Question 1/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(5x^2-4x+t=0\) के वास्तविक और समान मूलों के लिए (t) क्या होगा?
What is (t) for real and equal roots of \(5x^2-4x+t=0\)?
Explanation opens after your attempt
Correct Answer
A. \(\frac{4}{5}\)
Step 1
Concept
(D=(-4)2-4(5)t=0) gives \(t=\frac{4}{5}\). Always set (D=0) for equal roots.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{4}{5}\). (D=(-4)2-4(5)t=0) gives \(t=\frac{4}{5}\). Always set (D=0) for equal roots.
Step 3
Exam Tip
(D=(-4)2-4(5)t=0) से \(t=\frac{4}{5}\) मिलता है। समान मूलों के लिए हमेशा (D=0) रखें।
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Question 2/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2-3x+s=0\) के समान वास्तविक मूलों के लिए (s) का मान क्या होगा?
What is the value of (s) for equal real roots of \(x^2-3x+s=0\)?
Explanation opens after your attempt
Correct Answer
A. \(\frac{9}{4}\)
Step 1
Concept
For equal roots (D=0), so ((-3)2-4s=0) gives \(s=\frac{9}{4}\). Do not fear fractional answers.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{9}{4}\). For equal roots (D=0), so ((-3)2-4s=0) gives \(s=\frac{9}{4}\). Do not fear fractional answers.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए ((-3)2-4s=0) से \(s=\frac{9}{4}\)। भिन्न उत्तर से न डरें।
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Question 3/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2+14x+49=0\) के लिए सही उत्तर चुनिए।
Choose the correct answer for \(x^2+14x+49=0\).
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और समान/two real and equal
Step 1
Concept
(D=142-4(1)(49)=0). Hence the roots are equal and real.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और समान / two real and equal. (D=142-4(1)(49)=0). Hence the roots are equal and real.
Step 3
Exam Tip
(D=142-4(1)(49)=0) है। अतः मूल समान वास्तविक हैं।
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Question 4/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(2x^2+4x+2=0\) के लिए विविक्तकर का चिन्ह क्या है?
What is the sign of the discriminant for \(2x^2+4x+2=0\)?
Explanation opens after your attempt
Correct Answer
A. शून्य/zero
Step 1
Concept
(D=42-4(2)(2)=0). So this is the case of equal real roots.
Step 2
Why this answer is correct
The correct answer is A. शून्य / zero. (D=42-4(2)(2)=0). So this is the case of equal real roots.
Step 3
Exam Tip
(D=42-4(2)(2)=0) है। इसलिए यह समान वास्तविक मूलों की स्थिति है।
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Question 5/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2-6x+9=0\) के लिए कौन सा कथन सही है?
Which statement is correct for \(x^2-6x+9=0\)?
Explanation opens after your attempt
Correct Answer
A. दो समान वास्तविक मूल हैं/it has two equal real roots
Step 1
Concept
(D=(-6)2-4(1)(9)=0). Therefore it has two equal real roots.
Step 2
Why this answer is correct
The correct answer is A. दो समान वास्तविक मूल हैं / it has two equal real roots. (D=(-6)2-4(1)(9)=0). Therefore it has two equal real roots.
Step 3
Exam Tip
(D=(-6)2-4(1)(9)=0) है। इसलिए दो समान वास्तविक मूल हैं।
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Question 6/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
यदि किसी द्विघात समीकरण के दो समान वास्तविक मूल हैं, तो (D) का मान क्या होगा?
If a quadratic equation has two equal real roots, what will be the value of (D)?
Explanation opens after your attempt
Step 1
Concept
For equal real roots, (D=0) is necessary. This is the main rule for nature questions.
Step 2
Why this answer is correct
The correct answer is A. (0). For equal real roots, (D=0) is necessary. This is the main rule for nature questions.
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0) अनिवार्य है। प्रकृति वाले प्रश्नों में यही मुख्य नियम है।
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Question 7/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2+12x+36=0\) के बारे में सही कथन कौन सा है?
Which statement is correct about \(x^2+12x+36=0\)?
Explanation opens after your attempt
Correct Answer
A. यह समान वास्तविक मूल रखता है/it has equal real roots
Step 1
Concept
(x-2+12x+36=(x+6)2). Being a perfect square, it has equal real roots.
Step 2
Why this answer is correct
The correct answer is A. यह समान वास्तविक मूल रखता है / it has equal real roots. (x-2+12x+36=(x+6)2). Being a perfect square, it has equal real roots.
Step 3
Exam Tip
(x-2+12x+36=(x+6)2) है। पूर्ण वर्ग होने से मूल समान वास्तविक हैं।
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Question 8/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(3x^2+kx+12=0\) में समान वास्तविक मूलों के लिए (k) का कौन सा मान सही हो सकता है?
Which value of (k) can give equal real roots in \(3x^2+kx+12=0\)?
Explanation opens after your attempt
Step 1
Concept
For equal roots (k-2-4(3)(12)=0), so (k=12) or (k=-12). Among the options, (12) is correct.
Step 2
Why this answer is correct
The correct answer is A. (12). For equal roots (k-2-4(3)(12)=0), so (k=12) or (k=-12). Among the options, (12) is correct.
Step 3
Exam Tip
समान मूलों के लिए (k-2-4(3)(12)=0), इसलिए (k=12) या (k=-12)। दिए विकल्पों में (12) सही है।
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Question 9/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2-10x+r=0\) में समान वास्तविक मूलों के लिए (r) का मान चुनिए।
Choose the value of (r) for equal real roots in \(x^2-10x+r=0\).
Explanation opens after your attempt
Step 1
Concept
(D=(-10)2-4r=0) gives (r=25). Equal roots have zero discriminant.
Step 2
Why this answer is correct
The correct answer is A. (25). (D=(-10)2-4r=0) gives (r=25). Equal roots have zero discriminant.
Step 3
Exam Tip
(D=(-10)2-4r=0) से (r=25) मिलता है। समान मूलों में विविक्तकर शून्य होता है।
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Question 10/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(9x^2-6x+1=0\) में मूलों की प्रकृति क्या है?
What is the nature of roots in \(9x^2-6x+1=0\)?
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और समान/two real and equal
Step 1
Concept
(D=(-6)2-4(9)(1)=0). Therefore this is a case of equal real roots.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और समान / two real and equal. (D=(-6)2-4(9)(1)=0). Therefore this is a case of equal real roots.
Step 3
Exam Tip
(D=(-6)2-4(9)(1)=0) है। इसलिए यह समान वास्तविक मूलों का मामला है।
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Question 11/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
यदि (D=0) और \(a\neq0\) हो तो द्विघात समीकरण में कितने अलग-अलग वास्तविक मूल होंगे?
If (D=0) and \(a\neq0\), how many distinct real roots will the quadratic equation have?
Explanation opens after your attempt
Step 1
Concept
At (D=0), both roots are equal, so the number of distinct real roots is (1). Remember the root is repeated.
Step 2
Why this answer is correct
The correct answer is A. (1). At (D=0), both roots are equal, so the number of distinct real roots is (1). Remember the root is repeated.
Step 3
Exam Tip
(D=0) पर दोनों मूल समान होते हैं, इसलिए अलग-अलग वास्तविक मूलों की संख्या (1) है। ध्यान रखें मूल दो बार दोहरता है।
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Question 12/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(4x^2-12x+9=0\) को देखकर मूलों की प्रकृति क्या होगी?
By observing \(4x^2-12x+9=0\), what will be the nature of roots?
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और समान/two real and equal
Step 1
Concept
\(4x^2-12x+9\) is a perfect square ((2x-3)2). So the roots are equal and real.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और समान / two real and equal. \(4x^2-12x+9\) is a perfect square ((2x-3)2). So the roots are equal and real.
Step 3
Exam Tip
\(4x^2-12x+9\) एक पूर्ण वर्ग ((2x-3)2) है। इसलिए मूल समान वास्तविक हैं।
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Question 13/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
किस समीकरण के दो वास्तविक और समान मूल होंगे?
Which equation will have two real and equal roots?
Explanation opens after your attempt
Correct Answer
A. \(x^2+10x+25=0\)
Step 1
Concept
In the first equation, (D=102-4(1)(25)=0). A perfect square form often gives equal roots.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+10x+25=0\). In the first equation, (D=102-4(1)(25)=0). A perfect square form often gives equal roots.
Step 3
Exam Tip
पहले समीकरण में (D=102-4(1)(25)=0) है। पूर्ण वर्ग रूप अक्सर समान मूल देता है।
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Question 14/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2+kx+16=0\) के समान वास्तविक मूल होने के लिए (k) का कौन सा मान सही हो सकता है?
Which value of (k) can make \(x^2+kx+16=0\) have equal real roots?
Explanation opens after your attempt
Step 1
Concept
For equal roots \(k^2-64=0\), so (k=8) or (k=-8). Among the options, (8) is correct.
Step 2
Why this answer is correct
The correct answer is A. (8). For equal roots \(k^2-64=0\), so (k=8) or (k=-8). Among the options, (8) is correct.
Step 3
Exam Tip
समान मूलों के लिए \(k^2-64=0\) होता है, इसलिए (k=8) या (k=-8)। दिए विकल्पों में (8) सही है।
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Question 15/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2-8x+m=0\) में समान वास्तविक मूलों के लिए (m) क्या होगा?
In \(x^2-8x+m=0\), what is (m) for equal real roots?
Explanation opens after your attempt
Step 1
Concept
(D=(-8)2-4m=0) gives (m=16). Keep the discriminant zero for equal roots.
Step 2
Why this answer is correct
The correct answer is A. (16). (D=(-8)2-4m=0) gives (m=16). Keep the discriminant zero for equal roots.
Step 3
Exam Tip
(D=(-8)2-4m=0) से (m=16) मिलता है। बराबर मूलों के लिए विविक्तकर शून्य रखें।
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Question 16/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2+6x+k=0\) के समान वास्तविक मूल होने के लिए (k) का मान क्या होगा?
For \(x^2+6x+k=0\) to have equal real roots, what should be the value of (k)?
Explanation opens after your attempt
Step 1
Concept
For equal roots (D=0), so \(6^2-4k=0\) gives (k=9). Use (D=0) in such questions.
Step 2
Why this answer is correct
The correct answer is A. (9). For equal roots (D=0), so \(6^2-4k=0\) gives (k=9). Use (D=0) in such questions.
Step 3
Exam Tip
समान मूलों के लिए (D=0), इसलिए \(6^2-4k=0\) से (k=9)। ऐसे प्रश्न में (D=0) लगाएं।
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Question 17/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(3x^2+6x+3=0\) के मूल किस प्रकार के होंगे?
What type of roots will the equation \(3x^2+6x+3=0\) have?
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और समान/two real and equal
Step 1
Concept
(D=62-4(3)(3)=0). Hence both roots will be equal and real.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और समान / two real and equal. (D=62-4(3)(3)=0). Hence both roots will be equal and real.
Step 3
Exam Tip
(D=62-4(3)(3)=0) है। इसलिए दोनों मूल समान वास्तविक होंगे।
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Question 18/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2-4x+4=0\) के मूलों की प्रकृति पहचानिए।
Identify the nature of roots of the equation \(x^2-4x+4=0\).
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और समान/two real and equal
Step 1
Concept
Here (D=(-4)2-4(1)(4)=0). (D=0) means equal real roots.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और समान / two real and equal. Here (D=(-4)2-4(1)(4)=0). (D=0) means equal real roots.
Step 3
Exam Tip
यहां (D=(-4)2-4(1)(4)=0) है। (D=0) समान वास्तविक मूल बताता है।
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Question 19/92
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
यदि द्विघात समीकरण के लिए (D=0) हो तो मूल कैसे होंगे?
If (D=0) for a quadratic equation, how will the roots be?
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और समान/two real and equal
Step 1
Concept
When (D=0), both roots are equal. These are also called repeated real roots.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और समान / two real and equal. When (D=0), both roots are equal. These are also called repeated real roots.
Step 3
Exam Tip
(D=0) होने पर दोनों मूल बराबर होते हैं। इसे दोहराए गए वास्तविक मूल भी कहते हैं।
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Question 20/92
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(x^2-24x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-24x+m=0\) has real and equal roots, what is the value of (m)?
Explanation opens after your attempt
Correct Answer
A. (m=144)
Step 1
Concept
For real and equal roots, (D=0), so (576-4m=0) gives (m=144). In exams, equal roots indicate (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=144). For real and equal roots, (D=0), so (576-4m=0) gives (m=144). In exams, equal roots indicate (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (576-4m=0) से (m=144) है। परीक्षा में समान मूल का संकेत (D=0) होता है।
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Question 21/92
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(x^2-22x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-22x+m=0\) has real and equal roots, what is the value of (m)?
Explanation opens after your attempt
Correct Answer
A. (m=121)
Step 1
Concept
For real and equal roots, (D=0), so (484-4m=0) gives (m=121). In exams, equal roots indicate (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=121). For real and equal roots, (D=0), so (484-4m=0) gives (m=121). In exams, equal roots indicate (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (484-4m=0) से (m=121) है। परीक्षा में समान मूल का संकेत (D=0) होता है।
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Question 22/92
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(x^2-20x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-20x+m=0\) has real and equal roots, what is the value of (m)?
Explanation opens after your attempt
Correct Answer
A. (m=100)
Step 1
Concept
For real and equal roots, (D=0), so (400-4m=0) gives (m=100). In exams, equal roots indicate (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=100). For real and equal roots, (D=0), so (400-4m=0) gives (m=100). In exams, equal roots indicate (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (400-4m=0) से (m=100) है। परीक्षा में समान मूल का संकेत (D=0) होता है।
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Question 23/92
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि \(x^2-18x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-18x+m=0\) has real and equal roots, what is the value of (m)?
Explanation opens after your attempt
Step 1
Concept
For real and equal roots, (D=0), so (324-4m=0) gives (m=81). In exams, equal roots mean (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=81). For real and equal roots, (D=0), so (324-4m=0) gives (m=81). In exams, equal roots mean (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (324-4m=0) से (m=81) है। परीक्षा में समान मूल का मतलब (D=0) होता है।
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Question 24/92
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि \(x^2-14x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-14x+m=0\) has real and equal roots, what is the value of (m)?
Explanation opens after your attempt
Step 1
Concept
For real and equal roots, (D=0), so (196-4m=0) gives (m=49). In exams, equal roots mean (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=49). For real and equal roots, (D=0), so (196-4m=0) gives (m=49). In exams, equal roots mean (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (196-4m=0) से (m=49) है। परीक्षा में समान मूल का मतलब (D=0) होता है।
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Question 25/92
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि \(x^2-6x+m=0\) के मूल वास्तविक और समान हैं, तो (m) का मान क्या है?
If \(x^2-6x+m=0\) has real and equal roots, what is the value of (m)?
Explanation opens after your attempt
Step 1
Concept
For real and equal roots, (D=0), so (36-4m=0) gives (m=9). In exams, remember equal roots mean (D=0).
Step 2
Why this answer is correct
The correct answer is A. (m=9). For real and equal roots, (D=0), so (36-4m=0) gives (m=9). In exams, remember equal roots mean (D=0).
Step 3
Exam Tip
समान वास्तविक मूलों के लिए (D=0), इसलिए (36-4m=0) से (m=9) है। परीक्षा में समान मूल का मतलब (D=0) याद रखें।
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Question 26/92
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
यदि (D=0) और (a=4,b=-16), तो समान मूल क्या होगा?
If (D=0) and (a=4,b=-16), what will be the equal root?
Explanation opens after your attempt
Step 1
Concept
The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{16}{8}=2\). In exams, this short formula is useful when (D=0).
Step 2
Why this answer is correct
The correct answer is A. (x=2). The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{16}{8}=2\). In exams, this short formula is useful when (D=0).
Step 3
Exam Tip
समान मूल \(x=\frac{-b}{2a}\) होता है, इसलिए \(x=\frac{16}{8}=2\) है। परीक्षा में (D=0) पर यह छोटा सूत्र उपयोगी है।
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Question 27/92
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
यदि (D=0) और (a=3,b=-12), तो समान मूल क्या होगा?
If (D=0) and (a=3,b=-12), what will be the equal root?
Explanation opens after your attempt
Step 1
Concept
The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{12}{6}=2\). In exams, this short formula is useful when (D=0).
Step 2
Why this answer is correct
The correct answer is A. (x=2). The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{12}{6}=2\). In exams, this short formula is useful when (D=0).
Step 3
Exam Tip
समान मूल \(x=\frac{-b}{2a}\) होता है, इसलिए \(x=\frac{12}{6}=2\) है। परीक्षा में (D=0) पर यह छोटा सूत्र उपयोगी है।
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Question 28/92
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि (D=0) और (a=2,b=-8), तो समान मूल क्या होगा?
If (D=0) and (a=2,b=-8), what will be the equal root?
Explanation opens after your attempt
Step 1
Concept
The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{8}{4}=2\). In exams, this short formula is useful when (D=0).
Step 2
Why this answer is correct
The correct answer is A. (x=2). The equal root is \(x=\frac{-b}{2a}\), so \(x=\frac{8}{4}=2\). In exams, this short formula is useful when (D=0).
Step 3
Exam Tip
समान मूल \(x=\frac{-b}{2a}\) होता है, इसलिए \(x=\frac{8}{4}=2\) है। परीक्षा में (D=0) पर यह छोटा सूत्र उपयोगी है।
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Question 29/92
Easy Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
यदि (D=0), तो द्विघात समीकरण के मूल कैसे होते हैं?
If (D=0), what type of roots does a quadratic equation have?
Explanation opens after your attempt
Correct Answer
A. समान वास्तविक मूल/Equal real roots
Step 1
Concept
When (D=0), both roots are equal. In exams, (D) quickly tells the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. समान वास्तविक मूल / Equal real roots. When (D=0), both roots are equal. In exams, (D) quickly tells the nature of roots.
Step 3
Exam Tip
(D=0) होने पर दोनों मूल समान होते हैं। परीक्षा में (D) से मूलों की प्रकृति तुरंत पता चलती है।
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Question 30/92
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि (x-2+(m-2)x+25=0) की जड़ें समान हैं, तो (m) के मान क्या हैं?
If (x-2+(m-2)x+25=0) has equal roots, what are the values of (m)?
Explanation opens after your attempt
Correct Answer
A. (12) और (-8)/(12) and (-8)
Step 1
Concept
For equal roots, ((m-2)2-100=0). Thus \(m-2=\pm10\), so (m=12) or (m=-8).
Step 2
Why this answer is correct
The correct answer is A. (12) और (-8) / (12) and (-8). For equal roots, ((m-2)2-100=0). Thus \(m-2=\pm10\), so (m=12) or (m=-8).
Step 3
Exam Tip
समान जड़ों के लिए ((m-2)2-100=0) होगा। इसलिए \(m-2=\pm10\), अतः (m=12) या (m=-8)।
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