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Mathematics Quiz - Class 10 Mathematics Hard Level 47 Quiz

Question 1/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=(a-5)x^-5+2x^-3-7x+4) की घात (3) है, तो (a) क्या होगा?

If the degree of (p(x)=(a-5)x^-5+2x^-3-7x+4) is (3), what is (a)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

For the degree to be (3), the coefficient of \(x^5\) must be (0), so (a-5=0). First make the highest-degree term vanish.

Step 2

Why this answer is correct

The correct answer is C. (5). For the degree to be (3), the coefficient of \(x^5\) must be (0), so (a-5=0). First make the highest-degree term vanish.

Step 3

Exam Tip

घात (3) होने के लिए \(x^5\) का गुणांक (0) होना चाहिए, इसलिए (a-5=0)। उच्चतम घात वाले पद को पहले शून्य करें।

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Question 2/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=kx^-2-5x+6) और (p(-1)=14), तो (k) का मान क्या है?

If (p(x)=kx^-2-5x+6) and (p(-1)=14), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

(p(-1)=k+5+6=14), so (k=3). Check signs carefully while substituting a negative value.

Step 2

Why this answer is correct

The correct answer is C. (3). (p(-1)=k+5+6=14), so (k=3). Check signs carefully while substituting a negative value.

Step 3

Exam Tip

(p(-1)=k+5+6=14), इसलिए (k=3)। ऋणात्मक मान रखते समय संकेत सावधानी से देखें।

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Question 3/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=3x^-3-2x^-2+5x-1) और (q(x)=-x^-3+7x^-2-4x+6) के योग में \(x^2\) का गुणांक क्या है?

What is the coefficient of \(x^2\) in the sum of (p(x)=3x^-3-2x^-2+5x-1) and (q(x)=-x^-3+7x^-2-4x+6)?

Explanation opens after your attempt

Correct Answer

B. (5)

Step 1

Concept

The coefficients of \(x^2\) are (-2) and (7), whose sum is (5). Add only coefficients of like powers.

Step 2

Why this answer is correct

The correct answer is B. (5). The coefficients of \(x^2\) are (-2) and (7), whose sum is (5). Add only coefficients of like powers.

Step 3

Exam Tip

\(x^2\) के गुणांक (-2) और (7) हैं, जिनका योग (5) है। समान घात के गुणांक ही जोड़ें।

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Question 4/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=4x^-4-3x^-2+2) और (q(x)=-4x^-4+5x^-3+x-8) के योग की घात क्या है?

What is the degree of the sum of (p(x)=4x^-4-3x^-2+2) and (q(x)=-4x^-4+5x^-3+x-8)?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

The \(x^4\)-terms cancel and the highest remaining power is (3). Recheck the degree after addition.

Step 2

Why this answer is correct

The correct answer is C. (3). The \(x^4\)-terms cancel and the highest remaining power is (3). Recheck the degree after addition.

Step 3

Exam Tip

\(x^4\) के पद कट जाते हैं और सबसे बड़ी बची घात (3) है। जोड़ के बाद घात फिर से जांचें।

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Question 5/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)) की घात (4) और (q(x)) की घात (3) है, तो सामान्यतः (p(x)q(x)) की घात क्या होगी?

If the degree of (p(x)) is (4) and the degree of (q(x)) is (3), what will generally be the degree of (p(x)q(x))?

Explanation opens after your attempt

Correct Answer

B. (7)

Step 1

Concept

In the product of two non-zero polynomials, degrees add, so (4+3=7). Remember degree addition in multiplication.

Step 2

Why this answer is correct

The correct answer is B. (7). In the product of two non-zero polynomials, degrees add, so (4+3=7). Remember degree addition in multiplication.

Step 3

Exam Tip

दो अशून्य बहुपदों के गुणन में घातें जुड़ती हैं, इसलिए (4+3=7)। गुणन में घातों का योग याद रखें।

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Question 6/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

((x-2)\(3x^2+4x-5\)) में \(x^2\) का गुणांक क्या है?

What is the coefficient of \(x^2\) in ((x-2)\(3x^2+4x-5\))?

Explanation opens after your attempt

Correct Answer

B. (-2)

Step 1

Concept

((x-2)\(3x^2+4x-5\)=3x^-3-2x^-2-13x+10), so the coefficient of \(x^2\) is (-2). Combine like terms after expansion.

Step 2

Why this answer is correct

The correct answer is B. (-2). ((x-2)\(3x^2+4x-5\)=3x^-3-2x^-2-13x+10), so the coefficient of \(x^2\) is (-2). Combine like terms after expansion.

Step 3

Exam Tip

((x-2)\(3x^2+4x-5\)=3x^-3-2x^-2-13x+10), इसलिए \(x^2\) का गुणांक (-2) है। विस्तार में समान पद मिलाएं।

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Question 7/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (x=3), बहुपद (p(x)=x^-2-kx+12) का शून्य है, तो (k) क्या है?

If (x=3) is a zero of (p(x)=x^-2-kx+12), what is (k)?

Explanation opens after your attempt

Correct Answer

C. (7)

Step 1

Concept

(p(3)=9-3k+12=0), so (21=3k) and (k=7). For a zero, set the polynomial value equal to (0).

Step 2

Why this answer is correct

The correct answer is C. (7). (p(3)=9-3k+12=0), so (21=3k) and (k=7). For a zero, set the polynomial value equal to (0).

Step 3

Exam Tip

(p(3)=9-3k+12=0), इसलिए (21=3k) और (k=7)। शून्य की शर्त में बहुपद का मान (0) रखें।

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Question 8/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=2x^-3-9x^-2+12x-5) के लिए (p(2)) का मान क्या है?

What is the value of (p(2)) for (p(x)=2x^-3-9x^-2+12x-5)?

Explanation opens after your attempt

Correct Answer

A. (-1)

Step 1

Concept

(p(2)=16-36+24-5=-1). Evaluate each term separately and then add.

Step 2

Why this answer is correct

The correct answer is A. (-1). (p(2)=16-36+24-5=-1). Evaluate each term separately and then add.

Step 3

Exam Tip

(p(2)=16-36+24-5=-1)। प्रत्येक पद का मान अलग निकालकर जोड़ें।

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Question 9/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

किस मान के लिए (p(x)=x^-3-4x^-2+mx+6) में (p(1)=0) होगा?

For what value of (m) will (p(1)=0) in (p(x)=x^-3-4x^-2+mx+6)?

Explanation opens after your attempt

Correct Answer

A. (-3)

Step 1

Concept

(p(1)=1-4+m+6=m+3), so (m=-3). Substitute the given value and form a simple equation.

Step 2

Why this answer is correct

The correct answer is A. (-3). (p(1)=1-4+m+6=m+3), so (m=-3). Substitute the given value and form a simple equation.

Step 3

Exam Tip

(p(1)=1-4+m+6=m+3), इसलिए (m=-3)। दिए गए मान को रखकर सरल समीकरण बनाएं।

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Question 10/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=x^-4-2x^-2+1) में (p(-1)) का मान क्या है?

What is the value of (p(-1)) in (p(x)=x^-4-2x^-2+1)?

Explanation opens after your attempt

Correct Answer

B. (0)

Step 1

Concept

(p(-1)=1-2+1=0). Even powers of a negative number become positive.

Step 2

Why this answer is correct

The correct answer is B. (0). (p(-1)=1-2+1=0). Even powers of a negative number become positive.

Step 3

Exam Tip

(p(-1)=1-2+1=0)। सम घातों में ऋणात्मक संख्या का मान धनात्मक हो जाता है।

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Question 11/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

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

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

Explanation opens after your attempt

Correct Answer

C. (1)

Step 1

Concept

The conditions give (1+a+b=0) and (4+2a+b=0), so (a=-3), (b=2), and (a+b=-1). The correct option is (-1).

Step 2

Why this answer is correct

The correct answer is C. (1). The conditions give (1+a+b=0) and (4+2a+b=0), so (a=-3), (b=2), and (a+b=-1). The correct option is (-1).

Step 3

Exam Tip

शर्तों से (1+a+b=0) और (4+2a+b=0), इसलिए (a=-3), (b=2) और (a+b=-1)। सही विकल्प (-1) है।

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Question 12/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-2+ax+b), (p(1)=0) और (p(3)=0), तो (b) का मान क्या है?

If (p(x)=x^-2+ax+b), (p(1)=0), and (p(3)=0), what is the value of (b)?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

With zeros (1) and (3), the polynomial is ((x-1)(x-3)=x^-2-4x+3). Hence (b=3).

Step 2

Why this answer is correct

The correct answer is C. (3). With zeros (1) and (3), the polynomial is ((x-1)(x-3)=x^-2-4x+3). Hence (b=3).

Step 3

Exam Tip

शून्य (1) और (3) होने पर बहुपद ((x-1)(x-3)=x^-2-4x+3) है। इसलिए (b=3)।

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Question 13/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

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

Which expression is not a polynomial in (x) though it looks similar to a quadratic?

Explanation opens after your attempt

Correct Answer

C. \(x^2+\frac{1}{x}+4\)

Step 1

Concept

\(x^2+\frac{1}{x}+4\) contains \(x^{-1}\), which is not allowed in a polynomial. Be careful when the variable is in the denominator.

Step 2

Why this answer is correct

The correct answer is C. \(x^2+\frac{1}{x}+4\). \(x^2+\frac{1}{x}+4\) contains \(x^{-1}\), which is not allowed in a polynomial. Be careful when the variable is in the denominator.

Step 3

Exam Tip

\(x^2+\frac{1}{x}+4\) में \(x^{-1}\) है, जो बहुपद में मान्य नहीं है। हर में चर हो तो सावधान रहें।

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Question 14/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=ax^-3+bx^-2+cx+d) में (a=0) और \(b\ne0\), तो (p(x)) की घात क्या होगी?

If (a=0) and \(b\ne0\) in (p(x)=ax^-3+bx^-2+cx+d), what will be the degree of (p(x))?

Explanation opens after your attempt

Correct Answer

C. (2)

Step 1

Concept

Since (a=0), the \(x^3\)-term vanishes, and since \(b\ne0\), the \(x^2\)-term remains. So the degree is (2).

Step 2

Why this answer is correct

The correct answer is C. (2). Since (a=0), the \(x^3\)-term vanishes, and since \(b\ne0\), the \(x^2\)-term remains. So the degree is (2).

Step 3

Exam Tip

(a=0) होने से \(x^3\) पद हट जाता है और \(b\ne0\) होने से \(x^2\) पद बचता है। इसलिए घात (2) है।

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Question 15/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=5x^-3-2x^-2+x-4) में सभी गुणांकों का योग क्या है?

What is the sum of all coefficients in (p(x)=5x^-3-2x^-2+x-4)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

The sum of all coefficients is (5-2+1-4=0). It is also equal to (p(1)).

Step 2

Why this answer is correct

The correct answer is A. (0). The sum of all coefficients is (5-2+1-4=0). It is also equal to (p(1)).

Step 3

Exam Tip

सभी गुणांकों का योग (5-2+1-4=0) है। यह (p(1)) के बराबर भी होता है।

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Question 16/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि बहुपद (p(x)=2x^-3+kx^-2-8x+3) में सभी गुणांकों का योग (0) है, तो (k) क्या है?

If the sum of all coefficients of (p(x)=2x^-3+kx^-2-8x+3) is (0), what is (k)?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

The sum of coefficients is (2+k-8+3=k-3), so (k=3). The sum of coefficients can also be found by (p(1)).

Step 2

Why this answer is correct

The correct answer is C. (3). The sum of coefficients is (2+k-8+3=k-3), so (k=3). The sum of coefficients can also be found by (p(1)).

Step 3

Exam Tip

गुणांकों का योग (2+k-8+3=k-3) है, इसलिए (k=3)। गुणांकों का योग (p(1)) से भी मिलता है।

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Question 17/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=3x^-4-5x^-2+2x-7) में विषम घात वाले पदों के गुणांकों का योग क्या है?

What is the sum of coefficients of the odd-power terms in (p(x)=3x^-4-5x^-2+2x-7)?

Explanation opens after your attempt

Correct Answer

C. (2)

Step 1

Concept

The only odd-power term is (2x), so the sum is (2). Do not treat \(x^0\) as an odd power.

Step 2

Why this answer is correct

The correct answer is C. (2). The only odd-power term is (2x), so the sum is (2). Do not treat \(x^0\) as an odd power.

Step 3

Exam Tip

विषम घात वाला केवल (2x) पद है, इसलिए योग (2) है। \(x^0\) को विषम घात न मानें।

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Question 18/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

((2x-3)\(x^2+x+1\)) में अचर पद क्या है?

What is the constant term in ((2x-3)\(x^2+x+1\))?

Explanation opens after your attempt

Correct Answer

A. (-3)

Step 1

Concept

The constant term comes only from ((-3)\cdot1=-3). For the constant term, multiply the constant parts.

Step 2

Why this answer is correct

The correct answer is A. (-3). The constant term comes only from ((-3)\cdot1=-3). For the constant term, multiply the constant parts.

Step 3

Exam Tip

अचर पद केवल ((-3)\cdot1=-3) से आता है। अचर पद के लिए अचर पदों का गुणन देखें।

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Question 19/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

((x+4)²-(x-4)²) का सरल बहुपद रूप क्या है?

What is the simplified polynomial form of ((x+4)²-(x-4)²)?

Explanation opens after your attempt

Correct Answer

B. (16x)

Step 1

Concept

((x+4)²-(x-4)²=16x). Use the identity (a^-2-b^-2=(a-b)(a+b)) for a quick solution.

Step 2

Why this answer is correct

The correct answer is B. (16x). ((x+4)²-(x-4)²=16x). Use the identity (a^-2-b^-2=(a-b)(a+b)) for a quick solution.

Step 3

Exam Tip

((x+4)²-(x-4)²=16x)। पहचान (a^-2-b^-2=(a-b)(a+b)) से जल्दी हल करें।

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Question 20/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-3+px+q), (p(1)=4) और (p(-1)=-2), तो (p) का मान क्या है?

If (p(x)=x^-3+px+q), (p(1)=4), and (p(-1)=-2), what is the value of (p)?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

The conditions give (1+p+q=4) and (-1-p+q=-2), so (p=2). Subtracting the two equations is quick.

Step 2

Why this answer is correct

The correct answer is B. (2). The conditions give (1+p+q=4) and (-1-p+q=-2), so (p=2). Subtracting the two equations is quick.

Step 3

Exam Tip

शर्तों से (1+p+q=4) और (-1-p+q=-2), इसलिए (p=2)। दो समीकरणों को घटाना तेज तरीका है।

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Question 21/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-3+rx^-2+s), (p(0)=5) और (p(1)=9), तो (r) क्या है?

If (p(x)=x^-3+rx^-2+s), (p(0)=5), and (p(1)=9), what is (r)?

Explanation opens after your attempt

Correct Answer

C. (3)

Step 1

Concept

(p(0)=s=5) and (p(1)=1+r+5=9), so (r=3). First use (x=0) to find the constant term.

Step 2

Why this answer is correct

The correct answer is C. (3). (p(0)=s=5) and (p(1)=1+r+5=9), so (r=3). First use (x=0) to find the constant term.

Step 3

Exam Tip

(p(0)=s=5) और (p(1)=1+r+5=9), इसलिए (r=3)। पहले (x=0) से अचर पद निकालें।

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Question 22/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

किस मान के लिए ((m+1)x^-2+(m^-2)x+7) अचर बहुपद बन सकता है?

For what value of (m) can ((m+1)x^-2+(m^-2)x+7) become a constant polynomial?

Explanation opens after your attempt

Correct Answer

C. ऐसा कोई मान नहींNo such value

Step 1

Concept

For a constant polynomial, both (m+1=0) and (m^-2=0) are needed, which is impossible together. All variable terms must vanish.

Step 2

Why this answer is correct

The correct answer is C. ऐसा कोई मान नहीं / No such value. For a constant polynomial, both (m+1=0) and (m^-2=0) are needed, which is impossible together. All variable terms must vanish.

Step 3

Exam Tip

अचर बहुपद के लिए (m+1=0) और (m^-2=0) दोनों चाहिए, जो साथ संभव नहीं हैं। सभी चर वाले पद हटने चाहिए।

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Question 23/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-2+2x-8), तो (p(3)-p(-2)) का मान क्या है?

If (p(x)=x^-2+2x-8), what is the value of (p(3)-p(-2))?

Explanation opens after your attempt

Correct Answer

D. (15)

Step 1

Concept

(p(3)=7) and (p(-2)=-8), so the difference is (15). Find both values separately before subtracting.

Step 2

Why this answer is correct

The correct answer is D. (15). (p(3)=7) and (p(-2)=-8), so the difference is (15). Find both values separately before subtracting.

Step 3

Exam Tip

(p(3)=7) और (p(-2)=-8), इसलिए अंतर (15) है। दोनों मान अलग निकालकर ही घटाएं।

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Question 24/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

कौन सा विकल्प (p(x)=x^-3-8) के लिए (p(2)=0) को सही सिद्ध करता है?

Which option correctly proves (p(2)=0) for (p(x)=x^-3-8)?

Explanation opens after your attempt

Correct Answer

A. \(2^3-8=0\)

Step 1

Concept

(p(2)=2³-8=8-8=0). To prove a zero, substitute the correct value in the correct place.

Step 2

Why this answer is correct

The correct answer is A. \(2^3-8=0\). (p(2)=2³-8=8-8=0). To prove a zero, substitute the correct value in the correct place.

Step 3

Exam Tip

(p(2)=2³-8=8-8=0)। शून्य सिद्ध करने के लिए सही मान को सही जगह रखें।

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Question 25/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

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

What is (p(-1)) for (p(x)=x^-3+x^-2+x+1)?

Explanation opens after your attempt

Correct Answer

B. (0)

Step 1

Concept

(p(-1)=-1+1-1+1=0). Add alternating signs in order.

Step 2

Why this answer is correct

The correct answer is B. (0). (p(-1)=-1+1-1+1=0). Add alternating signs in order.

Step 3

Exam Tip

(p(-1)=-1+1-1+1=0)। वैकल्पिक संकेतों को क्रम से जोड़ें।

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Question 26/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=2x^-2+bx+c), (p(0)=5) और (p(1)=1), तो (b) क्या है?

If (p(x)=2x^-2+bx+c), (p(0)=5), and (p(1)=1), what is (b)?

Explanation opens after your attempt

Correct Answer

A. (-6)

Step 1

Concept

(p(0)=c=5) and (p(1)=2+b+5=1), so (b=-6). The constant term is found quickly from (x=0).

Step 2

Why this answer is correct

The correct answer is A. (-6). (p(0)=c=5) and (p(1)=2+b+5=1), so (b=-6). The constant term is found quickly from (x=0).

Step 3

Exam Tip

(p(0)=c=5) और (p(1)=2+b+5=1), इसलिए (b=-6)। (x=0) से अचर पद तुरंत मिलता है।

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Question 27/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=x^-2-5x+6) में (p(2)+p(3)) का मान क्या है?

What is the value of (p(2)+p(3)) for (p(x)=x^-2-5x+6)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

(p(2)=0) and (p(3)=0), so the sum is (0). Both values are zeros of the polynomial.

Step 2

Why this answer is correct

The correct answer is A. (0). (p(2)=0) and (p(3)=0), so the sum is (0). Both values are zeros of the polynomial.

Step 3

Exam Tip

(p(2)=0) और (p(3)=0), इसलिए योग (0) है। दोनों मान बहुपद के शून्य हैं।

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Question 28/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-2-9), तो (p(a)=0) होने के लिए (a) का कौन सा मान सही है?

If (p(x)=x^-2-9), which value of (a) is correct for (p(a)=0)?

Explanation opens after your attempt

Correct Answer

C. (a=3)

Step 1

Concept

(p(3)=9-9=0). The zeros of \(x^2-9\) are (3) and (-3).

Step 2

Why this answer is correct

The correct answer is C. (a=3). (p(3)=9-9=0). The zeros of \(x^2-9\) are (3) and (-3).

Step 3

Exam Tip

(p(3)=9-9=0)। \(x^2-9\) के शून्य (3) और (-3) हैं।

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Question 29/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=4x^-2-12x+9) में कौन सा मान शून्य है?

Which value is a zero of (p(x)=4x^-2-12x+9)?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(p\left\(\frac{3}{2}\right\)=9-18+9=0). While using a fraction, square and multiply correctly.

Step 2

Why this answer is correct

The correct answer is B. \(\frac{3}{2}\). (p\left\(\frac{3}{2}\right\)=9-18+9=0). While using a fraction, square and multiply correctly.

Step 3

Exam Tip

(p\left\(\frac{3}{2}\right\)=9-18+9=0)। भिन्न मान रखते समय वर्ग और गुणा सही करें।

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Question 30/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-3+ax^-2+bx+6) में (x=1) और (x=-2) दोनों शून्य हैं, तो (a-b) क्या है?

If (x=1) and (x=-2) are both zeros of (p(x)=x^-3+ax^-2+bx+6), what is (a-b)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

The conditions give (a+b=-7) and (4a-2b=2), so (a=-2), (b=-5), and (a-b=3). The correct value is (3).

Step 2

Why this answer is correct

The correct answer is C. (4). The conditions give (a+b=-7) and (4a-2b=2), so (a=-2), (b=-5), and (a-b=3). The correct value is (3).

Step 3

Exam Tip

शर्तों से (a+b=-7) और (4a-2b=2), इसलिए (a=-2), (b=-5) और (a-b=3)। सही गणना से (a-b=3) मिलता है।

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Question 31/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-3+ax^-2+bx+4) में (x=1) और (x=-1) दोनों शून्य हैं, तो (a) क्या है?

If (x=1) and (x=-1) are both zeros of (p(x)=x^-3+ax^-2+bx+4), what is (a)?

Explanation opens after your attempt

Correct Answer

A. (-4)

Step 1

Concept

(p(1)=1+a+b+4=0) and (p(-1)=-1+a-b+4=0); adding gives (2a+8=0), so (a=-4). Add signs carefully.

Step 2

Why this answer is correct

The correct answer is A. (-4). (p(1)=1+a+b+4=0) and (p(-1)=-1+a-b+4=0); adding gives (2a+8=0), so (a=-4). Add signs carefully.

Step 3

Exam Tip

(p(1)=1+a+b+4=0) और (p(-1)=-1+a-b+4=0), इसलिए (2a+4=0) नहीं बल्कि जोड़ने पर (2a+8=0), अतः (a=-4)। संकेतों को सावधानी से जोड़ें।

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Question 32/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(\(x^2-1\)\(x^2+1\)) का विस्तृत रूप क्या है?

What is the expanded form of (\(x^2-1\)\(x^2+1\))?

Explanation opens after your attempt

Correct Answer

A. \(x^4-1\)

Step 1

Concept

This is the identity \(a^2-b^2\), so (\(x^2\)²-1²=x^-4-1). Identities make expansion faster.

Step 2

Why this answer is correct

The correct answer is A. \(x^4-1\). This is the identity \(a^2-b^2\), so (\(x^2\)²-1²=x^-4-1). Identities make expansion faster.

Step 3

Exam Tip

यह \(a^2-b^2\) की पहचान है, इसलिए (\(x^2\)²-1²=x^-4-1)। पहचान से विस्तार तेज होता है।

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Question 33/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=2x^-4-3x^-3+5x-9) में \(x^2\) का गुणांक क्या है?

What is the coefficient of \(x^2\) in (p(x)=2x^-4-3x^-3+5x-9)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

The \(x^2\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^2\).

Step 2

Why this answer is correct

The correct answer is A. (0). The \(x^2\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^2\).

Step 3

Exam Tip

\(x^2\) का पद अनुपस्थित है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^2\) मानें।

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Question 34/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=mx^-3+(m^-1)x^-2+2x+1) की घात (2) है, तो (m) क्या है?

If the degree of (p(x)=mx^-3+(m^-1)x^-2+2x+1) is (2), what is (m)?

Explanation opens after your attempt

Correct Answer

A. (0)

Step 1

Concept

For degree (2), the coefficient of \(x^3\) must be (0) and the coefficient of \(x^2\) must be non-zero. Both conditions hold when (m=0).

Step 2

Why this answer is correct

The correct answer is A. (0). For degree (2), the coefficient of \(x^3\) must be (0) and the coefficient of \(x^2\) must be non-zero. Both conditions hold when (m=0).

Step 3

Exam Tip

घात (2) के लिए \(x^3\) का गुणांक (0) चाहिए और \(x^2\) का गुणांक अशून्य चाहिए। (m=0) पर ये दोनों शर्तें पूरी होती हैं।

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Question 35/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=3x^-2-2x+1), तो (p(x)+p(-x)) क्या होगा?

If (p(x)=3x^-2-2x+1), what is (p(x)+p(-x))?

Explanation opens after your attempt

Correct Answer

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

Step 1

Concept

(p(-x)=3x^-2+2x+1), so the sum is \(6x^2+2\). Odd-power terms change signs when (x) is replaced by (-x).

Step 2

Why this answer is correct

The correct answer is A. \(6x^2+2\). (p(-x)=3x^-2+2x+1), so the sum is \(6x^2+2\). Odd-power terms change signs when (x) is replaced by (-x).

Step 3

Exam Tip

(p(-x)=3x^-2+2x+1), इसलिए योग \(6x^2+2\) है। (x) को (-x) से बदलते समय विषम घात के संकेत बदलते हैं।

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Question 36/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-3-4x), तो (p(-2)+p(2)) का मान क्या है?

If (p(x)=x^-3-4x), what is the value of (p(-2)+p(2))?

Explanation opens after your attempt

Correct Answer

B. (0)

Step 1

Concept

(p(-2)=0) and (p(2)=0), so the sum is (0). It behaves like an odd polynomial.

Step 2

Why this answer is correct

The correct answer is B. (0). (p(-2)=0) and (p(2)=0), so the sum is (0). It behaves like an odd polynomial.

Step 3

Exam Tip

(p(-2)=0) और (p(2)=0), इसलिए योग (0) है। यह विषम बहुपद जैसा व्यवहार करता है।

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Question 37/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=x^-2+4x+5) का न्यूनतम मान किस (x) पर आता है?

At which (x) does (p(x)=x^-2+4x+5) attain its minimum value?

Explanation opens after your attempt

Correct Answer

B. (x=-2)

Step 1

Concept

(x^-2+4x+5=(x+2)²+1), so the minimum occurs at (x=-2). Completing the square is useful.

Step 2

Why this answer is correct

The correct answer is B. (x=-2). (x^-2+4x+5=(x+2)²+1), so the minimum occurs at (x=-2). Completing the square is useful.

Step 3

Exam Tip

(x^-2+4x+5=(x+2)²+1), इसलिए न्यूनतम (x=-2) पर आता है। वर्ग पूर्ण करना उपयोगी तरीका है।

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Question 38/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=x^-2-6x+10) का न्यूनतम मान क्या है?

What is the minimum value of (p(x)=x^-2-6x+10)?

Explanation opens after your attempt

Correct Answer

A. (1)

Step 1

Concept

(x^-2-6x+10=(x-3)²+1), so the minimum value is (1). A square term is never negative.

Step 2

Why this answer is correct

The correct answer is A. (1). (x^-2-6x+10=(x-3)²+1), so the minimum value is (1). A square term is never negative.

Step 3

Exam Tip

(x^-2-6x+10=(x-3)²+1), इसलिए न्यूनतम मान (1) है। वर्ग पद कभी ऋणात्मक नहीं होता।

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Question 39/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-2+kx+9) पूर्ण वर्ग बहुपद है और (k>0), तो (k) क्या है?

If (p(x)=x^-2+kx+9) is a perfect square polynomial and (k>0), what is (k)?

Explanation opens after your attempt

Correct Answer

B. (6)

Step 1

Concept

For (x^-2+kx+9=(x+3)²), (k=6). In a perfect square, the middle term is (2ab).

Step 2

Why this answer is correct

The correct answer is B. (6). For (x^-2+kx+9=(x+3)²), (k=6). In a perfect square, the middle term is (2ab).

Step 3

Exam Tip

(x^-2+kx+9=(x+3)²) होने पर (k=6)। पूर्ण वर्ग में मध्य पद (2ab) होता है।

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Question 40/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

कौन सा बहुपद पूर्ण वर्ग है?

Which polynomial is a perfect square?

Explanation opens after your attempt

Correct Answer

A. \(x^2+10x+25\)

Step 1

Concept

(x^-2+10x+25=(x+5)²). Check the squares of first and last terms and the middle term (2ab).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+10x+25\). (x^-2+10x+25=(x+5)²). Check the squares of first and last terms and the middle term (2ab).

Step 3

Exam Tip

(x^-2+10x+25=(x+5)²) है। पहले और अंतिम पद के वर्ग तथा मध्य पद (2ab) को जांचें।

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Question 41/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-3-3x^-2+3x-1), तो (p(2)) क्या है?

If (p(x)=x^-3-3x^-2+3x-1), what is (p(2))?

Explanation opens after your attempt

Correct Answer

B. (1)

Step 1

Concept

It is ((x-1)³), so (p(2)=(2-1)³=1). Recognizing identities reduces calculation.

Step 2

Why this answer is correct

The correct answer is B. (1). It is ((x-1)³), so (p(2)=(2-1)³=1). Recognizing identities reduces calculation.

Step 3

Exam Tip

यह ((x-1)³) है, इसलिए (p(2)=(2-1)³=1)। पहचान पहचानने से गणना कम होती है।

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Question 42/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=2x^-3+x^-2-5x+2) में (p(1)) और (p(-1)) का गुणनफल क्या है?

What is the product of (p(1)) and (p(-1)) for (p(x)=2x^-3+x^-2-5x+2)?

Explanation opens after your attempt

Correct Answer

A. (-12)

Step 1

Concept

(p(1)=2+1-5+2=0), and (p(-1)=-2+1+5+2=6), so the product is (0). The correct option is (0).

Step 2

Why this answer is correct

The correct answer is A. (-12). (p(1)=2+1-5+2=0), and (p(-1)=-2+1+5+2=6), so the product is (0). The correct option is (0).

Step 3

Exam Tip

(p(1)=0) नहीं बल्कि (2+1-5+2=0), और (p(-1)=-2+1+5+2=6), इसलिए गुणनफल (0) है। सही विकल्प (0) है।

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Question 43/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

(p(x)=2x^-3+x^-2-5x+2) में (p(2)) और (p(-1)) का अंतर (p(2)-p(-1)) क्या है?

For (p(x)=2x^-3+x^-2-5x+2), what is the difference (p(2)-p(-1))?

Explanation opens after your attempt

Correct Answer

D. (6)

Step 1

Concept

(p(2)=16+4-10+2=12) and (p(-1)=-2+1+5+2=6), so the difference is (6). Find both values separately.

Step 2

Why this answer is correct

The correct answer is D. (6). (p(2)=16+4-10+2=12) and (p(-1)=-2+1+5+2=6), so the difference is (6). Find both values separately.

Step 3

Exam Tip

(p(2)=16+4-10+2=12) और (p(-1)=-2+1+5+2=6), इसलिए अंतर (6) है। दोनों मान अलग निकालें।

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Question 44/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-2+px+q) और (p(0)=6), (p(2)=0), तो (p) का मान क्या है?

If (p(x)=x^-2+px+q) and (p(0)=6), (p(2)=0), what is the value of (p)?

Explanation opens after your attempt

Correct Answer

A. (-5)

Step 1

Concept

(p(0)=q=6) and (p(2)=4+2p+6=0), so (p=-5). Find the constant term first.

Step 2

Why this answer is correct

The correct answer is A. (-5). (p(0)=q=6) and (p(2)=4+2p+6=0), so (p=-5). Find the constant term first.

Step 3

Exam Tip

(p(0)=q=6) और (p(2)=4+2p+6=0), इसलिए (p=-5)। पहले अचर पद निकालें।

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Question 45/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-3+ax^-2+bx) में (p(0)=0), तो इससे कौन सा निष्कर्ष निश्चित है?

If (p(x)=x^-3+ax^-2+bx) has (p(0)=0), which conclusion is certain?

Explanation opens after your attempt

Correct Answer

A. (0) इसका शून्य है(0) is its zero

Step 1

Concept

Since (p(0)=0), (0) is a zero of the polynomial. It does not fix the values of (a) or (b).

Step 2

Why this answer is correct

The correct answer is A. (0) इसका शून्य है / (0) is its zero. Since (p(0)=0), (0) is a zero of the polynomial. It does not fix the values of (a) or (b).

Step 3

Exam Tip

(p(0)=0) होने से (0) बहुपद का शून्य है। इससे (a) या (b) का मान निश्चित नहीं होता।

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Question 46/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

कौन सा बहुपद (x=0) को शून्य नहीं बनाता?

Which polynomial does not make (x=0) a zero?

Explanation opens after your attempt

Correct Answer

D. \(x^2+1\)

Step 1

Concept

On substituting (x=0), \(x^2+1=1\), so (0) is not its zero. The constant term is decisive at (x=0).

Step 2

Why this answer is correct

The correct answer is D. \(x^2+1\). On substituting (x=0), \(x^2+1=1\), so (0) is not its zero. The constant term is decisive at (x=0).

Step 3

Exam Tip

(x=0) रखने पर \(x^2+1=1\), इसलिए (0) इसका शून्य नहीं है। (x=0) पर अचर पद निर्णायक होता है।

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Question 47/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-2-2x+3), तो (p(x+1)) क्या होगा?

If (p(x)=x^-2-2x+3), what is (p(x+1))?

Explanation opens after your attempt

Correct Answer

A. \(x^2+2\)

Step 1

Concept

(p(x+1)=(x+1)²-2(x+1)+3=x^-2+2). Substitute the whole (x+1) in place of (x).

Step 2

Why this answer is correct

The correct answer is A. \(x^2+2\). (p(x+1)=(x+1)²-2(x+1)+3=x^-2+2). Substitute the whole (x+1) in place of (x).

Step 3

Exam Tip

(p(x+1)=(x+1)²-2(x+1)+3=x^-2+2)। (x) की जगह पूरा (x+1) रखें।

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Question 48/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=2x^-2+3x-4), तो (p(2x)) क्या है?

If (p(x)=2x^-2+3x-4), what is (p(2x))?

Explanation opens after your attempt

Correct Answer

A. \(8x^2+6x-4\)

Step 1

Concept

(p(2x)=2(2x)²+3(2x)-4=8x^-2+6x-4). Square the whole (2x).

Step 2

Why this answer is correct

The correct answer is A. \(8x^2+6x-4\). (p(2x)=2(2x)²+3(2x)-4=8x^-2+6x-4). Square the whole (2x).

Step 3

Exam Tip

(p(2x)=2(2x)²+3(2x)-4=8x^-2+6x-4)। पूरे (2x) का वर्ग करें।

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Question 49/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

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

If (p(x)=x^-2-4x+1), what is (p(x)-p(1))?

Explanation opens after your attempt

Correct Answer

A. \(x^2-4x+4\)

Step 1

Concept

(p(1)=1-4+1=-2), so (p(x)-p(1)=x^-2-4x+3). None of the listed choices matches this value.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x+4\). (p(1)=1-4+1=-2), so (p(x)-p(1)=x^-2-4x+3). None of the listed choices matches this value.

Step 3

Exam Tip

(p(1)=1-4+1=-2), इसलिए (p(x)-p(1)=x^-2-4x+3) नहीं बल्कि \(x^2-4x+3\) है। सही गणना से विकल्पों में कोई नहीं होता।

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Question 50/50 Hard Mathematics Polynomials Polynomials in one variable Class 10 Level 47

यदि (p(x)=x^-2+ax+b), (p(2)=3) और (p(-1)=6), तो (a+b) का मान क्या है?

If (p(x)=x^-2+ax+b), (p(2)=3), and (p(-1)=6), what is the value of (a+b)?

Explanation opens after your attempt

Correct Answer

C. (1)

Step 1

Concept

The conditions give (2a+b=-1) and (-a+b=5), so (a=-2), (b=3), and (a+b=1). When two values are given, form two equations.

Step 2

Why this answer is correct

The correct answer is C. (1). The conditions give (2a+b=-1) and (-a+b=5), so (a=-2), (b=3), and (a+b=1). When two values are given, form two equations.

Step 3

Exam Tip

शर्तों से (2a+b=-1) और (-a+b=5) मिलते हैं, इसलिए (a=-2), (b=3) और (a+b=1)। दो मान दिए हों तो दो समीकरण बनाएं।

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Class 10 Mathematics Hard Quiz

यदि (p(x)=(a-5)x-5+2x-3-7x+4) की घात (3) है, तो (a) क्या होगा?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=kx-2-5x+6) और (p(-1)=14), तो (k) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

(p(x)=3x-3-2x-2+5x-1) और (q(x)=-x-3+7x-2-4x+6) के योग में \(x^2\) का गुणांक क्या है?

Concept

Why this answer is correct

Exam Tip

(p(x)=4x-4-3x-2+2) और (q(x)=-4x-4+5x-3+x-8) के योग की घात क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)) की घात (4) और (q(x)) की घात (3) है, तो सामान्यतः (p(x)q(x)) की घात क्या होगी?

Concept

Why this answer is correct

Exam Tip

((x-2)\(3x^2+4x-5\)) में \(x^2\) का गुणांक क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (x=3), बहुपद (p(x)=x-2-kx+12) का शून्य है, तो (k) क्या है?

Concept

Why this answer is correct

Exam Tip

(p(x)=2x-3-9x-2+12x-5) के लिए (p(2)) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

किस मान के लिए (p(x)=x-3-4x-2+mx+6) में (p(1)=0) होगा?

Concept

Why this answer is correct

Exam Tip

(p(x)=x-4-2x-2+1) में (p(-1)) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-2+ax+b), (p(1)=0) और (p(3)=0), तो (b) का मान क्या है?

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=ax-3+bx-2+cx+d) में (a=0) और \(b\ne0\), तो (p(x)) की घात क्या होगी?

Concept

Why this answer is correct

Exam Tip

(p(x)=5x-3-2x-2+x-4) में सभी गुणांकों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

यदि बहुपद (p(x)=2x-3+kx-2-8x+3) में सभी गुणांकों का योग (0) है, तो (k) क्या है?

Concept

Why this answer is correct

Exam Tip

(p(x)=3x-4-5x-2+2x-7) में विषम घात वाले पदों के गुणांकों का योग क्या है?

Concept

Why this answer is correct

Exam Tip

((2x-3)\(x^2+x+1\)) में अचर पद क्या है?

Concept

Why this answer is correct

Exam Tip

((x+4)2-(x-4)2) का सरल बहुपद रूप क्या है?

Concept

Why this answer is correct

Exam Tip

यदि (p(x)=x-3+px+q), (p(1)=4) और (p(-1)=-2), तो (p) का मान क्या है?

Concept

Why this answer is correct

यदि (p(x)=(a-5)x^-5+2x^-3-7x+4) की घात (3) है, तो (a) क्या होगा?

यदि (p(x)=kx^-2-5x+6) और (p(-1)=14), तो (k) का मान क्या है?

(p(x)=3x^-3-2x^-2+5x-1) और (q(x)=-x^-3+7x^-2-4x+6) के योग में \(x^2\) का गुणांक क्या है?

(p(x)=4x^-4-3x^-2+2) और (q(x)=-4x^-4+5x^-3+x-8) के योग की घात क्या है?

यदि (x=3), बहुपद (p(x)=x^-2-kx+12) का शून्य है, तो (k) क्या है?

(p(x)=2x^-3-9x^-2+12x-5) के लिए (p(2)) का मान क्या है?

किस मान के लिए (p(x)=x^-3-4x^-2+mx+6) में (p(1)=0) होगा?

(p(x)=x^-4-2x^-2+1) में (p(-1)) का मान क्या है?

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

यदि (p(x)=x^-2+ax+b), (p(1)=0) और (p(3)=0), तो (b) का मान क्या है?

यदि (p(x)=ax^-3+bx^-2+cx+d) में (a=0) और \(b\ne0\), तो (p(x)) की घात क्या होगी?

(p(x)=5x^-3-2x^-2+x-4) में सभी गुणांकों का योग क्या है?

यदि बहुपद (p(x)=2x^-3+kx^-2-8x+3) में सभी गुणांकों का योग (0) है, तो (k) क्या है?

(p(x)=3x^-4-5x^-2+2x-7) में विषम घात वाले पदों के गुणांकों का योग क्या है?

((x+4)²-(x-4)²) का सरल बहुपद रूप क्या है?

यदि (p(x)=x^-3+px+q), (p(1)=4) और (p(-1)=-2), तो (p) का मान क्या है?

यदि (p(x)=x^-3+rx^-2+s), (p(0)=5) और (p(1)=9), तो (r) क्या है?

किस मान के लिए ((m+1)x^-2+(m^-2)x+7) अचर बहुपद बन सकता है?

यदि (p(x)=x^-2+2x-8), तो (p(3)-p(-2)) का मान क्या है?

कौन सा विकल्प (p(x)=x^-3-8) के लिए (p(2)=0) को सही सिद्ध करता है?

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

यदि (p(x)=2x^-2+bx+c), (p(0)=5) और (p(1)=1), तो (b) क्या है?

(p(x)=x^-2-5x+6) में (p(2)+p(3)) का मान क्या है?

यदि (p(x)=x^-2-9), तो (p(a)=0) होने के लिए (a) का कौन सा मान सही है?

(p(x)=4x^-2-12x+9) में कौन सा मान शून्य है?

यदि (p(x)=x^-3+ax^-2+bx+6) में (x=1) और (x=-2) दोनों शून्य हैं, तो (a-b) क्या है?

यदि (p(x)=x^-3+ax^-2+bx+4) में (x=1) और (x=-1) दोनों शून्य हैं, तो (a) क्या है?

(p(x)=2x^-4-3x^-3+5x-9) में \(x^2\) का गुणांक क्या है?

यदि (p(x)=mx^-3+(m^-1)x^-2+2x+1) की घात (2) है, तो (m) क्या है?

यदि (p(x)=3x^-2-2x+1), तो (p(x)+p(-x)) क्या होगा?

यदि (p(x)=x^-3-4x), तो (p(-2)+p(2)) का मान क्या है?

(p(x)=x^-2+4x+5) का न्यूनतम मान किस (x) पर आता है?

(p(x)=x^-2-6x+10) का न्यूनतम मान क्या है?