Question 1/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(3x^2+10x+3=0\) के मूलों की प्रकृति क्या है?
What is the nature of roots of \(3x^2+10x+3=0\)?
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और असमान/two real and distinct
Step 1
Concept
(D=102-4(3)(3)=64>0). Therefore the roots are real and distinct.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और असमान / two real and distinct. (D=102-4(3)(3)=64>0). Therefore the roots are real and distinct.
Step 3
Exam Tip
(D=102-4(3)(3)=64>0) है। इसलिए मूल वास्तविक और असमान हैं।
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Question 2/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
कथन पढ़िए: \(x^2+1=0\) के वास्तविक मूल नहीं हैं क्योंकि (D<0)। यह कथन कैसा है?
Read the statement: \(x^2+1=0\) has no real roots because (D<0). How is this statement?
Explanation opens after your attempt
Correct Answer
A. सही/correct
Step 1
Concept
(D=02-4(1)(1)=-4<0). Hence the statement is correct and there are no real roots.
Step 2
Why this answer is correct
The correct answer is A. सही / correct. (D=02-4(1)(1)=-4<0). Hence the statement is correct and there are no real roots.
Step 3
Exam Tip
(D=02-4(1)(1)=-4<0) है। इसलिए कथन सही है और वास्तविक मूल नहीं हैं।
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Question 3/600
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 4/600
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 5/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2-4x+8=0\) के मूलों की प्रकृति बताइए।
State the nature of roots of \(x^2-4x+8=0\).
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं/no real roots
Step 1
Concept
(D=(-4)2-4(1)(8)=-16<0). So there are no real roots.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=(-4)2-4(1)(8)=-16<0). So there are no real roots.
Step 3
Exam Tip
(D=(-4)2-4(1)(8)=-16<0) है। इसलिए कोई वास्तविक मूल नहीं है।
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Question 6/600
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 7/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2-11x+30=0\) के लिए मूलों की प्रकृति क्या होगी?
What will be the nature of roots for \(x^2-11x+30=0\)?
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और असमान/two real and distinct
Step 1
Concept
(D=(-11)2-4(1)(30)=1>0). Therefore the roots will be real and distinct.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और असमान / two real and distinct. (D=(-11)2-4(1)(30)=1>0). Therefore the roots will be real and distinct.
Step 3
Exam Tip
(D=(-11)2-4(1)(30)=1>0) है। इसलिए मूल वास्तविक और असमान होंगे।
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Question 8/600
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 9/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(3x^2-2x+4=0\) के लिए विविक्तकर का चिन्ह क्या है?
What is the sign of the discriminant for \(3x^2-2x+4=0\)?
Explanation opens after your attempt
Correct Answer
A. ऋणात्मक/negative
Step 1
Concept
(D=(-2)2-4(3)(4)=-44<0). Hence the discriminant is negative.
Step 2
Why this answer is correct
The correct answer is A. ऋणात्मक / negative. (D=(-2)2-4(3)(4)=-44<0). Hence the discriminant is negative.
Step 3
Exam Tip
(D=(-2)2-4(3)(4)=-44<0) है। अतः विविक्तकर ऋणात्मक है।
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Question 10/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2+5x+6=0\) के लिए विविक्तकर और प्रकृति का सही युग्म कौन सा है?
Which pair of discriminant and nature is correct for \(x^2+5x+6=0\)?
Explanation opens after your attempt
Correct Answer
A. (D=1), दो वास्तविक और असमान/(D=1), two real and distinct
Step 1
Concept
(D=52-4(1)(6)=1). A positive (D) gives real and distinct roots.
Step 2
Why this answer is correct
The correct answer is A. (D=1), दो वास्तविक और असमान / (D=1), two real and distinct. (D=52-4(1)(6)=1). A positive (D) gives real and distinct roots.
Step 3
Exam Tip
(D=52-4(1)(6)=1) है। धनात्मक (D) से वास्तविक और असमान मूल होते हैं।
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Question 11/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(4x^2+4x+5=0\) के लिए सही प्रकृति कौन सी है?
Which is the correct nature for \(4x^2+4x+5=0\)?
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं/no real roots
Step 1
Concept
(D=42-4(4)(5)=-64<0). Therefore it has no real roots.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=42-4(4)(5)=-64<0). Therefore it has no real roots.
Step 3
Exam Tip
(D=42-4(4)(5)=-64<0) है। इसलिए इसके वास्तविक मूल नहीं हैं।
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Question 12/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(2x^2-7x+3=0\) के मूलों की प्रकृति क्या है?
What is the nature of roots of \(2x^2-7x+3=0\)?
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और असमान/two real and distinct
Step 1
Concept
(D=(-7)2-4(2)(3)=25>0). Hence the roots are real and distinct.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और असमान / two real and distinct. (D=(-7)2-4(2)(3)=25>0). Hence the roots are real and distinct.
Step 3
Exam Tip
(D=(-7)2-4(2)(3)=25>0) है। इसलिए मूल वास्तविक और असमान हैं।
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Question 13/600
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 14/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
यदि किसी द्विघात समीकरण के वास्तविक मूल नहीं हैं, तो (D) के लिए सही शर्त क्या है?
If a quadratic equation has no real roots, what is the correct condition for (D)?
Explanation opens after your attempt
Step 1
Concept
When there are no real roots, (D<0). The condition \(D\geq0\) indicates real roots.
Step 2
Why this answer is correct
The correct answer is A. (D<0). When there are no real roots, (D<0). The condition \(D\geq0\) indicates real roots.
Step 3
Exam Tip
वास्तविक मूल न होने पर (D<0) होता है। \(D\geq0\) वास्तविक मूलों की स्थिति बताता है।
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Question 15/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
यदि किसी द्विघात समीकरण के दो असमान वास्तविक मूल हैं, तो (D) कैसा होगा?
If a quadratic equation has two distinct real roots, how will (D) be?
Explanation opens after your attempt
Step 1
Concept
For distinct real roots, (D>0). Do not add the equality sign by mistake.
Step 2
Why this answer is correct
The correct answer is A. (D>0). For distinct real roots, (D>0). Do not add the equality sign by mistake.
Step 3
Exam Tip
असमान वास्तविक मूलों के लिए (D>0) होता है। बराबर का चिन्ह गलती से न लगाएं।
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Question 16/600
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 17/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(2x^2+8=0\) के मूलों की प्रकृति क्या होगी?
What will be the nature of roots of \(2x^2+8=0\)?
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं/no real roots
Step 1
Concept
(D=02-4(2)(8)=-64<0). Therefore the equation will have no real roots.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=02-4(2)(8)=-64<0). Therefore the equation will have no real roots.
Step 3
Exam Tip
(D=02-4(2)(8)=-64<0) है। इसलिए समीकरण के वास्तविक मूल नहीं होंगे।
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Question 18/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(4x^2-1=0\) के मूल कैसे होंगे?
How will the roots of \(4x^2-1=0\) be?
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और असमान/two real and distinct
Step 1
Concept
(D=02-4(4)(-1)=16>0). Hence two distinct real roots will be obtained.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और असमान / two real and distinct. (D=02-4(4)(-1)=16>0). Hence two distinct real roots will be obtained.
Step 3
Exam Tip
(D=02-4(4)(-1)=16>0) है। इसलिए दो असमान वास्तविक मूल मिलेंगे।
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Question 19/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2+9=0\) के लिए सही विकल्प चुनिए।
Choose the correct option for \(x^2+9=0\).
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं/no real roots
Step 1
Concept
Here (D=02-4(1)(9)=-36<0). Therefore there are no real roots.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं / no real roots. Here (D=02-4(1)(9)=-36<0). Therefore there are no real roots.
Step 3
Exam Tip
यहां (D=02-4(1)(9)=-36<0) है। इसलिए वास्तविक मूल नहीं हैं।
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Question 20/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2-9=0\) के मूलों की प्रकृति क्या है?
What is the nature of roots of \(x^2-9=0\)?
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और असमान/two real and distinct
Step 1
Concept
Here (D=02-4(1)(-9)=36>0). So the roots are real and distinct.
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और असमान / two real and distinct. Here (D=02-4(1)(-9)=36>0). So the roots are real and distinct.
Step 3
Exam Tip
यहां (D=02-4(1)(-9)=36>0) है। इसलिए मूल वास्तविक और असमान हैं।
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Question 21/600
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 22/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(2x^2+3x+\lambda=0\) के वास्तविक और असमान मूलों के लिए कौन सी शर्त सही है?
For \(2x^2+3x+\lambda=0\) to have real and distinct roots, which condition is correct?
Explanation opens after your attempt
Correct Answer
A. \(\lambda<\frac{9}{8}\)
Step 1
Concept
(D=32-4(2)\lambda=9-8\lambda). From (D>0), we get \(\lambda<\frac{9}{8}\).
Step 2
Why this answer is correct
The correct answer is A. \(\lambda<\frac{9}{8}\). (D=32-4(2)\lambda=9-8\lambda). From (D>0), we get \(\lambda<\frac{9}{8}\).
Step 3
Exam Tip
(D=32-4(2)\lambda=9-8\lambda) है। (D>0) से \(\lambda<\frac{9}{8}\) मिलता है।
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Question 23/600
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 24/600
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 25/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2+4x+p=0\) के वास्तविक मूल न होने के लिए कौन सी शर्त सही है?
For \(x^2+4x+p=0\) to have no real roots, which condition is correct?
Explanation opens after your attempt
Step 1
Concept
For no real roots (D<0), so (16-4p<0) gives (p>4). A negative discriminant gives no real roots.
Step 2
Why this answer is correct
The correct answer is A. (p>4). For no real roots (D<0), so (16-4p<0) gives (p>4). A negative discriminant gives no real roots.
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0), इसलिए (16-4p<0) से (p>4)। ऋणात्मक विविक्तकर पर वास्तविक मूल नहीं होते।
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Question 26/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2-2x+n=0\) के दो वास्तविक और असमान मूल होने के लिए कौन सी शर्त सही है?
For \(x^2-2x+n=0\) to have two real and distinct roots, which condition is correct?
Explanation opens after your attempt
Step 1
Concept
For distinct real roots (D>0), so ((-2)2-4n>0) gives (n<1). Use a strict inequality for distinct roots.
Step 2
Why this answer is correct
The correct answer is A. (n<1). For distinct real roots (D>0), so ((-2)2-4n>0) gives (n<1). Use a strict inequality for distinct roots.
Step 3
Exam Tip
असमान वास्तविक मूलों के लिए (D>0), इसलिए ((-2)2-4n>0) से (n<1)। असमान के लिए कड़ाई वाली असमता लगती है।
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Question 27/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(7x^2+2x+3=0\) के लिए सही निष्कर्ष क्या है?
What is the correct conclusion for \(7x^2+2x+3=0\)?
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं/no real roots
Step 1
Concept
(D=22-4(7)(3)=-80<0). So this equation has no real roots.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=22-4(7)(3)=-80<0). So this equation has no real roots.
Step 3
Exam Tip
(D=22-4(7)(3)=-80<0) है। इसलिए यह समीकरण वास्तविक मूल नहीं रखता।
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Question 28/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(6x^2-5x+1=0\) का विविक्तकर क्या है?
What is the discriminant of \(6x^2-5x+1=0\)?
Explanation opens after your attempt
Step 1
Concept
(D=(-5)2-4(6)(1)=1). This gives two real and distinct roots.
Step 2
Why this answer is correct
The correct answer is A. (1). (D=(-5)2-4(6)(1)=1). This gives two real and distinct roots.
Step 3
Exam Tip
(D=(-5)2-4(6)(1)=1) है। इससे दो वास्तविक और असमान मूल होंगे।
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Question 29/600
Easy Mathematics
Quadratic Equations Nature of Roots Class 10 Level 37
समीकरण \(x^2+x+3=0\) के मूलों की प्रकृति क्या होगी?
What will be the nature of roots of \(x^2+x+3=0\)?
Explanation opens after your attempt
Correct Answer
A. वास्तविक मूल नहीं/no real roots
Step 1
Concept
(D=12-4(1)(3)=-11<0). Hence real roots will not be obtained.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक मूल नहीं / no real roots. (D=12-4(1)(3)=-11<0). Hence real roots will not be obtained.
Step 3
Exam Tip
(D=12-4(1)(3)=-11<0) है। इसलिए वास्तविक मूल नहीं मिलेंगे।
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Question 30/600
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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