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100 results found for "variable-classification" in Class 10.

एक चर के बहुपद में चर की घातें कैसी होनी चाहिए?

What should the powers of the variable be in a polynomial in one variable?

Explanation opens after your attempt
Correct Answer

C. अऋणात्मक पूर्णांकNon-negative integers

Step 1

Concept

In a polynomial, powers of the variable are non-negative integers like \(0,1,2,\ldots\). This is the basic identification rule.

Step 2

Why this answer is correct

The correct answer is C. अऋणात्मक पूर्णांक / Non-negative integers. In a polynomial, powers of the variable are non-negative integers like \(0,1,2,\ldots\). This is the basic identification rule.

Step 3

Exam Tip

बहुपद में चर की घातें \(0,1,2,\ldots\) जैसी अऋणात्मक पूर्णांक होती हैं। यही बहुपद की मूल पहचान है।

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बहुपद (p(u)=13u-3-2u+9) में चर कौन सा है?

What is the variable in the polynomial (p(u)=13u-3-2u+9)?

Explanation opens after your attempt
Correct Answer

B. (u)

Step 1

Concept

The letter whose values can change is the variable. Here the variable is (u).

Step 2

Why this answer is correct

The correct answer is B. (u). The letter whose values can change is the variable. Here the variable is (u).

Step 3

Exam Tip

जिस अक्षर के मान बदल सकते हैं वह चर होता है। यहां चर (u) है।

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बहुपद (p(t)=6t-2-7t+3) में चर कौन सा है?

What is the variable in the polynomial (p(t)=6t-2-7t+3)?

Explanation opens after your attempt
Correct Answer

B. (t)

Step 1

Concept

The letter whose value can vary is the variable. Here the variable is (t).

Step 2

Why this answer is correct

The correct answer is B. (t). The letter whose value can vary is the variable. Here the variable is (t).

Step 3

Exam Tip

जिस अक्षर का मान बदल सकता है वह चर है। यहां चर (t) है।

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कौन सा विकल्प एक चर में बहुपद है लेकिन रैखिक नहीं है?

Which option is a polynomial in one variable but not linear?

Explanation opens after your attempt
Correct Answer

B. \(x^2+2x+3\)

Step 1

Concept

\(x^2+2x+3\) is a polynomial and its degree is (2). Therefore it is not linear.

Step 2

Why this answer is correct

The correct answer is B. \(x^2+2x+3\). \(x^2+2x+3\) is a polynomial and its degree is (2). Therefore it is not linear.

Step 3

Exam Tip

\(x^2+2x+3\) बहुपद है और इसकी घात (2) है। इसलिए यह रैखिक नहीं है।

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कौन सा विकल्प एक चर में बहुपद है लेकिन द्विघात नहीं है?

Which option is a polynomial in one variable but not quadratic?

Explanation opens after your attempt
Correct Answer

B. \(4x^3+x-9\)

Step 1

Concept

\(4x^3+x-9\) is a polynomial and its degree is (3). Therefore it is not quadratic.

Step 2

Why this answer is correct

The correct answer is B. \(4x^3+x-9\). \(4x^3+x-9\) is a polynomial and its degree is (3). Therefore it is not quadratic.

Step 3

Exam Tip

\(4x^3+x-9\) बहुपद है और इसकी घात (3) है। इसलिए यह द्विघात नहीं है।

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निम्न में से एक चर वाला बहुपद कौन सा नहीं है?

Which of the following is not a polynomial in one variable?

Explanation opens after your attempt
Correct Answer

C. \(x^2+y+1\)

Step 1

Concept

\(x^2+y+1\) has two variables (x) and (y). Therefore it is not a polynomial in one variable.

Step 2

Why this answer is correct

The correct answer is C. \(x^2+y+1\). \(x^2+y+1\) has two variables (x) and (y). Therefore it is not a polynomial in one variable.

Step 3

Exam Tip

\(x^2+y+1\) में दो चर (x) और (y) हैं। इसलिए यह एक चर वाला बहुपद नहीं है।

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इनमें से कौन सा एक चर में बहुपद है?

Which of the following is a polynomial in one variable?

Explanation opens after your attempt
Correct Answer

A. (p(x)=3x-2-5x+7)

Step 1

Concept

In a polynomial in one variable, powers of the variable are non-negative integers. In exams, reject negative powers and roots of the variable.

Step 2

Why this answer is correct

The correct answer is A. (p(x)=3x-2-5x+7). In a polynomial in one variable, powers of the variable are non-negative integers. In exams, reject negative powers and roots of the variable.

Step 3

Exam Tip

एक चर के बहुपद में चर की घात केवल अशून्य पूर्णांक या शून्य होती है। परीक्षा में ऋणात्मक घात और मूल से बचें।

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कौन सा बहुपद एक चर (x) में है?

Which polynomial is in one variable (x)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+2x+1\)

Step 1

Concept

A polynomial in one variable (x) contains only the variable (x). The other options have more than one variable.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+2x+1\). A polynomial in one variable (x) contains only the variable (x). The other options have more than one variable.

Step 3

Exam Tip

एक चर (x) में बहुपद में केवल (x) चर होता है। अन्य विकल्पों में एक से अधिक चर हैं।

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बहुपद (p(t)=8t-2-3t+4) में चर कौन-सा है?

Which is the variable in the polynomial (p(t)=8t-2-3t+4)?

Explanation opens after your attempt
Correct Answer

B. (t)

Step 1

Concept

In (p(t)), the changing symbol is (t). So the variable is (t).

Step 2

Why this answer is correct

The correct answer is B. (t). In (p(t)), the changing symbol is (t). So the variable is (t).

Step 3

Exam Tip

(p(t)) में बदलने वाला चिन्ह (t) है। इसलिए चर (t) है।

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कौन सा व्यंजक बहुपद नहीं है क्योंकि चर की घात भिन्न है?

Which expression is not a polynomial because the variable has a fractional power?

Explanation opens after your attempt
Correct Answer

C. \(x^{\frac{3}{2}}+x+1\)

Step 1

Concept

In \(x^{\frac{3}{2}}\), the power of the variable is fractional, so it is not a polynomial. In a polynomial, powers are non-negative integers.

Step 2

Why this answer is correct

The correct answer is C. \(x^{\frac{3}{2}}+x+1\). In \(x^{\frac{3}{2}}\), the power of the variable is fractional, so it is not a polynomial. In a polynomial, powers are non-negative integers.

Step 3

Exam Tip

\(x^{\frac{3}{2}}\) में चर की घात भिन्न है, इसलिए यह बहुपद नहीं है। बहुपद में घातें अऋणात्मक पूर्णांक होती हैं।

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निम्न में से कौन सा बहुपद (x) में है लेकिन (y) में नहीं है?

Which of the following is a polynomial in (x) but not in (y)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+3x+1\)

Step 1

Concept

\(x^2+3x+1\) has only the variable (x). So it is a one-variable polynomial in (x).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+3x+1\). \(x^2+3x+1\) has only the variable (x). So it is a one-variable polynomial in (x).

Step 3

Exam Tip

\(x^2+3x+1\) में केवल (x) चर है। इसलिए यह (x) में एक चर वाला बहुपद है।

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कौन-सा व्यंजक एक चर वाला बहुपद है जिसमें वास्तविक गुणांक हैं?

Which expression is a polynomial in one variable with real coefficients?

Explanation opens after your attempt
Correct Answer

A. \(\sqrt{2}x^2-3x+1\)

Step 1

Concept

\(\sqrt{2}\) is a real number and the powers of (x) are whole numbers. So it is a polynomial.

Step 2

Why this answer is correct

The correct answer is A. \(\sqrt{2}x^2-3x+1\). \(\sqrt{2}\) is a real number and the powers of (x) are whole numbers. So it is a polynomial.

Step 3

Exam Tip

\(\sqrt{2}\) एक वास्तविक संख्या है और (x) की घातें पूर्ण संख्याएँ हैं। इसलिए यह बहुपद है।

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कौन-सा व्यंजक बहुपद नहीं है क्योंकि चर हर में है?

Which expression is not a polynomial because the variable is in the denominator?

Explanation opens after your attempt
Correct Answer

B. \(\frac{3}{x}+1\)

Step 1

Concept

\(\frac{3}{x}=3x^{-1}\), so the variable has a negative power. Therefore it is not a polynomial.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{3}{x}+1\). \(\frac{3}{x}=3x^{-1}\), so the variable has a negative power. Therefore it is not a polynomial.

Step 3

Exam Tip

\(\frac{3}{x}=3x^{-1}\) है और चर की घात ऋणात्मक है। इसलिए यह बहुपद नहीं है।

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कौन-सा व्यंजक (z) में एक चर वाला बहुपद है?

Which expression is a polynomial in one variable (z)?

Explanation opens after your attempt
Correct Answer

A. \(z^4-2z+1\)

Step 1

Concept

The expression \(z^4-2z+1\) has only (z) and no negative powers. So it is a polynomial in (z).

Step 2

Why this answer is correct

The correct answer is A. \(z^4-2z+1\). The expression \(z^4-2z+1\) has only (z) and no negative powers. So it is a polynomial in (z).

Step 3

Exam Tip

\(z^4-2z+1\) में केवल (z) है और घातें ऋणात्मक नहीं हैं। इसलिए यह (z) में बहुपद है।

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\(2x^2+3xy+1\) एक चर वाला बहुपद क्यों नहीं है?

Why is \(2x^2+3xy+1\) not a polynomial in one variable?

Explanation opens after your attempt
Correct Answer

A. क्योंकि इसमें दो चर हैंBecause it has two variables

Step 1

Concept

It contains both (x) and (y). A polynomial in one variable should contain only one variable.

Step 2

Why this answer is correct

The correct answer is A. क्योंकि इसमें दो चर हैं / Because it has two variables. It contains both (x) and (y). A polynomial in one variable should contain only one variable.

Step 3

Exam Tip

इसमें (x) और (y) दोनों चर हैं। एक चर वाले बहुपद में केवल एक ही चर होना चाहिए।

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कौन-सा व्यंजक (x) में एक चर वाला बहुपद है?

Which expression is a polynomial in one variable (x)?

Explanation opens after your attempt
Correct Answer

A. \(3x^2-5x+7\)

Step 1

Concept

The expression \(3x^2-5x+7\) has only (x) and non-negative integer powers. In exams, the variable power must not be negative or fractional.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-5x+7\). The expression \(3x^2-5x+7\) has only (x) and non-negative integer powers. In exams, the variable power must not be negative or fractional.

Step 3

Exam Tip

\(3x^2-5x+7\) में केवल (x) है और घातें पूर्ण संख्याएँ हैं। परीक्षा में चर की घात ऋणात्मक या भिन्न नहीं होनी चाहिए।

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जनगणना और जातीय वर्गीकरण उपनिवेशवाद में विवादास्पद क्यों थे?

Why were census and ethnic classification controversial in colonialism?

Explanation opens after your attempt
Correct Answer

A. उन्होंने समाज को प्रशासनिक श्रेणियों में बांटकर पहचान राजनीति को प्रभावित कियाThey affected identity politics by dividing society into administrative categories

Step 1

Concept

Colonial classification could affect both rule and identity. For exams write the relation between knowledge and power.

Step 2

Why this answer is correct

The correct answer is A. उन्होंने समाज को प्रशासनिक श्रेणियों में बांटकर पहचान राजनीति को प्रभावित किया / They affected identity politics by dividing society into administrative categories. Colonial classification could affect both rule and identity. For exams write the relation between knowledge and power.

Step 3

Exam Tip

औपनिवेशिक वर्गीकरण शासन और पहचान दोनों को प्रभावित कर सकता था। परीक्षा में ज्ञान और सत्ता का संबंध लिखें।

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जनगणना और वर्गीकरण ने औपनिवेशिक शासन को कैसे मदद दी?

How did census and classification help colonial rule?

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Correct Answer

A. समाज को श्रेणियों में समझकर प्रशासन और नियंत्रण आसान हुआAdministration and control became easier by understanding society in categories

Step 1

Concept

Colonial knowledge collection could become a tool of rule. For exams link knowledge power and administration.

Step 2

Why this answer is correct

The correct answer is A. समाज को श्रेणियों में समझकर प्रशासन और नियंत्रण आसान हुआ / Administration and control became easier by understanding society in categories. Colonial knowledge collection could become a tool of rule. For exams link knowledge power and administration.

Step 3

Exam Tip

औपनिवेशिक ज्ञान संग्रह शासन का साधन बन सकता था। परीक्षा में ज्ञान सत्ता और प्रशासन को साथ जोड़ें।

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यदि \(a_1/a_2=b_1/b_2=c_1/c_2\), तो युग्म का वर्गीकरण क्या होगा?

If \(a_1/a_2=b_1/b_2=c_1/c_2\), what will be the classification of the pair?

Explanation opens after your attempt
Correct Answer

C. संगत और आश्रितConsistent and dependent

Step 1

Concept

When all three ratios are equal, both equations form the same line. Therefore, the pair is consistent and dependent.

Step 2

Why this answer is correct

The correct answer is C. संगत और आश्रित / Consistent and dependent. When all three ratios are equal, both equations form the same line. Therefore, the pair is consistent and dependent.

Step 3

Exam Tip

तीनों अनुपात बराबर होने पर दोनों समीकरण एक ही रेखा बनाते हैं। इसलिए युग्म संगत और आश्रित होता है।

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यदि (p(x)=x-2+6x+6) है, तो उसके शून्यकों का सही वर्गीकरण क्या है?

If (p(x)=x-2+6x+6), what is the correct classification of its zeroes?

Explanation opens after your attempt
Correct Answer

A. वास्तविक और अपरिमेयReal and irrational

Step 1

Concept

(D=36-24=12), which is positive but not a perfect square. Hence the zeroes are real and irrational.

Step 2

Why this answer is correct

The correct answer is A. वास्तविक और अपरिमेय / Real and irrational. (D=36-24=12), which is positive but not a perfect square. Hence the zeroes are real and irrational.

Step 3

Exam Tip

(D=36-24=12) है, जो धनात्मक है पर पूर्ण वर्ग नहीं है। इसलिए शून्यक वास्तविक और अपरिमेय हैं।

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दशमलव \(0.505000500005000005\ldots\) के लिए सही वर्गीकरण कौन-सा है?

What is the correct classification of the decimal \(0.505000500005000005\ldots\)?

Explanation opens after your attempt
Correct Answer

C. असांत अनावर्ती अपरिमेयNon-terminating non-recurring irrational

Step 1

Concept

This decimal does not end, and the number of zeros keeps changing. Since there is no fixed repeating block, it is non-terminating non-recurring.

Step 2

Why this answer is correct

The correct answer is C. असांत अनावर्ती अपरिमेय / Non-terminating non-recurring irrational. This decimal does not end, and the number of zeros keeps changing. Since there is no fixed repeating block, it is non-terminating non-recurring.

Step 3

Exam Tip

यह दशमलव समाप्त नहीं होता और शून्यों की संख्या बदलती जाती है। स्थिर आवर्ती खंड न होने से यह असांत अनावर्ती है।

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दशमलव \(0.303000300003000003\ldots\) के लिए सही वर्गीकरण कौन-सा है?

What is the correct classification of the decimal \(0.303000300003000003\ldots\)?

Explanation opens after your attempt
Correct Answer

C. असांत अनावर्ती अपरिमेयNon-terminating non-recurring irrational

Step 1

Concept

This decimal does not end, and the number of zeros keeps changing. Since there is no fixed repeating block, it is non-terminating non-recurring.

Step 2

Why this answer is correct

The correct answer is C. असांत अनावर्ती अपरिमेय / Non-terminating non-recurring irrational. This decimal does not end, and the number of zeros keeps changing. Since there is no fixed repeating block, it is non-terminating non-recurring.

Step 3

Exam Tip

यह दशमलव समाप्त नहीं होता और शून्यों की संख्या बदलती जाती है। स्थिर आवर्ती खंड न होने से यह असांत अनावर्ती है।

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दशमलव \(0.202002000200002\ldots\) के लिए सही वर्गीकरण कौन-सा है?

What is the correct classification of the decimal \(0.202002000200002\ldots\)?

Explanation opens after your attempt
Correct Answer

C. असांत अनावर्ती अपरिमेयNon-terminating non-recurring irrational

Step 1

Concept

This decimal does not end, and the number of zeros between the (2)'s keeps changing. Since there is no fixed repeating block, it is non-terminating non-recurring.

Step 2

Why this answer is correct

The correct answer is C. असांत अनावर्ती अपरिमेय / Non-terminating non-recurring irrational. This decimal does not end, and the number of zeros between the (2)'s keeps changing. Since there is no fixed repeating block, it is non-terminating non-recurring.

Step 3

Exam Tip

यह दशमलव समाप्त नहीं होता और (2) के बीच शून्यों की संख्या बदलती रहती है। स्थिर आवर्ती खंड न होने से यह असांत अनावर्ती है।

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दशमलव \(0.123456789101112\ldots\) के लिए सबसे उचित वर्गीकरण कौन-सा है?

What is the most suitable classification of the decimal \(0.123456789101112\ldots\)?

Explanation opens after your attempt
Correct Answer

C. असांत अनावर्ती अपरिमेयNon-terminating non-recurring irrational

Step 1

Concept

This decimal does not terminate.

Step 2

Why this answer is correct

No fixed repeating block appears because natural numbers are being joined in order. So it is treated as non-terminating non-recurring.

Step 3

Exam Tip

In a long digit pattern, check for a fixed repeating block. चरण 1: यह दशमलव समाप्त नहीं होता। चरण 2: अंकों में कोई स्थिर आवर्ती खंड नहीं दिखता, क्योंकि प्राकृतिक संख्याएँ क्रम से जुड़ती जा रही हैं। इसलिए इसे असांत अनावर्ती माना जाएगा। चरण 3: लंबी संख्या-श्रृंखला में आवर्ती खंड की जाँच जरूरी है।

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दशमलव \(0.101001000100001\ldots\) के लिए सही वर्गीकरण कौन-सा है?

What is the correct classification of the decimal \(0.101001000100001\ldots\)?

Explanation opens after your attempt
Correct Answer

C. असांत अनावर्ती अपरिमेयNon-terminating non-recurring irrational

Step 1

Concept

This decimal does not terminate.

Step 2

Why this answer is correct

The number of zeros between the (1)'s keeps changing, so there is no fixed repeating block. Hence it is non-terminating non-recurring.

Step 3

Exam Tip

Do not call a decimal rational unless a repeating block is present. चरण 1: यह दशमलव समाप्त नहीं होता। चरण 2: इसमें (1) के बीच शून्यों की संख्या बदलती जा रही है, इसलिए कोई स्थिर आवर्ती खंड नहीं है। अतः यह असांत अनावर्ती है। चरण 3: आवर्ती खंड न मिले तो उसे परिमेय मानने की जल्दी न करें।

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वर्गीकरण को विकास का सहायक प्रमाण तो माना जाता है पर अकेला अंतिम प्रमाण क्यों नहीं?

Why is classification considered supportive evidence of evolution but not the final proof alone?

Explanation opens after your attempt
Correct Answer

A. क्योंकि समानताओं के साथ जीवाश्म संरचना और अन्य प्रमाण भी देखने पड़ते हैंBecause along with similarities fossils structure and other evidence must also be studied

Step 1

Concept

Classification arranges similarities among organisms.

Step 2

Why this answer is correct

Similarity can suggest evolutionary relationship.

Step 3

Exam Tip

Correct conclusions require several types of evidence together. चरण 1: वर्गीकरण जीवों की समानताओं को व्यवस्थित करता है। चरण 2: समानता विकास संबंध का संकेत दे सकती है। चरण 3: सही निष्कर्ष के लिए कई प्रकार के प्रमाण साथ देखने चाहिए।

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वर्गीकरण विकास संबंध समझने में कैसे सहायक है लेकिन अकेला अंतिम प्रमाण क्यों नहीं है?

How does classification help in understanding evolutionary relationships but is not the only final proof?

Explanation opens after your attempt
Correct Answer

A. यह समानताओं को व्यवस्थित करता है पर जीवाश्म संरचना और अन्य प्रमाण भी चाहिएIt arranges similarities but fossils structure and other evidence are also needed

Step 1

Concept

Classification shows similarities among organisms.

Step 2

Why this answer is correct

Similarity helps infer relationships.

Step 3

Exam Tip

For a correct conclusion several evidences should be studied together. चरण 1: वर्गीकरण जीवों की समानता दिखाता है। चरण 2: समानता से संबंध का अनुमान मिलता है। चरण 3: सही निष्कर्ष के लिए अनेक प्रमाणों को साथ देखना चाहिए।

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विकास को समझने में वर्गीकरण कैसे सहायता करता है?

How does classification help in understanding evolution?

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Correct Answer

A. यह जीवों की समानता और संबंधों को व्यवस्थित रूप से दिखाता हैIt systematically shows similarities and relationships among organisms

Step 1

Concept

Classification arranges organisms based on similarities.

Step 2

Why this answer is correct

Greater similarity can suggest closer relationship.

Step 3

Exam Tip

Therefore classification helps understand evolutionary relationships. चरण 1: वर्गीकरण जीवों को समानताओं के आधार पर व्यवस्थित करता है। चरण 2: अधिक समानता निकट संबंध का संकेत दे सकती है। चरण 3: इसलिए वर्गीकरण विकास संबंधों को समझने में मदद करता है।

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निम्न में से कौन-सा (x) में रेखीय बहुपद है?

Which of the following is a linear polynomial in (x)?

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Correct Answer

A. (5x-9)

Step 1

Concept

A linear polynomial has degree (1), so (5x-9) is linear. Its leading coefficient must be non-zero.

Step 2

Why this answer is correct

The correct answer is A. (5x-9). A linear polynomial has degree (1), so (5x-9) is linear. Its leading coefficient must be non-zero.

Step 3

Exam Tip

रेखीय बहुपद की घात (1) होती है, इसलिए (5x-9) रेखीय है। प्रमुख गुणांक शून्य नहीं होना चाहिए।

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यदि (p(x)=\sqrt{5}x-3-\frac{2}{3}x+1), तो यह किस प्रकार का बहुपद है?

If (p(x)=\sqrt{5}x-3-\frac{2}{3}x+1), what type of polynomial is it?

Explanation opens after your attempt
Correct Answer

A. घन बहुपदCubic polynomial

Step 1

Concept

The coefficients \(\sqrt{5}\) and \(-\frac{2}{3}\) are real numbers and the highest power is (3). Hence it is a cubic polynomial.

Step 2

Why this answer is correct

The correct answer is A. घन बहुपद / Cubic polynomial. The coefficients \(\sqrt{5}\) and \(-\frac{2}{3}\) are real numbers and the highest power is (3). Hence it is a cubic polynomial.

Step 3

Exam Tip

गुणांक \(\sqrt{5}\) और \(-\frac{2}{3}\) वास्तविक संख्याएँ हैं और सबसे बड़ी घात (3) है। इसलिए यह घन बहुपद है।

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कौन सा व्यंजक (x) में बहुपद है लेकिन (x) में द्विघात नहीं है?

Which expression is a polynomial in (x) but not quadratic in (x)?

Explanation opens after your attempt
Correct Answer

B. \(6x^3-2x+9\)

Step 1

Concept

\(6x^3-2x+9\) is a polynomial and its degree is (3), so it is not quadratic. Classify by degree.

Step 2

Why this answer is correct

The correct answer is B. \(6x^3-2x+9\). \(6x^3-2x+9\) is a polynomial and its degree is (3), so it is not quadratic. Classify by degree.

Step 3

Exam Tip

\(6x^3-2x+9\) बहुपद है और इसकी घात (3) है, इसलिए यह द्विघात नहीं है। घात से वर्गीकरण करें।

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कौन सा कथन (p(x)=x-3+1) के बारे में सही है?

Which statement about (p(x)=x-3+1) is correct?

Explanation opens after your attempt
Correct Answer

C. यह घन बहुपद हैIt is a cubic polynomial

Step 1

Concept

In (p(x)=x-3+1), the highest power is (3), so it is a cubic polynomial. Decide the type of a polynomial by its degree.

Step 2

Why this answer is correct

The correct answer is C. यह घन बहुपद है / It is a cubic polynomial. In (p(x)=x-3+1), the highest power is (3), so it is a cubic polynomial. Decide the type of a polynomial by its degree.

Step 3

Exam Tip

(p(x)=x-3+1) में सबसे बड़ी घात (3) है इसलिए यह घन बहुपद है। बहुपद का प्रकार उसकी घात से तय करें।

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\(12x^2-7x+4\) किस प्रकार का बहुपद है?

What type of polynomial is \(12x^2-7x+4\)?

Explanation opens after your attempt
Correct Answer

C. त्रिपदीTrinomial

Step 1

Concept

It has (3) effective terms, so it is a trinomial. The name is identified by the number of terms.

Step 2

Why this answer is correct

The correct answer is C. त्रिपदी / Trinomial. It has (3) effective terms, so it is a trinomial. The name is identified by the number of terms.

Step 3

Exam Tip

इसमें (3) प्रभावी पद हैं इसलिए यह त्रिपदी है। पदों की संख्या से नाम पहचाना जाता है।

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कौन सा विकल्प \(x^3-1\) के प्रकार को सही बताता है?

Which option correctly describes the type of \(x^3-1\)?

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Correct Answer

C. त्रिघात द्विपदीCubic binomial

Step 1

Concept

\(x^3-1\) has degree (3) and (2) terms. So it is a cubic binomial.

Step 2

Why this answer is correct

The correct answer is C. त्रिघात द्विपदी / Cubic binomial. \(x^3-1\) has degree (3) and (2) terms. So it is a cubic binomial.

Step 3

Exam Tip

\(x^3-1\) की घात (3) है और इसमें (2) पद हैं। इसलिए यह त्रिघात द्विपदी है।

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निम्न में से किस बहुपद में प्रमुख गुणांक (1) नहीं है?

Which of the following polynomials does not have leading coefficient (1)?

Explanation opens after your attempt
Correct Answer

C. \(3x^2+x+1\)

Step 1

Concept

The leading term of \(3x^2+x+1\) is \(3x^2\). Its leading coefficient is (3), not (1).

Step 2

Why this answer is correct

The correct answer is C. \(3x^2+x+1\). The leading term of \(3x^2+x+1\) is \(3x^2\). Its leading coefficient is (3), not (1).

Step 3

Exam Tip

\(3x^2+x+1\) का प्रमुख पद \(3x^2\) है। इसका प्रमुख गुणांक (3) है, (1) नहीं।

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\(x^2+1\), \(x^3+x\), (5x-2) में सबसे कम घात वाला बहुपद कौन सा है?

Among \(x^2+1\), \(x^3+x\), and (5x-2), which polynomial has the least degree?

Explanation opens after your attempt
Correct Answer

C. (5x-2)

Step 1

Concept

Their degrees are (2), (3), and (1) respectively. The least degree is (1).

Step 2

Why this answer is correct

The correct answer is C. (5x-2). Their degrees are (2), (3), and (1) respectively. The least degree is (1).

Step 3

Exam Tip

इनकी घातें क्रमशः (2), (3) और (1) हैं। सबसे कम घात (1) है।

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निम्न में से कौन सा बहुपद नियत बहुपद नहीं है?

Which of the following is not a constant polynomial?

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Correct Answer

D. (2x+1)

Step 1

Concept

(2x+1) contains the variable (x), so it is not a constant polynomial. A constant polynomial has no variable term.

Step 2

Why this answer is correct

The correct answer is D. (2x+1). (2x+1) contains the variable (x), so it is not a constant polynomial. A constant polynomial has no variable term.

Step 3

Exam Tip

(2x+1) में चर (x) है इसलिए यह नियत बहुपद नहीं है। नियत बहुपद में चर वाला पद नहीं होता।

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कौन सा कथन \(5x^2-3x+7\) के लिए सही है?

Which statement is correct for \(5x^2-3x+7\)?

Explanation opens after your attempt
Correct Answer

B. यह द्विघात बहुपद हैIt is a quadratic polynomial

Step 1

Concept

The highest power of (x) is (2). Therefore it is a quadratic polynomial.

Step 2

Why this answer is correct

The correct answer is B. यह द्विघात बहुपद है / It is a quadratic polynomial. The highest power of (x) is (2). Therefore it is a quadratic polynomial.

Step 3

Exam Tip

इसमें (x) की सबसे बड़ी घात (2) है। इसलिए यह द्विघात बहुपद है।

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कौन सा कथन (p(x)=x-2+1) के बारे में सही है?

Which statement about (p(x)=x-2+1) is correct?

Explanation opens after your attempt
Correct Answer

B. यह द्विघात बहुपद हैIt is a quadratic polynomial

Step 1

Concept

In (p(x)=x-2+1), the highest power is (2), so it is a quadratic polynomial. Classify by degree.

Step 2

Why this answer is correct

The correct answer is B. यह द्विघात बहुपद है / It is a quadratic polynomial. In (p(x)=x-2+1), the highest power is (2), so it is a quadratic polynomial. Classify by degree.

Step 3

Exam Tip

(p(x)=x-2+1) में सबसे बड़ी घात (2) है इसलिए यह द्विघात बहुपद है। घात से वर्गीकरण करें।

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बहुपद \(8x^2-3x+1\) किस प्रकार का है?

What type of polynomial is \(8x^2-3x+1\)?

Explanation opens after your attempt
Correct Answer

C. त्रिपदीTrinomial

Step 1

Concept

It has three terms, so it is a trinomial. Identify the type by counting terms.

Step 2

Why this answer is correct

The correct answer is C. त्रिपदी / Trinomial. It has three terms, so it is a trinomial. Identify the type by counting terms.

Step 3

Exam Tip

इसमें तीन पद हैं इसलिए यह त्रिपदी है। पदों की संख्या से प्रकार पहचानें।

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निम्न में से कौन सा त्रिपदी है?

Which of the following is a trinomial?

Explanation opens after your attempt
Correct Answer

B. \(x^2-2x+1\)

Step 1

Concept

A polynomial with three terms is a trinomial. \(x^2-2x+1\) has three terms.

Step 2

Why this answer is correct

The correct answer is B. \(x^2-2x+1\). A polynomial with three terms is a trinomial. \(x^2-2x+1\) has three terms.

Step 3

Exam Tip

तीन पदों वाला बहुपद त्रिपदी कहलाता है। \(x^2-2x+1\) में तीन पद हैं।

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निम्न में से कौन सा द्विपदी है?

Which of the following is a binomial?

Explanation opens after your attempt
Correct Answer

A. \(x^2+3\)

Step 1

Concept

A polynomial with two terms is a binomial. \(x^2+3\) has two terms.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+3\). A polynomial with two terms is a binomial. \(x^2+3\) has two terms.

Step 3

Exam Tip

दो पदों वाला बहुपद द्विपदी कहलाता है। \(x^2+3\) में दो पद हैं।

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निम्न में से कौन सा एकपदी है?

Which of the following is a monomial?

Explanation opens after your attempt
Correct Answer

A. \(3x^2\)

Step 1

Concept

A polynomial with one term is called a monomial. \(3x^2\) has only one term.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2\). A polynomial with one term is called a monomial. \(3x^2\) has only one term.

Step 3

Exam Tip

एक पद वाला बहुपद एकपदी कहलाता है। \(3x^2\) में केवल एक पद है।

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बहुपद \(3x^2+2x-1\) में कितने पद हैं?

How many terms are there in the polynomial \(3x^2+2x-1\)?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

The terms are \(3x^2\), (2x), and (-1). Separate terms by plus or minus signs.

Step 2

Why this answer is correct

The correct answer is C. (3). The terms are \(3x^2\), (2x), and (-1). Separate terms by plus or minus signs.

Step 3

Exam Tip

यहाँ पद \(3x^2\), (2x) और (-1) हैं। पदों को जोड़ या घटाव के संकेतों से अलग करें।

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कौन-सा कथन (p(x)=0) के लिए सही है?

Which statement is correct for (p(x)=0)?

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Correct Answer

A. यह शून्य बहुपद हैIt is the zero polynomial

Step 1

Concept

(p(x)=0) is called the zero polynomial. Its degree is undefined.

Step 2

Why this answer is correct

The correct answer is A. यह शून्य बहुपद है / It is the zero polynomial. (p(x)=0) is called the zero polynomial. Its degree is undefined.

Step 3

Exam Tip

(p(x)=0) को शून्य बहुपद कहते हैं। इसकी घात परिभाषित नहीं होती।

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यदि (p(x)=ax-2+bx+c) और \(a\neq0\), तो (p(x)) किस प्रकार का बहुपद है?

If (p(x)=ax-2+bx+c) and \(a\neq0\), what type of polynomial is (p(x))?

Explanation opens after your attempt
Correct Answer

B. द्विघातQuadratic

Step 1

Concept

Since \(a\neq0\), the \(x^2\) term is present. So the degree is (2) and it is a quadratic polynomial.

Step 2

Why this answer is correct

The correct answer is B. द्विघात / Quadratic. Since \(a\neq0\), the \(x^2\) term is present. So the degree is (2) and it is a quadratic polynomial.

Step 3

Exam Tip

क्योंकि \(a\neq0\), \(x^2\) वाला पद उपस्थित है। इसलिए घात (2) है और यह द्विघात बहुपद है।

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कौन-सा बहुपद स्थिर बहुपद है?

Which polynomial is a constant polynomial?

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Correct Answer

C. \(-7\)

Step 1

Concept

A constant polynomial has no variable. The number (-7) is a non-zero constant polynomial.

Step 2

Why this answer is correct

The correct answer is C. \(-7\). A constant polynomial has no variable. The number (-7) is a non-zero constant polynomial.

Step 3

Exam Tip

स्थिर बहुपद में चर नहीं होता। (-7) शून्य से भिन्न स्थिर बहुपद है।

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कौन-सा बहुपद घन बहुपद है?

Which polynomial is a cubic polynomial?

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Correct Answer

A. \(x^3-2x+1\)

Step 1

Concept

A cubic polynomial has degree (3). The highest power in \(x^3-2x+1\) is (3).

Step 2

Why this answer is correct

The correct answer is A. \(x^3-2x+1\). A cubic polynomial has degree (3). The highest power in \(x^3-2x+1\) is (3).

Step 3

Exam Tip

घन बहुपद की घात (3) होती है। \(x^3-2x+1\) की सबसे बड़ी घात (3) है।

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कौन-सा बहुपद त्रिपदी है?

Which polynomial is a trinomial?

Explanation opens after your attempt
Correct Answer

A. \(x^2+x+1\)

Step 1

Concept

A trinomial has three terms. The expression \(x^2+x+1\) has three terms.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+x+1\). A trinomial has three terms. The expression \(x^2+x+1\) has three terms.

Step 3

Exam Tip

त्रिपदी में तीन पद होते हैं। \(x^2+x+1\) में तीन पद हैं।

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कौन-सा बहुपद द्विपदी है?

Which polynomial is a binomial?

Explanation opens after your attempt
Correct Answer

B. (5x-7)

Step 1

Concept

A binomial has two terms. The expression (5x-7) has the two terms (5x) and (-7).

Step 2

Why this answer is correct

The correct answer is B. (5x-7). A binomial has two terms. The expression (5x-7) has the two terms (5x) and (-7).

Step 3

Exam Tip

द्विपदी में दो पद होते हैं। (5x-7) में (5x) और (-7) दो पद हैं।

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कौन-सा बहुपद एकपदी है?

Which polynomial is a monomial?

Explanation opens after your attempt
Correct Answer

A. \(3x^2\)

Step 1

Concept

A monomial has only one term. The expression \(3x^2\) has one term.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2\). A monomial has only one term. The expression \(3x^2\) has one term.

Step 3

Exam Tip

एकपदी में केवल एक पद होता है। \(3x^2\) एक ही पद है।

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कौन-सा बहुपद रैखिक बहुपद है?

Which polynomial is a linear polynomial?

Explanation opens after your attempt
Correct Answer

B. (3x-8)

Step 1

Concept

A linear polynomial has degree (1). The highest power in (3x-8) is (1).

Step 2

Why this answer is correct

The correct answer is B. (3x-8). A linear polynomial has degree (1). The highest power in (3x-8) is (1).

Step 3

Exam Tip

रैखिक बहुपद की घात (1) होती है। (3x-8) की सबसे बड़ी घात (1) है।

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कौन-सा बहुपद द्विघात बहुपद है?

Which polynomial is a quadratic polynomial?

Explanation opens after your attempt
Correct Answer

B. \(x^2-4x+1\)

Step 1

Concept

A quadratic polynomial has degree (2). In \(x^2-4x+1\), the highest power is (2).

Step 2

Why this answer is correct

The correct answer is B. \(x^2-4x+1\). A quadratic polynomial has degree (2). In \(x^2-4x+1\), the highest power is (2).

Step 3

Exam Tip

द्विघात बहुपद की घात (2) होती है। \(x^2-4x+1\) में सबसे बड़ी घात (2) है।

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यदि (p(x)=x-4-5x-2+4) है, तो (p(x)) का घात कितना है?

If (p(x)=x-4-5x-2+4), what is the degree of (p(x))?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

The highest power is \(x^4\), so the degree is (4). Terms with zero coefficients do not affect the degree.

Step 2

Why this answer is correct

The correct answer is A. (4). The highest power is \(x^4\), so the degree is (4). Terms with zero coefficients do not affect the degree.

Step 3

Exam Tip

सबसे बड़ी घात \(x^4\) है, इसलिए घात (4) है। शून्य गुणांक वाले पदों को घात तय करने में नहीं गिनते।

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यदि (p(x)=ax-2+bx+c) में \(a\neq0\) है और (p(1)=p(-1)=0) है, तो (b) का मान क्या होगा?

If (p(x)=ax-2+bx+c) with \(a\neq0\) and (p(1)=p(-1)=0), what is the value of (b)?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

(p(1)=a+b+c) and (p(-1)=a-b+c); subtracting gives (2b=0). In exams, use addition or subtraction for symmetric inputs.

Step 2

Why this answer is correct

The correct answer is A. (0). (p(1)=a+b+c) and (p(-1)=a-b+c); subtracting gives (2b=0). In exams, use addition or subtraction for symmetric inputs.

Step 3

Exam Tip

(p(1)=a+b+c) और (p(-1)=a-b+c) हैं, घटाने पर (2b=0) मिलता है। परीक्षा में सममित मानों पर जोड़-घटाव जल्दी करें।

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निम्न में से (y) में बहुपद कौन सा है?

Which of the following is a polynomial in (y)?

Explanation opens after your attempt
Correct Answer

A. \(y^2-3y+2\)

Step 1

Concept

In \(y^2-3y+2\), the powers of (y) are whole numbers. A polynomial can be in one variable such as (y).

Step 2

Why this answer is correct

The correct answer is A. \(y^2-3y+2\). In \(y^2-3y+2\), the powers of (y) are whole numbers. A polynomial can be in one variable such as (y).

Step 3

Exam Tip

\(y^2-3y+2\) में (y) की घातें पूर्ण संख्याएँ हैं। बहुपद किसी एक चर जैसे (y) में भी हो सकता है।

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क्या \(4x^2-3\sqrt{x}+1\) (x) में बहुपद है?

Is \(4x^2-3\sqrt{x}+1\) a polynomial in (x)?

Explanation opens after your attempt
Correct Answer

B. नहींNo

Step 1

Concept

\(\sqrt{x}=x^{\frac{1}{2}}\), and \(\frac{1}{2}\) is not a whole number. So it is not a polynomial in (x).

Step 2

Why this answer is correct

The correct answer is B. नहीं / No. \(\sqrt{x}=x^{\frac{1}{2}}\), and \(\frac{1}{2}\) is not a whole number. So it is not a polynomial in (x).

Step 3

Exam Tip

\(\sqrt{x}=x^{\frac{1}{2}}\) है और \(\frac{1}{2}\) पूर्ण संख्या नहीं है। इसलिए यह (x) में बहुपद नहीं है।

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(p(x)=x-2+3x+2) के लिए (p(1)) का मान क्या है?

For (p(x)=x-2+3x+2), what is the value of (p(1))?

Explanation opens after your attempt
Correct Answer

C. (6)

Step 1

Concept

(p(1)=12+3\cdot1+2=6). While evaluating, replace every (x) with the given number.

Step 2

Why this answer is correct

The correct answer is C. (6). (p(1)=12+3\cdot1+2=6). While evaluating, replace every (x) with the given number.

Step 3

Exam Tip

(p(1)=12+3\cdot1+2=6) है। मान निकालते समय हर (x) की जगह दी गई संख्या रखें।

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यदि (p(x)=2x-3-5x+9) है, तो इसमें \(x^2\) का गुणांक क्या है?

If (p(x)=2x-3-5x+9), what is the coefficient of \(x^2\)?

Explanation opens after your attempt
Correct Answer

D. (0)

Step 1

Concept

There is no \(x^2\)-term in this polynomial, so its coefficient is (0). The coefficient of a missing term is always taken as (0).

Step 2

Why this answer is correct

The correct answer is D. (0). There is no \(x^2\)-term in this polynomial, so its coefficient is (0). The coefficient of a missing term is always taken as (0).

Step 3

Exam Tip

इस बहुपद में \(x^2\) पद नहीं है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद का गुणांक हमेशा (0) माना जाता है।

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निम्न में से कौन सा (x) में बहुपद है?

Which of the following is a polynomial in (x)?

Explanation opens after your attempt
Correct Answer

A. \(x^2+3x+5\)

Step 1

Concept

A polynomial has only non-negative integer powers of (x). In exams check the power of every term.

Step 2

Why this answer is correct

The correct answer is A. \(x^2+3x+5\). A polynomial has only non-negative integer powers of (x). In exams check the power of every term.

Step 3

Exam Tip

बहुपद में (x) की घात केवल पूर्णांक और अशून्य नहीं बल्कि ऋणात्मक नहीं होनी चाहिए। परीक्षा में हर पद की घात जांचें।

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कर्नाटक और तेलंगाना पठारों का सही व्यापक वर्गीकरण क्या है?

What is the correct broad classification of Karnataka and Telangana Plateaus?

Explanation opens after your attempt
Correct Answer

B. दक्कन पठार के क्षेत्रीय भागRegional parts of Deccan Plateau

Step 1

Concept

Karnataka and Telangana Plateaus are regional parts of the Deccan Plateau. For exams, connect them with the southern Peninsular Plateau.

Step 2

Why this answer is correct

The correct answer is B. दक्कन पठार के क्षेत्रीय भाग / Regional parts of Deccan Plateau. Karnataka and Telangana Plateaus are regional parts of the Deccan Plateau. For exams, connect them with the southern Peninsular Plateau.

Step 3

Exam Tip

कर्नाटक और तेलंगाना पठार दक्कन पठार के क्षेत्रीय भाग हैं। परीक्षा में इन्हें दक्षिणी प्रायद्वीपीय पठार से जोड़ें।

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कर्नाटक और तेलंगाना पठारों का व्यापक भौतिक वर्गीकरण क्या है?

What is the broad physical classification of the Karnataka and Telangana Plateaus?

Explanation opens after your attempt
Correct Answer

C. दक्कन पठार के क्षेत्रीय भागRegional parts of the Deccan Plateau

Step 1

Concept

Karnataka and Telangana Plateaus are regional parts of the Deccan Plateau. For exams, connect them with the southern Peninsular Plateau.

Step 2

Why this answer is correct

The correct answer is C. दक्कन पठार के क्षेत्रीय भाग / Regional parts of the Deccan Plateau. Karnataka and Telangana Plateaus are regional parts of the Deccan Plateau. For exams, connect them with the southern Peninsular Plateau.

Step 3

Exam Tip

कर्नाटक और तेलंगाना पठार दक्कन पठार के क्षेत्रीय भाग हैं। परीक्षा में इन्हें दक्षिणी प्रायद्वीपीय पठार से जोड़ें।

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कर्नाटक और तेलंगाना पठार का सबसे सही व्यापक वर्गीकरण क्या है?

What is the most correct broad classification of the Karnataka and Telangana Plateaus?

Explanation opens after your attempt
Correct Answer

C. दक्कन पठार के क्षेत्रीय भागRegional parts of the Deccan Plateau

Step 1

Concept

Karnataka and Telangana Plateaus are regional parts of the Deccan Plateau. For exams, connect them with the southern Peninsular Plateau.

Step 2

Why this answer is correct

The correct answer is C. दक्कन पठार के क्षेत्रीय भाग / Regional parts of the Deccan Plateau. Karnataka and Telangana Plateaus are regional parts of the Deccan Plateau. For exams, connect them with the southern Peninsular Plateau.

Step 3

Exam Tip

कर्नाटक और तेलंगाना पठार दक्कन पठार के क्षेत्रीय भाग हैं। परीक्षा में इन्हें दक्षिणी प्रायद्वीपीय पठार से जोड़ें।

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घाघरा गंडक और कोसी का सही वर्गीकरण क्या है?

What is the correct classification of Ghaghara Gandak and Kosi?

Explanation opens after your attempt
Correct Answer

B. गंगा की हिमालयी बाएं तट सहायक नदियांHimalayan left bank tributaries of Ganga

Step 1

Concept

Ghaghara Gandak and Kosi are Himalayan left bank tributaries of Ganga. For exams remember their Nepal Himalaya link.

Step 2

Why this answer is correct

The correct answer is B. गंगा की हिमालयी बाएं तट सहायक नदियां / Himalayan left bank tributaries of Ganga. Ghaghara Gandak and Kosi are Himalayan left bank tributaries of Ganga. For exams remember their Nepal Himalaya link.

Step 3

Exam Tip

घाघरा गंडक और कोसी गंगा की हिमालयी बाएं तट सहायक नदियां हैं। परीक्षा में इनका नेपाल हिमालय संबंध याद रखें।

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घाघरा गंडक और कोसी का गंगा तंत्र में सही वर्गीकरण कौन सा है?

What is the correct classification of Ghaghara Gandak and Kosi in the Ganga system?

Explanation opens after your attempt
Correct Answer

D. हिमालयी बाएं तट सहायक नदियांHimalayan left bank tributaries

Step 1

Concept

Ghaghara Gandak and Kosi are Himalayan left bank tributaries of Ganga. For exams remember their Nepal Himalaya link.

Step 2

Why this answer is correct

The correct answer is D. हिमालयी बाएं तट सहायक नदियां / Himalayan left bank tributaries. Ghaghara Gandak and Kosi are Himalayan left bank tributaries of Ganga. For exams remember their Nepal Himalaya link.

Step 3

Exam Tip

घाघरा गंडक और कोसी गंगा की बाएं तट की हिमालयी सहायक नदियां हैं। परीक्षा में इनका नेपाल हिमालय संबंध याद रखें।

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नलसरोवर और दीपोर बील का सही वर्गीकरण क्या है?

What is the correct classification of Nalsarovar and Deepor Beel?

Explanation opens after your attempt
Correct Answer

C. आर्द्रभूमि झीलेंWetland lakes

Step 1

Concept

Nalsarovar in Gujarat and Deepor Beel in Assam are famous wetland lakes. For exams connect wetlands with biodiversity.

Step 2

Why this answer is correct

The correct answer is C. आर्द्रभूमि झीलें / Wetland lakes. Nalsarovar in Gujarat and Deepor Beel in Assam are famous wetland lakes. For exams connect wetlands with biodiversity.

Step 3

Exam Tip

नलसरोवर गुजरात और दीपोर बील असम की प्रसिद्ध आर्द्रभूमि झीलें हैं। परीक्षा में आर्द्रभूमि को जैव विविधता से जोड़ें।

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माजुली सुंदरवन और लक्षद्वीप की तुलना किस भौतिक वर्गीकरण को स्पष्ट करती है?

Comparison of Majuli Sundarbans and Lakshadweep clarifies which physical classification?

Explanation opens after your attempt
Correct Answer

A. नदी द्वीप डेल्टा और प्रवाल द्वीप का अंतरDifference among river island delta and coral island

Step 1

Concept

Majuli is a river island Sundarbans is a delta and Lakshadweep is a coral island. For exams keep landform types separate.

Step 2

Why this answer is correct

The correct answer is A. नदी द्वीप डेल्टा और प्रवाल द्वीप का अंतर / Difference among river island delta and coral island. Majuli is a river island Sundarbans is a delta and Lakshadweep is a coral island. For exams keep landform types separate.

Step 3

Exam Tip

माजुली नदी द्वीप है सुंदरवन डेल्टा है और लक्षद्वीप प्रवाल द्वीप है। परीक्षा में स्थलरूप प्रकार अलग रखें।

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माजुली और बैरन द्वीप की तुलना में कौन सा वर्गीकरण विशेषज्ञ स्तर पर सही है?

Which classification is correct at expert level when comparing Majuli and Barren Island?

Explanation opens after your attempt
Correct Answer

A. माजुली नदी द्वीप और बैरन ज्वालामुखीय द्वीपMajuli river island and Barren volcanic island

Step 1

Concept

Majuli is a river island linked with Brahmaputra and Barren is a volcanic island of Andaman. For exams keep island types separate.

Step 2

Why this answer is correct

The correct answer is A. माजुली नदी द्वीप और बैरन ज्वालामुखीय द्वीप / Majuli river island and Barren volcanic island. Majuli is a river island linked with Brahmaputra and Barren is a volcanic island of Andaman. For exams keep island types separate.

Step 3

Exam Tip

माजुली ब्रह्मपुत्र से जुड़ा नदी द्वीप है और बैरन अंडमान का ज्वालामुखीय द्वीप है। परीक्षा में द्वीप प्रकार अलग रखें।

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कोंकण कन्नड़ और मालाबार का क्रम किस भौतिक वर्गीकरण को सटीक बनाता है?

The sequence Konkan Kannad and Malabar makes which physical classification precise?

Explanation opens after your attempt
Correct Answer

A. पश्चिमी तटीय मैदान का उत्तर दक्षिण विभाजनNorth south division of western coastal plain

Step 1

Concept

These are regional parts of the western coastal plain. For exams remember the north to south sequence.

Step 2

Why this answer is correct

The correct answer is A. पश्चिमी तटीय मैदान का उत्तर दक्षिण विभाजन / North south division of western coastal plain. These are regional parts of the western coastal plain. For exams remember the north to south sequence.

Step 3

Exam Tip

ये पश्चिमी तटीय मैदान के क्षेत्रीय भाग हैं। परीक्षा में उत्तर से दक्षिण क्रम याद रखें।

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माजुली और सुंदरवन का सही तुलनात्मक वर्गीकरण कौन सा है?

Which is the correct comparative classification of Majuli and Sundarbans?

Explanation opens after your attempt
Correct Answer

A. माजुली नदी द्वीप है और सुंदरवन ज्वारीय मैंग्रोव डेल्टा हैMajuli is a river island and Sundarbans is a tidal mangrove delta

Step 1

Concept

Majuli is a river island of Brahmaputra and Sundarbans is a mangrove delta region. For exams keep island and delta separate.

Step 2

Why this answer is correct

The correct answer is A. माजुली नदी द्वीप है और सुंदरवन ज्वारीय मैंग्रोव डेल्टा है / Majuli is a river island and Sundarbans is a tidal mangrove delta. Majuli is a river island of Brahmaputra and Sundarbans is a mangrove delta region. For exams keep island and delta separate.

Step 3

Exam Tip

माजुली ब्रह्मपुत्र का नदी द्वीप है और सुंदरवन डेल्टा का मैंग्रोव क्षेत्र है। परीक्षा में द्वीप और डेल्टा अलग रखें।

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माजुली और लक्षद्वीप की तुलना में सही भौतिक वर्गीकरण कौन सा है?

What is the correct physical classification when comparing Majuli and Lakshadweep?

Explanation opens after your attempt
Correct Answer

A. माजुली नदी द्वीप और लक्षद्वीप प्रवाल समुद्री द्वीपMajuli river island and Lakshadweep coral marine island

Step 1

Concept

Majuli is a river island in Brahmaputra and Lakshadweep is a coral island in Arabian Sea. For exams identify island types separately.

Step 2

Why this answer is correct

The correct answer is A. माजुली नदी द्वीप और लक्षद्वीप प्रवाल समुद्री द्वीप / Majuli river island and Lakshadweep coral marine island. Majuli is a river island in Brahmaputra and Lakshadweep is a coral island in Arabian Sea. For exams identify island types separately.

Step 3

Exam Tip

माजुली ब्रह्मपुत्र में नदी द्वीप है और लक्षद्वीप अरब सागर में प्रवाल द्वीप है। परीक्षा में द्वीप प्रकार अलग पहचानें।

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मेगस्थनीज की इंडिका में भारतीय समाज के वर्गीकरण को सीधे स्वीकार करने में समस्या क्यों है?

Why is it problematic to directly accept the social classification in Megasthenes' Indica?

Explanation opens after your attempt
Correct Answer

A. विदेशी दृष्टि और सीमित समझ का प्रभाव हो सकता हैIt may reflect foreign perspective and limited understanding

Step 1

Concept

Indica is useful but has the limits of a foreign observer. For exams, always apply source criticism.

Step 2

Why this answer is correct

The correct answer is A. विदेशी दृष्टि और सीमित समझ का प्रभाव हो सकता है / It may reflect foreign perspective and limited understanding. Indica is useful but has the limits of a foreign observer. For exams, always apply source criticism.

Step 3

Exam Tip

इंडिका उपयोगी है लेकिन विदेशी पर्यवेक्षक की सीमाएं रखती है। परीक्षा में स्रोत की आलोचना अवश्य करें।

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यदि किसी अभिक्रिया में ऊष्मा उत्पादों की ओर लिखी है और केवल एक उत्पाद बनता है तो कौन सा वर्गीकरण संभव है?

If heat is written on the product side and only one product forms which classification is possible?

Explanation opens after your attempt
Correct Answer

A. ऊष्माक्षेपी संयोजनExothermic combination

Step 1

Concept

Heat on the product side shows heat release.

Step 2

Why this answer is correct

Formation of only one product can indicate combination.

Step 3

Exam Tip

Therefore it can be exothermic combination. चरण 1: उत्पादों की ओर ऊष्मा लिखना ऊष्मा निकलने को दिखाता है। चरण 2: केवल एक उत्पाद बनना संयोजन की पहचान हो सकती है। चरण 3: इसलिए यह ऊष्माक्षेपी संयोजन हो सकता है।

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यदि (p(x)=x-2-4x+6), तो (p(x+1)-p(x)) का मान क्या है?

If (p(x)=x-2-4x+6), what is the value of (p(x+1)-p(x))?

Explanation opens after your attempt
Correct Answer

A. (2x-3)

Step 1

Concept

(p(x+1)=x-2-2x+3) and (p(x+1)-p(x)=2x-3). In such questions, substitute (x+1) carefully first.

Step 2

Why this answer is correct

The correct answer is A. (2x-3). (p(x+1)=x-2-2x+3) and (p(x+1)-p(x)=2x-3). In such questions, substitute (x+1) carefully first.

Step 3

Exam Tip

(p(x+1)=x-2-2x+3) और (p(x+1)-p(x)=2x-3) है। ऐसे प्रश्नों में पहले (x+1) को सावधानी से प्रतिस्थापित करें।

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यदि (p(x)=x-2-8x+16) है, तो (p(4+t)) का मान क्या है?

If (p(x)=x-2-8x+16), what is the value of (p(4+t))?

Explanation opens after your attempt
Correct Answer

A. \(t^2\)

Step 1

Concept

(p(x)=(x-4)2), so (p(4+t)=t-2). In such questions, first form a perfect square.

Step 2

Why this answer is correct

The correct answer is A. \(t^2\). (p(x)=(x-4)2), so (p(4+t)=t-2). In such questions, first form a perfect square.

Step 3

Exam Tip

(p(x)=(x-4)2), इसलिए (p(4+t)=t-2)। ऐसे प्रश्नों में पहले पूर्ण वर्ग बनाना आसान होता है।

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यदि (p(x)=x-3-1), तो निम्न में से कौन-सा रैखिक गुणनखंड है?

If (p(x)=x-3-1), which of the following is a linear factor?

Explanation opens after your attempt
Correct Answer

A. (x-1)

Step 1

Concept

(x-3-1=(x-1)\(x^2+x+1\)). Therefore (x-1) is a linear factor.

Step 2

Why this answer is correct

The correct answer is A. (x-1). (x-3-1=(x-1)\(x^2+x+1\)). Therefore (x-1) is a linear factor.

Step 3

Exam Tip

(x-3-1=(x-1)\(x^2+x+1\)) है। इसलिए (x-1) रैखिक गुणनखंड है।

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यदि (p(x)=x-2-ax+b) के शून्यक (a) और (b) हैं, तो कौन-सा संबंध सही है?

If the zeroes of (p(x)=x-2-ax+b) are (a) and (b), which relation is correct?

Explanation opens after your attempt
Correct Answer

A. (a+b=a) और (ab=b)(a+b=a) and (ab=b)

Step 1

Concept

The sum of zeroes from the polynomial is (a) and the product is (b). Hence if the zeroes are (a,b), then (a+b=a) and (ab=b).

Step 2

Why this answer is correct

The correct answer is A. (a+b=a) और (ab=b) / (a+b=a) and (ab=b). The sum of zeroes from the polynomial is (a) and the product is (b). Hence if the zeroes are (a,b), then (a+b=a) and (ab=b).

Step 3

Exam Tip

शून्यकों का योग बहुपद से (a) और गुणनफल (b) है। इसलिए यदि शून्यक (a,b) हैं, तो (a+b=a) और (ab=b) होना चाहिए।

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यदि (p(x)=x-2+px+q) और (p(1)=0,\ p(2)=0), तो (p+q) क्या है?

If (p(x)=x-2+px+q) and (p(1)=0,\ p(2)=0), what is (p+q)?

Explanation opens after your attempt
Correct Answer

A. -(1)

Step 1

Concept

The zeroes are (1) and (2), so the polynomial is \(x^2-3x+2\). Thus (p=-3,\ q=2), and (p+q=-1).

Step 2

Why this answer is correct

The correct answer is A. -(1). The zeroes are (1) and (2), so the polynomial is \(x^2-3x+2\). Thus (p=-3,\ q=2), and (p+q=-1).

Step 3

Exam Tip

शून्यक (1) और (2) हैं, इसलिए बहुपद \(x^2-3x+2\) है। अतः (p=-3,\ q=2) और (p+q=-1)।

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यदि (p(x)=2x-2+x-6), तो (2p(1)-p(-2)) का मान क्या है?

If (p(x)=2x-2+x-6), what is the value of (2p(1)-p(-2))?

Explanation opens after your attempt
Correct Answer

A. -(6)

Step 1

Concept

(p(1)=2+1-6=-3) and (p(-2)=8-2-6=0). Therefore (2p(1)-p(-2)=-6).

Step 2

Why this answer is correct

The correct answer is A. -(6). (p(1)=2+1-6=-3) and (p(-2)=8-2-6=0). Therefore (2p(1)-p(-2)=-6).

Step 3

Exam Tip

(p(1)=2+1-6=-3) और (p(-2)=8-2-6=0)। इसलिए (2p(1)-p(-2)=-6)।

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यदि (p(x)=x-2-6x+8), तो शून्यकों के वर्गों से बना मोनिक बहुपद कौन-सा है?

If (p(x)=x-2-6x+8), which monic polynomial has the squares of its zeroes as zeroes?

Explanation opens after your attempt
Correct Answer

A. \(x^2-20x+64\)

Step 1

Concept

The original zeroes are (2) and (4), so the new zeroes are (4) and (16). The new polynomial is \(x^2-20x+64\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-20x+64\). The original zeroes are (2) and (4), so the new zeroes are (4) and (16). The new polynomial is \(x^2-20x+64\).

Step 3

Exam Tip

मूल शून्यक (2) और (4) हैं, इसलिए नए शून्यक (4) और (16) हैं। नया बहुपद \(x^2-20x+64\) है।

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यदि (p(x)=x-2+2x+c) का कोई वास्तविक शून्यक नहीं है, तो (c) के लिए कौन-सी शर्त सही है?

If (p(x)=x-2+2x+c) has no real zero, which condition on (c) is correct?

Explanation opens after your attempt
Correct Answer

A. (c>1)

Step 1

Concept

For no real zero, the discriminant must satisfy (4-4c<0). This gives (c>1).

Step 2

Why this answer is correct

The correct answer is A. (c>1). For no real zero, the discriminant must satisfy (4-4c<0). This gives (c>1).

Step 3

Exam Tip

कोई वास्तविक शून्यक नहीं होने के लिए विविक्तकर (4-4c<0) चाहिए। इससे (c>1) मिलता है।

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यदि (p(x)=x-2-7x+12) है, तो (p(x)) का ग्राफ (x)-अक्ष को किन बिंदुओं पर काटेगा?

If (p(x)=x-2-7x+12), at which points will the graph of (p(x)) cut the (x)-axis?

Explanation opens after your attempt
Correct Answer

A. ((3,0),(4,0))

Step 1

Concept

(x-2-7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). The (x)-axis points are ((3,0)) and ((4,0)).

Step 2

Why this answer is correct

The correct answer is A. ((3,0),(4,0)). (x-2-7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). The (x)-axis points are ((3,0)) and ((4,0)).

Step 3

Exam Tip

(x-2-7x+12=(x-3)(x-4)), इसलिए शून्यक (3) और (4) हैं। (x)-अक्ष पर बिंदु ((3,0)) और ((4,0)) होंगे।

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यदि (p(x)=x-2+5x+6) और (r(x)=p(-x)), तो (r(x)) के शून्यक कौन-से हैं?

If (p(x)=x-2+5x+6) and (r(x)=p(-x)), what are the zeroes of (r(x))?

Explanation opens after your attempt
Correct Answer

A. (2,3)

Step 1

Concept

The zeroes of (p(x)) are (-2) and (-3). For (p(-x)=0), (-x=-2) or (-x=-3), so (x=2,3).

Step 2

Why this answer is correct

The correct answer is A. (2,3). The zeroes of (p(x)) are (-2) and (-3). For (p(-x)=0), (-x=-2) or (-x=-3), so (x=2,3).

Step 3

Exam Tip

(p(x)) के शून्यक (-2) और (-3) हैं। (p(-x)=0) के लिए (-x=-2) या (-x=-3), इसलिए (x=2,3)।

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यदि (p(x)=x-3-3x-2-4x+12), तो पूर्ण गुणनखंड रूप क्या है?

If (p(x)=x-3-3x-2-4x+12), what is the complete factor form?

Explanation opens after your attempt
Correct Answer

A. ((x-3)(x-2)(x+2))

Step 1

Concept

By grouping, (x-2(x-3)-4(x-3)=(x-3)\(x^2-4\)). Thus the factors are ((x-3)(x-2)(x+2)).

Step 2

Why this answer is correct

The correct answer is A. ((x-3)(x-2)(x+2)). By grouping, (x-2(x-3)-4(x-3)=(x-3)\(x^2-4\)). Thus the factors are ((x-3)(x-2)(x+2)).

Step 3

Exam Tip

समूहीकरण से (x-2(x-3)-4(x-3)=(x-3)\(x^2-4\)) मिलता है। इसलिए गुणनखंड ((x-3)(x-2)(x+2)) हैं।

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यदि (p(x)=x-2-4x+3) है, तो कौन-सा मान (p(x)<0) बनाता है?

If (p(x)=x-2-4x+3), which value makes (p(x)<0)?

Explanation opens after your attempt
Correct Answer

A. (2)

Step 1

Concept

(p(x)=(x-1)(x-3)), and it is negative for (1<x<3). Therefore (x=2) is correct.

Step 2

Why this answer is correct

The correct answer is A. (2). (p(x)=(x-1)(x-3)), and it is negative for (1<x<3). Therefore (x=2) is correct.

Step 3

Exam Tip

(p(x)=(x-1)(x-3)) है और (1<x<3) में मान ऋणात्मक होता है। इसलिए (x=2) सही है।

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यदि (p(x)=x-2-2x+k) का न्यूनतम मान (3) है, तो (k) क्या है?

If the minimum value of (p(x)=x-2-2x+k) is (3), what is (k)?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

(x-2-2x+k=(x-1)2+k-1), so the minimum value is (k-1). From (k-1=3), (k=4).

Step 2

Why this answer is correct

The correct answer is A. (4). (x-2-2x+k=(x-1)2+k-1), so the minimum value is (k-1). From (k-1=3), (k=4).

Step 3

Exam Tip

(x-2-2x+k=(x-1)2+k-1), इसलिए न्यूनतम मान (k-1) है। (k-1=3) से (k=4)।

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यदि (p(x)=x-2+ax+a) में (p(1)=0), तो (a) क्या है?

If (p(x)=x-2+ax+a) and (p(1)=0), what is (a)?

Explanation opens after your attempt
Correct Answer

A. -\(\frac{1}{2}\)

Step 1

Concept

(p(1)=1+a+a=0), so (2a=-1). Therefore \(a=-\frac{1}{2}\).

Step 2

Why this answer is correct

The correct answer is A. -\(\frac{1}{2}\). (p(1)=1+a+a=0), so (2a=-1). Therefore \(a=-\frac{1}{2}\).

Step 3

Exam Tip

(p(1)=1+a+a=0), इसलिए (2a=-1)। अतः \(a=-\frac{1}{2}\) है।

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यदि (p(x)=x-4-16), तो \(x^2+4\) के कारण वास्तविक शून्यकों पर क्या प्रभाव पड़ता है?

For (p(x)=x-4-16), what effect does \(x^2+4\) have on real zeroes?

Explanation opens after your attempt
Correct Answer

A. यह कोई वास्तविक शून्यक नहीं देताIt gives no real zero

Step 1

Concept

(x-4-16=\(x^2-4\)\(x^2+4\)). The factor \(x^2+4\) is never (0) for real (x).

Step 2

Why this answer is correct

The correct answer is A. यह कोई वास्तविक शून्यक नहीं देता / It gives no real zero. (x-4-16=\(x^2-4\)\(x^2+4\)). The factor \(x^2+4\) is never (0) for real (x).

Step 3

Exam Tip

(x-4-16=\(x^2-4\)\(x^2+4\)) है। \(x^2+4\) वास्तविक (x) के लिए कभी (0) नहीं होता।

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यदि (p(x)=5x-2-20x+20), तो इसके शून्यकों का योग क्या है?

If (p(x)=5x-2-20x+20), what is the sum of its zeroes?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

The sum is \(-\frac{b}{a}=-\frac{-20}{5}=4\). Even if a common factor is removed first, the sum remains the same.

Step 2

Why this answer is correct

The correct answer is A. (4). The sum is \(-\frac{b}{a}=-\frac{-20}{5}=4\). Even if a common factor is removed first, the sum remains the same.

Step 3

Exam Tip

योग \(-\frac{b}{a}=-\frac{-20}{5}=4\) है। पहले सामान्य गुणनखंड निकालना चाहें तो भी योग वही रहेगा।

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यदि (p(x)=x-2+2x-24), तो (p(x)) का कौन-सा गुणनखंड है?

If (p(x)=x-2+2x-24), which is a factor of (p(x))?

Explanation opens after your attempt
Correct Answer

A. (x-4)

Step 1

Concept

(x-2+2x-24=(x-4)(x+6)). Therefore (x-4) is a factor.

Step 2

Why this answer is correct

The correct answer is A. (x-4). (x-2+2x-24=(x-4)(x+6)). Therefore (x-4) is a factor.

Step 3

Exam Tip

(x-2+2x-24=(x-4)(x+6)) है। इसलिए (x-4) एक गुणनखंड है।

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यदि (p(x)=x-2-12x+35), तो \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}\) क्या है, जहाँ \(\alpha,\beta\) शून्यक हैं?

If (p(x)=x-2-12x+35), what is \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}\), where \(\alpha,\beta\) are zeroes?

Explanation opens after your attempt
Correct Answer

D. \(\frac{11}{24}\)

Step 1

Concept

\(\alpha+\beta=12\) and \(\alpha\beta=35\). \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}=\frac{\alpha+\beta-2}{\alpha\beta-\alpha-\beta+1}=\frac{10}{24}=\frac{5}{12}\).

Step 2

Why this answer is correct

The correct answer is D. \(\frac{11}{24}\). \(\alpha+\beta=12\) and \(\alpha\beta=35\). \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}=\frac{\alpha+\beta-2}{\alpha\beta-\alpha-\beta+1}=\frac{10}{24}=\frac{5}{12}\).

Step 3

Exam Tip

\(\alpha+\beta=12\) और \(\alpha\beta=35\) हैं। \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}=\frac{\alpha+\beta-2}{\alpha\beta-\alpha-\beta+1}=\frac{10}{24}=\frac{5}{12}\)।

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यदि (p(x)=x-3+px-2+qx+15) के शून्यक (-1,3,-5) हैं, तो (p+q) क्या है?

If the zeroes of (p(x)=x-3+px-2+qx+15) are (-1,3,-5), what is (p+q)?

Explanation opens after your attempt
Correct Answer

B. (2)

Step 1

Concept

The sum of zeroes is (-3), so (p=3). The pairwise product sum is (-3+5-15=-13), so (q=-13) and (p+q=-10).

Step 2

Why this answer is correct

The correct answer is B. (2). The sum of zeroes is (-3), so (p=3). The pairwise product sum is (-3+5-15=-13), so (q=-13) and (p+q=-10).

Step 3

Exam Tip

शून्यकों का योग (-3) है, इसलिए (p=3)। युग्म गुणनफलों का योग (-3+5-15=-13), इसलिए (q=-13) और (p+q=-10)।

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यदि (p(x)=x-2+4x+4), तो (p(-2+h)) का मान क्या है?

If (p(x)=x-2+4x+4), what is the value of (p(-2+h))?

Explanation opens after your attempt
Correct Answer

A. \(h^2\)

Step 1

Concept

(p(x)=(x+2)2), so (p(-2+h)=h-2). Perfect square form makes substitution easier.

Step 2

Why this answer is correct

The correct answer is A. \(h^2\). (p(x)=(x+2)2), so (p(-2+h)=h-2). Perfect square form makes substitution easier.

Step 3

Exam Tip

(p(x)=(x+2)2), इसलिए (p(-2+h)=h-2)। पूर्ण वर्ग रूप से प्रतिस्थापन आसान हो जाता है।

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यदि (x=2) पर (p(x)=x-3+mx-10) का मान (0) है, तो (m) क्या है?

If the value of (p(x)=x-3+mx-10) at (x=2) is (0), what is (m)?

Explanation opens after your attempt
Correct Answer

A. (1)

Step 1

Concept

(p(2)=8+2m-10=0). This gives (2m=2) and (m=1).

Step 2

Why this answer is correct

The correct answer is A. (1). (p(2)=8+2m-10=0). This gives (2m=2) and (m=1).

Step 3

Exam Tip

(p(2)=8+2m-10=0) है। इससे (2m=2) और (m=1) मिलता है।

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यदि (p(x)=2x-2-7x+5), तो शून्यकों के योग और गुणनफल का अंतर क्या है?

If (p(x)=2x-2-7x+5), what is the difference between the sum and product of its zeroes?

Explanation opens after your attempt
Correct Answer

A. (1)

Step 1

Concept

The sum is \(\frac{7}{2}\) and the product is \(\frac{5}{2}\). Their difference is \(\frac{7}{2}-\frac{5}{2}=1\).

Step 2

Why this answer is correct

The correct answer is A. (1). The sum is \(\frac{7}{2}\) and the product is \(\frac{5}{2}\). Their difference is \(\frac{7}{2}-\frac{5}{2}=1\).

Step 3

Exam Tip

योग \(\frac{7}{2}\) और गुणनफल \(\frac{5}{2}\) है। उनका अंतर \(\frac{7}{2}-\frac{5}{2}=1\) है।

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यदि (p(x)=x-2-kx+36) के शून्यक धनात्मक और अनुपात (1:4) में हैं, तो (k) क्या है?

If the zeroes of (p(x)=x-2-kx+36) are positive and in the ratio (1:4), what is (k)?

Explanation opens after your attempt
Correct Answer

A. (15)

Step 1

Concept

Let the zeroes be (t) and (4t), then \(4t^2=36\) gives (t=3). The sum is (15), so (k=15).

Step 2

Why this answer is correct

The correct answer is A. (15). Let the zeroes be (t) and (4t), then \(4t^2=36\) gives (t=3). The sum is (15), so (k=15).

Step 3

Exam Tip

शून्यक (t) और (4t) मानें, तो \(4t^2=36\) से (t=3) है। योग (15) है, इसलिए (k=15)।

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यदि (p(x)=ax-2+bx+c) और (p(1)=p(2)=p(3)=0), तो कौन-सा निष्कर्ष सही है?

If (p(x)=ax-2+bx+c) and (p(1)=p(2)=p(3)=0), which conclusion is correct?

Explanation opens after your attempt
Correct Answer

A. (p(x)) शून्य बहुपद है(p(x)) is the zero polynomial

Step 1

Concept

A polynomial of degree at most (2) can have three distinct zeroes only if it is the zero polynomial. A non-zero polynomial cannot have more distinct zeroes than its degree.

Step 2

Why this answer is correct

The correct answer is A. (p(x)) शून्य बहुपद है / (p(x)) is the zero polynomial. A polynomial of degree at most (2) can have three distinct zeroes only if it is the zero polynomial. A non-zero polynomial cannot have more distinct zeroes than its degree.

Step 3

Exam Tip

अधिकतम द्विघात बहुपद के तीन अलग-अलग शून्यक तभी हो सकते हैं जब वह शून्य बहुपद हो। घात से अधिक अलग शून्यक असंभव होते हैं।

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यदि (p(x)=x-2-5x+6), तो (p(2)+p(3)) का मान क्या है?

If (p(x)=x-2-5x+6), what is the value of (p(2)+p(3))?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

(2) and (3) are zeroes of (p(x)), so (p(2)=0) and (p(3)=0). Hence the sum is (0).

Step 2

Why this answer is correct

The correct answer is A. (0). (2) and (3) are zeroes of (p(x)), so (p(2)=0) and (p(3)=0). Hence the sum is (0).

Step 3

Exam Tip

(2) और (3), (p(x)) के शून्यक हैं, इसलिए (p(2)=0) और (p(3)=0)। इसलिए योग (0) है।

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यदि (p(x)=x-2-2x-8), तो (p(x+3)) के शून्यक कौन-से हैं?

If (p(x)=x-2-2x-8), what are the zeroes of (p(x+3))?

Explanation opens after your attempt
Correct Answer

A. -(5,1)

Step 1

Concept

The zeroes of (p(x)) are (4) and (-2). From (x+3=4) or (x+3=-2), the zeroes are (1) and (-5).

Step 2

Why this answer is correct

The correct answer is A. -(5,1). The zeroes of (p(x)) are (4) and (-2). From (x+3=4) or (x+3=-2), the zeroes are (1) and (-5).

Step 3

Exam Tip

(p(x)) के शून्यक (4) और (-2) हैं। (x+3=4) या (x+3=-2) से शून्यक (1) और (-5) मिलते हैं।

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यदि (p(x)=x-3-9x), तो इसके कितने भिन्न वास्तविक शून्यक हैं?

If (p(x)=x-3-9x), how many distinct real zeroes does it have?

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

(x-3-9x=x(x-3)(x+3)), so the zeroes are (-3,0,3). Hence there are (3) distinct real zeroes.

Step 2

Why this answer is correct

The correct answer is A. (3). (x-3-9x=x(x-3)(x+3)), so the zeroes are (-3,0,3). Hence there are (3) distinct real zeroes.

Step 3

Exam Tip

(x-3-9x=x(x-3)(x+3)), इसलिए शून्यक (-3,0,3) हैं। अतः भिन्न वास्तविक शून्यक (3) हैं।

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