Question 1/9
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि \(x=1-\sqrt{5}\), तो \(x^2-2x-4\) का मान क्या है?
If \(x=1-\sqrt{5}\), what is the value of \(x^2-2x-4\)?
#irrational root
#polynomial value
#algebra
A (0)
B \(-2\sqrt{5}\)
C \(2\sqrt{5}\)
D (4)
Explanation opens after your attempt
Step 1
Concept
Since \(x-1=-\sqrt{5}\), ((x-1)2 =5), so \(x^2-2x-4=0\). Isolate the irrational part and square in exams.
Step 2
Why this answer is correct
The correct answer is A. (0). Since \(x-1=-\sqrt{5}\), ((x-1)2 =5), so \(x^2-2x-4=0\). Isolate the irrational part and square in exams.
Step 3
Exam Tip
\(x-1=-\sqrt{5}\), इसलिए ((x-1)2 =5) से \(x^2-2x-4=0\) मिलता है। परीक्षा में अपरिमेय भाग अलग करके वर्ग करें।
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Question 2/9
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि \(x=\sqrt{3}\), तो \(2x^2-x-6\) का मान क्या है?
If \(x=\sqrt{3}\), what is the value of \(2x^2-x-6\)?
#polynomial value
#substitution
#irrational
A \(-\sqrt{3}\)
B (0)
C \(\sqrt{3}\)
D \(6-\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(-\sqrt{3}\)
Step 1
Concept
\(2x^2-x-6=2\cdot3-\sqrt{3}-6=-\sqrt{3}\). Simplify \(x^2\) first in exams.
Step 2
Why this answer is correct
The correct answer is A. \(-\sqrt{3}\). \(2x^2-x-6=2\cdot3-\sqrt{3}-6=-\sqrt{3}\). Simplify \(x^2\) first in exams.
Step 3
Exam Tip
\(2x^2-x-6=2\cdot3-\sqrt{3}-6=-\sqrt{3}\) है। परीक्षा में \(x^2\) को पहले सरल करें।
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Question 3/9
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि \(x=\sqrt{11}\), तो \(x^4-121\) का मान क्या है?
If \(x=\sqrt{11}\), what is the value of \(x^4-121\)?
#powers
#irrational
#polynomial value
A (0)
B (11)
C \(\sqrt{11}\)
D \(121\sqrt{11}\)
Explanation opens after your attempt
Step 1
Concept
Since \(x^2=11\), \(x^4=121\), so the value is (0). In exams reduce higher powers using \(x^2\).
Step 2
Why this answer is correct
The correct answer is A. (0). Since \(x^2=11\), \(x^4=121\), so the value is (0). In exams reduce higher powers using \(x^2\).
Step 3
Exam Tip
\(x^2=11\), इसलिए \(x^4=121\) और मान (0) है। परीक्षा में उच्च घात को \(x^2\) से सरल करें।
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Question 4/9
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि \(x=2+\sqrt{5}\), तो \(x^2-4x-1\) का मान क्या होगा?
If \(x=2+\sqrt{5}\), what is the value of \(x^2-4x-1\)?
#irrational equation
#polynomial value
#zero
A (0)
B (1)
C \(\sqrt{5}\)
D \(4\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
Since \(x-2=\sqrt{5}\), squaring gives ((x-2)2 =5), so \(x^2-4x-1=0\). In exams square to remove the radical.
Step 2
Why this answer is correct
The correct answer is A. (0). Since \(x-2=\sqrt{5}\), squaring gives ((x-2)2 =5), so \(x^2-4x-1=0\). In exams square to remove the radical.
Step 3
Exam Tip
\(x-2=\sqrt{5}\), इसलिए ((x-2)2 =5) से \(x^2-4x-1=0\) मिलता है। परीक्षा में वर्ग करके अपरिमेय हटाएं।
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Question 5/9
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि (p(x)=x-2 -7) है, तो (p\(\sqrt{7}+1\)) का मान किस रूप में है?
If (p(x)=x-2 -7), what is the form of (p\(\sqrt{7}+1\))?
#polynomial value
#surds
#expansion
A \(1+2\sqrt{7}\)
B (8)
C \(2\sqrt{7}\)
D \(7+2\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
A. \(1+2\sqrt{7}\)
Step 1
Concept
(\(\sqrt{7}+1\)2 -7=8+2\sqrt{7}-7=1+2\sqrt{7}). Use ((a+b)2 ) carefully in exams.
Step 2
Why this answer is correct
The correct answer is A. \(1+2\sqrt{7}\). (\(\sqrt{7}+1\)2 -7=8+2\sqrt{7}-7=1+2\sqrt{7}). Use ((a+b)2 ) carefully in exams.
Step 3
Exam Tip
(\(\sqrt{7}+1\)2 -7=8+2\sqrt{7}-7=1+2\sqrt{7}) है। परीक्षा में ((a+b)2 ) सावधानी से लगाएं।
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Question 6/9
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि \(x=\sqrt{3}\) है, तो \(x^2-3\) का मान क्या है?
If \(x=\sqrt{3}\), what is the value of \(x^2-3\)?
#substitution
#square root
#polynomial value
A \(\sqrt{3}\)
B (0)
C \(3\sqrt{3}\)
D (6)
Explanation opens after your attempt
Step 1
Concept
Since (\(\sqrt{3}\)2 =3), \(x^2-3=0\). In exams the square of a square root gives the radicand.
Step 2
Why this answer is correct
The correct answer is B. (0). Since (\(\sqrt{3}\)2 =3), \(x^2-3=0\). In exams the square of a square root gives the radicand.
Step 3
Exam Tip
क्योंकि (\(\sqrt{3}\)2 =3), इसलिए \(x^2-3=0\) है। परीक्षा में वर्गमूल का वर्ग मूलांक देता है।
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Question 7/9
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि (p(x)=x-2 -5x+6) है, तो (p\(\sqrt{2}\)) किस प्रकार की संख्या है?
If (p(x)=x-2 -5x+6), what type of number is (p\(\sqrt{2}\))?
#polynomial value
#irrational numbers
#substitution
A परिमेय / Rational
B अपरिमेय / Irrational
C शून्य / Zero
D पूर्णांक / Integer
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
(p\(\sqrt{2}\)=2-5\sqrt{2}+6=8-5\sqrt{2}), which is irrational. In exams substitute first and then simplify the radical.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय / Irrational. (p\(\sqrt{2}\)=2-5\sqrt{2}+6=8-5\sqrt{2}), which is irrational. In exams substitute first and then simplify the radical.
Step 3
Exam Tip
(p\(\sqrt{2}\)=2-5\sqrt{2}+6=8-5\sqrt{2}), जो अपरिमेय है। परीक्षा में पहले प्रतिस्थापन करें फिर वर्गमूल को सरल करें।
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Question 8/9
Expert Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि (p\(\sqrt{5}\)=0) और (p(x)=x-2 +ax-5) है, तो (a) का मान क्या है?
If (p\(\sqrt{5}\)=0) and (p(x)=x-2 +ax-5), what is the value of (a)?
#polynomial-value
#parameter
#irrational-input
A (0)
B \(\sqrt{5}\)
C \(-\sqrt{5}\)
D (5)
Explanation opens after your attempt
Step 1
Concept
Substitution gives \(5+a\sqrt{5}-5=0\), so \(a\sqrt{5}=0\) and (a=0). Simplify like terms first while substituting.
Step 2
Why this answer is correct
The correct answer is A. (0). Substitution gives \(5+a\sqrt{5}-5=0\), so \(a\sqrt{5}=0\) and (a=0). Simplify like terms first while substituting.
Step 3
Exam Tip
रखने पर \(5+a\sqrt{5}-5=0\), इसलिए \(a\sqrt{5}=0\) और (a=0)। मान रखते समय समान पद पहले सरल करें।
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Question 9/9
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि (p\(\sqrt{3}\)=0) और (p(x)=x-2 +ax+3) है, तो (a) का मान क्या होगा?
If (p\(\sqrt{3}\)=0) and (p(x)=x-2 +ax+3), what is the value of (a)?
#parameter
#polynomial-value
#irrational
A \(-2\sqrt{3}\)
B \(2\sqrt{3}\)
C \(-\sqrt{3}\)
D (0)
Explanation opens after your attempt
Correct Answer
A. \(-2\sqrt{3}\)
Step 1
Concept
From \(3+a\sqrt{3}+3=0\), \(a\sqrt{3}=-6\), so \(a=-2\sqrt{3}\). After substituting an irrational value, separate like terms carefully.
Step 2
Why this answer is correct
The correct answer is A. \(-2\sqrt{3}\). From \(3+a\sqrt{3}+3=0\), \(a\sqrt{3}=-6\), so \(a=-2\sqrt{3}\). After substituting an irrational value, separate like terms carefully.
Step 3
Exam Tip
\(3+a\sqrt{3}+3=0\) से \(a\sqrt{3}=-6\), इसलिए \(a=-2\sqrt{3}\) है। अपरिमेय मान रखने के बाद समान पद अलग करें।
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