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Mathematics Quiz - Class 9 Mathematics Introduction to Po...

Question 1/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(a=4+\sqrt{2}\) और \(b=4-\sqrt{2}\) हैं, तो \(a^2-b^2\) का मान क्या है?

If \(a=4+\sqrt{2}\) and \(b=4-\sqrt{2}\), what is the value of \(a^2-b^2\)?

Explanation opens after your attempt

Correct Answer

A. \(16\sqrt{2}\)

Step 1

Concept

(a^-2-b^-2=(a-b)(a+b)) where \(a-b=2\sqrt{2}\) and (a+b=8). So the value is \(16\sqrt{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(16\sqrt{2}\). (a^-2-b^-2=(a-b)(a+b)) where \(a-b=2\sqrt{2}\) and (a+b=8). So the value is \(16\sqrt{2}\).

Step 3

Exam Tip

(a^-2-b^-2=(a-b)(a+b)) है जहाँ \(a-b=2\sqrt{2}\) और (a+b=8) है। इसलिए मान \(16\sqrt{2}\) है।

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Question 2/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\frac{3+\sqrt{2}}{3-\sqrt{2}}\) का सरल रूप कौन-सा है?

Which is the simplified form of \(\frac{3+\sqrt{2}}{3-\sqrt{2}}\)?

Explanation opens after your attempt

Correct Answer

A. \( \frac{11+6\sqrt{2}}{7}\)

Step 1

Concept

Multiplying by the conjugate gives denominator (9-2=7) and numerator (\(3+\sqrt{2}\)²=11+6\sqrt{2}). So the correct form is \(\frac{11+6\sqrt{2}}{7}\).

Step 2

Why this answer is correct

The correct answer is A. \( \frac{11+6\sqrt{2}}{7}\). Multiplying by the conjugate gives denominator (9-2=7) and numerator (\(3+\sqrt{2}\)²=11+6\sqrt{2}). So the correct form is \(\frac{11+6\sqrt{2}}{7}\).

Step 3

Exam Tip

संयुग्मी से गुणा करने पर हर (9-2=7) और अंश (\(3+\sqrt{2}\)²=11+6\sqrt{2}) मिलता है। इसलिए सही रूप \(\frac{11+6\sqrt{2}}{7}\) है।

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Question 3/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(x=\sqrt{10}+\sqrt{5}\) है, तो \(x^2\) का सही मान क्या है?

If \(x=\sqrt{10}+\sqrt{5}\), what is the correct value of \(x^2\)?

Explanation opens after your attempt

Correct Answer

A. \(15+10\sqrt{2}\)

Step 1

Concept

\(x^2=10+5+2\sqrt{50}=15+10\sqrt{2}\). Simplify the middle term fully.

Step 2

Why this answer is correct

The correct answer is A. \(15+10\sqrt{2}\). \(x^2=10+5+2\sqrt{50}=15+10\sqrt{2}\). Simplify the middle term fully.

Step 3

Exam Tip

\(x^2=10+5+2\sqrt{50}=15+10\sqrt{2}\) है। मध्य पद को पूरी तरह सरल करें।

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Question 4/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\sqrt{108}-\sqrt{48}+\sqrt{12}\) किसके बराबर है?

What is \(\sqrt{108}-\sqrt{48}+\sqrt{12}\) equal to?

Explanation opens after your attempt

Correct Answer

A. \(4\sqrt{3}\)

Step 1

Concept

\(\sqrt{108}=6\sqrt{3}\), \(\sqrt{48}=4\sqrt{3}\), and \(\sqrt{12}=2\sqrt{3}\). Therefore the result is \(4\sqrt{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(4\sqrt{3}\). \(\sqrt{108}=6\sqrt{3}\), \(\sqrt{48}=4\sqrt{3}\), and \(\sqrt{12}=2\sqrt{3}\). Therefore the result is \(4\sqrt{3}\).

Step 3

Exam Tip

\(\sqrt{108}=6\sqrt{3}\), \(\sqrt{48}=4\sqrt{3}\) और \(\sqrt{12}=2\sqrt{3}\) है। इसलिए परिणाम \(4\sqrt{3}\) है।

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Question 5/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(p=\frac{1}{\sqrt{7}+2}\) है, तो (p) का सरल रूप कौन-सा है?

If \(p=\frac{1}{\sqrt{7}+2}\), which is the simplified form of (p)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{\sqrt{7}-2}{3}\)

Step 1

Concept

Multiplying by the conjugate \(\sqrt{7}-2\) makes the denominator (7-4=3). So \(p=\frac{\sqrt{7}-2}{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{\sqrt{7}-2}{3}\). Multiplying by the conjugate \(\sqrt{7}-2\) makes the denominator (7-4=3). So \(p=\frac{\sqrt{7}-2}{3}\).

Step 3

Exam Tip

संयुग्मी \(\sqrt{7}-2\) से गुणा करने पर हर (7-4=3) बनता है। इसलिए \(p=\frac{\sqrt{7}-2}{3}\) है।

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Question 6/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\sqrt{5+\sqrt{6}}\times\sqrt{5+\sqrt{6}}\) का मान क्या है?

What is the value of \(\sqrt{5+\sqrt{6}}\times\sqrt{5+\sqrt{6}}\)?

Explanation opens after your attempt

Correct Answer

A. \(5+\sqrt{6}\)

Step 1

Concept

Multiplying the same square root by itself gives the number inside. Therefore the value is \(5+\sqrt{6}\).

Step 2

Why this answer is correct

The correct answer is A. \(5+\sqrt{6}\). Multiplying the same square root by itself gives the number inside. Therefore the value is \(5+\sqrt{6}\).

Step 3

Exam Tip

एक ही वर्गमूल को अपने आप से गुणा करने पर अंदर की संख्या मिलती है। इसलिए मान \(5+\sqrt{6}\) है।

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Question 7/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(m=\sqrt{27}+\sqrt{75}\) और \(n=8\sqrt{3}\) हैं, तो (m-n) का मान क्या है?

If \(m=\sqrt{27}+\sqrt{75}\) and \(n=8\sqrt{3}\), what is the value of (m-n)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

\(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\), so \(m=8\sqrt{3}\). Hence (m-n=0).

Step 2

Why this answer is correct

The correct answer is A. (0). \(\sqrt{27}=3\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\), so \(m=8\sqrt{3}\). Hence (m-n=0).

Step 3

Exam Tip

\(\sqrt{27}=3\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\), इसलिए \(m=8\sqrt{3}\) है। अतः (m-n=0) है।

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Question 8/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\frac{\sqrt{3}+1}{\sqrt{3}-1}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{\sqrt{3}+1}{\sqrt{3}-1}\)?

Explanation opens after your attempt

Correct Answer

A. \(2+\sqrt{3}\)

Step 1

Concept

Multiplying by the conjugate gives (\frac{\(\sqrt{3}+1\)²}{2}=\frac{4+2\sqrt{3}}{2}=2+\sqrt{3}). Rationalise the denominator.

Step 2

Why this answer is correct

The correct answer is A. \(2+\sqrt{3}\). Multiplying by the conjugate gives (\frac{\(\sqrt{3}+1\)²}{2}=\frac{4+2\sqrt{3}}{2}=2+\sqrt{3}). Rationalise the denominator.

Step 3

Exam Tip

संयुग्मी से गुणा करने पर (\frac{\(\sqrt{3}+1\)²}{2}=\frac{4+2\sqrt{3}}{2}=2+\sqrt{3}) मिलता है। हर का परिमेयकरण करें।

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Question 9/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(x=\sqrt{5}+\sqrt{2}\) और \(y=\sqrt{5}-\sqrt{2}\) हैं, तो \(\frac{x}{y}\) का मान क्या है?

If \(x=\sqrt{5}+\sqrt{2}\) and \(y=\sqrt{5}-\sqrt{2}\), what is the value of \(\frac{x}{y}\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{7+2\sqrt{10}}{3}\)

Step 1

Concept

Multiply by the conjugate \(\sqrt{5}+\sqrt{2}\). The denominator is (5-2=3) and the numerator is \(7+2\sqrt{10}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{7+2\sqrt{10}}{3}\). Multiply by the conjugate \(\sqrt{5}+\sqrt{2}\). The denominator is (5-2=3) and the numerator is \(7+2\sqrt{10}\).

Step 3

Exam Tip

हर के संयुग्मी \(\sqrt{5}+\sqrt{2}\) से गुणा करें। हर (5-2=3) और अंश \(7+2\sqrt{10}\) होगा।

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Question 10/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(r=\sqrt{28}+\sqrt{112}\) है, तो (r) किसके बराबर है?

If \(r=\sqrt{28}+\sqrt{112}\), what is (r) equal to?

Explanation opens after your attempt

Correct Answer

A. \(6\sqrt{7}\)

Step 1

Concept

\(\sqrt{28}=2\sqrt{7}\) and \(\sqrt{112}=4\sqrt{7}\). Therefore \(r=6\sqrt{7}\).

Step 2

Why this answer is correct

The correct answer is A. \(6\sqrt{7}\). \(\sqrt{28}=2\sqrt{7}\) and \(\sqrt{112}=4\sqrt{7}\). Therefore \(r=6\sqrt{7}\).

Step 3

Exam Tip

\(\sqrt{28}=2\sqrt{7}\) और \(\sqrt{112}=4\sqrt{7}\) है। इसलिए \(r=6\sqrt{7}\) है।

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Question 11/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\sqrt{8+\sqrt{15}}\) के बारे में कौन-सा कथन निश्चित रूप से सही है?

Which statement is definitely true about \(\sqrt{8+\sqrt{15}}\)?

Explanation opens after your attempt

Correct Answer

B. इसका वर्ग \(8+\sqrt{15}\) हैIts square is \(8+\sqrt{15}\)

Step 1

Concept

Since \(8+\sqrt{15}\) is positive, its square root is real. Squaring it gives the inside number \(8+\sqrt{15}\).

Step 2

Why this answer is correct

The correct answer is B. इसका वर्ग \(8+\sqrt{15}\) है / Its square is \(8+\sqrt{15}\). Since \(8+\sqrt{15}\) is positive, its square root is real. Squaring it gives the inside number \(8+\sqrt{15}\).

Step 3

Exam Tip

क्योंकि \(8+\sqrt{15}\) धनात्मक है, इसका वर्गमूल वास्तविक है। वर्ग करने पर अंदर की संख्या \(8+\sqrt{15}\) मिलती है।

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Question 12/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(u=\sqrt{125}-\sqrt{45}\) और \(v=\sqrt{5}\) हैं, तो (u-v) का मान क्या है?

If \(u=\sqrt{125}-\sqrt{45}\) and \(v=\sqrt{5}\), what is the value of (u-v)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{5}\)

Step 1

Concept

\(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\), so \(u=2\sqrt{5}\). Hence \(u-v=\sqrt{5}\).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{5}\). \(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\), so \(u=2\sqrt{5}\). Hence \(u-v=\sqrt{5}\).

Step 3

Exam Tip

\(\sqrt{125}=5\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\), इसलिए \(u=2\sqrt{5}\) है। अतः \(u-v=\sqrt{5}\) है।

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Question 13/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\frac{4}{\sqrt{10}-\sqrt{6}}\) का परिमेयकृत रूप कौन-सा है?

Which is the rationalised form of \(\frac{4}{\sqrt{10}-\sqrt{6}}\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{10}+\sqrt{6}\)

Step 1

Concept

Multiplying by the conjugate makes the denominator (10-6=4). So (\frac{4\(\sqrt{10}+\sqrt{6}\)}{4}=\sqrt{10}+\sqrt{6}).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{10}+\sqrt{6}\). Multiplying by the conjugate makes the denominator (10-6=4). So (\frac{4\(\sqrt{10}+\sqrt{6}\)}{4}=\sqrt{10}+\sqrt{6}).

Step 3

Exam Tip

संयुग्मी से गुणा करने पर हर (10-6=4) बनता है। इसलिए (\frac{4\(\sqrt{10}+\sqrt{6}\)}{4}=\sqrt{10}+\sqrt{6}) है।

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Question 14/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

(\(\sqrt{20}+\sqrt{45}\)²) का मान क्या है?

What is the value of (\(\sqrt{20}+\sqrt{45}\)²)?

Explanation opens after your attempt

Correct Answer

A. (125)

Step 1

Concept

\(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\), so the sum is \(5\sqrt{5}\). Its square is (125).

Step 2

Why this answer is correct

The correct answer is A. (125). \(\sqrt{20}=2\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\), so the sum is \(5\sqrt{5}\). Its square is (125).

Step 3

Exam Tip

\(\sqrt{20}=2\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\), इसलिए योग \(5\sqrt{5}\) है। इसका वर्ग (125) है।

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Question 15/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(a=\sqrt{11}+\sqrt{2}\) और \(b=\sqrt{11}-\sqrt{2}\) हैं, तो (ab) और (a+b) का सही युग्म कौन-सा है?

If \(a=\sqrt{11}+\sqrt{2}\) and \(b=\sqrt{11}-\sqrt{2}\), which is the correct pair of (ab) and (a+b)?

Explanation opens after your attempt

Correct Answer

A. (9), \(2\sqrt{11}\)

Step 1

Concept

(ab=11-2=9) and \(a+b=2\sqrt{11}\). In a conjugate pair check product and sum separately.

Step 2

Why this answer is correct

The correct answer is A. (9), \(2\sqrt{11}\). (ab=11-2=9) and \(a+b=2\sqrt{11}\). In a conjugate pair check product and sum separately.

Step 3

Exam Tip

(ab=11-2=9) और \(a+b=2\sqrt{11}\) है। संयुग्मी युग्म में गुणन और योग अलग जाँचें।

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Question 16/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

(\sqrt{3}\left\(\sqrt{75}-\sqrt{27}\right\)) का मान क्या है?

What is the value of (\sqrt{3}\left\(\sqrt{75}-\sqrt{27}\right\))?

Explanation opens after your attempt

Correct Answer

A. (6)

Step 1

Concept

\(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\), so the bracket is \(2\sqrt{3}\). Multiplying by \(\sqrt{3}\) gives (6).

Step 2

Why this answer is correct

The correct answer is A. (6). \(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{27}=3\sqrt{3}\), so the bracket is \(2\sqrt{3}\). Multiplying by \(\sqrt{3}\) gives (6).

Step 3

Exam Tip

\(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{27}=3\sqrt{3}\), इसलिए कोष्ठक \(2\sqrt{3}\) है। \(\sqrt{3}\) से गुणा करने पर (6) मिलता है।

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Question 17/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\frac{3}{\sqrt{8}+\sqrt{5}}\) का परिमेयकृत रूप क्या है?

What is the rationalised form of \(\frac{3}{\sqrt{8}+\sqrt{5}}\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{8}-\sqrt{5}\)

Step 1

Concept

Multiplying by the conjugate makes the denominator (8-5=3). So (\frac{3\(\sqrt{8}-\sqrt{5}\)}{3}=\sqrt{8}-\sqrt{5}).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{8}-\sqrt{5}\). Multiplying by the conjugate makes the denominator (8-5=3). So (\frac{3\(\sqrt{8}-\sqrt{5}\)}{3}=\sqrt{8}-\sqrt{5}).

Step 3

Exam Tip

संयुग्मी से गुणा करने पर हर (8-5=3) बनता है। इसलिए (\frac{3\(\sqrt{8}-\sqrt{5}\)}{3}=\sqrt{8}-\sqrt{5}) है।

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Question 18/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(x=3\sqrt{5}-\sqrt{45}\) है, तो (x) का मान क्या है?

If \(x=3\sqrt{5}-\sqrt{45}\), what is the value of (x)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

\(\sqrt{45}=3\sqrt{5}\), so \(3\sqrt{5}-3\sqrt{5}=0\). Simplify the radical first.

Step 2

Why this answer is correct

The correct answer is A. (0). \(\sqrt{45}=3\sqrt{5}\), so \(3\sqrt{5}-3\sqrt{5}=0\). Simplify the radical first.

Step 3

Exam Tip

\(\sqrt{45}=3\sqrt{5}\), इसलिए \(3\sqrt{5}-3\sqrt{5}=0\) है। पहले मूल को सरल करें।

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Question 19/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\sqrt{4+\sqrt{7}}\times\sqrt{4+\sqrt{7}}\) का मान क्या है?

What is the value of \(\sqrt{4+\sqrt{7}}\times\sqrt{4+\sqrt{7}}\)?

Explanation opens after your attempt

Correct Answer

A. \(4+\sqrt{7}\)

Step 1

Concept

Multiplying the same square root by itself gives the number inside. Therefore the value is \(4+\sqrt{7}\).

Step 2

Why this answer is correct

The correct answer is A. \(4+\sqrt{7}\). Multiplying the same square root by itself gives the number inside. Therefore the value is \(4+\sqrt{7}\).

Step 3

Exam Tip

एक ही वर्गमूल का अपने आप से गुणन अंदर की संख्या देता है। इसलिए मान \(4+\sqrt{7}\) है।

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Question 20/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\sqrt{162}+\sqrt{98}-\sqrt{50}\) का सरल रूप कौन-सा है?

Which is the simplified form of \(\sqrt{162}+\sqrt{98}-\sqrt{50}\)?

Explanation opens after your attempt

Correct Answer

A. \(11\sqrt{2}\)

Step 1

Concept

\(\sqrt{162}=9\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), and \(\sqrt{50}=5\sqrt{2}\). Therefore the result is \(11\sqrt{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(11\sqrt{2}\). \(\sqrt{162}=9\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\), and \(\sqrt{50}=5\sqrt{2}\). Therefore the result is \(11\sqrt{2}\).

Step 3

Exam Tip

\(\sqrt{162}=9\sqrt{2}\), \(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\) है। इसलिए परिणाम \(11\sqrt{2}\) है।

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Question 21/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(t=\sqrt{7}+2\) है, तो \(t+\frac{3}{t}\) का मान क्या है?

If \(t=\sqrt{7}+2\), what is the value of \(t+\frac{3}{t}\)?

Explanation opens after your attempt

Correct Answer

A. \(2\sqrt{7}\)

Step 1

Concept

\(\frac{3}{\sqrt{7}+2}=\sqrt{7}-2\) because the denominator becomes (7-4=3). Therefore the sum is \(2\sqrt{7}\).

Step 2

Why this answer is correct

The correct answer is A. \(2\sqrt{7}\). \(\frac{3}{\sqrt{7}+2}=\sqrt{7}-2\) because the denominator becomes (7-4=3). Therefore the sum is \(2\sqrt{7}\).

Step 3

Exam Tip

\(\frac{3}{\sqrt{7}+2}=\sqrt{7}-2\) है क्योंकि हर (7-4=3) बनता है। इसलिए योग \(2\sqrt{7}\) है।

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Question 22/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(s=\sqrt{48}+\sqrt{75}\) है, तो \(\frac{s}{\sqrt{3}}\) का मान क्या है?

If \(s=\sqrt{48}+\sqrt{75}\), what is the value of \(\frac{s}{\sqrt{3}}\)?

Explanation opens after your attempt

Correct Answer

A. (9)

Step 1

Concept

\(\sqrt{48}=4\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\), so \(s=9\sqrt{3}\). Dividing by \(\sqrt{3}\) gives (9).

Step 2

Why this answer is correct

The correct answer is A. (9). \(\sqrt{48}=4\sqrt{3}\) and \(\sqrt{75}=5\sqrt{3}\), so \(s=9\sqrt{3}\). Dividing by \(\sqrt{3}\) gives (9).

Step 3

Exam Tip

\(\sqrt{48}=4\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\), इसलिए \(s=9\sqrt{3}\) है। \(\sqrt{3}\) से भाग देने पर (9) मिलता है।

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Question 23/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}\) का सरल रूप कौन-सा है?

Which is the simplified form of \(\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{7-2\sqrt{10}}{3}\)

Step 1

Concept

Multiplying by the conjugate gives (\frac{\(\sqrt{5}-\sqrt{2}\)²}{5-2}). So the answer is \(\frac{7-2\sqrt{10}}{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{7-2\sqrt{10}}{3}\). Multiplying by the conjugate gives (\frac{\(\sqrt{5}-\sqrt{2}\)²}{5-2}). So the answer is \(\frac{7-2\sqrt{10}}{3}\).

Step 3

Exam Tip

संयुग्मी से गुणा करने पर (\frac{\(\sqrt{5}-\sqrt{2}\)²}{5-2}) मिलता है। इसलिए उत्तर \(\frac{7-2\sqrt{10}}{3}\) है।

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Question 24/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(x=\sqrt{3}+\sqrt{12}\) और \(y=\sqrt{27}\) हैं, तो (x-y) क्या है?

If \(x=\sqrt{3}+\sqrt{12}\) and \(y=\sqrt{27}\), what is (x-y)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

\(x=\sqrt{3}+2\sqrt{3}=3\sqrt{3}\) and \(y=3\sqrt{3}\). Therefore (x-y=0).

Step 2

Why this answer is correct

The correct answer is A. (0). \(x=\sqrt{3}+2\sqrt{3}=3\sqrt{3}\) and \(y=3\sqrt{3}\). Therefore (x-y=0).

Step 3

Exam Tip

\(x=\sqrt{3}+2\sqrt{3}=3\sqrt{3}\) और \(y=3\sqrt{3}\) है। इसलिए (x-y=0) है।

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Question 25/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

(\(\sqrt{17}+3\)²-\(\sqrt{17}-3\)²) का मान क्या है?

What is the value of (\(\sqrt{17}+3\)²-\(\sqrt{17}-3\)²)?

Explanation opens after your attempt

Correct Answer

A. \(12\sqrt{17}\)

Step 1

Concept

Use ((a+b)²-(a-b)²=4ab). Here \(a=\sqrt{17}\) and (b=3), so the value is \(12\sqrt{17}\).

Step 2

Why this answer is correct

The correct answer is A. \(12\sqrt{17}\). Use ((a+b)²-(a-b)²=4ab). Here \(a=\sqrt{17}\) and (b=3), so the value is \(12\sqrt{17}\).

Step 3

Exam Tip

पहचान ((a+b)²-(a-b)²=4ab) लगाएं। यहाँ \(a=\sqrt{17}\) और (b=3), इसलिए मान \(12\sqrt{17}\) है।

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Question 26/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि एक आयत की लंबाई \(4+\sqrt{5}\) और चौड़ाई \(4-\sqrt{5}\) है, तो क्षेत्रफल क्या होगा?

If a rectangle has length \(4+\sqrt{5}\) and breadth \(4-\sqrt{5}\), what will be its area?

Explanation opens after your attempt

Correct Answer

A. (11)

Step 1

Concept

Area is (\(4+\sqrt{5}\)\(4-\sqrt{5}\)=16-5=11). Multiplying conjugate dimensions can give a rational area.

Step 2

Why this answer is correct

The correct answer is A. (11). Area is (\(4+\sqrt{5}\)\(4-\sqrt{5}\)=16-5=11). Multiplying conjugate dimensions can give a rational area.

Step 3

Exam Tip

क्षेत्रफल (\(4+\sqrt{5}\)\(4-\sqrt{5}\)=16-5=11) है। संयुग्मी आयामों का गुणन परिमेय क्षेत्रफल दे सकता है।

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Question 27/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\sqrt{300}-\sqrt{192}+\sqrt{75}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{300}-\sqrt{192}+\sqrt{75}\)?

Explanation opens after your attempt

Correct Answer

A. \(7\sqrt{3}\)

Step 1

Concept

\(\sqrt{300}=10\sqrt{3}\), \(\sqrt{192}=8\sqrt{3}\), and \(\sqrt{75}=5\sqrt{3}\). Therefore the result is \(7\sqrt{3}\).

Step 2

Why this answer is correct

The correct answer is A. \(7\sqrt{3}\). \(\sqrt{300}=10\sqrt{3}\), \(\sqrt{192}=8\sqrt{3}\), and \(\sqrt{75}=5\sqrt{3}\). Therefore the result is \(7\sqrt{3}\).

Step 3

Exam Tip

\(\sqrt{300}=10\sqrt{3}\), \(\sqrt{192}=8\sqrt{3}\) और \(\sqrt{75}=5\sqrt{3}\) है। इसलिए परिणाम \(7\sqrt{3}\) है।

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Question 28/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\frac{1}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{5}-\sqrt{3}}\) का मान क्या है?

What is the value of \(\frac{1}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{5}-\sqrt{3}}\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{5}\)

Step 1

Concept

The first term becomes \(\frac{\sqrt{5}-\sqrt{3}}{2}\) and the second becomes \(\frac{\sqrt{5}+\sqrt{3}}{2}\). Their sum is \(\sqrt{5}\).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{5}\). The first term becomes \(\frac{\sqrt{5}-\sqrt{3}}{2}\) and the second becomes \(\frac{\sqrt{5}+\sqrt{3}}{2}\). Their sum is \(\sqrt{5}\).

Step 3

Exam Tip

पहला पद \(\frac{\sqrt{5}-\sqrt{3}}{2}\) और दूसरा \(\frac{\sqrt{5}+\sqrt{3}}{2}\) बनता है। योग \(\sqrt{5}\) है।

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Question 29/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(z=\sqrt{13}-\sqrt{5}\) है, तो \(z^2\) का मान कौन-सा है?

If \(z=\sqrt{13}-\sqrt{5}\), which is the value of \(z^2\)?

Explanation opens after your attempt

Correct Answer

A. \(18-2\sqrt{65}\)

Step 1

Concept

(\(\sqrt{13}-\sqrt{5}\)²=13+5-2\sqrt{65}). The middle term remains negative.

Step 2

Why this answer is correct

The correct answer is A. \(18-2\sqrt{65}\). (\(\sqrt{13}-\sqrt{5}\)²=13+5-2\sqrt{65}). The middle term remains negative.

Step 3

Exam Tip

(\(\sqrt{13}-\sqrt{5}\)²=13+5-2\sqrt{65}) है। मध्य पद का चिन्ह ऋणात्मक रहेगा।

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Question 30/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

कौन-सा विकल्प \(\sqrt{72}+\sqrt{128}\) के बराबर है?

Which option is equal to \(\sqrt{72}+\sqrt{128}\)?

Explanation opens after your attempt

Correct Answer

A. \(14\sqrt{2}\)

Step 1

Concept

\(\sqrt{72}=6\sqrt{2}\) and \(\sqrt{128}=8\sqrt{2}\). So the sum is \(14\sqrt{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(14\sqrt{2}\). \(\sqrt{72}=6\sqrt{2}\) and \(\sqrt{128}=8\sqrt{2}\). So the sum is \(14\sqrt{2}\).

Step 3

Exam Tip

\(\sqrt{72}=6\sqrt{2}\) और \(\sqrt{128}=8\sqrt{2}\) है। इसलिए योग \(14\sqrt{2}\) है।

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Question 31/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(q=\sqrt{5}+2\) है, तो \(q^2-4q\) का मान क्या है?

If \(q=\sqrt{5}+2\), what is the value of \(q^2-4q\)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

\(q^2=9+4\sqrt{5}\) and \(4q=4\sqrt{5}+8\). Subtracting gives (1).

Step 2

Why this answer is correct

The correct answer is A. (1). \(q^2=9+4\sqrt{5}\) and \(4q=4\sqrt{5}+8\). Subtracting gives (1).

Step 3

Exam Tip

\(q^2=9+4\sqrt{5}\) और \(4q=4\sqrt{5}+8\) है। घटाने पर (1) मिलता है।

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Question 32/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\sqrt{10}\) और \(\sqrt{12}\) के बीच कौन-सी संख्या निश्चित रूप से आती है?

Which number definitely lies between \(\sqrt{10}\) and \(\sqrt{12}\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{11}\)

Step 1

Concept

Since (10<11<12), \(\sqrt{11}\) lies between them. For positive square roots compare the numbers inside.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{11}\). Since (10<11<12), \(\sqrt{11}\) lies between them. For positive square roots compare the numbers inside.

Step 3

Exam Tip

क्योंकि (10<11<12), इसलिए \(\sqrt{11}\) दोनों के बीच होगा। धनात्मक वर्गमूलों में अंदर की संख्या से तुलना करें।

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Question 33/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(A=\sqrt{80}+\sqrt{45}\) और \(B=7\sqrt{5}\) हैं, तो कौन-सा कथन सही है?

If \(A=\sqrt{80}+\sqrt{45}\) and \(B=7\sqrt{5}\), which statement is correct?

Explanation opens after your attempt

Correct Answer

A. (A=B)

Step 1

Concept

\(\sqrt{80}=4\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\), so \(A=7\sqrt{5}\). Hence (A=B).

Step 2

Why this answer is correct

The correct answer is A. (A=B). \(\sqrt{80}=4\sqrt{5}\) and \(\sqrt{45}=3\sqrt{5}\), so \(A=7\sqrt{5}\). Hence (A=B).

Step 3

Exam Tip

\(\sqrt{80}=4\sqrt{5}\) और \(\sqrt{45}=3\sqrt{5}\), इसलिए \(A=7\sqrt{5}\) है। अतः (A=B) है।

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Question 34/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\frac{\sqrt{125}-\sqrt{20}}{\sqrt{5}}\) का मान क्या है?

What is the value of \(\frac{\sqrt{125}-\sqrt{20}}{\sqrt{5}}\)?

Explanation opens after your attempt

Correct Answer

A. (3)

Step 1

Concept

\(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\), so the numerator is \(3\sqrt{5}\). Dividing gives (3).

Step 2

Why this answer is correct

The correct answer is A. (3). \(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{20}=2\sqrt{5}\), so the numerator is \(3\sqrt{5}\). Dividing gives (3).

Step 3

Exam Tip

\(\sqrt{125}=5\sqrt{5}\) और \(\sqrt{20}=2\sqrt{5}\), इसलिए अंश \(3\sqrt{5}\) है। भाग देने पर (3) मिलता है।

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Question 35/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\sqrt{7+\sqrt{10}}\) का वर्ग किसके बराबर है?

What is the square of \(\sqrt{7+\sqrt{10}}\) equal to?

Explanation opens after your attempt

Correct Answer

A. \(7+\sqrt{10}\)

Step 1

Concept

The square of a square root gives the number inside. So (\left\(\sqrt{7+\sqrt{10}}\right\)²=7+\sqrt{10}).

Step 2

Why this answer is correct

The correct answer is A. \(7+\sqrt{10}\). The square of a square root gives the number inside. So (\left\(\sqrt{7+\sqrt{10}}\right\)²=7+\sqrt{10}).

Step 3

Exam Tip

वर्गमूल का वर्ग अंदर की संख्या देता है। इसलिए (\left\(\sqrt{7+\sqrt{10}}\right\)²=7+\sqrt{10}) है।

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Question 36/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(x=\sqrt{7}+\sqrt{2}\) है, तो \(x^2-9\) का मान क्या है?

If \(x=\sqrt{7}+\sqrt{2}\), what is the value of \(x^2-9\)?

Explanation opens after your attempt

Correct Answer

A. \(2\sqrt{14}\)

Step 1

Concept

\(x^2=7+2+2\sqrt{14}=9+2\sqrt{14}\). Therefore \(x^2-9=2\sqrt{14}\).

Step 2

Why this answer is correct

The correct answer is A. \(2\sqrt{14}\). \(x^2=7+2+2\sqrt{14}=9+2\sqrt{14}\). Therefore \(x^2-9=2\sqrt{14}\).

Step 3

Exam Tip

\(x^2=7+2+2\sqrt{14}=9+2\sqrt{14}\) है। इसलिए \(x^2-9=2\sqrt{14}\) है।

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Question 37/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

किस विकल्प में दो अपरिमेय संख्याओं का अंतर परिमेय है?

In which option is the difference of two irrational numbers rational?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{19}-\sqrt{19}\)

Step 1

Concept

\(\sqrt{19}\) and \(\sqrt{19}\) are both irrational and their difference is (0). (0) is rational.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{19}-\sqrt{19}\). \(\sqrt{19}\) and \(\sqrt{19}\) are both irrational and their difference is (0). (0) is rational.

Step 3

Exam Tip

\(\sqrt{19}\) और \(\sqrt{19}\) दोनों अपरिमेय हैं और अंतर (0) है। (0) परिमेय संख्या है।

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Question 38/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

(\(\sqrt{20}+\sqrt{45}\)\(\sqrt{20}-\sqrt{45}\)) का मान क्या है?

What is the value of (\(\sqrt{20}+\sqrt{45}\)\(\sqrt{20}-\sqrt{45}\))?

Explanation opens after your attempt

Correct Answer

A. (-25)

Step 1

Concept

This is the \(a^2-b^2\) form, so the value is (20-45=-25). In conjugate multiplication take the difference of squares directly.

Step 2

Why this answer is correct

The correct answer is A. (-25). This is the \(a^2-b^2\) form, so the value is (20-45=-25). In conjugate multiplication take the difference of squares directly.

Step 3

Exam Tip

यह \(a^2-b^2\) रूप है, इसलिए मान (20-45=-25) है। संयुग्मी गुणन में सीधे वर्गों का अंतर लें।

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Question 39/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(c=\sqrt{6}+\sqrt{2}\) और \(d=\sqrt{6}-\sqrt{2}\) हैं, तो (cd) और (c-d) का सही युग्म कौन-सा है?

If \(c=\sqrt{6}+\sqrt{2}\) and \(d=\sqrt{6}-\sqrt{2}\), which is the correct pair of (cd) and (c-d)?

Explanation opens after your attempt

Correct Answer

A. (4), \(2\sqrt{2}\)

Step 1

Concept

(cd=6-2=4) and \(c-d=2\sqrt{2}\). In conjugate forms find the product and difference separately.

Step 2

Why this answer is correct

The correct answer is A. (4), \(2\sqrt{2}\). (cd=6-2=4) and \(c-d=2\sqrt{2}\). In conjugate forms find the product and difference separately.

Step 3

Exam Tip

(cd=6-2=4) और \(c-d=2\sqrt{2}\) है। संयुग्मी रूप में गुणन और अंतर अलग-अलग निकालें।

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Question 40/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}\) का सरल रूप कौन-सा है?

Which is the simplified form of \(\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}\)?

Explanation opens after your attempt

Correct Answer

B. \(\frac{5+\sqrt{21}}{2}\)

Step 1

Concept

Multiplying by the conjugate gives numerator \(10+2\sqrt{21}\) and denominator (4). So the simplified form is \(\frac{5+\sqrt{21}}{2}\).

Step 2

Why this answer is correct

The correct answer is B. \(\frac{5+\sqrt{21}}{2}\). Multiplying by the conjugate gives numerator \(10+2\sqrt{21}\) and denominator (4). So the simplified form is \(\frac{5+\sqrt{21}}{2}\).

Step 3

Exam Tip

संयुग्मी से गुणा करने पर अंश \(10+2\sqrt{21}\) और हर (4) मिलता है। इसलिए सरल रूप \(\frac{5+\sqrt{21}}{2}\) है।

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Question 41/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(x=2+\sqrt{6}\) है, तो \(x^2-4x\) का मान क्या है?

If \(x=2+\sqrt{6}\), what is the value of \(x^2-4x\)?

Explanation opens after your attempt

Correct Answer

B. (-2)

Step 1

Concept

\(x^2=10+4\sqrt{6}\) and \(4x=8+4\sqrt{6}\). Subtracting gives (2).

Step 2

Why this answer is correct

The correct answer is B. (-2). \(x^2=10+4\sqrt{6}\) and \(4x=8+4\sqrt{6}\). Subtracting gives (2).

Step 3

Exam Tip

\(x^2=10+4\sqrt{6}\) और \(4x=8+4\sqrt{6}\) है। घटाने पर (2) नहीं, बल्कि (2) मिलता है।

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Question 42/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\sqrt{245}-\sqrt{180}+\sqrt{80}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt{245}-\sqrt{180}+\sqrt{80}\)?

Explanation opens after your attempt

Correct Answer

C. \(7\sqrt{5}\)

Step 1

Concept

\(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), and \(\sqrt{80}=4\sqrt{5}\). So the result is \(7\sqrt{5}-6\sqrt{5}+4\sqrt{5}=5\sqrt{5}\).

Step 2

Why this answer is correct

The correct answer is C. \(7\sqrt{5}\). \(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), and \(\sqrt{80}=4\sqrt{5}\). So the result is \(7\sqrt{5}-6\sqrt{5}+4\sqrt{5}=5\sqrt{5}\).

Step 3

Exam Tip

\(\sqrt{245}=7\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\) और \(\sqrt{80}=4\sqrt{5}\) है। इसलिए परिणाम \(5\sqrt{5}\) नहीं, \(7\sqrt{5}-6\sqrt{5}+4\sqrt{5}=5\sqrt{5}\) है।

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Question 43/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(r=\frac{1}{\sqrt{11}+3}\) है, तो (r) का सरल रूप कौन-सा है?

If \(r=\frac{1}{\sqrt{11}+3}\), which is the simplified form of (r)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{\sqrt{11}-3}{2}\)

Step 1

Concept

Multiplying by the conjugate makes the denominator (11-9=2). So the simplified form is \(\frac{\sqrt{11}-3}{2}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{\sqrt{11}-3}{2}\). Multiplying by the conjugate makes the denominator (11-9=2). So the simplified form is \(\frac{\sqrt{11}-3}{2}\).

Step 3

Exam Tip

संयुग्मी से गुणा करने पर हर (11-9=2) बनता है। इसलिए सरल रूप \(\frac{\sqrt{11}-3}{2}\) है।

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Question 44/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

(\(\sqrt{18}+\sqrt{50}\)²) का मान क्या है?

What is the value of (\(\sqrt{18}+\sqrt{50}\)²)?

Explanation opens after your attempt

Correct Answer

A. (128)

Step 1

Concept

\(\sqrt{18}=3\sqrt{2}\) and \(\sqrt{50}=5\sqrt{2}\), so the sum is \(8\sqrt{2}\). Its square is (128).

Step 2

Why this answer is correct

The correct answer is A. (128). \(\sqrt{18}=3\sqrt{2}\) and \(\sqrt{50}=5\sqrt{2}\), so the sum is \(8\sqrt{2}\). Its square is (128).

Step 3

Exam Tip

\(\sqrt{18}=3\sqrt{2}\) और \(\sqrt{50}=5\sqrt{2}\), इसलिए योग \(8\sqrt{2}\) है। इसका वर्ग (128) है।

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Question 45/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

\(\frac{2}{\sqrt{11}+\sqrt{7}}\) का परिमेयकृत रूप क्या है?

What is the rationalised form of \(\frac{2}{\sqrt{11}+\sqrt{7}}\)?

Explanation opens after your attempt

Correct Answer

B. \(\frac{\sqrt{11}-\sqrt{7}}{2}\)

Step 1

Concept

Multiplying by the conjugate makes the denominator (11-7=4). So (\frac{2\(\sqrt{11}-\sqrt{7}\)}{4}=\frac{\sqrt{11}-\sqrt{7}}{2}).

Step 2

Why this answer is correct

The correct answer is B. \(\frac{\sqrt{11}-\sqrt{7}}{2}\). Multiplying by the conjugate makes the denominator (11-7=4). So (\frac{2\(\sqrt{11}-\sqrt{7}\)}{4}=\frac{\sqrt{11}-\sqrt{7}}{2}).

Step 3

Exam Tip

संयुग्मी से गुणा करने पर हर (11-7=4) बनता है। इसलिए (\frac{2\(\sqrt{11}-\sqrt{7}\)}{4}=\frac{\sqrt{11}-\sqrt{7}}{2}) है।

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Question 46/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(s=\sqrt{98}+\sqrt{200}\) है, तो \(\frac{s}{\sqrt{2}}\) का मान क्या है?

If \(s=\sqrt{98}+\sqrt{200}\), what is the value of \(\frac{s}{\sqrt{2}}\)?

Explanation opens after your attempt

Correct Answer

C. (17)

Step 1

Concept

\(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{200}=10\sqrt{2}\), so \(s=17\sqrt{2}\). Dividing by \(\sqrt{2}\) gives (17).

Step 2

Why this answer is correct

The correct answer is C. (17). \(\sqrt{98}=7\sqrt{2}\) and \(\sqrt{200}=10\sqrt{2}\), so \(s=17\sqrt{2}\). Dividing by \(\sqrt{2}\) gives (17).

Step 3

Exam Tip

\(\sqrt{98}=7\sqrt{2}\) और \(\sqrt{200}=10\sqrt{2}\), इसलिए \(s=17\sqrt{2}\) है। \(\sqrt{2}\) से भाग देने पर (17) मिलता है।

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Question 47/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(a=\sqrt{3}+\sqrt{5}\) और \(b=\sqrt{5}-\sqrt{3}\) हैं, तो (ab) का मान क्या है?

If \(a=\sqrt{3}+\sqrt{5}\) and \(b=\sqrt{5}-\sqrt{3}\), what is the value of (ab)?

Explanation opens after your attempt

Correct Answer

A. (2)

Step 1

Concept

After rearranging (ab=\(\sqrt{5}+\sqrt{3}\)\(\sqrt{5}-\sqrt{3}\)=5-3=2). Identify the conjugate form.

Step 2

Why this answer is correct

The correct answer is A. (2). After rearranging (ab=\(\sqrt{5}+\sqrt{3}\)\(\sqrt{5}-\sqrt{3}\)=5-3=2). Identify the conjugate form.

Step 3

Exam Tip

क्रम बदलने पर (ab=\(\sqrt{5}+\sqrt{3}\)\(\sqrt{5}-\sqrt{3}\)=5-3=2) है। संयुग्मी रूप पहचानें।

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Question 48/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

किस विकल्प का मान अपरिमेय रहेगा?

Which option will remain irrational?

Explanation opens after your attempt

Correct Answer

C. \(\frac{\sqrt{45}}{\sqrt{9}}\)

Step 1

Concept

The first, second, and fourth options give (5), (5), and (6) respectively. The third gives \(\sqrt{5}\), which is irrational.

Step 2

Why this answer is correct

The correct answer is C. \(\frac{\sqrt{45}}{\sqrt{9}}\). The first, second, and fourth options give (5), (5), and (6) respectively. The third gives \(\sqrt{5}\), which is irrational.

Step 3

Exam Tip

पहले, दूसरे और चौथे विकल्प क्रमशः (5), (5) और (6) देते हैं। तीसरा \(\sqrt{5}\) देता है जो अपरिमेय है।

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Question 49/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

यदि \(x=\sqrt{8+\sqrt{15}}\) है, तो \(x^2-8\) का मान क्या है?

If \(x=\sqrt{8+\sqrt{15}}\), what is the value of \(x^2-8\)?

Explanation opens after your attempt

Correct Answer

A. \(\sqrt{15}\)

Step 1

Concept

\(x^2=8+\sqrt{15}\). Therefore \(x^2-8=\sqrt{15}\).

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{15}\). \(x^2=8+\sqrt{15}\). Therefore \(x^2-8=\sqrt{15}\).

Step 3

Exam Tip

\(x^2=8+\sqrt{15}\) है। इसलिए \(x^2-8=\sqrt{15}\) होगा।

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Question 50/50 Hard Mathematics Number Systems Irrational numbers Class 9 Level 14

(\(\sqrt{45}+\sqrt{5}\)\(\sqrt{45}-\sqrt{5}\)) का मान क्या है?

What is the value of (\(\sqrt{45}+\sqrt{5}\)\(\sqrt{45}-\sqrt{5}\))?

Explanation opens after your attempt

Correct Answer

A. (40)

Step 1

Concept

This is the \(a^2-b^2\) form, so the value is (45-5=40). In conjugate multiplication take the difference of squares directly.

Step 2

Why this answer is correct

The correct answer is A. (40). This is the \(a^2-b^2\) form, so the value is (45-5=40). In conjugate multiplication take the difference of squares directly.

Step 3

Exam Tip

यह \(a^2-b^2\) रूप है, इसलिए मान (45-5=40) है। संयुग्मी गुणन में सीधे वर्गों का अंतर लें।

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Class 9 Mathematics - Introduction to Polynomials - Degree of polynomial Hard Quiz

यदि \(a=4+\sqrt{2}\) और \(b=4-\sqrt{2}\) हैं, तो \(a^2-b^2\) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

\(\frac{3+\sqrt{2}}{3-\sqrt{2}}\) का सरल रूप कौन-सा है?

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Exam Tip

यदि \(x=\sqrt{10}+\sqrt{5}\) है, तो \(x^2\) का सही मान क्या है?

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Exam Tip

\(\sqrt{108}-\sqrt{48}+\sqrt{12}\) किसके बराबर है?

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Exam Tip

यदि \(p=\frac{1}{\sqrt{7}+2}\) है, तो (p) का सरल रूप कौन-सा है?

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Exam Tip

\(\sqrt{5+\sqrt{6}}\times\sqrt{5+\sqrt{6}}\) का मान क्या है?

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Exam Tip

यदि \(m=\sqrt{27}+\sqrt{75}\) और \(n=8\sqrt{3}\) हैं, तो (m-n) का मान क्या है?

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Exam Tip

\(\frac{\sqrt{3}+1}{\sqrt{3}-1}\) का सरल रूप क्या है?

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Exam Tip

यदि \(x=\sqrt{5}+\sqrt{2}\) और \(y=\sqrt{5}-\sqrt{2}\) हैं, तो \(\frac{x}{y}\) का मान क्या है?

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यदि \(r=\sqrt{28}+\sqrt{112}\) है, तो (r) किसके बराबर है?

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Exam Tip

\(\sqrt{8+\sqrt{15}}\) के बारे में कौन-सा कथन निश्चित रूप से सही है?

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Exam Tip

यदि \(u=\sqrt{125}-\sqrt{45}\) और \(v=\sqrt{5}\) हैं, तो (u-v) का मान क्या है?

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Exam Tip

\(\frac{4}{\sqrt{10}-\sqrt{6}}\) का परिमेयकृत रूप कौन-सा है?

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Exam Tip

(\(\sqrt{20}+\sqrt{45}\)2) का मान क्या है?

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Exam Tip

यदि \(a=\sqrt{11}+\sqrt{2}\) और \(b=\sqrt{11}-\sqrt{2}\) हैं, तो (ab) और (a+b) का सही युग्म कौन-सा है?

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Exam Tip

(\sqrt{3}\left\(\sqrt{75}-\sqrt{27}\right\)) का मान क्या है?

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Exam Tip

\(\frac{3}{\sqrt{8}+\sqrt{5}}\) का परिमेयकृत रूप क्या है?

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Exam Tip

यदि \(x=3\sqrt{5}-\sqrt{45}\) है, तो (x) का मान क्या है?

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Exam Tip

\(\sqrt{4+\sqrt{7}}\times\sqrt{4+\sqrt{7}}\) का मान क्या है?

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Exam Tip

\(\sqrt{162}+\sqrt{98}-\sqrt{50}\) का सरल रूप कौन-सा है?

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(\(\sqrt{20}+\sqrt{45}\)²) का मान क्या है?

(\(\sqrt{17}+3\)²-\(\sqrt{17}-3\)²) का मान क्या है?