100 results found for "Geometric Progression" in Class 10.
किस स्थिति में ज्यामितीय आकार भाव को कमजोर कर सकते हैं?
In which situation can geometric shapes weaken the mood?
#geometric shape
#organic form
#nature
A मशीन का पोस्टर बनाते समय / While making a machine poster
B यातायात संकेत बनाते समय / While making a traffic sign
C प्राकृतिक बादलों की मुक्तता दिखाते समय / While showing freedom of natural clouds
D इमारत की योजना बनाते समय / While making a building plan
Explanation opens after your attempt
Correct Answer
C. प्राकृतिक बादलों की मुक्तता दिखाते समय / While showing freedom of natural clouds
Step 1
Concept
Cloud-like subjects need organic and irregular forms. Exam tip: connect shape with nature of subject.
Step 2
Why this answer is correct
The correct answer is C. प्राकृतिक बादलों की मुक्तता दिखाते समय / While showing freedom of natural clouds. Cloud-like subjects need organic and irregular forms. Exam tip: connect shape with nature of subject.
Step 3
Exam Tip
बादल जैसे विषय जैविक और अनियमित रूप मांगते हैं। परीक्षा में आकार को विषय के स्वभाव से जोड़ें।
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एक ही विषय में ज्यामितीय और जैविक आकार साथ रखने से क्या गहरा प्रभाव बन सकता है?
What deeper effect can be created by placing geometric and organic shapes together in one subject?
#shape contrast
#geometric organic
#symbolism
A प्रकृति और मानव निर्मित व्यवस्था का विरोध / Contrast between nature and human-made order
B रंगत्व का अभाव / Absence of hue
C कागज का भार / Paper weight
D स्पर्श बनावट / Tactile texture
Explanation opens after your attempt
Correct Answer
A. प्रकृति और मानव निर्मित व्यवस्था का विरोध / Contrast between nature and human-made order
Step 1
Concept
Contrast of two shape types can create meaning. Exam tip: connect shape contrast with symbolism.
Step 2
Why this answer is correct
The correct answer is A. प्रकृति और मानव निर्मित व्यवस्था का विरोध / Contrast between nature and human-made order. Contrast of two shape types can create meaning. Exam tip: connect shape contrast with symbolism.
Step 3
Exam Tip
दो आकार वर्गों का विरोध अर्थ बना सकता है। परीक्षा में shape contrast को symbolism से जोड़ें।
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किस स्थिति में ज्यामितीय आकारों का अधिक उपयोग विषय को अधिक प्रभावी बनाएगा?
In which situation will heavy use of geometric shapes make the subject more effective?
#geometric shapes
#technology
#poster
A विज्ञान और तकनीक पर आधारित पोस्टर में / In a science and technology poster
B जंगल की अनियमित झाड़ियों में / In irregular forest bushes
C बादलों की प्राकृतिक आकृति में / In natural cloud shapes
D पानी की मुक्त लहरों में / In free water waves
Explanation opens after your attempt
Correct Answer
A. विज्ञान और तकनीक पर आधारित पोस्टर में / In a science and technology poster
Step 1
Concept
Geometric shapes give order and technical feeling. Exam tip: choose shapes based on subject.
Step 2
Why this answer is correct
The correct answer is A. विज्ञान और तकनीक पर आधारित पोस्टर में / In a science and technology poster. Geometric shapes give order and technical feeling. Exam tip: choose shapes based on subject.
Step 3
Exam Tip
ज्यामितीय आकार व्यवस्था और तकनीकी भाव देते हैं। परीक्षा में subject based shape selection करें।
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किस स्थिति में जैविक आकारों की तुलना में ज्यामितीय आकार अधिक अर्थपूर्ण होंगे?
In which situation will geometric shapes be more meaningful than organic shapes?
#geometric shape
#technology
#discipline
A प्रकृति का नरम दृश्य / Soft nature scene
B तकनीक और अनुशासन दिखाने वाला पोस्टर / Poster showing technology and discipline
C बादलों का मुक्त अध्ययन / Free study of clouds
D फूलों का प्राकृतिक चित्र / Natural drawing of flowers
Explanation opens after your attempt
Correct Answer
B. तकनीक और अनुशासन दिखाने वाला पोस्टर / Poster showing technology and discipline
Step 1
Concept
Geometric shapes give order and technical mood. Exam tip: choose shape category according to subject.
Step 2
Why this answer is correct
The correct answer is B. तकनीक और अनुशासन दिखाने वाला पोस्टर / Poster showing technology and discipline. Geometric shapes give order and technical mood. Exam tip: choose shape category according to subject.
Step 3
Exam Tip
ज्यामितीय आकार व्यवस्था और तकनीकी भाव देते हैं। परीक्षा में subject के अनुसार shape category चुनें।
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ज्यामितीय और जैविक आकारों को साथ रखने से रचना में कौन सा गुण बढ़ता है?
Which quality increases in composition by placing geometric and organic shapes together?
#geometric shape
#organic shape
#variety
A विविधता / Variety
B कागज की मोटाई / Paper thickness
C सिर्फ रंगत्व / Only hue
D पूर्ण एकरसता / Complete monotony
Explanation opens after your attempt
Correct Answer
A. विविधता / Variety
Step 1
Concept
Two different types of shapes increase visual interest and variety. Exam tip: connect shape contrast with variety.
Step 2
Why this answer is correct
The correct answer is A. विविधता / Variety. Two different types of shapes increase visual interest and variety. Exam tip: connect shape contrast with variety.
Step 3
Exam Tip
दो अलग प्रकार के आकार दृश्य रुचि और विविधता बढ़ाते हैं। परीक्षा में shape contrast को variety से जोड़ें।
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ज्यामितीय आकारों से बना पोस्टर किस भाव को अधिक दे सकता है?
A poster made with geometric shapes can give more of which feeling?
#geometric shapes
#order
#poster
A अनियमित प्राकृतिकता / Irregular naturalness
B व्यवस्था और स्पष्टता / Order and clarity
C सिर्फ धुंधलापन / Only blur
D कांटेदार सतह / Thorny surface
Explanation opens after your attempt
Correct Answer
B. व्यवस्था और स्पष्टता / Order and clarity
Step 1
Concept
Geometric shapes are regular and clear. Exam tip: connect geometric shapes with order.
Step 2
Why this answer is correct
The correct answer is B. व्यवस्था और स्पष्टता / Order and clarity. Geometric shapes are regular and clear. Exam tip: connect geometric shapes with order.
Step 3
Exam Tip
ज्यामितीय आकार नियमित और स्पष्ट होते हैं। परीक्षा में geometric shapes को order से जोड़ें।
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यदि ज्यामितीय और जैविक आकार साथ रखे जाएं तो क्या बन सकता है?
What can be created when geometric and organic shapes are placed together?
#geometric organic
#shape contrast
#variety
A सिर्फ एकरसता / Only monotony
B रंग का नाम / Colour name
C विविधता और विरोध / Variety and contrast
D कागज की कीमत / Paper price
Explanation opens after your attempt
Correct Answer
C. विविधता और विरोध / Variety and contrast
Step 1
Concept
Different types of shapes create variety and visual interest. Exam tip: connect shape contrast with variety.
Step 2
Why this answer is correct
The correct answer is C. विविधता और विरोध / Variety and contrast. Different types of shapes create variety and visual interest. Exam tip: connect shape contrast with variety.
Step 3
Exam Tip
अलग प्रकार के आकार विविधता और दृश्य रुचि बनाते हैं। परीक्षा में shape contrast को variety से जोड़ें।
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पोस्टर में सरल ज्यामितीय आकारों का प्रयोग क्यों प्रभावी होता है?
Why is the use of simple geometric shapes effective in a poster?
#poster
#geometric shape
#clarity
A वे पढ़ने में बाधा बनते हैं / They create reading problem
B वे हमेशा छिप जाते हैं / They always get hidden
C वे दूर से साफ और जल्दी पहचाने जाते हैं / They are clear and quickly recognized from distance
D वे रंग नष्ट करते हैं / They destroy colour
Explanation opens after your attempt
Correct Answer
C. वे दूर से साफ और जल्दी पहचाने जाते हैं / They are clear and quickly recognized from distance
Step 1
Concept
Simple shapes remain clear even from distance. Exam tip: give importance to clarity in poster design.
Step 2
Why this answer is correct
The correct answer is C. वे दूर से साफ और जल्दी पहचाने जाते हैं / They are clear and quickly recognized from distance. Simple shapes remain clear even from distance. Exam tip: give importance to clarity in poster design.
Step 3
Exam Tip
सरल आकार दूर से भी स्पष्ट दिखते हैं। परीक्षा में poster design में clarity को महत्व दें।
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किस कारण से वर्ग को ज्यामितीय आकार कहा जाता है?
Why is a square called a geometric shape?
#geometric shape
#square
#regular
A क्योंकि वह हमेशा लाल होता है / Because it is always red
B क्योंकि उसमें सतह छू सकते हैं / Because its surface can be touched
C क्योंकि उसकी भुजाएं और कोण नियमित होते हैं / Because its sides and angles are regular
D क्योंकि वह केवल छाया है / Because it is only shadow
Explanation opens after your attempt
Correct Answer
C. क्योंकि उसकी भुजाएं और कोण नियमित होते हैं / Because its sides and angles are regular
Step 1
Concept
A square is a regular rule-based shape. Exam tip: treat measured and regular shapes as geometric.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि उसकी भुजाएं और कोण नियमित होते हैं / Because its sides and angles are regular. A square is a regular rule-based shape. Exam tip: treat measured and regular shapes as geometric.
Step 3
Exam Tip
वर्ग नियमित नियमों वाला आकार है। परीक्षा में measured and regular shapes को geometric मानें।
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किस विकल्प में ज्यामितीय आकारों का समूह है?
Which option is a group of geometric shapes?
#geometric shapes
#square circle triangle
A पत्ती बादल धुआं / Leaf cloud smoke
B कपड़ा पानी लहर / Cloth water wave
C बाल फर शाखा / Hair fur branch
D वर्ग वृत्त त्रिभुज / Square circle triangle
Explanation opens after your attempt
Correct Answer
D. वर्ग वृत्त त्रिभुज / Square circle triangle
Step 1
Concept
Square circle and triangle are regular geometric shapes. Exam tip: remember measured shapes as geometric.
Step 2
Why this answer is correct
The correct answer is D. वर्ग वृत्त त्रिभुज / Square circle triangle. Square circle and triangle are regular geometric shapes. Exam tip: remember measured shapes as geometric.
Step 3
Exam Tip
वर्ग वृत्त और त्रिभुज नियमित ज्यामितीय आकार हैं। परीक्षा में मापित आकारों को ज्यामितीय याद रखें।
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ज्यामितीय आकार की पहचान किससे होती है?
How is a geometric shape identified?
#geometric shape
#regular
#shape
A नियमित और माप योग्य रूपरेखा से / By regular and measurable outline
B केवल प्राकृतिक पत्ती से / Only by a natural leaf
C सिर्फ धुंधले रंग से / Only by dull colour
D बिना किसी सीमा से / By no boundary
Explanation opens after your attempt
Correct Answer
A. नियमित और माप योग्य रूपरेखा से / By regular and measurable outline
Step 1
Concept
Geometric shapes are based on regular rules. Exam tip: remember square circle and triangle.
Step 2
Why this answer is correct
The correct answer is A. नियमित और माप योग्य रूपरेखा से / By regular and measurable outline. Geometric shapes are based on regular rules. Exam tip: remember square circle and triangle.
Step 3
Exam Tip
ज्यामितीय आकार नियमित नियमों पर आधारित होते हैं। परीक्षा में वर्ग वृत्त और त्रिभुज याद रखें।
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संख्या रेखा पर \( \sqrt{2} \) बनाने की ज्यामितीय विधि में किस लंबाई को कर्ण के रूप में लिया जाता है?
In the geometric construction of \( \sqrt{2} \) on the number line, which length is taken as the hypotenuse?
#number-line
#geometric-construction
#square-root
A \( \sqrt{1^2+1^2}\)
B (1+1)
C \( \sqrt{2^2+2^2}\)
D \(2^2\)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{1^2+1^2}\)
Step 1
Concept
With perpendicular sides (1) and (1), the hypotenuse is \( \sqrt{2}\). Understand the construction using Pythagoras theorem.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{1^2+1^2}\). With perpendicular sides (1) and (1), the hypotenuse is \( \sqrt{2}\). Understand the construction using Pythagoras theorem.
Step 3
Exam Tip
समकोण त्रिभुज में भुजाएँ (1) और (1) लेने पर कर्ण \( \sqrt{2}\) होता है। पायथागोरस प्रमेय से निर्माण समझें।
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किसी समांतर श्रेणी में पहले और अंतिम पद का योग (144) है और कुल पद (18) हैं। श्रेणी का योग कितना होगा?
In an arithmetic progression, the sum of the first and last terms is (144), and there are (18) terms. What will be the sum of the progression?
#first_last_sum
#ap_sum
#formula
A (1276)
B (1286)
C (1296)
D (1306)
Explanation opens after your attempt
Step 1
Concept
Using (S_n=\frac{n}{2}(a+l)), \(S_{18}=\frac{18}{2}\times144=1296\). If (a+l) is directly given, use it immediately.
Step 2
Why this answer is correct
The correct answer is C. (1296). Using (S_n=\frac{n}{2}(a+l)), \(S_{18}=\frac{18}{2}\times144=1296\). If (a+l) is directly given, use it immediately.
Step 3
Exam Tip
(S_n=\frac{n}{2}(a+l)) से \(S_{18}=\frac{18}{2}\times144=1296\)। (a+l) सीधे दिया हो तो उसे तुरंत उपयोग करें।
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यदि (5a-2, 3a+6, a+18) अंकगणितीय श्रेणी में हैं तो सार्व अंतर क्या होगा?
If (5a-2, 3a+6, a+18) are in an arithmetic progression, what will be the common difference?
#arithmetic progression
#no solution
#algebraic check
#hard
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(2(3a+6)=(5a-2)+(a+18)) gives (a=2). Then the terms (8,12,20) do not have equal differences, so no arithmetic progression is formed.
Step 2
Why this answer is correct
The correct answer is B. (4). (2(3a+6)=(5a-2)+(a+18)) gives (a=2). Then the terms (8,12,20) do not have equal differences, so no arithmetic progression is formed.
Step 3
Exam Tip
(2(3a+6)=(5a-2)+(a+18)) से (a=2) मिलता है। तब पद (8,12,20) नहीं बल्कि (8,12,20) समान अंतर नहीं देते, इसलिए सही जांच से कोई अंकगणितीय श्रेणी नहीं बनती।
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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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किस विकल्प में क्रम समांतर श्रेणी नहीं है, हालांकि पहले दो अंतर बराबर हैं?
In which option is the sequence not an arithmetic progression although the first two differences are equal?
#arithmetic progression
#common difference
#class 10
A (2, 6, 10, 14)
B (5, 9, 13, 20)
C (1, 1, 1, 1)
D (-3, 0, 3, 6)
Explanation opens after your attempt
Correct Answer
B. (5, 9, 13, 20)
Step 1
Concept
In (5,9,13,20), the first two differences are (4,4), but the third difference is (7). It is necessary to check all consecutive differences.
Step 2
Why this answer is correct
The correct answer is B. (5, 9, 13, 20). In (5,9,13,20), the first two differences are (4,4), but the third difference is (7). It is necessary to check all consecutive differences.
Step 3
Exam Tip
(5,9,13,20) में पहले दो अंतर (4,4) हैं लेकिन तीसरा अंतर (7) है। सभी लगातार अंतर जांचना जरूरी है।
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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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किस (k) के लिए (k+7, 2k+3, 4k-5) समांतर श्रेणी है?
For which (k) is (k+7, 2k+3, 4k-5) an arithmetic progression?
#arithmetic progression
#common difference
#class 10
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The differences are (k-4) and (2k-8). Equating them gives (k=4).
Step 2
Why this answer is correct
The correct answer is C. (4). The differences are (k-4) and (2k-8). Equating them gives (k=4).
Step 3
Exam Tip
अंतर (k-4) और (2k-8) हैं। बराबर करने पर (k=4) मिलता है।
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यदि (x-5, x+3, x+11, x+19) समांतर श्रेणी है, तो पहले दो पदों का अंतर और अंतिम दो पदों का अंतर क्या है?
If (x-5, x+3, x+11, x+19) is an arithmetic progression, what are the differences of the first two and last two terms?
#arithmetic progression
#common difference
#class 10
A (8) और (8) / (8) and (8)
B (6) और (10) / (6) and (10)
C (x) और (8) / (x) and (8)
D (8x) और (8x) / (8x) and (8x)
Explanation opens after your attempt
Correct Answer
A. (8) और (8) / (8) and (8)
Step 1
Concept
Every consecutive difference is (8), and (x) cancels out. For terms with the same variable part, compare the constant parts.
Step 2
Why this answer is correct
The correct answer is A. (8) और (8) / (8) and (8). Every consecutive difference is (8), and (x) cancels out. For terms with the same variable part, compare the constant parts.
Step 3
Exam Tip
हर लगातार अंतर (8) है और (x) कट जाता है। समान चर वाले पदों में स्थिर भाग का अंतर देखें।
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किस (y) के लिए (5y+2, 3y+10, y+18) समांतर श्रेणी में हैं?
For which (y) are (5y+2, 3y+10, y+18) in an arithmetic progression?
#arithmetic progression
#common difference
#class 10
A हर (y) के लिए / For every (y)
B केवल (y=0) / Only (y=0)
C केवल (y=4) / Only (y=4)
D किसी भी (y) के लिए नहीं / For no (y)
Explanation opens after your attempt
Correct Answer
A. हर (y) के लिए / For every (y)
Step 1
Concept
The first difference is (-2y+8), and the second difference is also (-2y+8). They are equal for every (y).
Step 2
Why this answer is correct
The correct answer is A. हर (y) के लिए / For every (y). The first difference is (-2y+8), and the second difference is also (-2y+8). They are equal for every (y).
Step 3
Exam Tip
पहला अंतर (-2y+8) और दूसरा अंतर (-2y+8) है। दोनों हर (y) के लिए बराबर हैं।
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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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यदि (10, 10+d, 10+2d, 10+4d) समांतर श्रेणी है, तो कौन-सा निष्कर्ष सही है?
If (10, 10+d, 10+2d, 10+4d) is an arithmetic progression, which conclusion is correct?
#arithmetic progression
#common difference
#class 10
A (d=0)
B (d=2)
C (d=4)
D (d) कोई भी वास्तविक संख्या / (d) can be any real number
Explanation opens after your attempt
Step 1
Concept
The differences are (d, d, 2d). All three are equal only when (d=0).
Step 2
Why this answer is correct
The correct answer is A. (d=0). The differences are (d, d, 2d). All three are equal only when (d=0).
Step 3
Exam Tip
अंतर (d, d, 2d) हैं। तीनों बराबर तभी होंगे जब (d=0).
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यदि (2, x+1, 3x+4, 5x+7) समांतर श्रेणी है, तो (x) का मान क्या है?
If (2, x+1, 3x+4, 5x+7) is an arithmetic progression, what is the value of (x)?
#arithmetic progression
#common difference
#class 10
A यह (x=0) पर संभव है / It is possible at (x=0)
B यह (x=1) पर संभव है / It is possible at (x=1)
C यह (x=2) पर संभव है / It is possible at (x=2)
D ऐसा कोई (x) नहीं है / No such (x) exists
Explanation opens after your attempt
Correct Answer
D. ऐसा कोई (x) नहीं है / No such (x) exists
Step 1
Concept
The differences are (x-1, 2x+3, 2x+3). Equating the first two gives (x=-4), but then all differences do not stay equal.
Step 2
Why this answer is correct
The correct answer is D. ऐसा कोई (x) नहीं है / No such (x) exists. The differences are (x-1, 2x+3, 2x+3). Equating the first two gives (x=-4), but then all differences do not stay equal.
Step 3
Exam Tip
अंतर (x-1, 2x+3, 2x+3) हैं। पहले दो बराबर करने पर (x=-4), लेकिन तब सभी अंतर बराबर नहीं बनते।
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किस (a) के लिए (a+4, 2a+1, 5a-8) समांतर श्रेणी है?
For which (a) is (a+4, 2a+1, 5a-8) an arithmetic progression?
#arithmetic progression
#common difference
#class 10
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The differences are (a-3) and (3a-9). Equating them gives (a=3).
Step 2
Why this answer is correct
The correct answer is C. (3). The differences are (a-3) and (3a-9). Equating them gives (a=3).
Step 3
Exam Tip
अंतर (a-3) और (3a-9) हैं। बराबर करने पर (a=3) मिलता है।
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यदि (a, b, c) समांतर श्रेणी में हैं, तो (a-2b+c) का मान क्या होगा?
If (a, b, c) are in an arithmetic progression, what is the value of (a-2b+c)?
#arithmetic progression
#common difference
#class 10
A (-1)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
In an arithmetic progression, (2b=a+c). Therefore (a-2b+c=0).
Step 2
Why this answer is correct
The correct answer is B. (0). In an arithmetic progression, (2b=a+c). Therefore (a-2b+c=0).
Step 3
Exam Tip
समांतर श्रेणी में (2b=a+c). इसलिए (a-2b+c=0).
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यदि (5-2t, 7-t, 12+t) समांतर श्रेणी में हैं, तो (t) का मान क्या है?
If (5-2t, 7-t, 12+t) are in an arithmetic progression, what is the value of (t)?
#arithmetic progression
#common difference
#class 10
A (-3)
B (-2)
C (1)
D (3)
Explanation opens after your attempt
Step 1
Concept
The differences are not (t+2) and (t+5); the correct second difference is (5+2t). From (t+2=5+2t), (t=-3).
Step 2
Why this answer is correct
The correct answer is A. (-3). The differences are not (t+2) and (t+5); the correct second difference is (5+2t). From (t+2=5+2t), (t=-3).
Step 3
Exam Tip
अंतर (t+2) और (t+5) नहीं, सही दूसरा अंतर (5+2t) है। (t+2=5+2t) से (t=-3).
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यदि (1, 1+2p, 1+5p, 1+9p) समांतर श्रेणी है, तो (p) के बारे में सही बात क्या है?
If (1, 1+2p, 1+5p, 1+9p) is an arithmetic progression, what is correct about (p)?
#arithmetic progression
#common difference
#class 10
A (p=0)
B (p=1)
C (p=2)
D (p) कोई भी वास्तविक संख्या / (p) can be any real number
Explanation opens after your attempt
Step 1
Concept
The differences are (2p, 3p, 4p). They are equal only when (p=0).
Step 2
Why this answer is correct
The correct answer is A. (p=0). The differences are (2p, 3p, 4p). They are equal only when (p=0).
Step 3
Exam Tip
अंतर (2p, 3p, 4p) हैं। ये बराबर केवल (p=0) पर होंगे।
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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 (s) पर \(\frac{s}{2}, s+3, 3s-1\) समांतर श्रेणी बनेगी?
For which (s) will \(\frac{s}{2}, s+3, 3s-1\) form an arithmetic progression?
#arithmetic progression
#common difference
#class 10
A (4)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
The first difference is \(\frac{s}{2}+3\), and the second is (2s-4). Equating them gives (s=8).
Step 2
Why this answer is correct
The correct answer is C. (8). The first difference is \(\frac{s}{2}+3\), and the second is (2s-4). Equating them gives (s=8).
Step 3
Exam Tip
पहला अंतर \(\frac{s}{2}+3\) और दूसरा अंतर (2s-4) है। बराबर करने पर (s=8) मिलता है।
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यदि (x, x+6, 3x-2) समांतर श्रेणी में हैं, तो (x) का सही मान क्या है?
If (x, x+6, 3x-2) are in an arithmetic progression, what is the correct value of (x)?
#arithmetic progression
#common difference
#class 10
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The differences (6) and (2x-8) must be equal. Thus (2x-8=6), giving (x=7).
Step 2
Why this answer is correct
The correct answer is C. (7). The differences (6) and (2x-8) must be equal. Thus (2x-8=6), giving (x=7).
Step 3
Exam Tip
अंतर (6) और (2x-8) बराबर होने चाहिए। इसलिए (2x-8=6) से (x=7).
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यदि (x, x+6, 3x-2) समांतर श्रेणी में हैं, तो तीसरा पद क्या है?
If (x, x+6, 3x-2) are in an arithmetic progression, what is the third term?
#arithmetic progression
#common difference
#class 10
A (14)
B (16)
C (18)
D (20)
Explanation opens after your attempt
Step 1
Concept
From (2(x+6)=x+(3x-2)), (x=7). The third term is (3x-2=19), so none of the options is correct.
Step 2
Why this answer is correct
The correct answer is B. (16). From (2(x+6)=x+(3x-2)), (x=7). The third term is (3x-2=19), so none of the options is correct.
Step 3
Exam Tip
(2(x+6)=x+(3x-2)) से (x=9). तीसरा पद (3x-2=25) नहीं, इसलिए विकल्पों में सही मान नहीं 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 (2, 5, 10, 17) को समांतर श्रेणी कहा जाए, तो सही जांच क्या बताती है?
If (2, 5, 10, 17) is called an arithmetic progression, what does the correct check show?
#arithmetic progression
#common difference
#class 10
A यह समांतर श्रेणी है क्योंकि सभी पद बढ़ रहे हैं / It is an arithmetic progression because all terms increase
B यह समांतर श्रेणी है क्योंकि अंतर धनात्मक हैं / It is an arithmetic progression because differences are positive
C यह समांतर श्रेणी नहीं है क्योंकि अंतर (3,5,7) हैं / It is not an arithmetic progression because the differences are (3,5,7)
D यह समांतर श्रेणी नहीं है क्योंकि पहला पद छोटा है / It is not an arithmetic progression because the first term is small
Explanation opens after your attempt
Correct Answer
C. यह समांतर श्रेणी नहीं है क्योंकि अंतर (3,5,7) हैं / It is not an arithmetic progression because the differences are (3,5,7)
Step 1
Concept
For an arithmetic progression, every consecutive difference must be equal. Here (3,5,7) are not equal.
Step 2
Why this answer is correct
The correct answer is C. यह समांतर श्रेणी नहीं है क्योंकि अंतर (3,5,7) हैं / It is not an arithmetic progression because the differences are (3,5,7). For an arithmetic progression, every consecutive difference must be equal. Here (3,5,7) are not equal.
Step 3
Exam Tip
समांतर श्रेणी के लिए हर लगातार अंतर समान होना चाहिए। यहाँ (3,5,7) समान नहीं हैं।
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क्रम (81, 27, 9, 3) को समांतर श्रेणी मानने में कौन-सी गलती होगी?
What mistake is made if (81, 27, 9, 3) is considered an arithmetic progression?
#arithmetic progression
#common difference
#class 10
A पद घट रहे हैं / The terms are decreasing
B अनुपात समान है, अंतर समान नहीं / The ratio is constant, not the difference
C पहला पद बड़ा है / The first term is large
D सभी पद पूर्णांक हैं / All terms are integers
Explanation opens after your attempt
Correct Answer
B. अनुपात समान है, अंतर समान नहीं / The ratio is constant, not the difference
Step 1
Concept
This sequence has ratio \(\frac{1}{3}\), but differences (-54, -18, -6) are not equal. In an arithmetic progression, check difference, not ratio.
Step 2
Why this answer is correct
The correct answer is B. अनुपात समान है, अंतर समान नहीं / The ratio is constant, not the difference. This sequence has ratio \(\frac{1}{3}\), but differences (-54, -18, -6) are not equal. In an arithmetic progression, check difference, not ratio.
Step 3
Exam Tip
इस क्रम में अनुपात \(\frac{1}{3}\) है, पर अंतर (-54, -18, -6) बराबर नहीं हैं। समांतर श्रेणी में अनुपात नहीं, अंतर देखें।
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यदि (3z, z+10, 22-z) समांतर श्रेणी में हैं, तो पहला पद क्या है?
If (3z, z+10, 22-z) are in an arithmetic progression, what is the first term?
#arithmetic progression
#common difference
#class 10
A (6)
B (9)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
From (2(z+10)=3z+(22-z)), (z=4). The first term is (3z=12).
Step 2
Why this answer is correct
The correct answer is C. (12). From (2(z+10)=3z+(22-z)), (z=4). The first term is (3z=12).
Step 3
Exam Tip
(2(z+10)=3z+(22-z)) से (z=4). पहला पद (3z=12) है।
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किस (n) पर (n+2, 2n+5, 4n+8) समांतर श्रेणी बनेगी?
For which (n) will (n+2, 2n+5, 4n+8) form an arithmetic progression?
#arithmetic progression
#common difference
#class 10
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
The consecutive differences are (n+3) and (2n+3). Equating them gives (n=0).
Step 2
Why this answer is correct
The correct answer is A. (0). The consecutive differences are (n+3) and (2n+3). Equating them gives (n=0).
Step 3
Exam Tip
लगातार अंतर (n+3) और (2n+3) हैं। बराबर करने पर (n=0) 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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क्रम (2, 2+k, 2+4k, 2+9k) समांतर श्रेणी हो सकता है। किस शर्त पर?
The sequence (2, 2+k, 2+4k, 2+9k) can be an arithmetic progression. Under what condition?
#arithmetic progression
#common difference
#class 10
A (k=0)
B (k=1)
C (k=2)
D (k=-1)
Explanation opens after your attempt
Step 1
Concept
The differences are (k, 3k, 5k). They are all equal only when (k=0).
Step 2
Why this answer is correct
The correct answer is A. (k=0). The differences are (k, 3k, 5k). They are all equal only when (k=0).
Step 3
Exam Tip
अंतर (k, 3k, 5k) हैं। ये सभी बराबर केवल (k=0) पर होंगे।
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यदि (u, v, w) समांतर श्रेणी में हैं और (u+w=48), तो (v) का मान क्या है?
If (u, v, w) are in an arithmetic progression and (u+w=48), what is the value of (v)?
#arithmetic progression
#common difference
#class 10
A (16)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
In a three-term arithmetic progression, (2v=u+w). Therefore (v=24).
Step 2
Why this answer is correct
The correct answer is D. (24). In a three-term arithmetic progression, (2v=u+w). Therefore (v=24).
Step 3
Exam Tip
तीन पदों वाली समांतर श्रेणी में (2v=u+w). इसलिए (v=24).
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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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यदि किसी समांतर श्रेणी के पद (a, a+d, a+2d) हैं और (a+d=0), तो पहले और तीसरे पद का योग क्या होगा?
If the terms of an arithmetic progression are (a, a+d, a+2d) and (a+d=0), what is the sum of the first and third terms?
#arithmetic progression
#common difference
#class 10
A (-2d)
B (0)
C (2d)
D (a+d)
Explanation opens after your attempt
Step 1
Concept
In a three-term arithmetic progression, the first and third terms sum to twice the middle term. Here (2(a+d)=0).
Step 2
Why this answer is correct
The correct answer is B. (0). In a three-term arithmetic progression, the first and third terms sum to twice the middle term. Here (2(a+d)=0).
Step 3
Exam Tip
तीन पदों वाली समांतर श्रेणी में पहला और तीसरा पद मिलकर दूसरे पद का दोगुना देते हैं। यहाँ (2(a+d)=0).
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यदि (12, b, 2b-3, 39) समांतर श्रेणी में हैं, तो (b) का मान क्या है?
If (12, b, 2b-3, 39) are in an arithmetic progression, what is the value of (b)?
#arithmetic progression
#common difference
#class 10
A (18)
B (20)
C (21)
D (24)
Explanation opens after your attempt
Step 1
Concept
From the first to the fourth term, there are three equal gaps, so (d=9). The second term is (12+9=21), hence (b=21).
Step 2
Why this answer is correct
The correct answer is C. (21). From the first to the fourth term, there are three equal gaps, so (d=9). The second term is (12+9=21), hence (b=21).
Step 3
Exam Tip
पहले से चौथे पद तक तीन समान अंतर हैं, इसलिए (d=9). दूसरा पद (12+9=21), अतः (b=21).
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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 (5, 5+t, 5+3t, 5+6t) समांतर श्रेणी है, तो (t) का कौन-सा मान संभव है?
If (5, 5+t, 5+3t, 5+6t) is an arithmetic progression, which value of (t) is possible?
#arithmetic progression
#common difference
#class 10
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
The differences are (t, 2t, 3t), and all are equal only when (t=0). In such questions, check every consecutive difference.
Step 2
Why this answer is correct
The correct answer is A. (0). The differences are (t, 2t, 3t), and all are equal only when (t=0). In such questions, check every consecutive difference.
Step 3
Exam Tip
अंतर (t, 2t, 3t) हैं और तीनों बराबर तभी होंगे जब (t=0). ऐसे प्रश्नों में सभी लगातार अंतर जांचें।
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क्रम (18, 18-c, 18-3c) समांतर श्रेणी है। (c) के बारे में सही निष्कर्ष क्या है?
The sequence (18, 18-c, 18-3c) is an arithmetic progression. What is the correct conclusion about (c)?
#arithmetic progression
#common difference
#class 10
A (c=0)
B (c=1)
C (c=3)
D (c) कोई भी वास्तविक संख्या / (c) can be any real number
Explanation opens after your attempt
Step 1
Concept
The consecutive differences are (-c) and (-2c). They are equal only when (c=0).
Step 2
Why this answer is correct
The correct answer is A. (c=0). The consecutive differences are (-c) and (-2c). They are equal only when (c=0).
Step 3
Exam Tip
लगातार अंतर (-c) और (-2c) हैं। बराबर होने के लिए (c=0) होना चाहिए।
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यदि (2a+3, 5a-1, 11a-13) समांतर श्रेणी में हैं, तो दूसरा पद क्या है?
If (2a+3, 5a-1, 11a-13) are in an arithmetic progression, what is the second term?
#arithmetic progression
#common difference
#class 10
A (9)
B (11)
C (14)
D (19)
Explanation opens after your attempt
Step 1
Concept
From (2(5a-1)=(2a+3)+(11a-13)), (a=3). The second term is (5a-1=14).
Step 2
Why this answer is correct
The correct answer is C. (14). From (2(5a-1)=(2a+3)+(11a-13)), (a=3). The second term is (5a-1=14).
Step 3
Exam Tip
(2(5a-1)=(2a+3)+(11a-13)) से (a=3). दूसरा पद (5a-1=14) है।
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क्रम \(\frac{1}{2}, \frac{1}{2}+u, \frac{5}{2}+3u\) समांतर श्रेणी में है। (u) का मान क्या है?
The sequence \(\frac{1}{2}, \frac{1}{2}+u, \frac{5}{2}+3u\) is in an arithmetic progression. What is the value of (u)?
#arithmetic progression
#common difference
#class 10
A \(-\frac{5}{2}\)
B (-2)
C (-1)
D (2)
Explanation opens after your attempt
Step 1
Concept
The first difference is (u), and the second difference is (2+2u). Equating them gives (u=-2).
Step 2
Why this answer is correct
The correct answer is B. (-2). The first difference is (u), and the second difference is (2+2u). Equating them gives (u=-2).
Step 3
Exam Tip
पहला अंतर (u) है और दूसरा अंतर (2+2u) है। बराबर करने पर (u=-2) मिलता है।
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किस (q) के लिए \(q^2, q^2+q, q^2+3q-2\) समांतर श्रेणी में होंगे?
For which (q) will \(q^2, q^2+q, q^2+3q-2\) be in an arithmetic progression?
#arithmetic progression
#common difference
#class 10
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
The consecutive differences are (q) and (2q-2). Equating them gives (q=2).
Step 2
Why this answer is correct
The correct answer is C. (2). The consecutive differences are (q) and (2q-2). Equating them gives (q=2).
Step 3
Exam Tip
लगातार अंतर (q) और (2q-2) हैं। बराबर करने पर (q=2) मिलता है।
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यदि (4, r, s, 31) समांतर श्रेणी में हैं, तो (s-r) का मान क्या है?
If (4, r, s, 31) are in an arithmetic progression, what is the value of (s-r)?
#arithmetic progression
#common difference
#class 10
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
From the first to the fourth term, there are three equal gaps, so \(d=\frac{31-4}{3}=9\). Therefore (s-r=d=9).
Step 2
Why this answer is correct
The correct answer is C. (9). From the first to the fourth term, there are three equal gaps, so \(d=\frac{31-4}{3}=9\). Therefore (s-r=d=9).
Step 3
Exam Tip
चार पदों में पहले से चौथे तक तीन समान अंतर हैं, इसलिए \(d=\frac{31-4}{3}=9\). अतः (s-r=d=9).
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क्रम (m+1, 3m-2, 6m-8) समांतर श्रेणी नहीं है। नीचे दिए गए किस (m) पर यह बात गलत हो जाएगी?
The sequence (m+1, 3m-2, 6m-8) is not an arithmetic progression. For which value of (m) will this statement become false?
#arithmetic progression
#common difference
#class 10
A (1)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
The statement becomes false when the three terms form an arithmetic progression. From (2(3m-2)=(m+1)+(6m-8)), (m=2).
Step 2
Why this answer is correct
The correct answer is B. (2). The statement becomes false when the three terms form an arithmetic progression. From (2(3m-2)=(m+1)+(6m-8)), (m=2).
Step 3
Exam Tip
वाक्य गलत तब होगा जब तीनों पद समांतर श्रेणी में हों। (2(3m-2)=(m+1)+(6m-8)) से (m=2).
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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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क्रम (7, x, 23, y, 39) समांतर श्रेणी है। (x+y) का मान क्या है?
The sequence (7, x, 23, y, 39) is an arithmetic progression. What is the value of (x+y)?
#arithmetic progression
#common difference
#class 10
A (42)
B (46)
C (50)
D (54)
Explanation opens after your attempt
Step 1
Concept
There are four equal gaps between the first and fifth terms, so (d=8). Hence (x=15) and (y=31).
Step 2
Why this answer is correct
The correct answer is B. (46). There are four equal gaps between the first and fifth terms, so (d=8). Hence (x=15) and (y=31).
Step 3
Exam Tip
पहले और पांचवें पद के बीच चार समान अंतर हैं, इसलिए (d=8). तब (x=15) और (y=31).
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यदि (a, a+2d, a+5d) समांतर श्रेणी में हैं और \(d \neq 0\), तो कौन-सा कथन सही है?
If (a, a+2d, a+5d) are in an arithmetic progression and \(d \neq 0\), which statement is correct?
#arithmetic progression
#common difference
#class 10
A यह हमेशा समांतर श्रेणी है / It is always an arithmetic progression
B यह कभी समांतर श्रेणी नहीं है / It is never an arithmetic progression
C यह केवल (a=0) पर समांतर श्रेणी है / It is an arithmetic progression only when (a=0)
D यह केवल (d=1) पर समांतर श्रेणी है / It is an arithmetic progression only when (d=1)
Explanation opens after your attempt
Correct Answer
B. यह कभी समांतर श्रेणी नहीं है / It is never an arithmetic progression
Step 1
Concept
The consecutive differences are (2d) and (3d), which cannot be equal when \(d \neq 0\). In exams, compare consecutive differences directly.
Step 2
Why this answer is correct
The correct answer is B. यह कभी समांतर श्रेणी नहीं है / It is never an arithmetic progression. The consecutive differences are (2d) and (3d), which cannot be equal when \(d \neq 0\). In exams, compare consecutive differences directly.
Step 3
Exam Tip
लगातार अंतर (2d) और (3d) हैं, जो \(d \neq 0\) पर बराबर नहीं हो सकते। परीक्षा में पदों के अंतर अलग-अलग निकालें।
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किस मान पर (3k-2, 5k+1, 8k-3) समांतर श्रेणी में होंगे?
For what value of (k) will (3k-2, 5k+1, 8k-3) be in an arithmetic progression?
#arithmetic progression
#common difference
#class 10
A (4)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
In an arithmetic progression, the middle term is the average of the extremes, so (2(5k+1)=(3k-2)+(8k-3)). For three terms, this is the fastest exam rule.
Step 2
Why this answer is correct
The correct answer is B. (6). In an arithmetic progression, the middle term is the average of the extremes, so (2(5k+1)=(3k-2)+(8k-3)). For three terms, this is the fastest exam rule.
Step 3
Exam Tip
समांतर श्रेणी में बीच का पद दोनों सिरों का औसत होता है, इसलिए (2(5k+1)=(3k-2)+(8k-3)). परीक्षा में तीन पदों के लिए यह सबसे तेज नियम है।
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यदि किसी समांतर श्रेढ़ी में (a=28) और दूसरा पद (19) है, तो सार्व अंतर क्या है?
If an arithmetic progression has (a=28) and second term (19), what is the common difference?
#arithmetic-progression
#find-d
#class10
A (9)
B (-9)
C (19)
D (47)
Explanation opens after your attempt
Step 1
Concept
The common difference is (19-28=-9). Find (d) by subtracting the first term from the second term.
Step 2
Why this answer is correct
The correct answer is B. (-9). The common difference is (19-28=-9). Find (d) by subtracting the first term from the second term.
Step 3
Exam Tip
सार्व अंतर (19-28=-9) है। दूसरे पद से पहले पद को घटाकर (d) निकालें।
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यदि समांतर श्रेढ़ी का दूसरा पद (18) और पहला पद (11) है, तो (d) क्या होगा?
If the second term of an arithmetic progression is (18) and the first term is (11), what will (d) be?
#arithmetic-progression
#find-d
#class10
A (6)
B (7)
C (18)
D (29)
Explanation opens after your attempt
Step 1
Concept
The common difference is (18-11=7). For (d), subtract the first term from the second term.
Step 2
Why this answer is correct
The correct answer is B. (7). The common difference is (18-11=7). For (d), subtract the first term from the second term.
Step 3
Exam Tip
सार्व अंतर (18-11=7) है। (d) के लिए दूसरा पद घटा पहला पद करें।
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समांतर श्रेढ़ी \(a-2,a+1,a+4,a+7,\ldots\) का सार्व अंतर क्या है?
What is the common difference of the arithmetic progression \(a-2,a+1,a+4,a+7,\ldots\)?
#arithmetic-progression
#algebraic-ap
#class10
A (2)
B (3)
C (a)
D (a+3)
Explanation opens after your attempt
Step 1
Concept
The difference of consecutive terms is ((a+1)-(a-2)=3). Like terms cancel in variable terms.
Step 2
Why this answer is correct
The correct answer is B. (3). The difference of consecutive terms is ((a+1)-(a-2)=3). Like terms cancel in variable terms.
Step 3
Exam Tip
लगातार पदों का अंतर ((a+1)-(a-2)=3) है। चर वाले पदों में समान पद कट जाते हैं।
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कौन-सा अनुक्रम (d=0.25) वाली समांतर श्रेढ़ी है?
Which sequence is an arithmetic progression with (d=0.25)?
#arithmetic-progression
#decimal-ap
#class10
A \(1,1.5,2,2.5,\ldots\)
B \(0.25,0.5,0.75,1.0,\ldots\)
C \(2,2.25,2.75,3.5,\ldots\)
D \(0.25,1,4,16,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(0.25,0.5,0.75,1.0,\ldots\)
Step 1
Concept
(0.5-0.25=0.25), and the same difference continues. Hence this is the correct arithmetic progression.
Step 2
Why this answer is correct
The correct answer is B. \(0.25,0.5,0.75,1.0,\ldots\). (0.5-0.25=0.25), and the same difference continues. Hence this is the correct arithmetic progression.
Step 3
Exam Tip
(0.5-0.25=0.25) और आगे भी यही अंतर है। इसलिए यह सही समांतर श्रेढ़ी है।
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समांतर श्रेढ़ी \(\frac{1}{3},\frac{2}{3},1,\frac{4}{3},\ldots\) में (d) क्या है?
What is (d) in the arithmetic progression \(\frac{1}{3},\frac{2}{3},1,\frac{4}{3},\ldots\)?
#arithmetic-progression
#fraction-common-difference
#class10
A \(\frac{1}{3}\)
B \(\frac{2}{3}\)
C (1)
D \(\frac{4}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{3}\)
Step 1
Concept
\(\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\). For fractions, find the difference of the first two terms.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{3}\). \(\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\). For fractions, find the difference of the first two terms.
Step 3
Exam Tip
\(\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\) है। भिन्नों में पहले दो पदों का अंतर निकालें।
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यदि किसी समांतर श्रेढ़ी में (d=-1.5) है और प्रथम पद (10) है, तो दूसरा पद क्या होगा?
If an arithmetic progression has (d=-1.5) and first term (10), what is the second term?
#arithmetic-progression
#decimal-negative-d
#class10
A (8.5)
B (9.5)
C (11.5)
D (-8.5)
Explanation opens after your attempt
Step 1
Concept
The second term is (10+(-1.5)=8.5). Take care of both decimals and negative signs.
Step 2
Why this answer is correct
The correct answer is A. (8.5). The second term is (10+(-1.5)=8.5). Take care of both decimals and negative signs.
Step 3
Exam Tip
दूसरा पद (10+(-1.5)=8.5) है। दशमलव और ऋणात्मक चिन्ह दोनों का ध्यान रखें।
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किसी समांतर श्रेढ़ी में (a=3) और (d=0) है। पहले तीन पद कौन-से होंगे?
In an arithmetic progression, (a=3) and (d=0). What are the first three terms?
#arithmetic-progression
#zero-difference
#class10
A (3,0,0)
B (0,3,6)
C (3,3,3)
D (3,6,9)
Explanation opens after your attempt
Correct Answer
C. (3,3,3)
Step 1
Concept
When (d=0), every term remains equal. Therefore, the first three terms are (3,3,3).
Step 2
Why this answer is correct
The correct answer is C. (3,3,3). When (d=0), every term remains equal. Therefore, the first three terms are (3,3,3).
Step 3
Exam Tip
(d=0) होने पर हर पद समान रहता है। इसलिए पहले तीन पद (3,3,3) हैं।
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समांतर श्रेढ़ी \(17,13,9,5,\ldots\) में पहले पद और सार्व अंतर का गुणनफल क्या है?
In the arithmetic progression \(17,13,9,5,\ldots\), what is the product of the first term and the common difference?
#arithmetic-progression
#first-term-common-difference
#class10
A (68)
B (-68)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
Here the first term is (17) and (d=-4). Therefore, the product is \(17\times(-4)=-68\).
Step 2
Why this answer is correct
The correct answer is B. (-68). Here the first term is (17) and (d=-4). Therefore, the product is \(17\times(-4)=-68\).
Step 3
Exam Tip
यहाँ पहला पद (17) और (d=-4) है। इसलिए गुणनफल \(17\times(-4)=-68\) होगा।
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यदि (d>0) है और प्रथम पद धनात्मक है, तो समांतर श्रेढ़ी के पद सामान्यतः कैसे बदलेंगे?
If (d>0) and the first term is positive, how will the terms of an arithmetic progression generally change?
#arithmetic-progression
#positive-difference
#class10
A घटेंगे / They will decrease
B समान रहेंगे / They will remain equal
C बढ़ेंगे / They will increase
D अनियमित होंगे / They will be irregular
Explanation opens after your attempt
Correct Answer
C. बढ़ेंगे / They will increase
Step 1
Concept
Positive (d) means adding each time. Therefore, the terms generally keep increasing.
Step 2
Why this answer is correct
The correct answer is C. बढ़ेंगे / They will increase. Positive (d) means adding each time. Therefore, the terms generally keep increasing.
Step 3
Exam Tip
धनात्मक (d) का अर्थ हर बार जोड़ना है। इसलिए पद सामान्यतः बढ़ते जाते हैं।
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कौन-सा अनुक्रम (d=-5) वाली समांतर श्रेढ़ी है?
Which sequence is an arithmetic progression with (d=-5)?
#arithmetic-progression
#negative-difference
#class10
A \(10,15,20,25,\ldots\)
B \(40,35,30,25,\ldots\)
C \(5,0,-6,-13,\ldots\)
D \(25,20,10,5,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(40,35,30,25,\ldots\)
Step 1
Concept
(35-40=-5), and the same difference continues. Equal negative difference forms a decreasing arithmetic progression.
Step 2
Why this answer is correct
The correct answer is B. \(40,35,30,25,\ldots\). (35-40=-5), and the same difference continues. Equal negative difference forms a decreasing arithmetic progression.
Step 3
Exam Tip
(35-40=-5) और आगे भी यही अंतर है। समान ऋणात्मक अंतर घटती समांतर श्रेढ़ी बनाता है।
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समांतर श्रेढ़ी \(3,9,15,21,\ldots\) में (a) और (d) का योग क्या है?
In the arithmetic progression \(3,9,15,21,\ldots\), what is the sum of (a) and (d)?
#arithmetic-progression
#first-term-common-difference
#class10
A (6)
B (9)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
Here (a=3) and (d=6). Therefore, (a+d=9).
Step 2
Why this answer is correct
The correct answer is B. (9). Here (a=3) and (d=6). Therefore, (a+d=9).
Step 3
Exam Tip
यहाँ (a=3) और (d=6) है। इसलिए (a+d=9) होगा।
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अनुक्रम \(11,16,22,29,\ldots\) समांतर श्रेढ़ी क्यों नहीं है?
Why is \(11,16,22,29,\ldots\) not an arithmetic progression?
#arithmetic-progression
#non-ap-reason
#class10
A क्योंकि पहला पद (11) है / Because the first term is (11)
B क्योंकि पद बढ़ रहे हैं / Because the terms are increasing
C क्योंकि अंतर (5,6,7) समान नहीं हैं / Because the differences (5,6,7) are not equal
D क्योंकि सभी पद धनात्मक हैं / Because all terms are positive
Explanation opens after your attempt
Correct Answer
C. क्योंकि अंतर (5,6,7) समान नहीं हैं / Because the differences (5,6,7) are not equal
Step 1
Concept
In an arithmetic progression, consecutive differences are equal. Here the differences change, so it is not an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि अंतर (5,6,7) समान नहीं हैं / Because the differences (5,6,7) are not equal. In an arithmetic progression, consecutive differences are equal. Here the differences change, so it is not an arithmetic progression.
Step 3
Exam Tip
समांतर श्रेढ़ी में लगातार अंतर समान होते हैं। यहाँ अंतर बदल रहे हैं इसलिए यह समांतर श्रेढ़ी नहीं है।
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यदि समांतर श्रेढ़ी \(x,x+4,x+8,x+12,\ldots\) है, तो सार्व अंतर क्या है?
If the arithmetic progression is \(x,x+4,x+8,x+12,\ldots\), what is the common difference?
#arithmetic-progression
#algebraic-ap
#class10
A (x)
B (2x)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The difference of consecutive terms is ((x+4)-x=4). The same rule applies to algebraic terms.
Step 2
Why this answer is correct
The correct answer is C. (4). The difference of consecutive terms is ((x+4)-x=4). The same rule applies to algebraic terms.
Step 3
Exam Tip
लगातार पदों का अंतर ((x+4)-x=4) है। अक्षर वाले पदों में भी वही नियम लगता है।
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समांतर श्रेढ़ी \(4,4,4,4,\ldots\) के बारे में कौन-सा कथन सही है?
Which statement is correct about the arithmetic progression \(4,4,4,4,\ldots\)?
#arithmetic-progression
#zero-difference
#class10
A इसका (d=4) है / Its (d=4)
B इसका (d=0) है / Its (d=0)
C यह समांतर श्रेढ़ी नहीं है / It is not an arithmetic progression
D इसका प्रथम पद (0) है / Its first term is (0)
Explanation opens after your attempt
Correct Answer
B. इसका (d=0) है / Its (d=0)
Step 1
Concept
The difference of consecutive terms is (4-4=0). A constant-term progression has (d=0).
Step 2
Why this answer is correct
The correct answer is B. इसका (d=0) है / Its (d=0). The difference of consecutive terms is (4-4=0). A constant-term progression has (d=0).
Step 3
Exam Tip
लगातार पदों का अंतर (4-4=0) है। समान पदों वाली श्रेढ़ी में (d=0) होता है।
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यदि (a=20) और (d=-3) है, तो समांतर श्रेढ़ी का तीसरा पद क्या होगा?
If (a=20) and (d=-3), what is the third term of the arithmetic progression?
#arithmetic-progression
#third-term
#class10
A (14)
B (17)
C (20)
D (23)
Explanation opens after your attempt
Step 1
Concept
The first three terms are (20,17,14). With negative (d), subtraction occurs each time.
Step 2
Why this answer is correct
The correct answer is A. (14). The first three terms are (20,17,14). With negative (d), subtraction occurs each time.
Step 3
Exam Tip
पहले तीन पद (20,17,14) होंगे। ऋणात्मक (d) में हर बार घटाव होता है।
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यदि किसी समांतर श्रेढ़ी के लगातार दो पद (18) और (25) हैं, तो सार्व अंतर क्या है?
If two consecutive terms of an arithmetic progression are (18) and (25), what is the common difference?
#arithmetic-progression
#consecutive-terms
#class10
A (5)
B (6)
C (7)
D (43)
Explanation opens after your attempt
Step 1
Concept
The common difference is (25-18=7). When consecutive terms are given, subtract directly.
Step 2
Why this answer is correct
The correct answer is C. (7). The common difference is (25-18=7). When consecutive terms are given, subtract directly.
Step 3
Exam Tip
सार्व अंतर (25-18=7) है। लगातार पद दिए हों तो सीधे घटाव करें।
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समांतर श्रेढ़ी \(31,27,23,19,\ldots\) में अगला पद क्या होगा?
What will be the next term in the arithmetic progression \(31,27,23,19,\ldots\)?
#arithmetic-progression
#next-term
#class10
A (16)
B (15)
C (14)
D (13)
Explanation opens after your attempt
Step 1
Concept
Here (d=-4). Therefore, the next term is (19-4=15).
Step 2
Why this answer is correct
The correct answer is B. (15). Here (d=-4). Therefore, the next term is (19-4=15).
Step 3
Exam Tip
यहाँ (d=-4) है। इसलिए अगला पद (19-4=15) होगा।
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यदि समांतर श्रेढ़ी का प्रथम पद (a=12) और सार्व अंतर (d=5) है, तो पहले चार पद कौन-से होंगे?
If the first term of an arithmetic progression is (a=12) and the common difference is (d=5), what are the first four terms?
#arithmetic-progression
#construct-ap
#class10
A (12,17,22,27)
B (5,12,19,26)
C (12,18,24,30)
D (17,22,27,32)
Explanation opens after your attempt
Correct Answer
A. (12,17,22,27)
Step 1
Concept
The first term is (12) and (5) is added each time. Hence the terms are (12,17,22,27).
Step 2
Why this answer is correct
The correct answer is A. (12,17,22,27). The first term is (12) and (5) is added each time. Hence the terms are (12,17,22,27).
Step 3
Exam Tip
पहला पद (12) है और हर बार (5) जोड़ना है। इसलिए पद (12,17,22,27) होंगे।
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यदि किसी समांतर श्रेढ़ी के लगातार पद (32) और (41) हैं तो सार्व अंतर (d) क्या होगा?
If consecutive terms of an arithmetic progression are (32) and (41), what will be the common difference (d)?
#arithmetic-progression
#consecutive-terms
#class10
A (7)
B (8)
C (9)
D (73)
Explanation opens after your attempt
Step 1
Concept
The common difference is (41-32=9). When consecutive terms are given, no long formula is needed.
Step 2
Why this answer is correct
The correct answer is C. (9). The common difference is (41-32=9). When consecutive terms are given, no long formula is needed.
Step 3
Exam Tip
सार्व अंतर (41-32=9) है। लगातार पद दिए हों तो कोई सूत्र लंबा लगाने की जरूरत नहीं होती।
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यदि (a=11) और (d=6) है तो समांतर श्रेढ़ी के पहले चार पद कौन-से होंगे?
If (a=11) and (d=6), what are the first four terms of the arithmetic progression?
#arithmetic-progression
#construct-ap
#class10
A (11,16,21,26)
B (6,11,16,21)
C (11,17,23,29)
D (17,23,29,35)
Explanation opens after your attempt
Correct Answer
C. (11,17,23,29)
Step 1
Concept
The first term is (11) and (6) is added each time. Therefore, the first four terms are (11,17,23,29).
Step 2
Why this answer is correct
The correct answer is C. (11,17,23,29). The first term is (11) and (6) is added each time. Therefore, the first four terms are (11,17,23,29).
Step 3
Exam Tip
पहला पद (11) है और हर बार (6) जोड़ना है। इसलिए पहले चार पद (11,17,23,29) हैं।
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कौन-सा अनुक्रम समांतर श्रेढ़ी है जिसका सार्व अंतर (-7) है?
Which sequence is an arithmetic progression with common difference (-7)?
#arithmetic-progression
#negative-difference
#class10
A \(49,42,35,28,\ldots\)
B \(7,14,21,28,\ldots\)
C \(49,40,31,22,\ldots\)
D \(28,35,42,49,\ldots\)
Explanation opens after your attempt
Correct Answer
A. \(49,42,35,28,\ldots\)
Step 1
Concept
(42-49=-7) so (7) is subtracted each time. In a decreasing progression, (d) is written as negative.
Step 2
Why this answer is correct
The correct answer is A. \(49,42,35,28,\ldots\). (42-49=-7) so (7) is subtracted each time. In a decreasing progression, (d) is written as negative.
Step 3
Exam Tip
(42-49=-7) है इसलिए हर बार (7) घट रहा है। घटती श्रेढ़ी में (d) ऋणात्मक लिखा जाता है।
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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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यदि कोई अनुक्रम \(12,12,12,12,\ldots\) है, तो वह किस प्रकार की समांतर श्रेढ़ी है?
If a sequence is \(12,12,12,12,\ldots\), what type of arithmetic progression is it?
#arithmetic-progression
#constant-ap
#class10
A बढ़ती हुई / Increasing
B घटती हुई / Decreasing
C समान पदों वाली / Constant terms
D समांतर श्रेढ़ी नहीं / Not an arithmetic progression
Explanation opens after your attempt
Correct Answer
C. समान पदों वाली / Constant terms
Step 1
Concept
All terms are equal, so (d=0). It is called an arithmetic progression with constant terms.
Step 2
Why this answer is correct
The correct answer is C. समान पदों वाली / Constant terms. All terms are equal, so (d=0). It is called an arithmetic progression with constant terms.
Step 3
Exam Tip
सभी पद समान हैं इसलिए (d=0) है। इसे समान पदों वाली समांतर श्रेढ़ी कहते हैं।
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समांतर श्रेढ़ी \(12,19,26,33,\ldots\) में प्रत्येक पद पिछले पद से कितना अधिक है?
In the arithmetic progression \(12,19,26,33,\ldots\), how much greater is each term than the previous term?
#arithmetic-progression
#common-difference
#class10
A (5)
B (6)
C (7)
D (12)
Explanation opens after your attempt
Step 1
Concept
Each next term is (7) greater than the previous term. This is the common difference of this progression.
Step 2
Why this answer is correct
The correct answer is C. (7). Each next term is (7) greater than the previous term. This is the common difference of this progression.
Step 3
Exam Tip
हर अगला पद पिछले पद से (7) अधिक है। यही इस श्रेढ़ी का सार्व अंतर है।
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अनुक्रम \(3,7,12,18,\ldots\) समांतर श्रेढ़ी है या नहीं?
Is the sequence \(3,7,12,18,\ldots\) an arithmetic progression or not?
#arithmetic-progression
#ap-check
#class10
A हाँ क्योंकि पद बढ़ते हैं / Yes because the terms increase
B हाँ क्योंकि पहला पद छोटा है / Yes because the first term is small
C नहीं क्योंकि अंतर समान नहीं हैं / No because the differences are not equal
D नहीं क्योंकि पद धनात्मक हैं / No because the terms are positive
Explanation opens after your attempt
Correct Answer
C. नहीं क्योंकि अंतर समान नहीं हैं / No because the differences are not equal
Step 1
Concept
Its differences are (4,5,6). Since the differences are not equal, it is not an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is C. नहीं क्योंकि अंतर समान नहीं हैं / No because the differences are not equal. Its differences are (4,5,6). Since the differences are not equal, it is not an arithmetic progression.
Step 3
Exam Tip
इसके अंतर (4,5,6) हैं। समान अंतर न होने के कारण यह समांतर श्रेढ़ी नहीं है।
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यदि समांतर श्रेढ़ी के लगातार दो पद (26) और (31) हैं, तो सार्व अंतर क्या है?
If two consecutive terms of an arithmetic progression are (26) and (31), what is the common difference?
#arithmetic-progression
#consecutive-terms
#class10
A (3)
B (5)
C (26)
D (57)
Explanation opens after your attempt
Step 1
Concept
The common difference is (31-26=5). When consecutive terms are given, directly find the difference.
Step 2
Why this answer is correct
The correct answer is B. (5). The common difference is (31-26=5). When consecutive terms are given, directly find the difference.
Step 3
Exam Tip
सार्व अंतर (31-26=5) है। लगातार पद दिए हों तो सीधा अंतर निकालें।
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यदि (d=0) है, तो समांतर श्रेढ़ी के लगातार पदों में क्या होगा?
If (d=0), what will happen to consecutive terms of an arithmetic progression?
#arithmetic-progression
#zero-difference
#class10
A वे बराबर होंगे / They will be equal
B वे दुगुने होंगे / They will double
C वे ऋणात्मक होंगे / They will be negative
D वे वर्ग होंगे / They will be squares
Explanation opens after your attempt
Correct Answer
A. वे बराबर होंगे / They will be equal
Step 1
Concept
(d=0) means there is no difference between consecutive terms. Therefore, all terms will be equal.
Step 2
Why this answer is correct
The correct answer is A. वे बराबर होंगे / They will be equal. (d=0) means there is no difference between consecutive terms. Therefore, all terms will be equal.
Step 3
Exam Tip
(d=0) का अर्थ है कि लगातार पदों में कोई अंतर नहीं है। इसलिए सभी पद बराबर होंगे।
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अनुक्रम \(5,10,20,40,\ldots\) समांतर श्रेढ़ी क्यों नहीं है?
Why is \(5,10,20,40,\ldots\) not an arithmetic progression?
#arithmetic-progression
#non-ap-reason
#class10
A क्योंकि पहला पद (5) है / Because the first term is (5)
B क्योंकि पद बढ़ रहे हैं / Because the terms are increasing
C क्योंकि लगातार अंतर (5,10,20) समान नहीं हैं / Because consecutive differences (5,10,20) are not equal
D क्योंकि सभी पद पूर्णांक हैं / Because all terms are integers
Explanation opens after your attempt
Correct Answer
C. क्योंकि लगातार अंतर (5,10,20) समान नहीं हैं / Because consecutive differences (5,10,20) are not equal
Step 1
Concept
In an arithmetic progression, all consecutive differences are equal. Here the differences are not equal, so it is not an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि लगातार अंतर (5,10,20) समान नहीं हैं / Because consecutive differences (5,10,20) are not equal. In an arithmetic progression, all consecutive differences are equal. Here the differences are not equal, so it is not an arithmetic progression.
Step 3
Exam Tip
समांतर श्रेढ़ी में सभी लगातार अंतर समान होते हैं। यहाँ अंतर समान नहीं हैं इसलिए यह समांतर श्रेढ़ी नहीं है।
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समांतर श्रेढ़ी की मुख्य पहचान क्या है?
What is the main identity of an arithmetic progression?
#arithmetic-progression
#definition
#class10
A हर पद पिछले पद का वर्ग होता है / Each term is the square of the previous term
B लगातार पदों का अंतर समान होता है / The difference of consecutive terms is equal
C लगातार पदों का अनुपात समान होता है / The ratio of consecutive terms is equal
D सभी पद अवश्य धनात्मक होते हैं / All terms are necessarily positive
Explanation opens after your attempt
Correct Answer
B. लगातार पदों का अंतर समान होता है / The difference of consecutive terms is equal
Step 1
Concept
In an arithmetic progression, differences like \(a_2-a_1\) remain constant. This should be checked first.
Step 2
Why this answer is correct
The correct answer is B. लगातार पदों का अंतर समान होता है / The difference of consecutive terms is equal. In an arithmetic progression, differences like \(a_2-a_1\) remain constant. This should be checked first.
Step 3
Exam Tip
समांतर श्रेढ़ी में \(a_2-a_1\) जैसा अंतर स्थिर रहता है। यही सबसे पहले जाँचना चाहिए।
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समांतर श्रेढ़ी \(3,9,15,21,\ldots\) में तीसरा पद कौन-सा है?
Which is the third term in the arithmetic progression \(3,9,15,21,\ldots\)?
#arithmetic-progression
#term-position
#class10
A (3)
B (9)
C (15)
D (21)
Explanation opens after your attempt
Step 1
Concept
In the written order, the third term is (15). Do not skip the first term while counting positions.
Step 2
Why this answer is correct
The correct answer is C. (15). In the written order, the third term is (15). Do not skip the first term while counting positions.
Step 3
Exam Tip
लिखे क्रम में तीसरा पद (15) है। पद की स्थिति गिनते समय पहला पद न छोड़ें।
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यदि समांतर श्रेढ़ी \(b,b+5,b+10,b+15,\ldots\) है, तो सार्व अंतर क्या है?
If the arithmetic progression is \(b,b+5,b+10,b+15,\ldots\), what is the common difference?
#arithmetic-progression
#algebraic-ap
#class10
A (b)
B (5)
C (10)
D (5b)
Explanation opens after your attempt
Step 1
Concept
The difference of consecutive terms is ((b+5)-b=5). For algebraic terms also, subtract to find (d).
Step 2
Why this answer is correct
The correct answer is B. (5). The difference of consecutive terms is ((b+5)-b=5). For algebraic terms also, subtract to find (d).
Step 3
Exam Tip
लगातार पदों का अंतर ((b+5)-b=5) है। अक्षर वाले पदों में भी घटाकर (d) निकालें।
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कौन-सा अनुक्रम (d=-2) वाली समांतर श्रेढ़ी है?
Which sequence is an arithmetic progression with (d=-2)?
#arithmetic-progression
#identify-d
#class10
A \(4,6,8,10,\ldots\)
B \(18,16,14,12,\ldots\)
C \(2,4,8,16,\ldots\)
D \(9,7,4,0,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(18,16,14,12,\ldots\)
Step 1
Concept
In \(18,16,14,12,\ldots\), (2) is subtracted each time. Hence (d=-2).
Step 2
Why this answer is correct
The correct answer is B. \(18,16,14,12,\ldots\). In \(18,16,14,12,\ldots\), (2) is subtracted each time. Hence (d=-2).
Step 3
Exam Tip
\(18,16,14,12,\ldots\) में हर बार (2) घटता है। इसलिए (d=-2) है।
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समांतर श्रेढ़ी \(6,13,20,27,\ldots\) का प्रथम पद क्या है?
What is the first term of the arithmetic progression \(6,13,20,27,\ldots\)?
#arithmetic-progression
#first-term
#class10
A (6)
B (7)
C (13)
D (20)
Explanation opens after your attempt
Step 1
Concept
The first written term is the first term (a). Here (a=6).
Step 2
Why this answer is correct
The correct answer is A. (6). The first written term is the first term (a). Here (a=6).
Step 3
Exam Tip
पहला लिखा हुआ पद ही प्रथम पद (a) होता है। यहाँ (a=6) है।
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कौन-सा अनुक्रम (d=0) वाली समांतर श्रेढ़ी है?
Which sequence is an arithmetic progression with (d=0)?
#arithmetic-progression
#zero-difference
#class10
A \(1,2,3,4,\ldots\)
B \(8,8,8,8,\ldots\)
C \(10,8,6,4,\ldots\)
D \(2,4,8,16,\ldots\)
Explanation opens after your attempt
Correct Answer
B. \(8,8,8,8,\ldots\)
Step 1
Concept
In \(8,8,8,8,\ldots\), every difference is (0). Hence it is an arithmetic progression with (d=0).
Step 2
Why this answer is correct
The correct answer is B. \(8,8,8,8,\ldots\). In \(8,8,8,8,\ldots\), every difference is (0). Hence it is an arithmetic progression with (d=0).
Step 3
Exam Tip
\(8,8,8,8,\ldots\) में हर अंतर (0) है। इसलिए यह (d=0) वाली समांतर श्रेढ़ी है।
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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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किसी समांतर श्रेढ़ी में (d<0) होने पर पद सामान्यतः कैसे बदलते हैं?
In an arithmetic progression, when (d<0), how do the terms generally change?
#arithmetic-progression
#negative-difference
#class10
A बढ़ते हैं / They increase
B समान रहते हैं / They remain equal
C घटते हैं / They decrease
D दुगुने होते हैं / They double
Explanation opens after your attempt
Correct Answer
C. घटते हैं / They decrease
Step 1
Concept
Negative (d) means subtraction occurs each time. Therefore, the terms decrease.
Step 2
Why this answer is correct
The correct answer is C. घटते हैं / They decrease. Negative (d) means subtraction occurs each time. Therefore, the terms decrease.
Step 3
Exam Tip
ऋणात्मक (d) का अर्थ हर बार घटाना है। इसलिए पद घटते हैं।
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किसी समांतर श्रेढ़ी में (d>0) होने पर पद सामान्यतः कैसे बदलते हैं?
In an arithmetic progression, when (d>0), how do the terms generally change?
#arithmetic-progression
#positive-difference
#class10
A घटते हैं / They decrease
B बढ़ते हैं / They increase
C सदैव (0) होते हैं / They are always (0)
D बदलते नहीं हैं / They do not change
Explanation opens after your attempt
Correct Answer
B. बढ़ते हैं / They increase
Step 1
Concept
Positive (d) means something is added each time. Therefore, the terms increase.
Step 2
Why this answer is correct
The correct answer is B. बढ़ते हैं / They increase. Positive (d) means something is added each time. Therefore, the terms increase.
Step 3
Exam Tip
धनात्मक (d) का अर्थ हर बार कुछ जोड़ना है। इसलिए पद बढ़ते हैं।
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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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यदि कोई अनुक्रम \(5,5,5,5,\ldots\) है, तो वह किस प्रकार की समांतर श्रेढ़ी है?
If a sequence is \(5,5,5,5,\ldots\), what type of arithmetic progression is it?
#arithmetic-progression
#constant-ap
#class10
A घटती हुई / Decreasing
B बढ़ती हुई / Increasing
C समान पदों वाली / Constant terms
D समांतर श्रेढ़ी नहीं / Not an arithmetic progression
Explanation opens after your attempt
Correct Answer
C. समान पदों वाली / Constant terms
Step 1
Concept
All terms are equal, so (d=0). It can be called an arithmetic progression with constant terms.
Step 2
Why this answer is correct
The correct answer is C. समान पदों वाली / Constant terms. All terms are equal, so (d=0). It can be called an arithmetic progression with constant terms.
Step 3
Exam Tip
सभी पद समान हैं इसलिए (d=0) है। इसे समान पदों वाली समांतर श्रेढ़ी कह सकते हैं।
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समांतर श्रेढ़ी \(18,21,24,27,\ldots\) में कौन-सा पद दिया गया नहीं है?
Which term is not given in the arithmetic progression \(18,21,24,27,\ldots\)?
#arithmetic-progression
#given-terms
#class10
A (18)
B (21)
C (24)
D (30)
Explanation opens after your attempt
Step 1
Concept
The written terms are (18,21,24,27). (30) can be the next term but is not among the given terms.
Step 2
Why this answer is correct
The correct answer is D. (30). The written terms are (18,21,24,27). (30) can be the next term but is not among the given terms.
Step 3
Exam Tip
लिखे हुए पद (18,21,24,27) हैं। (30) अगला पद हो सकता है पर दिए गए पदों में नहीं है।
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समांतर श्रेढ़ी \(1,4,7,10,\ldots\) में प्रत्येक पद पिछले पद से कितना अधिक है?
In the arithmetic progression \(1,4,7,10,\ldots\), how much greater is each term than the previous term?
#arithmetic-progression
#common-difference
#class10
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Each next term is (3) greater than the previous term. This is the common difference of the sequence.
Step 2
Why this answer is correct
The correct answer is C. (3). Each next term is (3) greater than the previous term. This is the common difference of the sequence.
Step 3
Exam Tip
हर अगला पद पिछले पद से (3) अधिक है। यही इस श्रेढ़ी का सार्व अंतर है।
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अनुक्रम \(4,8,13,19,\ldots\) समांतर श्रेढ़ी है या नहीं?
Is the sequence \(4,8,13,19,\ldots\) an arithmetic progression or not?
#arithmetic-progression
#ap-check
#class10
A हाँ क्योंकि पद बढ़ रहे हैं / Yes because terms are increasing
B हाँ क्योंकि सभी पद धनात्मक हैं / Yes because all terms are positive
C नहीं क्योंकि अंतर समान नहीं हैं / No because differences are not equal
D नहीं क्योंकि पहला पद सम है / No because the first term is even
Explanation opens after your attempt
Correct Answer
C. नहीं क्योंकि अंतर समान नहीं हैं / No because differences are not equal
Step 1
Concept
Its differences are (4,5,6). Since the differences are not equal, it is not an arithmetic progression.
Step 2
Why this answer is correct
The correct answer is C. नहीं क्योंकि अंतर समान नहीं हैं / No because differences are not equal. Its differences are (4,5,6). Since the differences are not equal, it is not an arithmetic progression.
Step 3
Exam Tip
इसके अंतर (4,5,6) हैं। समान अंतर न होने से यह समांतर श्रेढ़ी नहीं है।
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