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100 results found for "ap-index-variable-hard" in Class 10.

Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 48

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

Explanation

Simple Explanation

बहुपद में चर की घातें \(0,1,2,\ldots\) जैसी अऋणात्मक पूर्णांक होती हैं। यही बहुपद की मूल पहचान है। / In a polynomial, powers of the variable are non-negative integers like \(0,1,2,\ldots\). This is the basic identification rule.

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 48

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)

Explanation

Simple Explanation

जिस अक्षर के मान बदल सकते हैं वह चर होता है। यहां चर (u) है। / The letter whose values can change is the variable. Here the variable is (u).

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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)

Explanation

Simple Explanation

जिस अक्षर का मान बदल सकता है वह चर है। यहां चर (t) है। / The letter whose value can vary is the variable. Here the variable is (t).

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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

Explanation

Simple Explanation

\(x^2+y+1\) में दो चर (x) और (y) हैं। इसलिए यह एक चर वाला बहुपद नहीं है। / \(x^2+y+1\) has two variables (x) and (y). Therefore it is not a polynomial in one variable.

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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)

Explanation

Simple Explanation

एक चर के बहुपद में चर की घात केवल अशून्य पूर्णांक या शून्य होती है। परीक्षा में ऋणात्मक घात और मूल से बचें। / In a polynomial in one variable, powers of the variable are non-negative integers. In exams, reject negative powers and roots of the variable.

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

कौन सा बहुपद एक चर (x) में है?

Which polynomial is in one variable (x)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

एक चर (x) में बहुपद में केवल (x) चर होता है। अन्य विकल्पों में एक से अधिक चर हैं। / A polynomial in one variable (x) contains only the variable (x). The other options have more than one variable.

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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)

Explanation

Simple Explanation

(p(t)) में बदलने वाला चिन्ह (t) है। इसलिए चर (t) है। / In (p(t)), the changing symbol is (t). So the variable is (t).

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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 47

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

Explanation

Simple Explanation

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

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 48

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

Explanation

Simple Explanation

\(x^2+2x+3\) बहुपद है और इसकी घात (2) है। इसलिए यह रैखिक नहीं है। / \(x^2+2x+3\) is a polynomial and its degree is (2). Therefore it is not linear.

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 47

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

Explanation

Simple Explanation

\(x^2+3x+1\) में केवल (x) चर है। इसलिए यह (x) में एक चर वाला बहुपद है। / \(x^2+3x+1\) has only the variable (x). So it is a one-variable polynomial in (x).

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Question Medium Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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

Explanation

Simple Explanation

\(4x^3+x-9\) बहुपद है और इसकी घात (3) है। इसलिए यह द्विघात नहीं है। / \(4x^3+x-9\) is a polynomial and its degree is (3). Therefore it is not quadratic.

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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

Explanation

Simple Explanation

\(\sqrt{2}\) एक वास्तविक संख्या है और (x) की घातें पूर्ण संख्याएँ हैं। इसलिए यह बहुपद है। / \(\sqrt{2}\) is a real number and the powers of (x) are whole numbers. So it is a polynomial.

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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

Explanation

Simple Explanation

\(\frac{3}{x}=3x^{-1}\) है और चर की घात ऋणात्मक है। इसलिए यह बहुपद नहीं है। / \(\frac{3}{x}=3x^{-1}\), so the variable has a negative power. Therefore it is not a polynomial.

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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

Explanation

Simple Explanation

\(z^4-2z+1\) में केवल (z) है और घातें ऋणात्मक नहीं हैं। इसलिए यह (z) में बहुपद है। / The expression \(z^4-2z+1\) has only (z) and no negative powers. So it is a polynomial in (z).

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

\(2x^2+3xy+1\) 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

Explanation

Simple Explanation

इसमें (x) और (y) दोनों चर हैं। एक चर वाले बहुपद में केवल एक ही चर होना चाहिए। / It contains both (x) and (y). A polynomial in one variable should contain only one variable.

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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

Explanation

Simple Explanation

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

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_1=8\), (d=9) और \(a_{3n+2}=197\) है तो (n) का मान क्या है?

If \(a_1=8\), (d=9), and \(a_{3n+2}=197\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

(197=8+(3n+1)9) से (189=27n+9) इसलिए \(n=\frac{20}{3}\) नहीं आता। सूचकांक ठीक पढ़ना जरूरी है। / (197=8+(3n+1)9), so (189=27n+9) and \(n=\frac{20}{3}\). Read the index carefully before selecting an integer option.

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_1=5\), (d=7) और \(a_{2n+3}=159\) है तो (n) का मान क्या है?

If \(a_1=5\), (d=7), and \(a_{2n+3}=159\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (10)

Explanation

Simple Explanation

(159=5+(2n+2)7) से (154=14n+14)। इसलिए (n=10)। / From (159=5+(2n+2)7), (154=14n+14). Therefore (n=10).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_1=3\) और \(a_{2n+1}=123\) है तथा (d=4) है तो (n) का मान क्या है?

If \(a_1=3\), \(a_{2n+1}=123\), and (d=4), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (15)

Explanation

Simple Explanation

\(123=3+2n\cdot4\) से (120=8n) इसलिए (n=15)। सूचकांक (2n+1) में (1) घटाकर गुणक लें। / From \(123=3+2n\cdot4\), (120=8n), so (n=15). In index (2n+1), subtract (1) to get the multiplier.

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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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)

Explanation

Simple Explanation

सबसे बड़ी घात \(x^4\) है, इसलिए घात (4) है। शून्य गुणांक वाले पदों को घात तय करने में नहीं गिनते। / The highest power is \(x^4\), so the degree is (4). Terms with zero coefficients do not affect the degree.

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Question Expert Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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)

Explanation

Simple Explanation

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

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 47

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

Explanation

Simple Explanation

\(y^2-3y+2\) में (y) की घातें पूर्ण संख्याएँ हैं। बहुपद किसी एक चर जैसे (y) में भी हो सकता है। / In \(y^2-3y+2\), the powers of (y) are whole numbers. A polynomial can be in one variable such as (y).

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 47

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

Explanation

Simple Explanation

\(\sqrt{x}=x^{\frac{1}{2}}\) है और \(\frac{1}{2}\) पूर्ण संख्या नहीं है। इसलिए यह (x) में बहुपद नहीं है। / \(\sqrt{x}=x^{\frac{1}{2}}\), and \(\frac{1}{2}\) is not a whole number. So it is not a polynomial in (x).

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

(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)

Explanation

Simple Explanation

(p(1)=12+3\cdot1+2=6) है। मान निकालते समय हर (x) की जगह दी गई संख्या रखें। / (p(1)=12+3\cdot1+2=6). While evaluating, replace every (x) with the given number.

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

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)

Explanation

Simple Explanation

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

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Question Easy Mathematics Polynomials Polynomials in one variable Class 10 Level 48

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

Explanation

Simple Explanation

बहुपद में (x) की घात केवल पूर्णांक और अशून्य नहीं बल्कि ऋणात्मक नहीं होनी चाहिए। परीक्षा में हर पद की घात जांचें। / A polynomial has only non-negative integer powers of (x). In exams check the power of every term.

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_1=23\), (d=14) और \(a_{5n+4}=527\) है, तो (n) का मान क्या है?

If \(a_1=23\), (d=14), and \(a_{5n+4}=527\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

(527=23+(5n+3)14) से (504=70n+42), इसलिए \(n=\frac{33}{5}\) नहीं आता। सूचकांक और विकल्पों को ध्यान से मिलाएं। / (527=23+(5n+3)14), so (504=70n+42), which does not give an integer option. Match the index and options carefully.

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_1=17\), (d=10) और \(a_{4n+3}=407\) है, तो (n) का मान क्या है?

If \(a_1=17\), (d=10), and \(a_{4n+3}=407\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (9)

Explanation

Simple Explanation

(407=17+(4n+2)10) से (390=40n+20), इसलिए \(n=\frac{37}{4}\) नहीं आता। सूचकांक और विकल्पों को सावधानी से मिलाएं। / (407=17+(4n+2)10), so (390=40n+20), which does not give an integer option. Match the index and options carefully.

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Question Expert Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_1=11\), (d=8) और \(a_{3n+4}=275\) है, तो (n) का मान क्या है?

If \(a_1=11\), (d=8), and \(a_{3n+4}=275\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (10)

Explanation

Simple Explanation

(275=11+(3n+3)8) से (264=24n+24), इसलिए (n=10)। सूचकांक से (1) घटाकर (d) का गुणक बनाएं। / From (275=11+(3n+3)8), (264=24n+24), so (n=10). Subtract (1) from the index to get the multiplier of (d).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि द्विघात बहुपद \(x^2-6x+k\) के शून्यक \(\alpha\) और \(\beta\) हैं तथा \(\alpha^2+\beta^2=20\) है, तो (k) का मान क्या होगा?

If \(\alpha\) and \(\beta\) are zeroes of the quadratic polynomial \(x^2-6x+k\) and \(\alpha^2+\beta^2=20\), what is the value of (k)?

Explanation opens after your attempt
Correct Answer

A. (8)

Explanation

Simple Explanation

\(\alpha+\beta=6\) और (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta) होता है। इसलिए (20=36-2k) से (k=8) मिलता है। / Here \(\alpha+\beta=6\) and (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta). So (20=36-2k), giving (k=8).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x-3+mx-2-4x-4) में (x+2) एक गुणनखंड है, तो (m) का मान क्या होगा?

If (x+2) is a factor of (p(x)=x-3+mx-2-4x-4), what is (m)?

Explanation opens after your attempt
Correct Answer

A. (1)

Explanation

Simple Explanation

(p(-2)=0) रखने पर (-8+4m+8-4=0) मिलता है। इससे (4m-4=0) और (m=1) है। / Putting (p(-2)=0) gives (-8+4m+8-4=0). Thus (4m-4=0), so (m=1).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

\(x^3-7x+6\) के लिए कौन सा कथन सही है?

Which statement is correct for \(x^3-7x+6\)?

Explanation opens after your attempt
Correct Answer

A. (x-1) और (x-2) दोनों गुणनखंड हैंBoth (x-1) and (x-2) are factors

Explanation

Simple Explanation

(p(1)=0) और (p(2)=0) दोनों हैं। इसलिए (x-1) और (x-2) दोनों गुणनखंड हैं। / Both (p(1)=0) and (p(2)=0). Hence (x-1) and (x-2) are both factors.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=4x-2-12x+9), तो इसके शून्यकों के बारे में कौन सा कथन सही है?

If (p(x)=4x-2-12x+9), which statement about its zeroes is correct?

Explanation opens after your attempt
Correct Answer

A. दोनों शून्यक \(\frac{3}{2}\) हैंBoth zeroes are \(\frac{3}{2}\)

Explanation

Simple Explanation

(4x-2-12x+9=(2x-3)2) है। इसलिए दोनों शून्यक \(\frac{3}{2}\) हैं। / (4x-2-12x+9=(2x-3)2). Therefore, both zeroes are \(\frac{3}{2}\).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(x^2-11x+30\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो (\(\alpha-\beta\)2) क्या है?

If \(\alpha\) and \(\beta\) are zeroes of \(x^2-11x+30\), what is (\(\alpha-\beta\)2)?

Explanation opens after your attempt
Correct Answer

A. (1)

Explanation

Simple Explanation

(\(\alpha-\beta\)2=\(\alpha+\beta\)2-4\alpha\beta) है। (121-120=1) मिलता है। / (\(\alpha-\beta\)2=\(\alpha+\beta\)2-4\alpha\beta). We get (121-120=1).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(x^2+mx+n\) का एक शून्यक (0) है और दूसरा शून्यक (5) है, तो (m+n) क्या होगा?

If one zero of \(x^2+mx+n\) is (0) and the other zero is (5), what is (m+n)?

Explanation opens after your attempt
Correct Answer

A. (-5)

Explanation

Simple Explanation

योग (5) है इसलिए (m=-5), और गुणनफल (0) है इसलिए (n=0)। अतः (m+n=-5)। / The sum is (5), so (m=-5), and the product is (0), so (n=0). Hence (m+n=-5).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x-4-5x-2+4), तो कौन सा मान (p(x)) का शून्यक नहीं है?

If (p(x)=x-4-5x-2+4), which value is not a zero of (p(x))?

Explanation opens after your attempt
Correct Answer

D. (3)

Explanation

Simple Explanation

(p(3)=81-45+4=40) है, इसलिए (3) शून्यक नहीं है। शेष (1), (-1) और (2) पर मान (0) मिलता है। / (p(3)=81-45+4=40), so (3) is not a zero. The values (1), (-1), and (2) make the polynomial (0).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

किस बहुपद के शून्यक (0), (2) और (-3) हैं?

Which polynomial has zeroes (0), (2), and (-3)?

Explanation opens after your attempt
Correct Answer

A. \(x^3+x^2-6x\)

Explanation

Simple Explanation

शून्यकों से बहुपद (x(x-2)(x+3)) बनेगा। इसे फैलाने पर \(x^3+x^2-6x\) मिलता है। / From the zeroes, the polynomial is (x(x-2)(x+3)). Expanding gives \(x^3+x^2-6x\).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(2x^2+5x-3\) को (\(x-\alpha\)\(x-\beta\)) के रूप में लिखा जाए, तो \(\alpha+\beta\) क्या होगा?

If \(2x^2+5x-3\) is considered with factors involving (\(x-\alpha\)\(x-\beta\)), what is \(\alpha+\beta\)?

Explanation opens after your attempt
Correct Answer

A. \(-\frac{5}{2}\)

Explanation

Simple Explanation

द्विघात \(ax^2+bx+c\) के लिए शून्यकों का योग \(-\frac{b}{a}\) होता है। इसलिए \(\alpha+\beta=-\frac{5}{2}\)। / For \(ax^2+bx+c\), the sum of zeroes is \(-\frac{b}{a}\). Hence \(\alpha+\beta=-\frac{5}{2}\).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(x^2-3x-10\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो \(\alpha^2\beta+\alpha\beta^2\) क्या है?

If \(\alpha\) and \(\beta\) are zeroes of \(x^2-3x-10\), what is \(\alpha^2\beta+\alpha\beta^2\)?

Explanation opens after your attempt
Correct Answer

A. (-30)

Explanation

Simple Explanation

(\alpha-2\beta+\alpha\beta-2=\alpha\beta\(\alpha+\beta\)) होता है। यहां \(\alpha\beta=-10\) और \(\alpha+\beta=3\), इसलिए मान (-30) है। / (\alpha-2\beta+\alpha\beta-2=\alpha\beta\(\alpha+\beta\)). Here \(\alpha\beta=-10\) and \(\alpha+\beta=3\), so the value is (-30).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x-3+ax-2+bx+8) के शून्यक (-1), (-2) और (-4) हैं, तो (a+b) क्या है?

If the zeroes of (p(x)=x-3+ax-2+bx+8) are (-1), (-2), and (-4), what is (a+b)?

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Correct Answer

A. (21)

Explanation

Simple Explanation

बहुपद ((x+1)(x+2)(x+4)=x-3+7x-2+14x+8) है। इसलिए (a+b=21)। / The polynomial is ((x+1)(x+2)(x+4)=x-3+7x-2+14x+8). Hence (a+b=21).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(x^2-10x+q\) के शून्यक (2r) और (3r) हैं, तो (q) का मान क्या है?

If the zeroes of \(x^2-10x+q\) are (2r) and (3r), what is (q)?

Explanation opens after your attempt
Correct Answer

A. (24)

Explanation

Simple Explanation

योग (5r=10) से (r=2) है। गुणनफल \(2r\cdot3r=6r^2=24\) है। / From the sum (5r=10), (r=2). The product is \(2r\cdot3r=6r^2=24\).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

द्विघात बहुपद \(kx^2+6x+4\) के शून्यकों का योग (-3) है। (k) का मान क्या है?

The sum of zeroes of the quadratic polynomial \(kx^2+6x+4\) is (-3). What is (k)?

Explanation opens after your attempt
Correct Answer

A. (2)

Explanation

Simple Explanation

योग \(-\frac{6}{k}\) है और यह (-3) है। इसलिए (k=2) होगा। / The sum is \(-\frac{6}{k}\), and it equals (-3). Therefore, (k=2).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(x^2-8x+k\) के शून्यक \(\alpha\) और \(\beta\) हैं तथा \(\alpha-\beta=2\), तो (k) क्या है?

If \(\alpha\) and \(\beta\) are zeroes of \(x^2-8x+k\) and \(\alpha-\beta=2\), what is (k)?

Explanation opens after your attempt
Correct Answer

A. (15)

Explanation

Simple Explanation

योग (8) और अंतर (2) से शून्यक (5) और (3) हैं। गुणनफल (15) है इसलिए (k=15)। / From sum (8) and difference (2), the zeroes are (5) and (3). Their product is (15), so (k=15).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

किस (k) के लिए \(x^2+kx+9\) का एक शून्यक दूसरे का तीन गुना है और दोनों धनात्मक हैं?

For which (k) does \(x^2+kx+9\) have one zero three times the other and both positive?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

शून्यक (t) और (3t) मानें, तो \(3t^2=9\) से \(t=\sqrt{3}\) है। योग \(4\sqrt{3}\) है इसलिए \(k=-4\sqrt{3}\)। / Let the zeroes be (t) and (3t), so \(3t^2=9\) gives \(t=\sqrt{3}\). The sum is \(4\sqrt{3}\), hence \(k=-4\sqrt{3}\).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(x^2-4x+1\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो \(\alpha^3+\beta^3\) का मान क्या है?

If \(\alpha\) and \(\beta\) are zeroes of \(x^2-4x+1\), what is \(\alpha^3+\beta^3\)?

Explanation opens after your attempt
Correct Answer

A. (52)

Explanation

Simple Explanation

\(\alpha+\beta=4\) और \(\alpha\beta=1\) है। (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=64-12=52)। / \(\alpha+\beta=4\) and \(\alpha\beta=1\). (\alpha-3+\beta-3=\(\alpha+\beta\)3-3\alpha\beta\(\alpha+\beta\)=64-12=52).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(x^2+5x+6\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो नया बहुपद जिसके शून्यक \(\alpha+1\) और \(\beta+1\) हैं, क्या है?

If \(\alpha\) and \(\beta\) are zeroes of \(x^2+5x+6\), what is the new polynomial whose zeroes are \(\alpha+1\) and \(\beta+1\)?

Explanation opens after your attempt
Correct Answer

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

Explanation

Simple Explanation

मूल शून्यक (-2) और (-3) हैं, इसलिए नए शून्यक (-1) और (-2) हैं। नया बहुपद \(x^2+3x+2\) है। / The original zeroes are (-2) and (-3), so the new zeroes are (-1) and (-2). The new polynomial is \(x^2+3x+2\).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x-3-2x-2-5x+6), तो निम्न में से कौन सा शून्यक नहीं है?

If (p(x)=x-3-2x-2-5x+6), which of the following is not a zero?

Explanation opens after your attempt
Correct Answer

B. (2)

Explanation

Simple Explanation

(p(2)=8-8-10+6=-4) है इसलिए (2) शून्यक नहीं है। बाकी विकल्पों को भी प्रतिस्थापन से जांच सकते हैं। / (p(2)=8-8-10+6=-4), so (2) is not a zero. The other options can be checked by substitution.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

बहुपद \(2x^3-9x^2+13x-6\) का एक गुणनखंड कौन सा है?

Which is a factor of \(2x^3-9x^2+13x-6\)?

Explanation opens after your attempt
Correct Answer

A. (x-1)

Explanation

Simple Explanation

(p(1)=2-9+13-6=0) है इसलिए (x-1) गुणनखंड है। विकल्प जांच में छोटे मान पहले लगाएं। / (p(1)=2-9+13-6=0), so (x-1) is a factor. In option checking, try small values first.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x-2-4x+k) और (p(1)=p(3)), तो (k) के बारे में क्या कहा जा सकता है?

If (p(x)=x-2-4x+k) and (p(1)=p(3)), what can be said about (k)?

Explanation opens after your attempt
Correct Answer

C. कोई भी वास्तविक मानAny real value

Explanation

Simple Explanation

(p(1)=k-3) और (p(3)=k-3) दोनों बराबर हैं। इसलिए (k) कोई भी वास्तविक मान हो सकता है। / (p(1)=k-3) and (p(3)=k-3), so they are equal. Hence (k) can be any real value.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(x^2+px+16\) के शून्यक परस्पर बराबर और ऋणात्मक हैं, तो (p) का मान क्या है?

If the zeroes of \(x^2+px+16\) are equal and negative, what is (p)?

Explanation opens after your attempt
Correct Answer

A. (8)

Explanation

Simple Explanation

बराबर ऋणात्मक शून्यक (-4) और (-4) होंगे क्योंकि गुणनफल (16) है। योग (-8) है इसलिए (p=8)। / The equal negative zeroes are (-4) and (-4) because the product is (16). The sum is (-8), so (p=8).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(3x^2+2x-1\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो (\(\alpha+\beta\)2) का मान क्या है?

If \(\alpha\) and \(\beta\) are zeroes of \(3x^2+2x-1\), what is (\(\alpha+\beta\)2)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{4}{9}\)

Explanation

Simple Explanation

\(\alpha+\beta=-\frac{2}{3}\) है। इसलिए (\(\alpha+\beta\)2=\frac{4}{9}) होगा। / \(\alpha+\beta=-\frac{2}{3}\). Therefore, (\(\alpha+\beta\)2=\frac{4}{9}).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(x^2-7x+10\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो \(\alpha^2+\beta^2\) क्या है?

If \(\alpha\) and \(\beta\) are zeroes of \(x^2-7x+10\), what is \(\alpha^2+\beta^2\)?

Explanation opens after your attempt
Correct Answer

A. (29)

Explanation

Simple Explanation

(\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta) होता है। (72-2(10)=29) है। / (\alpha-2+\beta-2=\(\alpha+\beta\)2-2\alpha\beta). Thus (72-2(10)=29).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(2x^2-3x-5\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो \(\frac{1}{\alpha}+\frac{1}{\beta}\) क्या होगा?

If \(\alpha\) and \(\beta\) are zeroes of \(2x^2-3x-5\), what is \(\frac{1}{\alpha}+\frac{1}{\beta}\)?

Explanation opens after your attempt
Correct Answer

A. \(-\frac{3}{5}\)

Explanation

Simple Explanation

\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\) है। यहां \(\frac{3}{2}\div-\frac{5}{2}=-\frac{3}{5}\)। / \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here \(\frac{3}{2}\div-\frac{5}{2}=-\frac{3}{5}\).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि द्विघात बहुपद के शून्यक \(\alpha\) और \(\beta\) हैं तथा \(\alpha+\beta=5\), \(\alpha\beta=6\), तो मोनिक बहुपद क्या है?

If a quadratic polynomial has zeroes \(\alpha\) and \(\beta\), with \(\alpha+\beta=5\) and \(\alpha\beta=6\), what is the monic polynomial?

Explanation opens after your attempt
Correct Answer

A. \(x^2-5x+6\)

Explanation

Simple Explanation

मोनिक बहुपद (x-2-\(\alpha+\beta\)x+\alpha\beta) होता है। इसलिए \(x^2-5x+6\) सही है। / The monic polynomial is (x-2-\(\alpha+\beta\)x+\alpha\beta). Hence \(x^2-5x+6\) is correct.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x-2-2x+5), तो (p(1)) का मान क्या है और क्या (1) शून्यक है?

If (p(x)=x-2-2x+5), what is (p(1)), and is (1) a zero?

Explanation opens after your attempt
Correct Answer

A. (4), नहीं(4), no

Explanation

Simple Explanation

(p(1)=1-2+5=4) है इसलिए (1) शून्यक नहीं है। शून्यक तभी होगा जब मान (0) हो। / (p(1)=1-2+5=4), so (1) is not a zero. A zero must make the value (0).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

\(x^4-1\) के रैखिक गुणनखंडों में से कौन सा गलत है?

Which one is not a linear factor of \(x^4-1\)?

Explanation opens after your attempt
Correct Answer

C. \(x^2+1\)

Explanation

Simple Explanation

\(x^2+1\) रैखिक नहीं है क्योंकि उसकी घात (2) है। वास्तविक संख्याओं में इसे रैखिक गुणनखंड नहीं माना जाता। / \(x^2+1\) is not linear because its degree is (2). Over real numbers, it is not a linear factor.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)) को (x-4) से भाग देने पर शेषफल (7) है, तो (p(4)) क्या होगा?

If the remainder when (p(x)) is divided by (x-4) is (7), what is (p(4))?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

शेषफल प्रमेय के अनुसार (x-4) से भाग देने पर शेषफल (p(4)) होता है। इसलिए (p(4)=7)। / By the remainder theorem, the remainder on division by (x-4) is (p(4)). Therefore, (p(4)=7).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

\(3x^3-2x^2+x+7\) को (x+2) से भाग देने पर शेषफल क्या है?

What is the remainder when \(3x^3-2x^2+x+7\) is divided by (x+2)?

Explanation opens after your attempt
Correct Answer

A. (-27)

Explanation

Simple Explanation

शेषफल (p(-2)) होगा। (3(-8)-2(4)-2+7=-27) है। / The remainder is (p(-2)). (3(-8)-2(4)-2+7=-27).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

\(x^3-5x^2+8x-4\) को (x-1) से भाग देने पर शेषफल क्या होगा?

What is the remainder when \(x^3-5x^2+8x-4\) is divided by (x-1)?

Explanation opens after your attempt
Correct Answer

A. (0)

Explanation

Simple Explanation

शेषफल प्रमेय से शेषफल (p(1)) है। (1-5+8-4=0) मिलता है। / By the remainder theorem, the remainder is (p(1)). We get (1-5+8-4=0).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (x+1) बहुपद \(2x^3+kx^2-5x+2\) का गुणनखंड है, तो (k) का सही मान क्या है?

If (x+1) is a factor of \(2x^3+kx^2-5x+2\), what is the correct value of (k)?

Explanation opens after your attempt
Correct Answer

A. (-5)

Explanation

Simple Explanation

(p(-1)=0) रखने पर (-2+k+5+2=0) मिलता है। इसलिए (k=-5) सही है। / Putting (p(-1)=0) gives (-2+k+5+2=0). Therefore, (k=-5) is correct.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (x+1) बहुपद \(2x^3+kx^2-5x+2\) का गुणनखंड है, तो (k) का मान क्या है?

If (x+1) is a factor of \(2x^3+kx^2-5x+2\), what is (k)?

Explanation opens after your attempt
Correct Answer

A. (5)

Explanation

Simple Explanation

(x+1) गुणनखंड होने पर (p(-1)=0) होगा। (-2+k+5+2=0) से (k=-5) नहीं बल्कि (k=-5) मिलता है। / If (x+1) is a factor, then (p(-1)=0). From (-2+k+5+2=0), we get (k=-5).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x-3-3x-2-4x+12) है, तो कौन सा (p(x)) का गुणनखंड है?

If (p(x)=x-3-3x-2-4x+12), which is a factor of (p(x))?

Explanation opens after your attempt
Correct Answer

A. (x-2)

Explanation

Simple Explanation

(p(2)=8-12-8+12=0) है इसलिए (x-2) गुणनखंड है। गुणनखंड प्रमेय का प्रयोग करें। / Since (p(2)=8-12-8+12=0), (x-2) is a factor. Use the factor theorem.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

बहुपद \(x^3-6x^2+11x-6\) के शून्यक कौन से हैं?

What are the zeroes of \(x^3-6x^2+11x-6\)?

Explanation opens after your attempt
Correct Answer

A. (1,2,3)

Explanation

Simple Explanation

यह ((x-1)(x-2)(x-3)) के बराबर है। अतः शून्यक (1), (2) और (3) हैं। / It equals ((x-1)(x-2)(x-3)). Therefore, the zeroes are (1), (2), and (3).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (x-a), (x-b) और (x-c) किसी घन बहुपद के गुणनखंड हैं, तो उसका एक संभावित बहुपद कौन सा है?

If (x-a), (x-b), and (x-c) are factors of a cubic polynomial, which is a possible polynomial?

Explanation opens after your attempt
Correct Answer

A. (x-3-(a+b+c)x-2+(ab+bc+ca)x-abc)

Explanation

Simple Explanation

((x-a)(x-b)(x-c)) फैलाने पर पहला रूप मिलता है। शून्यकों और गुणनखंडों का संबंध याद रखें। / Expanding ((x-a)(x-b)(x-c)) gives the first form. Remember the link between zeroes and factors.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

बहुपद \(x^2-6x+9\) के शून्यकों के बारे में सही कथन कौन सा है?

Which statement about the zeroes of \(x^2-6x+9\) is correct?

Explanation opens after your attempt
Correct Answer

B. दोनों शून्यक बराबर हैंBoth zeroes are equal

Explanation

Simple Explanation

(x-2-6x+9=(x-3)2) है इसलिए दोनों शून्यक (3) हैं। वर्ग रूप को पहचानना परीक्षा में तेज तरीका है। / (x-2-6x+9=(x-3)2), so both zeroes are (3). Recognizing square form is a fast exam method.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=3x-2-10x+m) के शून्यकों का गुणनफल \(\frac{4}{3}\) है, तो (m) का मान क्या है?

If the product of zeroes of (p(x)=3x-2-10x+m) is \(\frac{4}{3}\), what is (m)?

Explanation opens after your attempt
Correct Answer

A. (4)

Explanation

Simple Explanation

गुणनफल \(\frac{m}{3}\) है। \(\frac{m}{3}=\frac{4}{3}\) से (m=4) मिलता है। / The product is \(\frac{m}{3}\). From \(\frac{m}{3}=\frac{4}{3}\), we get (m=4).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=2x-2+kx+8) के शून्यकों का योग (3) है, तो (k) क्या होगा?

If the sum of zeroes of (p(x)=2x-2+kx+8) is (3), what is (k)?

Explanation opens after your attempt
Correct Answer

B. (-6)

Explanation

Simple Explanation

योग \(-\frac{k}{2}\) होता है और यह (3) है। इसलिए (k=-6) है। / The sum is \(-\frac{k}{2}\), and it equals (3). Hence (k=-6).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

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

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

Explanation opens after your attempt
Correct Answer

A. (0)

Explanation

Simple Explanation

(2) और (3) दोनों शून्यक हैं, इसलिए (p(3)=0) और (p(2)=0)। अतः अंतर (0) है। / Both (2) and (3) are zeroes, so (p(3)=0) and (p(2)=0). Therefore, the difference is (0).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

किस बहुपद की घात (4) है?

Which polynomial has degree (4)?

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Correct Answer

A. \(7x^4+0x^5-3x+1\)

Explanation

Simple Explanation

\(0x^5\) पद घात नहीं बढ़ाता क्योंकि उसका गुणांक (0) है। सबसे बड़ा शून्येतर घात (4) है। / The term \(0x^5\) does not affect degree because its coefficient is (0). The highest non-zero power is (4).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(x^2+ax+b\) के शून्यक (4) और (-7) हैं, तो (a-b) क्या होगा?

If the zeroes of \(x^2+ax+b\) are (4) and (-7), what is (a-b)?

Explanation opens after your attempt
Correct Answer

B. (31)

Explanation

Simple Explanation

योग (-3) है इसलिए (a=3) और गुणनफल (-28) है इसलिए (b=-28)। अतः (a-b=31) है। / The sum is (-3), so (a=3), and the product is (-28), so (b=-28). Hence (a-b=31).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

द्विघात बहुपद जिसके शून्यक \(\frac{2}{3}\) और \(-\frac{5}{4}\) हैं, कौन सा हो सकता है?

Which can be a quadratic polynomial whose zeroes are \(\frac{2}{3}\) and \(-\frac{5}{4}\)?

Explanation opens after your attempt
Correct Answer

A. \(12x^2+7x-10\)

Explanation

Simple Explanation

शून्यकों का योग \(-\frac{7}{12}\) और गुणनफल \(-\frac{5}{6}\) है। इसलिए \(12x^2+7x-10\) सही है। / The sum is \(-\frac{7}{12}\) and the product is \(-\frac{5}{6}\). So \(12x^2+7x-10\) is correct.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x-3+px-2+qx-6) के शून्यक (1), (2) और (3) हैं, तो (p+q) का सही मान क्या है?

If the zeroes of (p(x)=x-3+px-2+qx-6) are (1), (2), and (3), what is the correct value of (p+q)?

Explanation opens after your attempt
Correct Answer

A. (5)

Explanation

Simple Explanation

((x-1)(x-2)(x-3)=x-3-6x-2+11x-6) से (p=-6) और (q=11)। अतः (p+q=5) है। / From ((x-1)(x-2)(x-3)=x-3-6x-2+11x-6), (p=-6) and (q=11). Hence (p+q=5).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x-3+px-2+qx-6) के शून्यक (1), (2) और (3) हैं, तो (p+q) का मान क्या है?

If the zeroes of (p(x)=x-3+px-2+qx-6) are (1), (2), and (3), what is (p+q)?

Explanation opens after your attempt
Correct Answer

A. (-5)

Explanation

Simple Explanation

बहुपद ((x-1)(x-2)(x-3)=x-3-6x-2+11x-6) है। इसलिए (p=-6), (q=11) और (p+q=5) नहीं बल्कि (5) है। / The polynomial is ((x-1)(x-2)(x-3)=x-3-6x-2+11x-6). Hence (p=-6), (q=11), so (p+q=5).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

बहुपद \(x^3-4x^2+x+6\) में (x=2) रखने पर क्या निष्कर्ष निकलेगा?

What conclusion follows when (x=2) is substituted in \(x^3-4x^2+x+6\)?

Explanation opens after your attempt
Correct Answer

A. (2) शून्यक है(2) is a zero

Explanation

Simple Explanation

(p(2)=8-16+2+6=0) है इसलिए (2) शून्यक है। सीधे प्रतिस्थापन से जल्दी जांच होती है। / (p(2)=8-16+2+6=0), so (2) is a zero. Direct substitution is the quickest check.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि \(x^2-9x+k\) के शून्यक बराबर हैं, तो (k) का मान क्या है?

If the zeroes of \(x^2-9x+k\) are equal, what is the value of (k)?

Explanation opens after your attempt
Correct Answer

C. \(\frac{81}{4}\)

Explanation

Simple Explanation

बराबर शून्यकों के लिए विविक्तकर \(b^2-4ac=0\) होता है। इसलिए (81-4k=0) से \(k=\frac{81}{4}\) मिलता है। / For equal zeroes, the discriminant \(b^2-4ac=0\). Thus (81-4k=0), giving \(k=\frac{81}{4}\).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

द्विघात बहुपद \(2x^2-7x+3\) के शून्यकों का गुणनफल क्या है?

What is the product of the zeroes of the quadratic polynomial \(2x^2-7x+3\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{3}{2}\)

Explanation

Simple Explanation

द्विघात \(ax^2+bx+c\) में गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{3}{2}\) सही है। / For \(ax^2+bx+c\), the product is \(\frac{c}{a}\). Here, \(\frac{3}{2}\) is correct.

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=x-2-(m+3)x+12) के शून्यक (3) और (4) हैं, तो (m) का मान क्या है?

If the zeroes of (p(x)=x-2-(m+3)x+12) are (3) and (4), what is (m)?

Explanation opens after your attempt
Correct Answer

B. (4)

Explanation

Simple Explanation

शून्यकों का योग (7) है और यह (m+3) के बराबर है। इसलिए (m=4) मिलेगा। / The sum of zeroes is (7), which equals (m+3). Therefore, (m=4).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

यदि (p(x)=kx-2-5x+6) का एक शून्यक (2) है, तो (k) का मान क्या होगा?

If (2) is a zero of (p(x)=kx-2-5x+6), what is the value of (k)?

Explanation opens after your attempt
Correct Answer

A. (1)

Explanation

Simple Explanation

(p(2)=0) रखने पर (4k-10+6=0) से (k=1) मिलता है। शून्यक के लिए (p\(\alpha\)=0) लगाएं। / Putting (p(2)=0) gives (4k-10+6=0), so (k=1). For a zero, use (p\(\alpha\)=0).

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Question Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 46

बहुपद (p(x)=ax-3+bx-2+cx+d) में \(a\ne0\) है। यदि (p(x)) को रैखिक बहुपद कहा जाए, तो यह कथन क्यों गलत है?

In the polynomial (p(x)=ax-3+bx-2+cx+d), \(a\ne0\). Why is it wrong to call (p(x)) a linear polynomial?

Explanation opens after your attempt
Correct Answer

C. क्योंकि घात (3) हैBecause degree is (3)

Explanation

Simple Explanation

सबसे बड़ी घात (3) है इसलिए बहुपद घन है। परीक्षा में हमेशा सबसे बड़े शून्येतर घातांक को देखें। / The highest power is (3), so the polynomial is cubic. In exams, always check the highest non-zero exponent.

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_n=17n+c\) और \(a_7=145\) है तो \(a_{3r}=757\) होने पर (r) क्या है?

If \(a_n=17n+c\) and \(a_7=145\), what is (r) when \(a_{3r}=757\)?

Explanation opens after your attempt
Correct Answer

B. (14)

Explanation

Simple Explanation

(145=119+c) से (c=26)। (757=51r+26) से \(r=\frac{731}{51}\) आता है इसलिए विकल्पों की जांच जरूरी है। / From (145=119+c), (c=26). (757=51r+26), giving \(r=\frac{731}{51}\), so option checking is necessary.

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_n=11n-5\) है तो \(a_{4k}-a_k=198\) के लिए (k) क्या होगा?

If \(a_n=11n-5\), what is (k) for \(a_{4k}-a_k=198\)?

Explanation opens after your attempt
Correct Answer

C. (6)

Explanation

Simple Explanation

(a_{4k}-a_k=(44k-5)-(11k-5)=33k)। (33k=198) से (k=6)। / (a_{4k}-a_k=(44k-5)-(11k-5)=33k). From (33k=198), (k=6).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

समान्तर श्रेणी में \(a_{5n}=205\), \(a_n=49\) और (d=13) है। (n) क्या है?

In an AP, \(a_{5n}=205\), \(a_n=49\), and (d=13). What is (n)?

Explanation opens after your attempt
Correct Answer

A. (3)

Explanation

Simple Explanation

\(a_{5n}-a_n=4nd=156\)। (52n=156) से (n=3)। / \(a_{5n}-a_n=4nd=156\). From (52n=156), (n=3).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

एक समान्तर श्रेणी में \(a_5=27\) और \(a_{17}=111\) है। \(a_{5r}\) का मान (195) है तो (r) क्या है?

In an AP, \(a_5=27\) and \(a_{17}=111\). If \(a_{5r}=195\), what is (r)?

Explanation opens after your attempt
Correct Answer

A. (5)

Explanation

Simple Explanation

\(d=\frac{111-27}{12}=7\)। (195=27+(5r-5)7) से (5r=29) इसलिए \(r=\frac{29}{5}\)। / \(d=\frac{111-27}{12}=7\). From (195=27+(5r-5)7), (5r=29), so \(r=\frac{29}{5}\).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

यदि \(a_n=4n+9\) और \(a_m=137\) है तो \(a_{m+15}\) क्या होगा?

If \(a_n=4n+9\) and \(a_m=137\), what is \(a_{m+15}\)?

Explanation opens after your attempt
Correct Answer

C. (197)

Explanation

Simple Explanation

(4m+9=137) से (m=32)। \(a_{47}=4\times47+9=197\)। / From (4m+9=137), (m=32). \(a_{47}=4\times47+9=197\).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

किसी समान्तर श्रेणी में \(a_p=42\), \(a_{p+12}=150\) और (p=9) है। \(a_{40}\) क्या होगा?

In an AP, \(a_p=42\), \(a_{p+12}=150\), and (p=9). What is \(a_{40}\)?

Explanation opens after your attempt
Correct Answer

A. (321)

Explanation

Simple Explanation

(12d=108) से (d=9)। \(a_{40}=a_9+31d=42+279=321\)। / From (12d=108), (d=9). \(a_{40}=a_9+31d=42+279=321\).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 66

किसी समान्तर श्रेणी में \(a_{4m}=156\), \(a_m=48\) और (d=6) है। (m) का मान क्या है?

In an AP, \(a_{4m}=156\), \(a_m=48\), and (d=6). What is the value of (m)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{4m}-a_m=3md=108\) है। (18m=108) से (m=6)। / \(a_{4m}-a_m=3md=108\). From (18m=108), (m=6).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_n=13n+c\) और \(a_6=101\) है तो \(a_{4r}=465\) होने पर (r) क्या है?

If \(a_n=13n+c\) and \(a_6=101\), what is (r) when \(a_{4r}=465\)?

Explanation opens after your attempt
Correct Answer

B. (9)

Explanation

Simple Explanation

(101=78+c) से (c=23)। (465=52r+23) से \(r=\frac{442}{52}=8.5\)। / From (101=78+c), (c=23). (465=52r+23), so \(r=\frac{442}{52}=8.5\).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_n=9n+2\) है तो \(a_{3k}-a_k=144\) के लिए (k) क्या होगा?

If \(a_n=9n+2\), what is (k) for \(a_{3k}-a_k=144\)?

Explanation opens after your attempt
Correct Answer

C. (8)

Explanation

Simple Explanation

(a_{3k}-a_k=(27k+2)-(9k+2)=18k)। (18k=144) से (k=8)। / (a_{3k}-a_k=(27k+2)-(9k+2)=18k). From (18k=144), (k=8).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

समान्तर श्रेणी में \(a_{4n}=140\), \(a_n=32\) और (d=6) है। (n) क्या है?

In an AP, \(a_{4n}=140\), \(a_n=32\), and (d=6). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{4n}-a_n=3nd=108\)। (18n=108) से (n=6)। / \(a_{4n}-a_n=3nd=108\). From (18n=108), (n=6).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

एक समान्तर श्रेणी में \(a_4=18\) और \(a_{16}=78\) है। \(a_{4r}\) का मान (138) है तो (r) क्या है?

In an AP, \(a_4=18\) and \(a_{16}=78\). If \(a_{4r}=138\), what is (r)?

Explanation opens after your attempt
Correct Answer

A. (7)

Explanation

Simple Explanation

\(d=\frac{78-18}{12}=5\)। (138=18+(4r-4)5) से (4r=28) इसलिए (r=7)। / \(d=\frac{78-18}{12}=5\). From (138=18+(4r-4)5), (4r=28), so (r=7).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

यदि \(a_n=3n+4\) और \(a_m=91\) है तो \(a_{m+12}\) क्या होगा?

If \(a_n=3n+4\) and \(a_m=91\), what is \(a_{m+12}\)?

Explanation opens after your attempt
Correct Answer

C. (127)

Explanation

Simple Explanation

(3m+4=91) से (m=29)। \(a_{41}=3\times41+4=127\)। / From (3m+4=91), (m=29). \(a_{41}=3\times41+4=127\).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

किसी समान्तर श्रेणी में \(a_p=29\), \(a_{p+10}=99\) और (p=8) है। \(a_{35}\) क्या होगा?

In an AP, \(a_p=29\), \(a_{p+10}=99\), and (p=8). What is \(a_{35}\)?

Explanation opens after your attempt
Correct Answer

A. (218)

Explanation

Simple Explanation

(10d=70) से (d=7)। \(a_{35}=a_8+27d=29+189=218\)। / From (10d=70), (d=7). \(a_{35}=a_8+27d=29+189=218\).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 65

किसी समान्तर श्रेणी में \(a_{3m}=94\), \(a_m=34\) और (d=5) है। (m) का मान क्या है?

In an AP, \(a_{3m}=94\), \(a_m=34\), and (d=5). What is the value of (m)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{3m}-a_m=2md=60\) है। (10m=60) से (m=6)। / \(a_{3m}-a_m=2md=60\). From (10m=60), (m=6).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{n}=11n+c\) और \(a_{5}=72\) है तो \(a_{5r}\) का मान (512) होने पर (r) क्या है?

If \(a_n=11n+c\) and \(a_5=72\), what is (r) when \(a_{5r}=512\)?

Explanation opens after your attempt
Correct Answer

B. (9)

Explanation

Simple Explanation

(72=55+c) से (c=17)। (512=55r+17) से (r=9)। / From (72=55+c), (c=17). From (512=55r+17), (r=9).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_n=7n-4\) है तो \(a_{2k}-a_k=84\) के लिए (k) क्या होगा?

If \(a_n=7n-4\), what is (k) for \(a_{2k}-a_k=84\)?

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Correct Answer

C. (12)

Explanation

Simple Explanation

(a_{2k}-a_k=(14k-4)-(7k-4)=7k)। (7k=84) से (k=12)। / (a_{2k}-a_k=(14k-4)-(7k-4)=7k). From (7k=84), (k=12).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

समान्तर श्रेणी में \(a_{3n}=81\), \(a_n=21\) और (d=5) है। (n) क्या है?

In an AP, \(a_{3n}=81\), \(a_n=21\), and (d=5). What is (n)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

\(a_{3n}-a_n=2nd=60\)। (10n=60) से (n=6)। / \(a_{3n}-a_n=2nd=60\). From (10n=60), (n=6).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

एक समान्तर श्रेणी में \(a_3=11\) और \(a_{13}=51\) है। \(a_{3r}\) का मान (91) है तो (r) क्या है?

In an AP, \(a_3=11\) and \(a_{13}=51\). If \(a_{3r}=91\), what is (r)?

Explanation opens after your attempt
Correct Answer

C. (7)

Explanation

Simple Explanation

\(d=\frac{51-11}{10}=4\)। (91=11+(3r-3)4) से (3r=21) इसलिए (r=7)। / \(d=\frac{51-11}{10}=4\). From (91=11+(3r-3)4), (3r=21), so (r=7).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

यदि \(a_{n}=2n-1\) और \(a_m=63\) है तो \(a_{m+10}\) क्या होगा?

If \(a_n=2n-1\) and \(a_m=63\), what is \(a_{m+10}\)?

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Correct Answer

B. (83)

Explanation

Simple Explanation

(2m-1=63) से (m=32)। \(a_{42}=2\times42-1=83\)। / From (2m-1=63), (m=32). \(a_{42}=2\times42-1=83\).

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Question Hard Mathematics Arithmetic Progressions (AP) Finding the $n$th term of an AP Class 10 Level 64

किसी समान्तर श्रेणी में \(a_{p}=17\), \(a_{p+8}=65\) और (p=6) है। \(a_{30}\) क्या होगा?

In an AP, \(a_p=17\), \(a_{p+8}=65\), and (p=6). What is \(a_{30}\)?

Explanation opens after your attempt
Correct Answer

B. (161)

Explanation

Simple Explanation

(8d=48) से (d=6)। \(a_{30}=a_6+24d=17+144=161\)। / From (8d=48), (d=6). \(a_{30}=a_6+24d=17+144=161\).

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Question Hard Art Education Fundamentals of Visual Arts Elements of Art Class 10 Level 7

यदि कोई उत्तर केवल रंग का नाम बताता है तो hard level में क्या कमी है?

If an answer only names the colour what is lacking at hard level?

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Correct Answer

A. रंग का प्रभाव संदर्भ और प्रमाणColour effect context and evidence

Explanation

Simple Explanation

Hard level में रंग का असर भी समझाना चाहिए। परीक्षा में colour name से आगे mood लिखें। / At hard level colour effect should also be explained. Exam tip: write mood beyond colour name.

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