। पद संख्या पूछी हो तो दिए पद को \(a_n\) मानें।
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समान्तर श्रेणी \(27,24,21,\ldots\) का (n)वां पद (-30) है। (n) क्या है?
The (n)th term of the AP \(27,24,21,\ldots\) is (-30). What is (n)?
#ap
#negative-term
#term-number
#class10
A (18)
B (19)
C (20)
D (21)
Explanation opens after your attempt
Step 1
Concept
From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.
Step 2
Why this answer is correct
The correct answer is C. (20). From (-30=27+(n-1)(-3)), (57=3(n-1)), so (n=20). Handle signs carefully with a negative target term.
Step 3
Exam Tip
(-30=27+(n-1)(-3)) से (57=3(n-1)), इसलिए (n=20)। ऋणात्मक लक्ष्य पद में चिन्ह सावधानी से बदलें।
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यदि समान्तर श्रेणी \(x, x+4, x+8,\ldots\) का (10)वां पद (50) है, तो (x) का मान क्या है?
If the (10)th term of the AP \(x, x+4, x+8,\ldots\) is (50), what is the value of (x)?
#ap
#variable-first-term
#nth-term
#class10
A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(50=x+9\times4\), so (x=14). Treat the variable first term as (a) and apply the formula.
Step 2
Why this answer is correct
The correct answer is C. (14). \(50=x+9\times4\), so (x=14). Treat the variable first term as (a) and apply the formula.
Step 3
Exam Tip
\(50=x+9\times4\), इसलिए (x=14)। चर वाले पहले पद को (a) मानकर सूत्र लगाएं।
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एक समान्तर श्रेणी में (a=30) और (d=-2) है। कौन-सा पद (0) होगा?
In an AP, (a=30) and (d=-2). Which term will be (0)?
#ap
#zero-term
#nth-term
#class10
A (14)वां / (14)th
B (15)वां / (15)th
C (16)वां / (16)th
D (17)वां / (17)th
Explanation opens after your attempt
Correct Answer
C. (16)वां / (16)th
Step 1
Concept
From (0=30+(n-1)(-2)), (2(n-1)=30), so (n=16). Use the same nth-term formula even for the zero term.
Step 2
Why this answer is correct
The correct answer is C. (16)वां / (16)th. From (0=30+(n-1)(-2)), (2(n-1)=30), so (n=16). Use the same nth-term formula even for the zero term.
Step 3
Exam Tip
(0=30+(n-1)(-2)) से (2(n-1)=30), अतः (n=16)। शून्य पद के लिए भी वही (n)वां पद सूत्र लगाएं।
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समान्तर श्रेणी \(45,40,35,\ldots\) का प्रथम ऋणात्मक पद कौन-सा है?
Which is the first negative term of the AP \(45,40,35,\ldots\)?
#ap
#first-negative-term
#nth-term
#class10
A (10)वां / (10)th
B (11)वां / (11)th
C (12)वां / (12)th
D (13)वां / (13)th
Explanation opens after your attempt
Correct Answer
B. (11)वां / (11)th
Step 1
Concept
(a_n=45+(n-1)(-5)=50-5n). From \(a_n<0\), (n>10), so the first negative term is the (11)th.
Step 2
Why this answer is correct
The correct answer is B. (11)वां / (11)th. (a_n=45+(n-1)(-5)=50-5n). From \(a_n<0\), (n>10), so the first negative term is the (11)th.
Step 3
Exam Tip
(a_n=45+(n-1)(-5)=50-5n)। \(a_n<0\) से (n>10), इसलिए पहला ऋणात्मक पद (11)वां है।
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समान्तर श्रेणी \(15,21,27,\ldots\) का कौन-सा पद (111) है?
Which term of the AP \(15,21,27,\ldots\) is (111)?
#ap
#term-number
#nth-term
#class10
A (15)वां / (15)th
B (16)वां / (16)th
C (17)वां / (17)th
D (18)वां / (18)th
Explanation opens after your attempt
Correct Answer
C. (17)वां / (17)th
Step 1
Concept
(111=15+(n-1)6), so (96=6(n-1)) and (n=17). For term number, divide the difference by (d).
Step 2
Why this answer is correct
The correct answer is C. (17)वां / (17)th. (111=15+(n-1)6), so (96=6(n-1)) and (n=17). For term number, divide the difference by (d).
Step 3
Exam Tip
(111=15+(n-1)6), इसलिए (96=6(n-1)) और (n=17)। पद संख्या में अंतर को (d) से भाग दें।
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किसी समान्तर श्रेणी का (8)वां पद (35) और (d=4) है। \(a_1\) क्या होगा?
The (8)th term of an AP is (35) and (d=4). What is \(a_1\)?
#ap
#first-term
#nth-term
#class10
A (11)
B (9)
C (7)
D (13)
Explanation opens after your attempt
Step 1
Concept
\(35=a+7\times4\), so (a=7). For the (8)th term, subtract (7d).
Step 2
Why this answer is correct
The correct answer is C. (7). \(35=a+7\times4\), so (a=7). For the (8)th term, subtract (7d).
Step 3
Exam Tip
\(35=a+7\times4\), इसलिए (a=7)। (8)वें पद के लिए (7d) घटाएं।
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समान्तर श्रेणी \(3,8,13,\ldots\) का कौन-सा पद (88) है?
Which term of the AP \(3,8,13,\ldots\) is (88)?
#ap
#term-position
#nth-term
#class10
A (18)वां / (18)th
B (17)वां / (17)th
C (16)वां / (16)th
D (19)वां / (19)th
Explanation opens after your attempt
Correct Answer
A. (18)वां / (18)th
Step 1
Concept
From (88=3+(n-1)5), (85=5(n-1)), hence (n=18). In term-number questions, treat the given term as \(a_n\).
Step 2
Why this answer is correct
The correct answer is A. (18)वां / (18)th. From (88=3+(n-1)5), (85=5(n-1)), hence (n=18). In term-number questions, treat the given term as \(a_n\).
Step 3
Exam Tip
(88=3+(n-1)5) से (85=5(n-1)), अतः (n=18)। पद संख्या के प्रश्न में दिए पद को \(a_n\) मानें।
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समांतर श्रेढ़ी \(200,180,160,140,\ldots\) का (11)वाँ पद क्या है?
What is the (11)th term of the AP \(200,180,160,140,\ldots\)?
#ap decreasing
#nth term
#zero term
A (20)
B (40)
C (10)
D (0)
Explanation opens after your attempt
Step 1
Concept
Here (d=-20), so (a_{11}=200+10(-20)=0). In a decreasing AP, a term can also become zero.
Step 2
Why this answer is correct
The correct answer is D. (0). Here (d=-20), so (a_{11}=200+10(-20)=0). In a decreasing AP, a term can also become zero.
Step 3
Exam Tip
यहाँ (d=-20) है, इसलिए (a_{11}=200+10(-20)=0)। घटती श्रेढ़ी में पद शून्य भी हो सकता है।
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यदि \(a_n=4n+6\) है, तो (25)वाँ पद क्या होगा?
If \(a_n=4n+6\), what will be the (25)th term?
#ap general term
#nth term
#easy
A (106)
B (100)
C (104)
D (110)
Explanation opens after your attempt
Step 1
Concept
\(a_{25}=4\times25+6=106\). Put (n=25) in the given general term.
Step 2
Why this answer is correct
The correct answer is A. (106). \(a_{25}=4\times25+6=106\). Put (n=25) in the given general term.
Step 3
Exam Tip
\(a_{25}=4\times25+6=106\)। दिए गए सामान्य पद में (n=25) रखें।
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यदि (a=0) और (d=4) है, तो समांतर श्रेढ़ी का (26)वाँ पद क्या है?
If (a=0) and (d=4), what is the (26)th term of the AP?
#ap
#nth term
#zero first term
A (104)
B (96)
C (108)
D (100)
Explanation opens after your attempt
Step 1
Concept
\(a_{26}=0+25\times4=100\). Even with zero first term, (n-1) differences are added.
Step 2
Why this answer is correct
The correct answer is D. (100). \(a_{26}=0+25\times4=100\). Even with zero first term, (n-1) differences are added.
Step 3
Exam Tip
\(a_{26}=0+25\times4=100\)। शून्य प्रथम पद होने पर भी (n-1) अंतर जुड़ते हैं।
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एक समांतर श्रेढ़ी में \(a_1=13\) और (d=8) है। (10)वाँ पद क्या है?
In an AP, \(a_1=13\) and (d=8). What is the (10)th term?
#ap
#nth term
#first term
A (85)
B (93)
C (80)
D (77)
Explanation opens after your attempt
Step 1
Concept
\(a_{10}=13+9\times8=85\). \(a_1\) is the first term (a).
Step 2
Why this answer is correct
The correct answer is A. (85). \(a_{10}=13+9\times8=85\). \(a_1\) is the first term (a).
Step 3
Exam Tip
\(a_{10}=13+9\times8=85\)। \(a_1\) ही प्रथम पद (a) होता है।
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यदि \(a_n=30-3n\) है, तो (6)वाँ पद क्या होगा?
If \(a_n=30-3n\), what will be the (6)th term?
#ap nth term
#general term
#decreasing
A (18)
B (9)
C (15)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(a_6=30-3\times6=12\). Be careful with subtraction in a decreasing general term.
Step 2
Why this answer is correct
The correct answer is D. (12). \(a_6=30-3\times6=12\). Be careful with subtraction in a decreasing general term.
Step 3
Exam Tip
\(a_6=30-3\times6=12\)। घटते हुए सामान्य पद में घटाव सावधानी से करें।
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यदि \(a_n=5n-1\) हो, तो इस समांतर श्रेढ़ी का (20)वाँ पद क्या है?
If \(a_n=5n-1\), what is the (20)th term of this AP?
#ap nth term
#general term
#easy
A (101)
B (99)
C (95)
D (104)
Explanation opens after your attempt
Step 1
Concept
\(a_{20}=5\times20-1=99\). When \(a_n\) is given, put the value of (n) in it.
Step 2
Why this answer is correct
The correct answer is B. (99). \(a_{20}=5\times20-1=99\). When \(a_n\) is given, put the value of (n) in it.
Step 3
Exam Tip
\(a_{20}=5\times20-1=99\)। जब \(a_n\) दिया हो, तो सूत्र में (n) का मान रखें।
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समांतर श्रेढ़ी \(-10,-6,-2,2,\ldots\) का (18)वाँ पद कौन सा है?
Which is the (18)th term of the AP \(-10,-6,-2,2,\ldots\)?
#ap
#nth term
#negative first term
A (54)
B (62)
C (58)
D (68)
Explanation opens after your attempt
Step 1
Concept
Here (a=-10), (d=4), so \(a_{18}=-10+17\times4=58\). The formula remains the same even when terms move from negative to positive.
Step 2
Why this answer is correct
The correct answer is C. (58). Here (a=-10), (d=4), so \(a_{18}=-10+17\times4=58\). The formula remains the same even when terms move from negative to positive.
Step 3
Exam Tip
यहाँ (a=-10), (d=4) है, इसलिए \(a_{18}=-10+17\times4=58\)। ऋणात्मक से धनात्मक जाने पर भी सूत्र समान रहता है।
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यदि (p(x)=x-2 +ax+4) का स्थिर पद (4) है, तो स्थिर पद कौन-सा है?
If the constant term of (p(x)=x-2 +ax+4) is (4), which term is the constant term?
#constant_term
#parameter
#polynomials
A \(x^2\)
B (ax)
C (4)
D (a)
Explanation opens after your attempt
Step 1
Concept
The constant term does not contain (x). So (4) is the constant term.
Step 2
Why this answer is correct
The correct answer is C. (4). The constant term does not contain (x). So (4) is the constant term.
Step 3
Exam Tip
स्थिर पद में (x) नहीं होता। इसलिए (4) स्थिर पद है।
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रेखीय संतुलन में मोटी छोटी रेखा और पतली लंबी रेखा का संबंध कैसे देखा जाता है?
How is the relation between a thick short line and a thin long line seen in linear balance?
#visual balance
#line weight
#length
A लंबी रेखा हमेशा भारी होती है / Long line is always heavier
B दोनों का दृश्य भार अलग तरीके से संतुलित हो सकता है / Their visual weights can balance in different ways
C मोटी रेखा कभी प्रभावी नहीं होती / Thick line is never effective
D संतुलन में रेखा का कोई काम नहीं / Line has no role in balance
Explanation opens after your attempt
Correct Answer
B. दोनों का दृश्य भार अलग तरीके से संतुलित हो सकता है / Their visual weights can balance in different ways
Step 1
Concept
Visual weight comes not only from length but also thickness and placement. Exam tip: consider multiple qualities together.
Step 2
Why this answer is correct
The correct answer is B. दोनों का दृश्य भार अलग तरीके से संतुलित हो सकता है / Their visual weights can balance in different ways. Visual weight comes not only from length but also thickness and placement. Exam tip: consider multiple qualities together.
Step 3
Exam Tip
दृश्य भार केवल लंबाई नहीं, मोटाई और स्थिति से भी बनता है। परीक्षा में कई गुण साथ देखें।
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राजघाट पर महात्मा गांधी की समाधि पर कौन सा छोटा वाक्य अंकित है?
Which short phrase is inscribed on Mahatma Gandhi's memorial at Raj Ghat?
#raj ghat
#mahatma gandhi
#hey ram
A हे राम / Hey Ram
B सत्यमेव जयते / Satyameva Jayate
C जय जवान / Jai Jawan
D वंदे मातरम् / Vande Mataram
Explanation opens after your attempt
Correct Answer
A. हे राम / Hey Ram
Step 1
Concept
The phrase Hey Ram at Raj Ghat is linked with Mahatma Gandhi's memory. For exams remember symbols and phrases of national memorials.
Step 2
Why this answer is correct
The correct answer is A. हे राम / Hey Ram. The phrase Hey Ram at Raj Ghat is linked with Mahatma Gandhi's memory. For exams remember symbols and phrases of national memorials.
Step 3
Exam Tip
राजघाट पर हे राम वाक्य महात्मा गांधी की स्मृति से जुड़ा है। परीक्षा में राष्ट्रीय स्मारकों के प्रतीक और वाक्य याद रखें।
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यदि \(\sqrt{2}\) की जगह \(\sqrt{8}\) पर विचार किया जाए, तो \(\sqrt{8}\) के अपरिमेय होने का सबसे सही छोटा तर्क क्या है?
If \(\sqrt{8}\) is considered instead of \(\sqrt{2}\), what is the best short reason that \(\sqrt{8}\) is irrational?
#real-numbers
#root2
#root8
#application
A \(\sqrt{8}=4\sqrt{2}\), इसलिए अपरिमेय है / \(\sqrt{8}=4\sqrt{2}\), so it is irrational
B \(\sqrt{8}=2\sqrt{2}\), और परिमेय (2) को अपरिमेय \(\sqrt{2}\) से गुणा करने पर अपरिमेय संख्या मिलती है / \(\sqrt{8}=2\sqrt{2}\), and multiplying irrational \(\sqrt{2}\) by nonzero rational (2) gives an irrational number
C \(\sqrt{8}=8\), इसलिए अपरिमेय है / \(\sqrt{8}=8\), so it is irrational
D \(\sqrt{8}\) पूर्ण वर्ग है / \(\sqrt{8}\) is a perfect square
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{8}=2\sqrt{2}\), और परिमेय (2) को अपरिमेय \(\sqrt{2}\) से गुणा करने पर अपरिमेय संख्या मिलती है / \(\sqrt{8}=2\sqrt{2}\), and multiplying irrational \(\sqrt{2}\) by nonzero rational (2) gives an irrational number
Step 1
Concept
\(\sqrt{8}=\sqrt{4\cdot2}=2\sqrt{2}\).
Step 2
Why this answer is correct
\(\sqrt{2}\) is irrational and (2) is a nonzero rational number, so \(2\sqrt{2}\) remains irrational.
Step 3
Exam Tip
Separate perfect-square factors while simplifying roots. चरण 1: \(\sqrt{8}=\sqrt{4\cdot2}=2\sqrt{2}\)। चरण 2: \(\sqrt{2}\) अपरिमेय है और (2) शून्येतर परिमेय है, इसलिए \(2\sqrt{2}\) अपरिमेय रहेगा। चरण 3: सरलीकरण में पूर्ण वर्ग गुणनखंड अलग करें।
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कौन सा विकल्प \(\sqrt{2}\) की सिद्धि का सही संक्षिप्त ढांचा देता है?
Which option gives the correct short structure of the proof of \(\sqrt{2}\)?
#sqrt2 proof
#proof structure
#class 10
A परिमेय मानें, वर्ग करें, दोनों सम पाएं, सहअभाज्य से विरोधाभास / Assume rational, square, find both even, contradict coprime
B वर्ग करें, दशमलव निकालें, उत्तर याद करें / Square, find decimal, memorize answer
C पूर्ण वर्ग मानें, हर शून्य करें, निष्कर्ष लें / Assume perfect square, make denominator zero, conclude
D परिमेय मानें, (p=q) लिखें, प्रमाण पूरा करें / Assume rational, write (p=q), finish proof
Explanation opens after your attempt
Correct Answer
A. परिमेय मानें, वर्ग करें, दोनों सम पाएं, सहअभाज्य से विरोधाभास / Assume rational, square, find both even, contradict coprime
Step 1
Concept
Assume \(\sqrt{2}\) rational and write it as \(\frac{p}{q}\).
Step 2
Why this answer is correct
Squaring leads to both (p) and (q) being even.
Step 3
Exam Tip
Both even contradict the coprime condition. चरण 1: \(\sqrt{2}\) को परिमेय मानकर \(\frac{p}{q}\) लिखते हैं। चरण 2: वर्ग करने पर दोनों (p) और (q) सम निकलते हैं। चरण 3: दोनों सम होना सहअभाज्य शर्त से विरोधाभास देता है।
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कौन सा विकल्प \(\sqrt{5}\) की अपरिमेयता का सही संक्षिप्त कारण है?
Which option is the correct short reason for the irrationality of \(\sqrt{5}\)?
#sqrt5 explanation
#irrationality
#class 10
A परिमेय मानने पर अंश और हर दोनों (5) से विभाज्य हो जाते हैं / Assuming rational makes both numerator and denominator divisible by (5)
B क्योंकि (5) पूर्ण वर्ग है / Because (5) is a perfect square
C क्योंकि \(\sqrt{5}=25\) है / Because \(\sqrt{5}=25\)
D क्योंकि हर अभाज्य संख्या का वर्गमूल परिमेय होता है / Because the square root of every prime number is rational
Explanation opens after your attempt
Correct Answer
A. परिमेय मानने पर अंश और हर दोनों (5) से विभाज्य हो जाते हैं / Assuming rational makes both numerator and denominator divisible by (5)
Step 1
Concept
We assume \(\sqrt{5}\) rational and write it in lowest form.
Step 2
Why this answer is correct
The proof shows numerator and denominator both divisible by (5).
Step 3
Exam Tip
This contradicts lowest form, so \(\sqrt{5}\) is irrational. चरण 1: \(\sqrt{5}\) को परिमेय मानकर सरलतम भिन्न में लिखते हैं। चरण 2: प्रमाण से अंश और हर दोनों (5) से विभाज्य मिलते हैं। चरण 3: यह सरलतम रूप के विरुद्ध है, इसलिए \(\sqrt{5}\) अपरिमेय है।
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कौन सा विकल्प \(\sqrt{3}\) की अपरिमेयता का सही संक्षिप्त कारण है?
Which option is the correct short reason for the irrationality of \(\sqrt{3}\)?
#sqrt3 explanation
#irrationality
#class 10
A परिमेय मानने पर अंश और हर दोनों (3) से विभाज्य हो जाते हैं / Assuming rational makes both numerator and denominator divisible by (3)
B क्योंकि (3) सम संख्या है / Because (3) is an even number
C क्योंकि \(\sqrt{3}=3\) है / Because \(\sqrt{3}=3\)
D क्योंकि (3) पूर्ण वर्ग है / Because (3) is a perfect square
Explanation opens after your attempt
Correct Answer
A. परिमेय मानने पर अंश और हर दोनों (3) से विभाज्य हो जाते हैं / Assuming rational makes both numerator and denominator divisible by (3)
Step 1
Concept
Assuming \(\sqrt{3}=\frac{a}{b}\) and squaring gives \(a^2=3b^2\).
Step 2
Why this answer is correct
This makes both (a) and (b) divisible by (3).
Step 3
Exam Tip
This is impossible in a lowest-form fraction. चरण 1: \(\sqrt{3}\) को \(\frac{a}{b}\) मानकर वर्ग करने पर \(a^2=3b^2\) मिलता है। चरण 2: इससे (a) और (b) दोनों (3) से विभाज्य हो जाते हैं। चरण 3: सरलतम भिन्न में ऐसा होना असंभव है।
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यदि शरीर में जल की कमी हो तो नेफ्रॉन में जल पुनः अवशोषण पर क्या प्रभाव होना चाहिए?
If the body is short of water, what should happen to water reabsorption in nephrons?
#nephron
#water-balance
#reabsorption
#urine
A जल का पुनः अवशोषण बढ़ेगा / Water reabsorption will increase
B जल का पुनः अवशोषण पूरी तरह बंद होगा / Water reabsorption will completely stop
C नेफ्रॉन भोजन पचाएगा / Nephrons will digest food
D गुर्दे ऑक्सीजन बनाएँगे / Kidneys will produce oxygen
Explanation opens after your attempt
Correct Answer
A. जल का पुनः अवशोषण बढ़ेगा / Water reabsorption will increase
Step 1
Concept
Kidneys help maintain water balance.
Step 2
Why this answer is correct
During water shortage, the body must conserve more water.
Step 3
Exam Tip
Nephrons can return more water to blood, making urine more concentrated. चरण 1: गुर्दे शरीर के जल संतुलन में सहायता करते हैं। चरण 2: जल की कमी में शरीर को अधिक जल बचाना होता है। चरण 3: इसलिए नेफ्रॉन अधिक जल वापस रक्त में भेज सकते हैं और मूत्र अधिक गाढ़ा हो सकता है।
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एक समान्तर श्रेणी का प्रथम पद (19) है और \(S_{15}=810\) है। (15)वाँ पद क्या होगा?
The first term of an arithmetic progression is (19) and \(S_{15}=810\). What is the (15)th term?
#ap
#last-term-from-sum
#expert
A (87)
B (89)
C (91)
D (93)
Explanation opens after your attempt
Step 1
Concept
From (810=\frac{15}{2}(19+l)), (l=89). Exam tip: when the last term is needed, the (a+l) form is fast.
Step 2
Why this answer is correct
The correct answer is B. (89). From (810=\frac{15}{2}(19+l)), (l=89). Exam tip: when the last term is needed, the (a+l) form is fast.
Step 3
Exam Tip
(810=\frac{15}{2}(19+l)) से (l=89) मिलता है। परीक्षा में अंतिम पद चाहिए हो तो (a+l) वाला सूत्र तेज है।
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एक समान्तर श्रेणी का (8)वाँ पद (31) और (20)वाँ पद (79) है। पहले (20) पदों का योग कितना होगा?
The (8)th term of an arithmetic progression is (31) and the (20)th term is (79). What is the sum of the first (20) terms?
#ap
#term-sum
#expert
A (900)
B (940)
C (980)
D (1020)
Explanation opens after your attempt
Step 1
Concept
From the two terms (d=4) and (a=3). Hence \(S_{20}=980\); exam tip: find (a) and (d) before applying the sum formula.
Step 2
Why this answer is correct
The correct answer is C. (980). From the two terms (d=4) and (a=3). Hence \(S_{20}=980\); exam tip: find (a) and (d) before applying the sum formula.
Step 3
Exam Tip
दो पदों से (d=4) और (a=3) मिलता है इसलिए \(S_{20}=980\)। परीक्षा में पहले (a) और (d) निकालें फिर योग लगाएं।
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यदि किसी समांतर श्रेढ़ी में \(S_{28}=2576\) और \(S_{14}=770\), तो (15)वें पद से (28)वें पद तक का योग क्या होगा?
If in an AP \(S_{28}=2576\) and \(S_{14}=770\), what is the sum from the (15)th term to the (28)th term?
#partial sums
#term block
#ap
A (1778)
B (1806)
C (1834)
D (1862)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{28}-S_{14}=1806\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 2
Why this answer is correct
The correct answer is B. (1806). The required sum is \(S_{28}-S_{14}=1806\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 3
Exam Tip
आवश्यक योग \(S_{28}-S_{14}=1806\) है। लगातार पदों का योग आंशिक योगों के अंतर से तुरंत मिलता है।
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समांतर श्रेढ़ी \(-40,-31,-22,\ldots\) में (25)वें पद से (60)वें पद तक का योग कितना है?
In the AP \(-40,-31,-22,\ldots\), what is the sum from the (25)th term to the (60)th term?
#range sum
#negative first term
#ap
A (11826)
B (12006)
C (12186)
D (12366)
Explanation opens after your attempt
Correct Answer
B. (12006)
Step 1
Concept
The required sum is \(S_{60}-S_{24}=12006\). When starting from the (25)th term, subtract the sum up to (24) terms.
Step 2
Why this answer is correct
The correct answer is B. (12006). The required sum is \(S_{60}-S_{24}=12006\). When starting from the (25)th term, subtract the sum up to (24) terms.
Step 3
Exam Tip
मांगा गया योग \(S_{60}-S_{24}=12006\) है। (25)वें पद से शुरू होने पर (24) पदों तक का योग घटाएँ।
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किसी समांतर श्रेढ़ी में पहले (30) पदों का योग (3000) है और (30)वाँ पद (150) है। पहला पद ज्ञात कीजिए।
In an AP, the sum of the first (30) terms is (3000), and the (30)th term is (150). Find the first term.
#first term
#last term
#sum
#ap
A (45)
B (50)
C (55)
D (60)
Explanation opens after your attempt
Step 1
Concept
From (3000=15(a+150)), (a=50). Treat the (n)th term as the last term of the first (n) terms.
Step 2
Why this answer is correct
The correct answer is B. (50). From (3000=15(a+150)), (a=50). Treat the (n)th term as the last term of the first (n) terms.
Step 3
Exam Tip
(3000=15(a+150)) से (a=50) मिलता है। (n)वें पद को पहले (n) पदों का अंतिम पद मानें।
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यदि किसी समांतर श्रेढ़ी में \(S_{24}=1560\) और \(S_{12}=456\), तो (13)वें पद से (24)वें पद तक का योग क्या होगा?
If in an AP \(S_{24}=1560\) and \(S_{12}=456\), what is the sum from the (13)th term to the (24)th term?
#partial sums
#term block
#ap
A (1080)
B (1104)
C (1128)
D (1152)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{24}-S_{12}=1104\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 2
Why this answer is correct
The correct answer is B. (1104). The required sum is \(S_{24}-S_{12}=1104\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 3
Exam Tip
आवश्यक योग \(S_{24}-S_{12}=1104\) है। लगातार पदों का योग आंशिक योगों के अंतर से तुरंत मिलता है।
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समांतर श्रेढ़ी \(-30,-22,-14,\ldots\) में (18)वें पद से (50)वें पद तक का योग कितना है?
In the AP \(-30,-22,-14,\ldots\), what is the sum from the (18)th term to the (50)th term?
#range sum
#negative first term
#ap
A (7656)
B (7788)
C (7722)
D (7854)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{50}-S_{17}=7722\). When starting from the (18)th term, subtract the sum up to (17) terms.
Step 2
Why this answer is correct
The correct answer is C. (7722). The required sum is \(S_{50}-S_{17}=7722\). When starting from the (18)th term, subtract the sum up to (17) terms.
Step 3
Exam Tip
मांगा गया योग \(S_{50}-S_{17}=7722\) है। (18)वें पद से शुरू होने पर (17) पदों तक का योग घटाएँ।
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किसी समांतर श्रेढ़ी में पहले (25) पदों का योग (1625) है और (25)वाँ पद (113) है। पहला पद ज्ञात कीजिए।
In an AP, the sum of the first (25) terms is (1625), and the (25)th term is (113). Find the first term.
#first term
#last term
#sum
#ap
A (17)
B (15)
C (19)
D (21)
Explanation opens after your attempt
Step 1
Concept
From (1625=\frac{25}{2}(a+113)), (a=17). Treat the (n)th term as the last term of the first (n) terms.
Step 2
Why this answer is correct
The correct answer is A. (17). From (1625=\frac{25}{2}(a+113)), (a=17). Treat the (n)th term as the last term of the first (n) terms.
Step 3
Exam Tip
(1625=\frac{25}{2}(a+113)) से (a=17) मिलता है। (n)वें पद को पहले (n) पदों का अंतिम पद मानें।
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यदि किसी समांतर श्रेढ़ी में \(S_{16}=880\) और \(S_8=280\), तो (9)वें पद से (16)वें पद तक का योग क्या होगा?
If in an AP \(S_{16}=880\) and \(S_8=280\), what is the sum from the (9)th term to the (16)th term?
#partial sums
#term block
#ap
A (600)
B (580)
C (620)
D (640)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{16}-S_8=600\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 2
Why this answer is correct
The correct answer is A. (600). The required sum is \(S_{16}-S_8=600\). The sum of consecutive terms is quickly found by subtracting partial sums.
Step 3
Exam Tip
आवश्यक योग \(S_{16}-S_8=600\) है। लगातार पदों का योग आंशिक योगों के अंतर से तुरंत मिलता है।
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समांतर श्रेढ़ी \(-4,2,8,\ldots\) में (20)वें पद से (45)वें पद तक का योग कितना है?
In the AP \(-4,2,8,\ldots\), what is the sum from the (20)th term to the (45)th term?
#range sum
#negative first term
#ap
A (4720)
B (4810)
C (4900)
D (4990)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{45}-S_{19}=4810\). When starting from the (20)th term, subtract the sum up to (19) terms.
Step 2
Why this answer is correct
The correct answer is B. (4810). The required sum is \(S_{45}-S_{19}=4810\). When starting from the (20)th term, subtract the sum up to (19) terms.
Step 3
Exam Tip
मांगा गया योग \(S_{45}-S_{19}=4810\) है। (20)वें पद से शुरू होने पर (19) पदों तक का योग घटाएँ।
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यदि किसी समांतर श्रेढ़ी में \(S_{15}=465\) और \(S_{10}=240\), तो (11)वें पद से (15)वें पद तक का योग क्या होगा?
If in an AP \(S_{15}=465\) and \(S_{10}=240\), what is the sum from the (11)th term to the (15)th term?
#partial sums
#term block
#ap
A (205)
B (215)
C (235)
D (225)
Explanation opens after your attempt
Step 1
Concept
The required sum is \(S_{15}-S_{10}=225\). The sum of a consecutive block is found by subtracting partial sums.
Step 2
Why this answer is correct
The correct answer is D. (225). The required sum is \(S_{15}-S_{10}=225\). The sum of a consecutive block is found by subtracting partial sums.
Step 3
Exam Tip
आवश्यक योग \(S_{15}-S_{10}=225\) है। लगातार खंड का योग partial sums के अंतर से मिलता है।
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यदि किसी समांतर श्रेढ़ी का पहला पद (11), अंतिम पद (71) और योग (574) है, तो पदों की संख्या क्या है?
If an AP has first term (11), last term (71), and sum (574), what is the number of terms?
#find number of terms
#last term
#sum
A (12)
B (13)
C (14)
D (15)
Explanation opens after your attempt
Step 1
Concept
From (\frac{n}{2}(11+71)=574), (n=14). When the last term is given, the common difference is not needed.
Step 2
Why this answer is correct
The correct answer is C. (14). From (\frac{n}{2}(11+71)=574), (n=14). When the last term is given, the common difference is not needed.
Step 3
Exam Tip
(\frac{n}{2}(11+71)=574) से (n=14) मिलता है। अंतिम पद दिए होने पर सार्व अंतर की जरूरत नहीं होती।
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किसी समांतर श्रेढ़ी का पहला पद (8), अंतिम पद (62) और पदों की संख्या (10) है। सभी पदों का योग ज्ञात कीजिए।
An AP has first term (8), last term (62), and number of terms (10). Find the sum of all terms.
#first last term
#ap sum
#class 10
A (350)
B (360)
C (370)
D (340)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), the sum is (350). When the last term is given, this formula is faster.
Step 2
Why this answer is correct
The correct answer is A. (350). Using (S_n=\frac{n}{2}(a+l)), the sum is (350). When the last term is given, this formula is faster.
Step 3
Exam Tip
सूत्र (S_n=\frac{n}{2}(a+l)) से योग (350) आता है। जब अंतिम पद दिया हो तो यह सूत्र जल्दी काम करता है।
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