100 results found for "completing-square" in Class 10.
पूर्ण वर्ग बनाकर \(x^2+8x=0\) में \(x^2+8x+16\) किसके बराबर होगा?
By completing the square in \(x^2+8x=0\), what is \(x^2+8x+16\) equal to?
#quadratic
#completing-square
#perfect-square
A ((x+4)2 )
B ((x+8)2 )
C ((x-4)2 )
D ((x+16)2 )
Explanation opens after your attempt
Correct Answer
A. ((x+4)2 )
Step 1
Concept
(x-2 +8x+16=(x+4)2 ). In exams, take half of (8), which is (4), and add its square.
Step 2
Why this answer is correct
The correct answer is A. ((x+4)2 ). (x-2 +8x+16=(x+4)2 ). In exams, take half of (8), which is (4), and add its square.
Step 3
Exam Tip
(x-2 +8x+16=(x+4)2 ) होता है। परीक्षा में (8) का आधा (4) लेकर उसका वर्ग जोड़ें।
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यदि \(x^2+14x+10=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+14x+10=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+7)2 =39)
B ((x-7)2 =39)
C ((x+14)2 =10)
D ((x+7)2 =10)
Explanation opens after your attempt
Correct Answer
A. ((x+7)2 =39)
Step 1
Concept
Adding (49) to \(x^2+14x=-10\) gives ((x+7)2 =39). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+7)2 =39). Adding (49) to \(x^2+14x=-10\) gives ((x+7)2 =39). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+14x=-10\) में (49) जोड़ने पर ((x+7)2 =39) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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\(13x^2-52x+9=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(13x^2-52x+9=0\) by completing square method?
#quadratic
#completing-square
#irrational-roots
A \(x=2\pm\frac{\sqrt{559}}{13}\)
B \(x=-2\pm\frac{\sqrt{559}}{13}\)
C \(x=4\pm\sqrt{559}\)
D \(x=2\pm\frac{\sqrt{43}}{13}\)
Explanation opens after your attempt
Correct Answer
A. \(x=2\pm\frac{\sqrt{559}}{13}\)
Step 1
Concept
Since ((x-2)2 =\frac{43}{13}), \(x=2\pm\sqrt{\frac{43}{13}}=2\pm\frac{\sqrt{559}}{13}\). In exams, rationalize the denominator.
Step 2
Why this answer is correct
The correct answer is A. \(x=2\pm\frac{\sqrt{559}}{13}\). Since ((x-2)2 =\frac{43}{13}), \(x=2\pm\sqrt{\frac{43}{13}}=2\pm\frac{\sqrt{559}}{13}\). In exams, rationalize the denominator.
Step 3
Exam Tip
((x-2)2 =\frac{43}{13}), इसलिए \(x=2\pm\sqrt{\frac{43}{13}}=2\pm\frac{\sqrt{559}}{13}\) है। परीक्षा में हर को परिमेय बनाएं।
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\(13x^2-52x+9=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(13x^2-52x+9=0\) by completing the square?
#quadratic
#completing-square
#expert
A ((x-2)2 =\frac{43}{13})
B ((x+2)2 =\frac{43}{13})
C ((x-4)2 =\frac{9}{13})
D ((x-2)2 =4)
Explanation opens after your attempt
Correct Answer
A. ((x-2)2 =\frac{43}{13})
Step 1
Concept
First \(x^2-4x+\frac{9}{13}=0\) is obtained, then ((x-2)2 =\frac{43}{13}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. ((x-2)2 =\frac{43}{13}). First \(x^2-4x+\frac{9}{13}=0\) is obtained, then ((x-2)2 =\frac{43}{13}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-4x+\frac{9}{13}=0\) बनता है, फिर ((x-2)2 =\frac{43}{13}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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यदि \(3x^2+18x+5=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(3x^2+18x+5=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#expert
A ((x+3)2 =\frac{22}{3})
B ((x-3)2 =\frac{22}{3})
C ((x+6)2 =\frac{5}{3})
D ((x+3)2 =9)
Explanation opens after your attempt
Correct Answer
A. ((x+3)2 =\frac{22}{3})
Step 1
Concept
First \(x^2+6x+\frac{5}{3}=0\) is obtained, then adding (9) gives ((x+3)2 =\frac{22}{3}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. ((x+3)2 =\frac{22}{3}). First \(x^2+6x+\frac{5}{3}=0\) is obtained, then adding (9) gives ((x+3)2 =\frac{22}{3}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2+6x+\frac{5}{3}=0\) मिलता है, फिर (9) जोड़ने पर ((x+3)2 =\frac{22}{3}) बनता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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यदि \(x^2+12x+8=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+12x+8=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+6)2 =28)
B ((x-6)2 =28)
C ((x+12)2 =8)
D ((x+6)2 =8)
Explanation opens after your attempt
Correct Answer
A. ((x+6)2 =28)
Step 1
Concept
Adding (36) to \(x^2+12x=-8\) gives ((x+6)2 =28). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+6)2 =28). Adding (36) to \(x^2+12x=-8\) gives ((x+6)2 =28). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+12x=-8\) में (36) जोड़ने पर ((x+6)2 =28) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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\(11x^2-44x+7=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(11x^2-44x+7=0\) by completing square method?
#quadratic
#completing-square
#irrational-roots
A \(x=2\pm\frac{\sqrt{407}}{11}\)
B \(x=-2\pm\frac{\sqrt{407}}{11}\)
C \(x=4\pm\sqrt{407}\)
D \(x=2\pm\frac{\sqrt{37}}{11}\)
Explanation opens after your attempt
Correct Answer
A. \(x=2\pm\frac{\sqrt{407}}{11}\)
Step 1
Concept
Since ((x-2)2 =\frac{37}{11}), \(x=2\pm\sqrt{\frac{37}{11}}=2\pm\frac{\sqrt{407}}{11}\). In exams, rationalize the denominator.
Step 2
Why this answer is correct
The correct answer is A. \(x=2\pm\frac{\sqrt{407}}{11}\). Since ((x-2)2 =\frac{37}{11}), \(x=2\pm\sqrt{\frac{37}{11}}=2\pm\frac{\sqrt{407}}{11}\). In exams, rationalize the denominator.
Step 3
Exam Tip
((x-2)2 =\frac{37}{11}), इसलिए \(x=2\pm\sqrt{\frac{37}{11}}=2\pm\frac{\sqrt{407}}{11}\) है। परीक्षा में हर को परिमेय बनाएं।
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\(11x^2-44x+7=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(11x^2-44x+7=0\) by completing the square?
#quadratic
#completing-square
#expert
A ((x-2)2 =\frac{37}{11})
B ((x+2)2 =\frac{37}{11})
C ((x-4)2 =\frac{7}{11})
D ((x-2)2 =4)
Explanation opens after your attempt
Correct Answer
A. ((x-2)2 =\frac{37}{11})
Step 1
Concept
First \(x^2-4x+\frac{7}{11}=0\) is obtained, then ((x-2)2 =\frac{37}{11}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. ((x-2)2 =\frac{37}{11}). First \(x^2-4x+\frac{7}{11}=0\) is obtained, then ((x-2)2 =\frac{37}{11}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-4x+\frac{7}{11}=0\) बनता है, फिर ((x-2)2 =\frac{37}{11}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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यदि \(x^2+10x+6=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+10x+6=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+5)2 =19)
B ((x-5)2 =19)
C ((x+10)2 =6)
D ((x+5)2 =6)
Explanation opens after your attempt
Correct Answer
A. ((x+5)2 =19)
Step 1
Concept
Adding (25) to \(x^2+10x=-6\) gives ((x+5)2 =19). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+5)2 =19). Adding (25) to \(x^2+10x=-6\) gives ((x+5)2 =19). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+10x=-6\) में (25) जोड़ने पर ((x+5)2 =19) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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\(9x^2-30x+8=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(9x^2-30x+8=0\) by completing square method?
#quadratic
#completing-square
#irrational-roots
A \(x=\frac{5\pm\sqrt{17}}{3}\)
B \(x=\frac{-5\pm\sqrt{17}}{3}\)
C \(x=5\pm\sqrt{17}\)
D \(x=\frac{10\pm\sqrt{17}}{9}\)
Explanation opens after your attempt
Correct Answer
A. \(x=\frac{5\pm\sqrt{17}}{3}\)
Step 1
Concept
Since (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}), \(x=\frac{5\pm\sqrt{17}}{3}\). In exams, write the square root with the denominator correctly.
Step 2
Why this answer is correct
The correct answer is A. \(x=\frac{5\pm\sqrt{17}}{3}\). Since (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}), \(x=\frac{5\pm\sqrt{17}}{3}\). In exams, write the square root with the denominator correctly.
Step 3
Exam Tip
(\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}), इसलिए \(x=\frac{5\pm\sqrt{17}}{3}\) है। परीक्षा में वर्गमूल को हर के साथ सही लिखें।
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\(9x^2-30x+8=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(9x^2-30x+8=0\) by completing the square?
#quadratic
#completing-square
#expert
A (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9})
B (\left\(x+\frac{5}{3}\right\)2 =\frac{17}{9})
C (\left\(x-\frac{10}{3}\right\)2 =\frac{8}{9})
D (\left\(x-\frac{5}{3}\right\)2 =\frac{25}{9})
Explanation opens after your attempt
Correct Answer
A. (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9})
Step 1
Concept
First \(x^2-\frac{10}{3}x+\frac{8}{9}=0\) is obtained, then (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}). First \(x^2-\frac{10}{3}x+\frac{8}{9}=0\) is obtained, then (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-\frac{10}{3}x+\frac{8}{9}=0\) बनता है, फिर (\left\(x-\frac{5}{3}\right\)2 =\frac{17}{9}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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यदि \(x^2+8x+5=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+8x+5=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+4)2 =11)
B ((x-4)2 =11)
C ((x+8)2 =5)
D ((x+4)2 =5)
Explanation opens after your attempt
Correct Answer
A. ((x+4)2 =11)
Step 1
Concept
Adding (16) to \(x^2+8x=-5\) gives ((x+4)2 =11). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+4)2 =11). Adding (16) to \(x^2+8x=-5\) gives ((x+4)2 =11). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+8x=-5\) में (16) जोड़ने पर ((x+4)2 =11) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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\(7x^2-22x+7=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(7x^2-22x+7=0\) by completing the square?
#quadratic
#completing-square
#hard
A (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49})
B (\left\(x+\frac{11}{7}\right\)2 =\frac{72}{49})
C (\left\(x-\frac{22}{7}\right\)2 =1)
D (\left\(x-\frac{11}{7}\right\)2 =\frac{121}{49})
Explanation opens after your attempt
Correct Answer
A. (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49})
Step 1
Concept
First \(x^2-\frac{22}{7}x+1=0\) is obtained, then (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49}). First \(x^2-\frac{22}{7}x+1=0\) is obtained, then (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-\frac{22}{7}x+1=0\) बनता है, फिर (\left\(x-\frac{11}{7}\right\)2 =\frac{72}{49}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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यदि \(2x^2+10x+3=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(2x^2+10x+3=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#hard
A (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4})
B (\left\(x-\frac{5}{2}\right\)2 =\frac{19}{4})
C ((x+5)2 =\frac{3}{2})
D (\left\(x+\frac{5}{2}\right\)2 =\frac{25}{4})
Explanation opens after your attempt
Correct Answer
A. (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4})
Step 1
Concept
First \(x^2+5x+\frac{3}{2}=0\) is obtained, then adding \(\frac{25}{4}\) gives (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4}). First \(x^2+5x+\frac{3}{2}=0\) is obtained, then adding \(\frac{25}{4}\) gives (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2+5x+\frac{3}{2}=0\) मिलता है, फिर \(\frac{25}{4}\) जोड़ने पर (\left\(x+\frac{5}{2}\right\)2 =\frac{19}{4}) बनता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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यदि \(x^2+6x+2=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+6x+2=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+3)2 =7)
B ((x-3)2 =7)
C ((x+6)2 =2)
D ((x+3)2 =2)
Explanation opens after your attempt
Correct Answer
A. ((x+3)2 =7)
Step 1
Concept
Adding (9) to \(x^2+6x=-2\) gives ((x+3)2 =7). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+3)2 =7). Adding (9) to \(x^2+6x=-2\) gives ((x+3)2 =7). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+6x=-2\) में (9) जोड़ने पर ((x+3)2 =7) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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\(5x^2-18x+9=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(5x^2-18x+9=0\) by completing the square?
#quadratic
#completing-square
#hard
A (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25})
B (\left\(x+\frac{9}{5}\right\)2 =\frac{36}{25})
C (\left\(x-\frac{18}{5}\right\)2 =\frac{9}{5})
D (\left\(x-\frac{9}{5}\right\)2 =\frac{81}{25})
Explanation opens after your attempt
Correct Answer
A. (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25})
Step 1
Concept
First \(x^2-\frac{18}{5}x+\frac{9}{5}=0\) is obtained, then (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25}). First \(x^2-\frac{18}{5}x+\frac{9}{5}=0\) is obtained, then (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-\frac{18}{5}x+\frac{9}{5}=0\) बनता है, फिर (\left\(x-\frac{9}{5}\right\)2 =\frac{36}{25}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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\(2x^2+8x+1=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(2x^2+8x+1=0\) by completing the square method?
#quadratic
#completing-square
#irrational-roots
A \(x=-2\pm\frac{\sqrt{14}}{2}\)
B \(x=2\pm\frac{\sqrt{14}}{2}\)
C \(x=-4\pm\sqrt{14}\)
D \(x=-2\pm\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(x=-2\pm\frac{\sqrt{14}}{2}\)
Step 1
Concept
Since ((x+2)2 =\frac{7}{2}), \(x=-2\pm\sqrt{\frac{7}{2}}=-2\pm\frac{\sqrt{14}}{2}\). In exams, write the square root in simplified form.
Step 2
Why this answer is correct
The correct answer is A. \(x=-2\pm\frac{\sqrt{14}}{2}\). Since ((x+2)2 =\frac{7}{2}), \(x=-2\pm\sqrt{\frac{7}{2}}=-2\pm\frac{\sqrt{14}}{2}\). In exams, write the square root in simplified form.
Step 3
Exam Tip
((x+2)2 =\frac{7}{2}), इसलिए \(x=-2\pm\sqrt{\frac{7}{2}}=-2\pm\frac{\sqrt{14}}{2}\) है। परीक्षा में वर्गमूल को सरल रूप में लिखें।
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यदि \(2x^2+8x+1=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(2x^2+8x+1=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#hard
A ((x+2)2 =\frac{7}{2})
B ((x-2)2 =\frac{7}{2})
C ((x+4)2 =\frac{1}{2})
D ((x+2)2 =7)
Explanation opens after your attempt
Correct Answer
A. ((x+2)2 =\frac{7}{2})
Step 1
Concept
First \(x^2+4x+\frac{1}{2}=0\) is obtained, then adding (4) gives ((x+2)2 =\frac{7}{2}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. ((x+2)2 =\frac{7}{2}). First \(x^2+4x+\frac{1}{2}=0\) is obtained, then adding (4) gives ((x+2)2 =\frac{7}{2}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2+4x+\frac{1}{2}=0\) मिलता है, फिर (4) जोड़ने पर ((x+2)2 =\frac{7}{2}) बनता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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यदि \(x^2+4x+1=0\), तो पूर्ण वर्ग विधि से सही रूप कौनसा है?
If \(x^2+4x+1=0\), which form is correct by completing square?
#quadratic
#completing-square
#irrational-roots
A ((x+2)2 =3)
B ((x-2)2 =3)
C ((x+4)2 =1)
D ((x+2)2 =1)
Explanation opens after your attempt
Correct Answer
A. ((x+2)2 =3)
Step 1
Concept
Adding (4) to \(x^2+4x=-1\) gives ((x+2)2 =3). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+2)2 =3). Adding (4) to \(x^2+4x=-1\) gives ((x+2)2 =3). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2+4x=-1\) में (4) जोड़ने पर ((x+2)2 =3) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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\(3x^2-10x+3=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(3x^2-10x+3=0\) by completing the square?
#quadratic
#completing-square
#hard
A (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9})
B (\left\(x+\frac{5}{3}\right\)2 =\frac{16}{9})
C (\left\(x-\frac{10}{3}\right\)2 =1)
D (\left\(x-\frac{5}{3}\right\)2 =\frac{25}{9})
Explanation opens after your attempt
Correct Answer
A. (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9})
Step 1
Concept
First we get \(x^2-\frac{10}{3}x+1=0\), then (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9}). In exams, divide by (a) first when \(a\neq1\).
Step 2
Why this answer is correct
The correct answer is A. (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9}). First we get \(x^2-\frac{10}{3}x+1=0\), then (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9}). In exams, divide by (a) first when \(a\neq1\).
Step 3
Exam Tip
पहले \(x^2-\frac{10}{3}x+1=0\) बनता है और फिर (\left\(x-\frac{5}{3}\right\)2 =\frac{16}{9}) मिलता है। परीक्षा में \(a\neq1\) हो तो पहले (a) से भाग दें।
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\(x^2-24x+108=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(x^2-24x+108=0\) by completing the square method?
#quadratic
#completing-square
#roots
A (x=6,18)
B (x=-6,-18)
C (x=12,6)
D (x=24,108)
Explanation opens after your attempt
Correct Answer
A. (x=6,18)
Step 1
Concept
Since ((x-12)2 =36), \(x-12=\pm6\), so (x=6,18). In exams, use \(\pm\) to find both roots.
Step 2
Why this answer is correct
The correct answer is A. (x=6,18). Since ((x-12)2 =36), \(x-12=\pm6\), so (x=6,18). In exams, use \(\pm\) to find both roots.
Step 3
Exam Tip
((x-12)2 =36), इसलिए \(x-12=\pm6\) और (x=6,18) हैं। परीक्षा में \(\pm\) से दोनों मूल निकालें।
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यदि \(x^2-24x+108=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(x^2-24x+108=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#steps
A ((x-12)2 =36)
B ((x+12)2 =36)
C ((x-24)2 =108)
D ((x-12)2 =108)
Explanation opens after your attempt
Correct Answer
A. ((x-12)2 =36)
Step 1
Concept
Adding (144) to \(x^2-24x=-108\) gives ((x-12)2 =36). In exams, add the square of half the coefficient to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-12)2 =36). Adding (144) to \(x^2-24x=-108\) gives ((x-12)2 =36). In exams, add the square of half the coefficient to both sides.
Step 3
Exam Tip
\(x^2-24x=-108\) में (144) जोड़ने पर ((x-12)2 =36) मिलता है। परीक्षा में आधे गुणांक का वर्ग दोनों पक्षों में जोड़ें।
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\(x^2-6x+18=0\) में पूर्ण वर्ग बनाने पर कौनसा रूप बनेगा?
What form is obtained by completing the square in \(x^2-6x+18=0\)?
#quadratic
#completing-square
#no-real-roots
A ((x-3)2 +9=0)
B ((x+3)2 +9=0)
C ((x-3)2 -9=0)
D ((x+6)2 +3=0)
Explanation opens after your attempt
Correct Answer
A. ((x-3)2 +9=0)
Step 1
Concept
(x-2 -6x+18=(x-3)2 +9), so no real roots are obtained. In exams, use completed square form to understand the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. ((x-3)2 +9=0). (x-2 -6x+18=(x-3)2 +9), so no real roots are obtained. In exams, use completed square form to understand the nature of roots.
Step 3
Exam Tip
(x-2 -6x+18=(x-3)2 +9), इसलिए वास्तविक मूल नहीं मिलते। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति समझें।
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\(x^2+8x-33=0\) को पूर्ण वर्ग विधि से हल करने में सही चरण कौनसा है?
Which step is correct in solving \(x^2+8x-33=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x+4)2 =49)
B ((x-4)2 =49)
C ((x+8)2 =33)
D ((x+4)2 =33)
Explanation opens after your attempt
Correct Answer
A. ((x+4)2 =49)
Step 1
Concept
Adding (16) to \(x^2+8x=33\) gives ((x+4)2 =49). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. ((x+4)2 =49). Adding (16) to \(x^2+8x=33\) gives ((x+4)2 =49). In exams, add the square of half the coefficient.
Step 3
Exam Tip
\(x^2+8x=33\) में (16) जोड़ने पर ((x+4)2 =49) मिलता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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\(x^2-18x+45=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(x^2-18x+45=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x-9)2 =36)
B ((x+9)2 =36)
C ((x-18)2 =45)
D ((x-9)2 =45)
Explanation opens after your attempt
Correct Answer
A. ((x-9)2 =36)
Step 1
Concept
Adding (81) to \(x^2-18x=-45\) gives ((x-9)2 =36). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. ((x-9)2 =36). Adding (81) to \(x^2-18x=-45\) gives ((x-9)2 =36). In exams, add the square of half the coefficient.
Step 3
Exam Tip
\(x^2-18x=-45\) में (81) जोड़ने पर ((x-9)2 =36) मिलता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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\(x^2-10x+24=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(x^2-10x+24=0\) by completing the square?
#quadratic
#completing-square
#steps
A ((x-5)2 =1)
B ((x+5)2 =1)
C ((x-10)2 =24)
D ((x-5)2 =24)
Explanation opens after your attempt
Correct Answer
A. ((x-5)2 =1)
Step 1
Concept
Adding (25) to \(x^2-10x=-24\) gives ((x-5)2 =1). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-5)2 =1). Adding (25) to \(x^2-10x=-24\) gives ((x-5)2 =1). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2-10x=-24\) में (25) जोड़ने पर ((x-5)2 =1) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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\(x^2-6x-7=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What roots are obtained for \(x^2-6x-7=0\) by completing the square method?
#quadratic
#completing-square
#roots
A (x=7,-1)
B (x=-7,1)
C (x=3,4)
D (x=6,-7)
Explanation opens after your attempt
Correct Answer
A. (x=7,-1)
Step 1
Concept
Since ((x-3)2 =16), \(x-3=\pm4\), so (x=7,-1). In exams, use \(\pm\) to find both roots.
Step 2
Why this answer is correct
The correct answer is A. (x=7,-1). Since ((x-3)2 =16), \(x-3=\pm4\), so (x=7,-1). In exams, use \(\pm\) to find both roots.
Step 3
Exam Tip
((x-3)2 =16), इसलिए \(x-3=\pm4\) और (x=7,-1) हैं। परीक्षा में \(\pm\) से दोनों मूल निकालें।
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यदि \(x^2-6x-7=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(x^2-6x-7=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#steps
A ((x-3)2 =16)
B ((x+3)2 =16)
C ((x-6)2 =7)
D ((x-3)2 =7)
Explanation opens after your attempt
Correct Answer
A. ((x-3)2 =16)
Step 1
Concept
Adding (9) to \(x^2-6x=7\) gives ((x-3)2 =16). In exams, add the square of half the coefficient to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-3)2 =16). Adding (9) to \(x^2-6x=7\) gives ((x-3)2 =16). In exams, add the square of half the coefficient to both sides.
Step 3
Exam Tip
\(x^2-6x=7\) में (9) जोड़ने पर ((x-3)2 =16) मिलता है। परीक्षा में आधे गुणांक का वर्ग दोनों पक्षों में जोड़ें।
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\(x^2-4x+13=0\) में पूर्ण वर्ग बनाने पर कौनसा रूप बनेगा?
What form is obtained by completing the square in \(x^2-4x+13=0\)?
#quadratic
#completing-square
#no-real-roots
A ((x-2)2 +9=0)
B ((x+2)2 +9=0)
C ((x-2)2 -9=0)
D ((x+4)2 +2=0)
Explanation opens after your attempt
Correct Answer
A. ((x-2)2 +9=0)
Step 1
Concept
(x-2 -4x+13=(x-2)2 +9), so no real roots are obtained. In exams, use completed square form to understand the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. ((x-2)2 +9=0). (x-2 -4x+13=(x-2)2 +9), so no real roots are obtained. In exams, use completed square form to understand the nature of roots.
Step 3
Exam Tip
(x-2 -4x+13=(x-2)2 +9), इसलिए वास्तविक मूल नहीं मिलते। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति समझें।
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\(x^2+2x-24=0\) को पूर्ण वर्ग विधि से हल करने में सही चरण कौनसा है?
Which step is correct in solving \(x^2+2x-24=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x+1)2 =25)
B ((x-1)2 =25)
C ((x+2)2 =24)
D ((x+1)2 =24)
Explanation opens after your attempt
Correct Answer
A. ((x+1)2 =25)
Step 1
Concept
Adding (1) to \(x^2+2x=24\) gives ((x+1)2 =25). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. ((x+1)2 =25). Adding (1) to \(x^2+2x=24\) gives ((x+1)2 =25). In exams, add the square of half the coefficient.
Step 3
Exam Tip
\(x^2+2x=24\) में (1) जोड़ने पर ((x+1)2 =25) मिलता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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\(x^2-16x+28=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(x^2-16x+28=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x-8)2 =36)
B ((x+8)2 =36)
C ((x-16)2 =28)
D ((x-8)2 =28)
Explanation opens after your attempt
Correct Answer
A. ((x-8)2 =36)
Step 1
Concept
Adding (64) to \(x^2-16x=-28\) gives ((x-8)2 =36). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. ((x-8)2 =36). Adding (64) to \(x^2-16x=-28\) gives ((x-8)2 =36). In exams, add the square of half the coefficient.
Step 3
Exam Tip
\(x^2-16x=-28\) में (64) जोड़ने पर ((x-8)2 =36) मिलता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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\(x^2-8x+12=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(x^2-8x+12=0\) by completing the square?
#quadratic
#completing-square
#steps
A ((x-4)2 =4)
B ((x+4)2 =4)
C ((x-8)2 =12)
D ((x-4)2 =12)
Explanation opens after your attempt
Correct Answer
A. ((x-4)2 =4)
Step 1
Concept
Adding (16) to \(x^2-8x=-12\) gives ((x-4)2 =4). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-4)2 =4). Adding (16) to \(x^2-8x=-12\) gives ((x-4)2 =4). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2-8x=-12\) में (16) जोड़ने पर ((x-4)2 =4) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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\(x^2-8x+15=0\) के मूल पूर्ण वर्ग विधि से क्या मिलेंगे?
What roots are obtained for \(x^2-8x+15=0\) by completing the square method?
#quadratic
#completing-square
#roots
A (x=3,5)
B (x=-3,-5)
C (x=1,7)
D (x=4,1)
Explanation opens after your attempt
Correct Answer
A. (x=3,5)
Step 1
Concept
Since ((x-4)2 =1), \(x-4=\pm1\), so (x=3,5). In exams, use \(\pm\) to find both roots.
Step 2
Why this answer is correct
The correct answer is A. (x=3,5). Since ((x-4)2 =1), \(x-4=\pm1\), so (x=3,5). In exams, use \(\pm\) to find both roots.
Step 3
Exam Tip
((x-4)2 =1), इसलिए \(x-4=\pm1\) और (x=3,5) हैं। परीक्षा में \(\pm\) से दोनों मूल निकालें।
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यदि \(x^2-8x+15=0\) को पूर्ण वर्ग विधि से हल किया जाए, तो सही मध्य चरण कौनसा है?
If \(x^2-8x+15=0\) is solved by completing the square, which middle step is correct?
#quadratic
#completing-square
#steps
A ((x-4)2 =1)
B ((x+4)2 =1)
C ((x-8)2 =15)
D ((x-4)2 =15)
Explanation opens after your attempt
Correct Answer
A. ((x-4)2 =1)
Step 1
Concept
Adding (16) to \(x^2-8x=-15\) gives ((x-4)2 =1). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-4)2 =1). Adding (16) to \(x^2-8x=-15\) gives ((x-4)2 =1). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2-8x=-15\) में (16) जोड़ने पर ((x-4)2 =1) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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\(x^2-2x+5=0\) में पूर्ण वर्ग बनाने पर कौनसा रूप बनेगा?
What form is obtained by completing the square in \(x^2-2x+5=0\)?
#quadratic
#completing-square
#no-real-roots
A ((x-1)2 +4=0)
B ((x+1)2 +4=0)
C ((x-1)2 -4=0)
D ((x+2)2 +1=0)
Explanation opens after your attempt
Correct Answer
A. ((x-1)2 +4=0)
Step 1
Concept
(x-2 -2x+5=(x-1)2 +4), so no real roots are obtained. In exams, the completed square form also shows the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. ((x-1)2 +4=0). (x-2 -2x+5=(x-1)2 +4), so no real roots are obtained. In exams, the completed square form also shows the nature of roots.
Step 3
Exam Tip
(x-2 -2x+5=(x-1)2 +4), इसलिए वास्तविक मूल नहीं मिलते। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति समझ सकते हैं।
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\(x^2+4x-12=0\) को पूर्ण वर्ग विधि से हल करने में सही चरण कौनसा है?
Which step is correct in solving \(x^2+4x-12=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x+2)2 =16)
B ((x-2)2 =16)
C ((x+4)2 =12)
D ((x+2)2 =12)
Explanation opens after your attempt
Correct Answer
A. ((x+2)2 =16)
Step 1
Concept
Adding (4) to \(x^2+4x=12\) gives ((x+2)2 =16). In exams, add the same term to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x+2)2 =16). Adding (4) to \(x^2+4x=12\) gives ((x+2)2 =16). In exams, add the same term to both sides.
Step 3
Exam Tip
\(x^2+4x=12\) में (4) जोड़ने पर ((x+2)2 =16) मिलता है। परीक्षा में दोनों पक्षों में समान पद जोड़ें।
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\(x^2-12x+20=0\) को पूर्ण वर्ग विधि से हल करने में सही मध्य चरण कौनसा है?
Which middle step is correct while solving \(x^2-12x+20=0\) by completing square?
#quadratic
#completing-square
#steps
A ((x-6)2 =16)
B ((x+6)2 =16)
C ((x-12)2 =20)
D ((x-6)2 =36)
Explanation opens after your attempt
Correct Answer
A. ((x-6)2 =16)
Step 1
Concept
From \(x^2-12x+20=0\), \(x^2-12x=-20\), then adding (36) gives ((x-6)2 =16). In exams, add the same number to both sides.
Step 2
Why this answer is correct
The correct answer is A. ((x-6)2 =16). From \(x^2-12x+20=0\), \(x^2-12x=-20\), then adding (36) gives ((x-6)2 =16). In exams, add the same number to both sides.
Step 3
Exam Tip
\(x^2-12x+20=0\) से \(x^2-12x=-20\), फिर (36) जोड़कर ((x-6)2 =16) मिलता है। परीक्षा में दोनों पक्षों में समान संख्या जोड़ें।
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\(x^2+6x+1=0\) के मूल पूर्ण वर्ग विधि से क्या होंगे?
What are the roots of \(x^2+6x+1=0\) by completing the square method?
#quadratic
#completing-square
#irrational-roots
A \(x=-3\pm2\sqrt{2}\)
B \(x=3\pm2\sqrt{2}\)
C \(x=-6\pm\sqrt{2}\)
D \(x=-3\pm\sqrt{8}\)
Explanation opens after your attempt
Correct Answer
A. \(x=-3\pm2\sqrt{2}\)
Step 1
Concept
Since ((x+3)2 =8), \(x=-3\pm2\sqrt{2}\). In exams, simplify \(\sqrt{8}=2\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-3\pm2\sqrt{2}\). Since ((x+3)2 =8), \(x=-3\pm2\sqrt{2}\). In exams, simplify \(\sqrt{8}=2\sqrt{2}\).
Step 3
Exam Tip
((x+3)2 =8), इसलिए \(x=-3\pm2\sqrt{2}\) है। परीक्षा में \(\sqrt{8}=2\sqrt{2}\) सरल करें।
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\(x^2+6x+1=0\) को पूर्ण वर्ग विधि से हल करने पर कौनसा चरण सही है?
Which step is correct while solving \(x^2+6x+1=0\) by completing the square?
#quadratic
#completing-square
#steps
A ((x+3)2 =8)
B ((x+6)2 =35)
C ((x+3)2 =10)
D ((x-3)2 =8)
Explanation opens after your attempt
Correct Answer
A. ((x+3)2 =8)
Step 1
Concept
Adding (9) in \(x^2+6x+1=0\) gives ((x+3)2 =8). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. ((x+3)2 =8). Adding (9) in \(x^2+6x+1=0\) gives ((x+3)2 =8). In exams, add the square of half the coefficient.
Step 3
Exam Tip
\(x^2+6x+1=0\) में (9) जोड़ने पर ((x+3)2 =8) बनता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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पूर्ण वर्ग विधि में \(x^2+24x+17=0\) के लिए किस संख्या का प्रयोग होगा?
In completing square method for \(x^2+24x+17=0\), which number will be used?
#quadratic
#completing-square
#number-choice
A (144)
B (24)
C (12)
D (17)
Explanation opens after your attempt
Step 1
Concept
Half of (24) is (12), and \(12^2=144\). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. (144). Half of (24) is (12), and \(12^2=144\). In exams, add the square of half the coefficient.
Step 3
Exam Tip
(24) का आधा (12) है और \(12^2=144\) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ना होता है।
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पूर्ण वर्ग बनाते समय \(x^2-22x\) में कौनसा पद जोड़ना होगा?
While completing the square, which term must be added to \(x^2-22x\)?
#quadratic
#completing-square
#term
A (121)
B (22)
C (11)
D (44)
Explanation opens after your attempt
Step 1
Concept
Half of (-22) is (-11), and ((-11)2 =121). In exams, the square of half the coefficient is always positive.
Step 2
Why this answer is correct
The correct answer is A. (121). Half of (-22) is (-11), and ((-11)2 =121). In exams, the square of half the coefficient is always positive.
Step 3
Exam Tip
(-22) का आधा (-11) है और ((-11)2 =121) होता है। परीक्षा में आधे गुणांक का वर्ग हमेशा धनात्मक होता है।
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पूर्ण वर्ग विधि में \(x^2+20x+13=0\) के लिए कौनसी संख्या जोड़ी और घटाई जाएगी?
In completing square method for \(x^2+20x+13=0\), which number will be added and subtracted?
#quadratic
#completing-square
#number-choice
A (100)
B (20)
C (10)
D (13)
Explanation opens after your attempt
Step 1
Concept
Half of (20) is (10), and \(10^2=100\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 2
Why this answer is correct
The correct answer is A. (100). Half of (20) is (10), and \(10^2=100\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 3
Exam Tip
(20) का आधा (10) है और \(10^2=100\) होता है। परीक्षा में (\left\(\frac{b}{2}\right\)2 ) का प्रयोग करें।
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पूर्ण वर्ग विधि में \(x^2+16x+11=0\) के लिए किस संख्या का प्रयोग होगा?
In completing square method for \(x^2+16x+11=0\), which number will be used?
#quadratic
#completing-square
#number-choice
A (64)
B (16)
C (8)
D (11)
Explanation opens after your attempt
Step 1
Concept
Half of (16) is (8), and \(8^2=64\). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. (64). Half of (16) is (8), and \(8^2=64\). In exams, add the square of half the coefficient.
Step 3
Exam Tip
(16) का आधा (8) है और \(8^2=64\) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ना होता है।
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पूर्ण वर्ग बनाते समय \(x^2-18x\) में कौनसा पद जोड़ना होगा?
While completing the square, which term must be added to \(x^2-18x\)?
#quadratic
#completing-square
#term
A (81)
B (18)
C (9)
D (36)
Explanation opens after your attempt
Step 1
Concept
Half of (-18) is (-9), and ((-9)2 =81). In exams, the square of half the coefficient is always positive.
Step 2
Why this answer is correct
The correct answer is A. (81). Half of (-18) is (-9), and ((-9)2 =81). In exams, the square of half the coefficient is always positive.
Step 3
Exam Tip
(-18) का आधा (-9) है और ((-9)2 =81) होता है। परीक्षा में आधे गुणांक का वर्ग हमेशा धनात्मक होता है।
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पूर्ण वर्ग विधि में \(x^2+12x+7=0\) के लिए कौनसी संख्या जोड़ी और घटाई जाएगी?
In completing square method for \(x^2+12x+7=0\), which number will be added and subtracted?
#quadratic
#completing-square
#number-choice
A (36)
B (12)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Half of (12) is (6), and \(6^2=36\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 2
Why this answer is correct
The correct answer is A. (36). Half of (12) is (6), and \(6^2=36\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 3
Exam Tip
(12) का आधा (6) है और \(6^2=36\) होता है। परीक्षा में (\left\(\frac{b}{2}\right\)2 ) का प्रयोग करें।
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पूर्ण वर्ग विधि में \(x^2-10x+7=0\) के लिए किस संख्या का प्रयोग होगा?
In completing square method for \(x^2-10x+7=0\), which number will be used?
#quadratic
#completing-square
#number-choice
A (25)
B (10)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
Half of (-10) is (-5), and ((-5)2 =25). In exams, add the square of half the coefficient.
Step 2
Why this answer is correct
The correct answer is A. (25). Half of (-10) is (-5), and ((-5)2 =25). In exams, add the square of half the coefficient.
Step 3
Exam Tip
(-10) का आधा (-5) है और ((-5)2 =25) होता है। परीक्षा में आधे गुणांक का वर्ग जोड़ें।
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पूर्ण वर्ग विधि में \(x^2+6x+5=0\) के लिए किस संख्या को जोड़कर घटाया जाता है?
In completing square method for \(x^2+6x+5=0\), which number is added and subtracted?
#quadratic
#completing-square
#method
A (9)
B (6)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
Half of the coefficient (6) is (3), and \(3^2=9\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 2
Why this answer is correct
The correct answer is A. (9). Half of the coefficient (6) is (3), and \(3^2=9\). In exams, use (\left\(\frac{b}{2}\right\)2 ).
Step 3
Exam Tip
(x) के गुणांक (6) का आधा (3) है और \(3^2=9\) होता है। परीक्षा में (\left\(\frac{b}{2}\right\)2 ) का प्रयोग करें।
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कुतुब मीनार को पूरा कराने का श्रेय मुख्य रूप से किस शासक को दिया जाता है?
Who is mainly credited with completing the Qutb Minar?
#indian history
#medieval india
#qutb minar
A कुतुबुद्दीन ऐबक / Qutbuddin Aibak
B इल्तुतमिश / Iltutmish
C अलाउद्दीन खिलजी / Alauddin Khalji
D फिरोज शाह तुगलक / Firoz Shah Tughlaq
Explanation opens after your attempt
Correct Answer
B. इल्तुतमिश / Iltutmish
Step 1
Concept
Qutb Minar was started by Aibak and completed by Iltutmish. Exam tip: remember the difference between starting and completing it.
Step 2
Why this answer is correct
The correct answer is B. इल्तुतमिश / Iltutmish. Qutb Minar was started by Aibak and completed by Iltutmish. Exam tip: remember the difference between starting and completing it.
Step 3
Exam Tip
कुतुब मीनार की शुरुआत ऐबक ने की थी और इसे इल्तुतमिश ने पूरा कराया। परीक्षा में शुरुआत और पूर्णता में अंतर याद रखें।
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\(7x^2-14x+19=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(7x^2-14x+19=0\)?
#quadratic
#completing-square
#no-real-roots
A (7(x-1)2 +12=0)
B (7(x+1)2 +12=0)
C (7(x-1)2 -12=0)
D (7(x-2)2 +19=0)
Explanation opens after your attempt
Correct Answer
A. (7(x-1)2 +12=0)
Step 1
Concept
(7x-2 -14x+19=7(x-1)2 +12), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. (7(x-1)2 +12=0). (7x-2 -14x+19=7(x-1)2 +12), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 3
Exam Tip
(7x-2 -14x+19=7(x-1)2 +12), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति दिखती है।
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\(6x^2-12x+17=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(6x^2-12x+17=0\)?
#quadratic
#completing-square
#no-real-roots
A (6(x-1)2 +11=0)
B (6(x+1)2 +11=0)
C (6(x-1)2 -11=0)
D (6(x-2)2 +17=0)
Explanation opens after your attempt
Correct Answer
A. (6(x-1)2 +11=0)
Step 1
Concept
(6x-2 -12x+17=6(x-1)2 +11), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. (6(x-1)2 +11=0). (6x-2 -12x+17=6(x-1)2 +11), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 3
Exam Tip
(6x-2 -12x+17=6(x-1)2 +11), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति दिखती है।
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\(5x^2-10x+13=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(5x^2-10x+13=0\)?
#quadratic
#completing-square
#no-real-roots
A (5(x-1)2 +8=0)
B (5(x+1)2 +8=0)
C (5(x-1)2 -8=0)
D (5(x-2)2 +13=0)
Explanation opens after your attempt
Correct Answer
A. (5(x-1)2 +8=0)
Step 1
Concept
(5x-2 -10x+13=5(x-1)2 +8), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. (5(x-1)2 +8=0). (5x-2 -10x+13=5(x-1)2 +8), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 3
Exam Tip
(5x-2 -10x+13=5(x-1)2 +8), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति दिखती है।
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\(4x^2-8x+9=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(4x^2-8x+9=0\)?
#quadratic
#completing-square
#no-real-roots
A (4(x-1)2 +5=0)
B (4(x+1)2 +5=0)
C (4(x-1)2 -5=0)
D (4(x-2)2 +9=0)
Explanation opens after your attempt
Correct Answer
A. (4(x-1)2 +5=0)
Step 1
Concept
(4x-2 -8x+9=4(x-1)2 +5), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 2
Why this answer is correct
The correct answer is A. (4(x-1)2 +5=0). (4x-2 -8x+9=4(x-1)2 +5), so it cannot be zero for real (x). In exams, completed square form also shows the nature of roots.
Step 3
Exam Tip
(4x-2 -8x+9=4(x-1)2 +5), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी मूलों की प्रकृति दिखती है।
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\(3x^2-6x+7=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(3x^2-6x+7=0\)?
#quadratic
#completing-square
#no-real-roots
A (3(x-1)2 +4=0)
B (3(x+1)2 +4=0)
C (3(x-1)2 -4=0)
D (3(x-2)2 +7=0)
Explanation opens after your attempt
Correct Answer
A. (3(x-1)2 +4=0)
Step 1
Concept
(3x-2 -6x+7=3(x-1)2 +4), so it cannot be zero for real (x). In exams, completed square form also shows the nature of real roots.
Step 2
Why this answer is correct
The correct answer is A. (3(x-1)2 +4=0). (3x-2 -6x+7=3(x-1)2 +4), so it cannot be zero for real (x). In exams, completed square form also shows the nature of real roots.
Step 3
Exam Tip
(3x-2 -6x+7=3(x-1)2 +4), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी वास्तविक मूलों की प्रकृति दिखती है।
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\(2x^2-4x+5=0\) में पूर्ण वर्ग रूप कौनसा सही है?
Which completed square form is correct for \(2x^2-4x+5=0\)?
#quadratic
#completing-square
#no-real-roots
A (2(x-1)2 +3=0)
B (2(x+1)2 +3=0)
C (2(x-1)2 -3=0)
D (2(x-2)2 +5=0)
Explanation opens after your attempt
Correct Answer
A. (2(x-1)2 +3=0)
Step 1
Concept
(2x-2 -4x+5=2(x-1)2 +3), so it cannot be zero for real (x). In exams, completed square form also shows no real roots.
Step 2
Why this answer is correct
The correct answer is A. (2(x-1)2 +3=0). (2x-2 -4x+5=2(x-1)2 +3), so it cannot be zero for real (x). In exams, completed square form also shows no real roots.
Step 3
Exam Tip
(2x-2 -4x+5=2(x-1)2 +3), इसलिए यह वास्तविक (x) के लिए शून्य नहीं हो सकता। परीक्षा में पूर्ण वर्ग रूप से भी no real roots दिखता है।
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\(x^2+24x+144\) किसके बराबर है?
What is \(x^2+24x+144\) equal to?
#quadratic
#perfect-square
#completing-square
A ((x+12)2 )
B ((x-12)2 )
C ((x+24)2 )
D ((x-24)2 )
Explanation opens after your attempt
Correct Answer
A. ((x+12)2 )
Step 1
Concept
(x-2 +24x+144=(x+12)2 ). In exams, identify it using \(2\cdot12x=24x\).
Step 2
Why this answer is correct
The correct answer is A. ((x+12)2 ). (x-2 +24x+144=(x+12)2 ). In exams, identify it using \(2\cdot12x=24x\).
Step 3
Exam Tip
(x-2 +24x+144=(x+12)2 ) है। परीक्षा में \(2\cdot12x=24x\) से पहचान करें।
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\(x^2+16x+64\) किसके बराबर है?
What is \(x^2+16x+64\) equal to?
#quadratic
#perfect-square
#completing-square
A ((x+8)2 )
B ((x-8)2 )
C ((x+16)2 )
D ((x-16)2 )
Explanation opens after your attempt
Correct Answer
A. ((x+8)2 )
Step 1
Concept
(x-2 +16x+64=(x+8)2 ). In exams, identify it using \(2\cdot8x=16x\).
Step 2
Why this answer is correct
The correct answer is A. ((x+8)2 ). (x-2 +16x+64=(x+8)2 ). In exams, identify it using \(2\cdot8x=16x\).
Step 3
Exam Tip
(x-2 +16x+64=(x+8)2 ) है। परीक्षा में \(2\cdot8x=16x\) से पहचान करें।
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\(x^2-10x+25\) किसके बराबर है?
What is \(x^2-10x+25\) equal to?
#quadratic
#perfect-square
#completing-square
A ((x-5)2 )
B ((x+5)2 )
C ((x-10)2 )
D ((x+10)2 )
Explanation opens after your attempt
Correct Answer
A. ((x-5)2 )
Step 1
Concept
(x-2 -10x+25=(x-5)2 ). In exams, check the pattern using \(-2\cdot5x=-10x\).
Step 2
Why this answer is correct
The correct answer is A. ((x-5)2 ). (x-2 -10x+25=(x-5)2 ). In exams, check the pattern using \(-2\cdot5x=-10x\).
Step 3
Exam Tip
(x-2 -10x+25=(x-5)2 ) है। परीक्षा में \(-2\cdot5x=-10x\) से पैटर्न जांचें।
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एक वर्गाकार मैदान की भुजा (4) मीटर बढ़ाने पर क्षेत्रफल (96) वर्ग मीटर बढ़ जाता है। मूल भुजा कितनी थी?
When the side of a square field is increased by (4) m, its area increases by (96) square m. What was the original side?
#quadratic equations
#square
#area increase
A (8) मीटर / (8) m
B (10) मीटर / (10) m
C (12) मीटर / (12) m
D (14) मीटर / (14) m
Explanation opens after your attempt
Correct Answer
B. (10) मीटर / (10) m
Step 1
Concept
If the original side is (x), then ((x+4)2 -x-2 =96). Thus (8x+16=96), giving (x=10).
Step 2
Why this answer is correct
The correct answer is B. (10) मीटर / (10) m. If the original side is (x), then ((x+4)2 -x-2 =96). Thus (8x+16=96), giving (x=10).
Step 3
Exam Tip
मूल भुजा (x) हो तो ((x+4)2 -x-2 =96)। इससे (8x+16=96) और (x=10) मिलता है।
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एक वर्गाकार मैदान के अंदर समान चौड़ाई (x) मीटर की सीमा छोड़ने के बाद अंदर का वर्ग (60) मीटर भुजा का बचता है। बाहरी भुजा (92) मीटर है। (x) क्या है?
Inside a square field, after leaving a uniform border of width (x) m, the inner square has side (60) m. The outer side is (92) m. What is (x)?
#quadratic equations
#square border
#application
A (12) मीटर / (12) m
B (14) मीटर / (14) m
C (16) मीटर / (16) m
D (18) मीटर / (18) m
Explanation opens after your attempt
Correct Answer
C. (16) मीटर / (16) m
Step 1
Concept
The inner side is (92-2x) and (92-2x=60), so (x=16). The border is subtracted from both sides.
Step 2
Why this answer is correct
The correct answer is C. (16) मीटर / (16) m. The inner side is (92-2x) and (92-2x=60), so (x=16). The border is subtracted from both sides.
Step 3
Exam Tip
अंदर की भुजा (92-2x) है और (92-2x=60), इसलिए (x=16) है। सीमा दोनों तरफ से घटती है।
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एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (3025) वर्ग सेमी है। तार की लंबाई क्या है?
A wire is bent into a square and the area is (3025) square cm. What is the length of the wire?
#quadratic equations
#square
#wire
A (200) सेमी / (200) cm
B (210) सेमी / (210) cm
C (220) सेमी / (220) cm
D (240) सेमी / (240) cm
Explanation opens after your attempt
Correct Answer
C. (220) सेमी / (220) cm
Step 1
Concept
If the side of the square is (x), then \(x^2=3025\), so (x=55). The wire length is the perimeter (4x=220) cm.
Step 2
Why this answer is correct
The correct answer is C. (220) सेमी / (220) cm. If the side of the square is (x), then \(x^2=3025\), so (x=55). The wire length is the perimeter (4x=220) cm.
Step 3
Exam Tip
वर्ग की भुजा (x) हो तो \(x^2=3025\), इसलिए (x=55) है। तार की लंबाई परिमाप (4x=220) सेमी होगी।
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एक वर्ग की भुजा (x) सेमी है। भुजा (9) सेमी घटाने पर क्षेत्रफल (1681) वर्ग सेमी हो जाता है। मूल भुजा क्या है?
The side of a square is (x) cm. When the side is reduced by (9) cm, the area becomes (1681) square cm. What is the original side?
#quadratic equations
#square
#area change
A (41) सेमी / (41) cm
B (45) सेमी / (45) cm
C (50) सेमी / (50) cm
D (57) सेमी / (57) cm
Explanation opens after your attempt
Correct Answer
C. (50) सेमी / (50) cm
Step 1
Concept
((x-9)2 =1681) gives (x-9=41), so (x=50). Write the reduced side as (x-9).
Step 2
Why this answer is correct
The correct answer is C. (50) सेमी / (50) cm. ((x-9)2 =1681) gives (x-9=41), so (x=50). Write the reduced side as (x-9).
Step 3
Exam Tip
((x-9)2 =1681) से (x-9=41), इसलिए (x=50) है। घटाई गई भुजा को (x-9) लिखें।
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एक वर्गाकार टाइल की भुजा (x-12) सेमी है और क्षेत्रफल (1849) वर्ग सेमी है। (x) क्या है?
The side of a square tile is (x-12) cm and its area is (1849) square cm. What is (x)?
#quadratic equations
#square
#tile
A (43)
B (49)
C (55)
D (60)
Explanation opens after your attempt
Step 1
Concept
((x-12)2 =1849) and (x-12=43), so (x=55). Remember that the side must be positive.
Step 2
Why this answer is correct
The correct answer is C. (55). ((x-12)2 =1849) and (x-12=43), so (x=55). Remember that the side must be positive.
Step 3
Exam Tip
((x-12)2 =1849) और (x-12=43), इसलिए (x=55) है। भुजा धनात्मक होने की शर्त याद रखें।
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एक वर्ग की भुजा (x+17) सेमी है। उसका क्षेत्रफल (3249) वर्ग सेमी है। (x) का मान क्या है?
The side of a square is (x+17) cm. Its area is (3249) square cm. What is the value of (x)?
#quadratic equations
#square
#area
A (34)
B (38)
C (40)
D (57)
Explanation opens after your attempt
Step 1
Concept
((x+17)2 =3249) gives (x+17=57), so (x=40). Take the positive square root for length.
Step 2
Why this answer is correct
The correct answer is C. (40). ((x+17)2 =3249) gives (x+17=57), so (x=40). Take the positive square root for length.
Step 3
Exam Tip
((x+17)2 =3249) से (x+17=57), इसलिए (x=40) है। लंबाई के लिए धनात्मक वर्गमूल लें।
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एक वर्गाकार मैदान के अंदर समान चौड़ाई (x) मीटर की सीमा छोड़ने के बाद अंदर का वर्ग (44) मीटर भुजा का बचता है। बाहरी भुजा (68) मीटर है। (x) क्या है?
Inside a square field, after leaving a uniform border of width (x) m, the inner square has side (44) m. The outer side is (68) m. What is (x)?
#quadratic equations
#square border
#application
A (8) मीटर / (8) m
B (10) मीटर / (10) m
C (12) मीटर / (12) m
D (14) मीटर / (14) m
Explanation opens after your attempt
Correct Answer
C. (12) मीटर / (12) m
Step 1
Concept
The inner side is (68-2x) and (68-2x=44), so (x=12). The border is subtracted from both sides.
Step 2
Why this answer is correct
The correct answer is C. (12) मीटर / (12) m. The inner side is (68-2x) and (68-2x=44), so (x=12). The border is subtracted from both sides.
Step 3
Exam Tip
अंदर की भुजा (68-2x) है और (68-2x=44), इसलिए (x=12) है। सीमा दोनों तरफ से घटती है।
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एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (2025) वर्ग सेमी है। तार की लंबाई क्या है?
A wire is bent into a square and the area is (2025) square cm. What is the length of the wire?
#quadratic equations
#square
#wire
A (160) सेमी / (160) cm
B (180) सेमी / (180) cm
C (200) सेमी / (200) cm
D (225) सेमी / (225) cm
Explanation opens after your attempt
Correct Answer
B. (180) सेमी / (180) cm
Step 1
Concept
If the side of the square is (x), then \(x^2=2025\), so (x=45). The wire length is the perimeter (4x=180) cm.
Step 2
Why this answer is correct
The correct answer is B. (180) सेमी / (180) cm. If the side of the square is (x), then \(x^2=2025\), so (x=45). The wire length is the perimeter (4x=180) cm.
Step 3
Exam Tip
वर्ग की भुजा (x) हो तो \(x^2=2025\), इसलिए (x=45) है। तार की लंबाई परिमाप (4x=180) सेमी होगी।
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एक वर्ग की भुजा (x) सेमी है। भुजा (7) सेमी घटाने पर क्षेत्रफल (1296) वर्ग सेमी हो जाता है। मूल भुजा क्या है?
The side of a square is (x) cm. When the side is reduced by (7) cm, the area becomes (1296) square cm. What is the original side?
#quadratic equations
#square
#area change
A (36) सेमी / (36) cm
B (40) सेमी / (40) cm
C (43) सेमी / (43) cm
D (49) सेमी / (49) cm
Explanation opens after your attempt
Correct Answer
C. (43) सेमी / (43) cm
Step 1
Concept
((x-7)2 =1296) gives (x-7=36), so (x=43). Write the reduced side as (x-7).
Step 2
Why this answer is correct
The correct answer is C. (43) सेमी / (43) cm. ((x-7)2 =1296) gives (x-7=36), so (x=43). Write the reduced side as (x-7).
Step 3
Exam Tip
((x-7)2 =1296) से (x-7=36), इसलिए (x=43) है। घटाई गई भुजा को (x-7) लिखें।
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एक वर्गाकार टाइल की भुजा (x-13) सेमी है और क्षेत्रफल (1600) वर्ग सेमी है। (x) क्या है?
The side of a square tile is (x-13) cm and its area is (1600) square cm. What is (x)?
#quadratic equations
#square
#tile
A (40)
B (47)
C (53)
D (60)
Explanation opens after your attempt
Step 1
Concept
((x-13)2 =1600) and (x-13=40), so (x=53). Remember that the side must be positive.
Step 2
Why this answer is correct
The correct answer is C. (53). ((x-13)2 =1600) and (x-13=40), so (x=53). Remember that the side must be positive.
Step 3
Exam Tip
((x-13)2 =1600) और (x-13=40), इसलिए (x=53) है। भुजा धनात्मक होने की शर्त याद रखें।
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एक वर्ग की भुजा (x+12) सेमी है। उसका क्षेत्रफल (1764) वर्ग सेमी है। (x) का मान क्या है?
The side of a square is (x+12) cm. Its area is (1764) square cm. What is the value of (x)?
#quadratic equations
#square
#area
A (24)
B (28)
C (30)
D (42)
Explanation opens after your attempt
Step 1
Concept
((x+12)2 =1764) gives (x+12=42), so (x=30). Take the positive square root for length.
Step 2
Why this answer is correct
The correct answer is C. (30). ((x+12)2 =1764) gives (x+12=42), so (x=30). Take the positive square root for length.
Step 3
Exam Tip
((x+12)2 =1764) से (x+12=42), इसलिए (x=30) है। लंबाई के लिए धनात्मक वर्गमूल लें।
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एक वर्गाकार मैदान के अंदर समान चौड़ाई (x) मीटर की सीमा छोड़ने के बाद अंदर का वर्ग (36) मीटर भुजा का बचता है। बाहरी भुजा (52) मीटर है। (x) क्या है?
Inside a square field, after leaving a uniform border of width (x) m, the inner square has side (36) m. The outer side is (52) m. What is (x)?
#quadratic equations
#square border
#application
A (6) मीटर / (6) m
B (8) मीटर / (8) m
C (10) मीटर / (10) m
D (12) मीटर / (12) m
Explanation opens after your attempt
Correct Answer
B. (8) मीटर / (8) m
Step 1
Concept
The inner side is (52-2x) and (52-2x=36), so (x=8). The border is subtracted from both sides.
Step 2
Why this answer is correct
The correct answer is B. (8) मीटर / (8) m. The inner side is (52-2x) and (52-2x=36), so (x=8). The border is subtracted from both sides.
Step 3
Exam Tip
अंदर की भुजा (52-2x) है और (52-2x=36), इसलिए (x=8) है। सीमा दोनों तरफ से घटती है।
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एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (1296) वर्ग सेमी है। तार की लंबाई क्या है?
A wire is bent into a square and the area is (1296) square cm. What is the length of the wire?
#quadratic equations
#square
#wire
A (120) सेमी / (120) cm
B (132) सेमी / (132) cm
C (144) सेमी / (144) cm
D (156) सेमी / (156) cm
Explanation opens after your attempt
Correct Answer
C. (144) सेमी / (144) cm
Step 1
Concept
If the side of the square is (x), then \(x^2=1296\), so (x=36). The wire length is the perimeter (4x=144) cm.
Step 2
Why this answer is correct
The correct answer is C. (144) सेमी / (144) cm. If the side of the square is (x), then \(x^2=1296\), so (x=36). The wire length is the perimeter (4x=144) cm.
Step 3
Exam Tip
वर्ग की भुजा (x) हो तो \(x^2=1296\), इसलिए (x=36) है। तार की लंबाई परिमाप (4x=144) सेमी होगी।
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एक वर्ग की भुजा (x) सेमी है। भुजा (5) सेमी घटाने पर क्षेत्रफल (784) वर्ग सेमी हो जाता है। मूल भुजा क्या है?
The side of a square is (x) cm. When the side is reduced by (5) cm, the area becomes (784) square cm. What is the original side?
#quadratic equations
#square
#area change
A (28) सेमी / (28) cm
B (30) सेमी / (30) cm
C (33) सेमी / (33) cm
D (35) सेमी / (35) cm
Explanation opens after your attempt
Correct Answer
C. (33) सेमी / (33) cm
Step 1
Concept
((x-5)2 =784) gives (x-5=28), so (x=33). Write the reduced side as (x-5).
Step 2
Why this answer is correct
The correct answer is C. (33) सेमी / (33) cm. ((x-5)2 =784) gives (x-5=28), so (x=33). Write the reduced side as (x-5).
Step 3
Exam Tip
((x-5)2 =784) से (x-5=28), इसलिए (x=33) है। घटाई गई भुजा को (x-5) लिखें।
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एक वर्गाकार टाइल की भुजा (x-8) सेमी है और क्षेत्रफल (900) वर्ग सेमी है। (x) क्या है?
The side of a square tile is (x-8) cm and its area is (900) square cm. What is (x)?
#quadratic equations
#square
#tile
A (30)
B (34)
C (38)
D (42)
Explanation opens after your attempt
Step 1
Concept
((x-8)2 =900) and (x-8=30), so (x=38). Remember that the side must be positive.
Step 2
Why this answer is correct
The correct answer is C. (38). ((x-8)2 =900) and (x-8=30), so (x=38). Remember that the side must be positive.
Step 3
Exam Tip
((x-8)2 =900) और (x-8=30), इसलिए (x=38) है। भुजा धनात्मक होने की शर्त याद रखें।
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एक वर्ग की भुजा (x+6) सेमी है। उसका क्षेत्रफल (1225) वर्ग सेमी है। (x) का मान क्या है?
The side of a square is (x+6) cm. Its area is (1225) square cm. What is the value of (x)?
#quadratic equations
#square
#area
A (23)
B (25)
C (29)
D (35)
Explanation opens after your attempt
Step 1
Concept
((x+6)2 =1225) gives (x+6=35), so (x=29). Take the positive square root for length.
Step 2
Why this answer is correct
The correct answer is C. (29). ((x+6)2 =1225) gives (x+6=35), so (x=29). Take the positive square root for length.
Step 3
Exam Tip
((x+6)2 =1225) से (x+6=35), इसलिए (x=29) है। लंबाई के लिए धनात्मक वर्गमूल लें।
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एक वर्ग का क्षेत्रफल उसके परिमाप से (96) अधिक है। वर्ग की भुजा क्या है?
The area of a square is (96) more than its perimeter. What is the side of the square?
#quadratic-equations
#word-problems
#square
A (12)
B (8)
C (16)
D (24)
Explanation opens after your attempt
Step 1
Concept
If the side is (x), then \(x^2=4x+96\). This gives \(x^2-4x-96=0\), so the positive side is (12).
Step 2
Why this answer is correct
The correct answer is A. (12). If the side is (x), then \(x^2=4x+96\). This gives \(x^2-4x-96=0\), so the positive side is (12).
Step 3
Exam Tip
यदि भुजा (x) है, तो \(x^2=4x+96\)। इससे \(x^2-4x-96=0\), इसलिए धनात्मक भुजा (12) है।
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एक वर्गाकार मैदान के अंदर समान चौड़ाई (x) मीटर की सीमा छोड़ने के बाद अंदर का वर्ग (20) मीटर भुजा का बचता है। बाहरी भुजा (28) मीटर है। (x) क्या है?
Inside a square field, after leaving a uniform border of width (x) m, the inner square has side (20) m. The outer side is (28) m. What is (x)?
#quadratic equations
#square border
#application
A (3) मीटर / (3) m
B (4) मीटर / (4) m
C (5) मीटर / (5) m
D (6) मीटर / (6) m
Explanation opens after your attempt
Correct Answer
B. (4) मीटर / (4) m
Step 1
Concept
The inner side is (28-2x) and (28-2x=20), so (x=4). The border is subtracted from both sides.
Step 2
Why this answer is correct
The correct answer is B. (4) मीटर / (4) m. The inner side is (28-2x) and (28-2x=20), so (x=4). The border is subtracted from both sides.
Step 3
Exam Tip
अंदर की भुजा (28-2x) है और (28-2x=20), इसलिए (x=4) है। सीमा दोनों तरफ से घटती है।
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एक तार को वर्ग के रूप में मोड़ने पर क्षेत्रफल (625) वर्ग सेमी है। तार की लंबाई क्या है?
A wire is bent into a square and the area is (625) square cm. What is the length of the wire?
#quadratic equations
#square
#wire
A (80) सेमी / (80) cm
B (90) सेमी / (90) cm
C (100) सेमी / (100) cm
D (125) सेमी / (125) cm
Explanation opens after your attempt
Correct Answer
C. (100) सेमी / (100) cm
Step 1
Concept
If the side of the square is (x), then \(x^2=625\), so (x=25). The wire length is the perimeter (4x=100) cm.
Step 2
Why this answer is correct
The correct answer is C. (100) सेमी / (100) cm. If the side of the square is (x), then \(x^2=625\), so (x=25). The wire length is the perimeter (4x=100) cm.
Step 3
Exam Tip
वर्ग की भुजा (x) हो तो \(x^2=625\), इसलिए (x=25) है। तार की लंबाई परिमाप (4x=100) सेमी होगी।
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एक वर्ग की भुजा (x) सेमी है। भुजा (3) सेमी घटाने पर क्षेत्रफल (225) वर्ग सेमी हो जाता है। मूल भुजा क्या है?
The side of a square is (x) cm. When the side is reduced by (3) cm, the area becomes (225) square cm. What is the original side?
#quadratic equations
#square
#area change
A (15) सेमी / (15) cm
B (18) सेमी / (18) cm
C (21) सेमी / (21) cm
D (24) सेमी / (24) cm
Explanation opens after your attempt
Correct Answer
B. (18) सेमी / (18) cm
Step 1
Concept
((x-3)2 =225) gives (x-3=15), so (x=18). Write the reduced side as (x-3).
Step 2
Why this answer is correct
The correct answer is B. (18) सेमी / (18) cm. ((x-3)2 =225) gives (x-3=15), so (x=18). Write the reduced side as (x-3).
Step 3
Exam Tip
((x-3)2 =225) से (x-3=15), इसलिए (x=18) है। घटाई गई भुजा को (x-3) लिखें।
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एक वर्गाकार मैदान की भुजा (x) मीटर है। यदि भुजा (5) मीटर बढ़ाने पर क्षेत्रफल (425) वर्ग मीटर बढ़ता है, तो (x) क्या है?
A square field has side (x) m. If increasing the side by (5) m increases the area by (425) square m, what is (x)?
#quadratic equations
#square
#area increase
A (35)
B (38)
C (40)
D (45)
Explanation opens after your attempt
Step 1
Concept
The area increase is ((x+5)2 -x-2 =425). This gives (10x+25=425), so (x=40).
Step 2
Why this answer is correct
The correct answer is C. (40). The area increase is ((x+5)2 -x-2 =425). This gives (10x+25=425), so (x=40).
Step 3
Exam Tip
क्षेत्रफल वृद्धि ((x+5)2 -x-2 =425) है। इससे (10x+25=425), इसलिए (x=40) है।
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एक वर्गाकार टाइल की भुजा (x-3) सेमी है और क्षेत्रफल (441) वर्ग सेमी है। (x) क्या है?
The side of a square tile is (x-3) cm and its area is (441) square cm. What is (x)?
#quadratic equations
#square
#tile
A (18)
B (21)
C (24)
D (27)
Explanation opens after your attempt
Step 1
Concept
((x-3)2 =441) and (x-3=21), so (x=24). Remember that the side must be positive.
Step 2
Why this answer is correct
The correct answer is C. (24). ((x-3)2 =441) and (x-3=21), so (x=24). Remember that the side must be positive.
Step 3
Exam Tip
((x-3)2 =441) और (x-3=21), इसलिए (x=24) है। भुजा धनात्मक होने की शर्त याद रखें।
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एक वर्ग की भुजा (x+4) सेमी है। उसका क्षेत्रफल (576) वर्ग सेमी है। (x) का मान क्या है?
The side of a square is (x+4) cm. Its area is (576) square cm. What is the value of (x)?
#quadratic equations
#square
#area
A (16)
B (18)
C (20)
D (24)
Explanation opens after your attempt
Step 1
Concept
((x+4)2 =576) gives (x+4=24), so (x=20). Take the positive square root for length.
Step 2
Why this answer is correct
The correct answer is C. (20). ((x+4)2 =576) gives (x+4=24), so (x=20). Take the positive square root for length.
Step 3
Exam Tip
((x+4)2 =576) से (x+4=24), इसलिए (x=20) है। लंबाई के लिए धनात्मक वर्गमूल लें।
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एक वर्ग का क्षेत्रफल उसके परिमाप से (45) अधिक है। वर्ग की भुजा क्या है?
The area of a square is (45) more than its perimeter. What is the side of the square?
#quadratic-equations
#word-problems
#square
A (9)
B (5)
C (15)
D (6)
Explanation opens after your attempt
Step 1
Concept
If the side is (x), then \(x^2=4x+45\). This gives \(x^2-4x-45=0\), so the positive side is (9).
Step 2
Why this answer is correct
The correct answer is A. (9). If the side is (x), then \(x^2=4x+45\). This gives \(x^2-4x-45=0\), so the positive side is (9).
Step 3
Exam Tip
यदि भुजा (x) है, तो \(x^2=4x+45\)। इससे \(x^2-4x-45=0\), इसलिए धनात्मक भुजा (9) है।
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एक वर्गाकार खेत की भुजा (x) मीटर है। यदि क्षेत्रफल (729) वर्ग मीटर है, तो (x) क्या है?
A square field has side (x) m. If its area is (729) square m, what is (x)?
#quadratic equations
#square
#field
A (24)
B (25)
C (27)
D (29)
Explanation opens after your attempt
Step 1
Concept
\(x^2=729\) gives (x=27). In a square region, the side is the positive square root of area.
Step 2
Why this answer is correct
The correct answer is C. (27). \(x^2=729\) gives (x=27). In a square region, the side is the positive square root of area.
Step 3
Exam Tip
\(x^2=729\) से (x=27) है। वर्गाकार क्षेत्र में भुजा क्षेत्रफल का धनात्मक वर्गमूल होती है।
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एक वर्गाकार फर्श का क्षेत्रफल (625) वर्ग मीटर है। उसका परिमाप क्या है?
A square floor has area (625) square m. What is its perimeter?
#quadratic equations
#square
#perimeter
A (75) मीटर / (75) m
B (90) मीटर / (90) m
C (100) मीटर / (100) m
D (125) मीटर / (125) m
Explanation opens after your attempt
Correct Answer
C. (100) मीटर / (100) m
Step 1
Concept
From \(x^2=625\), the side is (25) m and perimeter is (4x=100) m. Keep area and perimeter formulas separate.
Step 2
Why this answer is correct
The correct answer is C. (100) मीटर / (100) m. From \(x^2=625\), the side is (25) m and perimeter is (4x=100) m. Keep area and perimeter formulas separate.
Step 3
Exam Tip
\(x^2=625\) से भुजा (25) मीटर है और परिमाप (4x=100) मीटर है। क्षेत्रफल और परिमाप के सूत्र अलग रखें।
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एक वर्गाकार हॉल का क्षेत्रफल (529) वर्ग मीटर है। उसकी भुजा क्या है?
A square hall has area (529) square m. What is its side?
#quadratic equations
#square
#area
A (21) मीटर / (21) m
B (22) मीटर / (22) m
C (23) मीटर / (23) m
D (24) मीटर / (24) m
Explanation opens after your attempt
Correct Answer
C. (23) मीटर / (23) m
Step 1
Concept
If the side is (x), then \(x^2=529\), so (x=23). For length, take only the positive square root.
Step 2
Why this answer is correct
The correct answer is C. (23) मीटर / (23) m. If the side is (x), then \(x^2=529\), so (x=23). For length, take only the positive square root.
Step 3
Exam Tip
भुजा (x) हो तो \(x^2=529\), इसलिए (x=23) है। लंबाई के लिए केवल धनात्मक वर्गमूल लें।
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एक वर्गाकार आँगन का क्षेत्रफल (400) वर्ग मीटर है। उसका परिमाप क्या है?
A square courtyard has area (400) square m. What is its perimeter?
#quadratic equations
#square
#perimeter
A (40) मीटर / (40) m
B (60) मीटर / (60) m
C (80) मीटर / (80) m
D (100) मीटर / (100) m
Explanation opens after your attempt
Correct Answer
C. (80) मीटर / (80) m
Step 1
Concept
\(x^2=400\) gives side (20) m and perimeter (4x=80) m. Area and perimeter formulas are different.
Step 2
Why this answer is correct
The correct answer is C. (80) मीटर / (80) m. \(x^2=400\) gives side (20) m and perimeter (4x=80) m. Area and perimeter formulas are different.
Step 3
Exam Tip
\(x^2=400\) से भुजा (20) मीटर और परिमाप (4x=80) मीटर है। क्षेत्रफल और परिमाप के सूत्र अलग होते हैं।
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एक वर्गाकार कार्ड का क्षेत्रफल (361) वर्ग सेमी है। उसकी भुजा क्या है?
A square card has area (361) square cm. What is its side?
#quadratic equations
#square
#card
A (17) सेमी / (17) cm
B (18) सेमी / (18) cm
C (19) सेमी / (19) cm
D (20) सेमी / (20) cm
Explanation opens after your attempt
Correct Answer
C. (19) सेमी / (19) cm
Step 1
Concept
\(x^2=361\) gives (x=19). While taking the square root, keep length positive.
Step 2
Why this answer is correct
The correct answer is C. (19) सेमी / (19) cm. \(x^2=361\) gives (x=19). While taking the square root, keep length positive.
Step 3
Exam Tip
\(x^2=361\) से (x=19) है। वर्गमूल लेते समय लंबाई को धनात्मक रखें।
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एक वर्गाकार मंच का क्षेत्रफल (289) वर्ग मीटर है। उसका परिमाप क्या है?
A square stage has area (289) square m. What is its perimeter?
#quadratic equations
#square
#perimeter
A (34) मीटर / (34) m
B (51) मीटर / (51) m
C (68) मीटर / (68) m
D (85) मीटर / (85) m
Explanation opens after your attempt
Correct Answer
C. (68) मीटर / (68) m
Step 1
Concept
From \(x^2=289\), the side is (17) m and perimeter is (4x=68) m. First find the side and then apply perimeter.
Step 2
Why this answer is correct
The correct answer is C. (68) मीटर / (68) m. From \(x^2=289\), the side is (17) m and perimeter is (4x=68) m. First find the side and then apply perimeter.
Step 3
Exam Tip
\(x^2=289\) से भुजा (17) मीटर है और परिमाप (4x=68) मीटर है। पहले भुजा निकालें और फिर परिमाप लगाएँ।
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एक वर्गाकार पार्क का क्षेत्रफल (196) वर्ग मीटर है। उसकी भुजा क्या है?
A square park has area (196) square m. What is its side?
#quadratic equations
#square
#area
A (12) मीटर / (12) m
B (13) मीटर / (13) m
C (14) मीटर / (14) m
D (16) मीटर / (16) m
Explanation opens after your attempt
Correct Answer
C. (14) मीटर / (14) m
Step 1
Concept
If the side is (x), then \(x^2=196\), so (x=14). The side of a square is always taken positive.
Step 2
Why this answer is correct
The correct answer is C. (14) मीटर / (14) m. If the side is (x), then \(x^2=196\), so (x=14). The side of a square is always taken positive.
Step 3
Exam Tip
भुजा (x) हो तो \(x^2=196\), इसलिए (x=14) है। वर्ग की भुजा हमेशा धनात्मक मानी जाती है।
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एक वर्गाकार शीट का क्षेत्रफल (144) वर्ग सेमी है। उसकी परिमाप क्या है?
A square sheet has area (144) square cm. What is its perimeter?
#quadratic equations
#square
#perimeter
A (36) सेमी / (36) cm
B (40) सेमी / (40) cm
C (44) सेमी / (44) cm
D (48) सेमी / (48) cm
Explanation opens after your attempt
Correct Answer
D. (48) सेमी / (48) cm
Step 1
Concept
\(x^2=144\) gives side (12) cm and perimeter (4x=48) cm. If perimeter is asked, do not stop after finding the side.
Step 2
Why this answer is correct
The correct answer is D. (48) सेमी / (48) cm. \(x^2=144\) gives side (12) cm and perimeter (4x=48) cm. If perimeter is asked, do not stop after finding the side.
Step 3
Exam Tip
\(x^2=144\) से भुजा (12) सेमी है और परिमाप (4x=48) सेमी है। परिमाप पूछे जाने पर केवल भुजा लिखकर न रुकें।
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एक वर्गाकार टाइल का क्षेत्रफल (64) वर्ग सेमी है। उसकी भुजा क्या है?
A square tile has area (64) square cm. What is its side?
#quadratic equations
#square
#tile
A (6) सेमी / (6) cm
B (7) सेमी / (7) cm
C (8) सेमी / (8) cm
D (9) सेमी / (9) cm
Explanation opens after your attempt
Correct Answer
C. (8) सेमी / (8) cm
Step 1
Concept
If the side is (x), then \(x^2=64\), so (x=8). In a square, area equals the square of the side.
Step 2
Why this answer is correct
The correct answer is C. (8) सेमी / (8) cm. If the side is (x), then \(x^2=64\), so (x=8). In a square, area equals the square of the side.
Step 3
Exam Tip
भुजा (x) हो तो \(x^2=64\), इसलिए (x=8) है। वर्ग में क्षेत्रफल भुजा के वर्ग के बराबर होता है।
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एक वर्गाकार मैदान का क्षेत्रफल (225) वर्ग मीटर है। उसकी परिमाप क्या है?
A square field has area (225) square m. What is its perimeter?
#quadratic equations
#square
#perimeter
A (30) मीटर / (30) m
B (45) मीटर / (45) m
C (60) मीटर / (60) m
D (75) मीटर / (75) m
Explanation opens after your attempt
Correct Answer
C. (60) मीटर / (60) m
Step 1
Concept
From \(x^2=225\), the side is (15) m and perimeter is (4x=60) m. First find the side, then apply perimeter.
Step 2
Why this answer is correct
The correct answer is C. (60) मीटर / (60) m. From \(x^2=225\), the side is (15) m and perimeter is (4x=60) m. First find the side, then apply perimeter.
Step 3
Exam Tip
\(x^2=225\) से भुजा (15) मीटर है और परिमाप (4x=60) मीटर है। पहले भुजा निकालें, फिर परिमाप लगाएँ।
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एक वर्गाकार बगीचे का क्षेत्रफल (169) वर्ग मीटर है। उसकी भुजा क्या है?
A square garden has area (169) square m. What is its side?
#quadratic equations
#square
#area
A (11) मीटर / (11) m
B (12) मीटर / (12) m
C (13) मीटर / (13) m
D (14) मीटर / (14) m
Explanation opens after your attempt
Correct Answer
C. (13) मीटर / (13) m
Step 1
Concept
If the side of the square is (x), then \(x^2=169\), so (x=13). A side length is always taken positive.
Step 2
Why this answer is correct
The correct answer is C. (13) मीटर / (13) m. If the side of the square is (x), then \(x^2=169\), so (x=13). A side length is always taken positive.
Step 3
Exam Tip
वर्ग की भुजा (x) हो तो \(x^2=169\), इसलिए (x=13) है। भुजा हमेशा धनात्मक ली जाती है।
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निम्न में से कौन सी संख्या पूर्ण वर्ग नहीं है और उसका वर्गमूल अपरिमेय सिद्ध किया जाता है?
Which of the following is not a perfect square and its square root is proved irrational?
#perfect square
#sqrt2
#class 10
A (2)
B (4)
C (9)
D (25)
Explanation opens after your attempt
Step 1
Concept
(4), (9), and (25) are perfect squares.
Step 2
Why this answer is correct
(2) is not a perfect square, so \(\sqrt{2}\) is proved irrational.
Step 3
Exam Tip
First identify perfect and non-perfect squares. चरण 1: (4), (9) और (25) पूर्ण वर्ग हैं। चरण 2: (2) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{2}\) अपरिमेय सिद्ध किया जाता है। चरण 3: पूर्ण वर्ग और अपूर्ण वर्ग की पहचान पहले करें।
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(p(x)=x-2 -12x+40) का न्यूनतम मान किस (x) पर आता है?
At which (x) does (p(x)=x-2 -12x+40) attain its minimum value?
#quadratic
#minimum
#completing square
A (x=4)
B (x=5)
C (x=6)
D (x=12)
Explanation opens after your attempt
Step 1
Concept
(x-2 -12x+40=(x-6)2 +4), so the minimum occurs at (x=6). Completing the square is useful.
Step 2
Why this answer is correct
The correct answer is C. (x=6). (x-2 -12x+40=(x-6)2 +4), so the minimum occurs at (x=6). Completing the square is useful.
Step 3
Exam Tip
(x-2 -12x+40=(x-6)2 +4), इसलिए न्यूनतम (x=6) पर आता है। वर्ग पूर्ण करना उपयोगी तरीका है।
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(p(x)=x-2 -8x+17) का न्यूनतम मान किस (x) पर आता है?
At which (x) does (p(x)=x-2 -8x+17) attain its minimum value?
#quadratic
#minimum
#completing square
A (x=-4)
B (x=0)
C (x=4)
D (x=8)
Explanation opens after your attempt
Step 1
Concept
(x-2 -8x+17=(x-4)2 +1), so the minimum occurs at (x=4). Completing the square is useful.
Step 2
Why this answer is correct
The correct answer is C. (x=4). (x-2 -8x+17=(x-4)2 +1), so the minimum occurs at (x=4). Completing the square is useful.
Step 3
Exam Tip
(x-2 -8x+17=(x-4)2 +1), इसलिए न्यूनतम (x=4) पर आता है। वर्ग पूर्ण करना उपयोगी तरीका है।
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(p(x)=x-2 +4x+5) का न्यूनतम मान किस (x) पर आता है?
At which (x) does (p(x)=x-2 +4x+5) attain its minimum value?
#quadratic
#minimum
#completing square
A (x=-4)
B (x=-2)
C (x=0)
D (x=2)
Explanation opens after your attempt
Step 1
Concept
(x-2 +4x+5=(x+2)2 +1), so the minimum occurs at (x=-2). Completing the square is useful.
Step 2
Why this answer is correct
The correct answer is B. (x=-2). (x-2 +4x+5=(x+2)2 +1), so the minimum occurs at (x=-2). Completing the square is useful.
Step 3
Exam Tip
(x-2 +4x+5=(x+2)2 +1), इसलिए न्यूनतम (x=-2) पर आता है। वर्ग पूर्ण करना उपयोगी तरीका है।
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\(x^2+14x+10=0\) के मूल क्या हैं?
What are the roots of \(x^2+14x+10=0\)?
#quadratic
#completing-square
#roots
A \(x=-7\pm\sqrt{39}\)
B \(x=7\pm\sqrt{39}\)
C \(x=-14\pm\sqrt{39}\)
D \(x=-7\pm39\)
Explanation opens after your attempt
Correct Answer
A. \(x=-7\pm\sqrt{39}\)
Step 1
Concept
Since ((x+7)2 =39), \(x=-7\pm\sqrt{39}\). In exams, write both values using \(\pm\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-7\pm\sqrt{39}\). Since ((x+7)2 =39), \(x=-7\pm\sqrt{39}\). In exams, write both values using \(\pm\).
Step 3
Exam Tip
((x+7)2 =39), इसलिए \(x=-7\pm\sqrt{39}\) है। परीक्षा में \(\pm\) के दोनों मान लिखें।
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\(x^2+12x+8=0\) के मूल क्या हैं?
What are the roots of \(x^2+12x+8=0\)?
#quadratic
#completing-square
#roots
A \(x=-6\pm2\sqrt{7}\)
B \(x=6\pm2\sqrt{7}\)
C \(x=-12\pm2\sqrt{7}\)
D \(x=-6\pm28\)
Explanation opens after your attempt
Correct Answer
A. \(x=-6\pm2\sqrt{7}\)
Step 1
Concept
Since ((x+6)2 =28), \(x=-6\pm2\sqrt{7}\). In exams, simplify \(\sqrt{28}=2\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-6\pm2\sqrt{7}\). Since ((x+6)2 =28), \(x=-6\pm2\sqrt{7}\). In exams, simplify \(\sqrt{28}=2\sqrt{7}\).
Step 3
Exam Tip
((x+6)2 =28), इसलिए \(x=-6\pm2\sqrt{7}\) है। परीक्षा में \(\sqrt{28}=2\sqrt{7}\) सरल करें।
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\(x^2+10x+6=0\) के मूल क्या हैं?
What are the roots of \(x^2+10x+6=0\)?
#quadratic
#completing-square
#roots
A \(x=-5\pm\sqrt{19}\)
B \(x=5\pm\sqrt{19}\)
C \(x=-10\pm\sqrt{19}\)
D \(x=-5\pm19\)
Explanation opens after your attempt
Correct Answer
A. \(x=-5\pm\sqrt{19}\)
Step 1
Concept
Since ((x+5)2 =19), \(x=-5\pm\sqrt{19}\). In exams, write both values using \(\pm\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-5\pm\sqrt{19}\). Since ((x+5)2 =19), \(x=-5\pm\sqrt{19}\). In exams, write both values using \(\pm\).
Step 3
Exam Tip
((x+5)2 =19), इसलिए \(x=-5\pm\sqrt{19}\) है। परीक्षा में \(\pm\) के दोनों मान लिखें।
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\(x^2+8x+5=0\) के मूल क्या हैं?
What are the roots of \(x^2+8x+5=0\)?
#quadratic
#completing-square
#roots
A \(x=-4\pm\sqrt{11}\)
B \(x=4\pm\sqrt{11}\)
C \(x=-8\pm\sqrt{11}\)
D \(x=-4\pm11\)
Explanation opens after your attempt
Correct Answer
A. \(x=-4\pm\sqrt{11}\)
Step 1
Concept
Since ((x+4)2 =11), \(x=-4\pm\sqrt{11}\). In exams, write both values using \(\pm\).
Step 2
Why this answer is correct
The correct answer is A. \(x=-4\pm\sqrt{11}\). Since ((x+4)2 =11), \(x=-4\pm\sqrt{11}\). In exams, write both values using \(\pm\).
Step 3
Exam Tip
((x+4)2 =11), इसलिए \(x=-4\pm\sqrt{11}\) है। परीक्षा में \(\pm\) के दोनों मान लिखें।
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