Class 9 Mathematics - Introduction to Polynomials - Algebraic expressions Expert Quiz

Mathematics Introduction to Polynomials Algebraic expressions Expert Class 9 Level 24

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Question 1/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

(3x-2-2x+7-\(x^2+5x-4\)) को सरल करने पर क्या मिलेगा?

What is obtained after simplifying (3x-2-2x+7-\(x^2+5x-4\))?

Explanation opens after your attempt
Correct Answer

B. \(2x^2-7x+11\)

Step 1

Concept

Signs inside change when the bracket is subtracted. The simplified form is \(3x^2-2x+7-x^2-5x+4=2x^2-7x+11\).

Step 2

Why this answer is correct

The correct answer is B. \(2x^2-7x+11\). Signs inside change when the bracket is subtracted. The simplified form is \(3x^2-2x+7-x^2-5x+4=2x^2-7x+11\).

Step 3

Exam Tip

कोष्ठक हटाते समय अंदर के चिन्ह बदलते हैं। सरल रूप \(3x^2-2x+7-x^2-5x+4=2x^2-7x+11\) है।

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Question 2/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (x=-1) हो, तो \(2x^4-3x^3+x-5\) का मान क्या होगा?

If (x=-1), what is the value of \(2x^4-3x^3+x-5\)?

Explanation opens after your attempt
Correct Answer

D. (-1)

Step 1

Concept

Even powers give positive values and odd powers keep the negative sign. The value is (2(1)-3(-1)-1-5=-1).

Step 2

Why this answer is correct

The correct answer is D. (-1). Even powers give positive values and odd powers keep the negative sign. The value is (2(1)-3(-1)-1-5=-1).

Step 3

Exam Tip

सम घात में मान धनात्मक और विषम घात में ऋणात्मक रहता है। मान (2(1)-3(-1)-1-5=-1) है।

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Question 3/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(6a^2b+2ab^2-4a^2b+9ab^2\) को सरल करने पर क्या मिलेगा?

What is obtained after simplifying \(6a^2b+2ab^2-4a^2b+9ab^2\)?

Explanation opens after your attempt
Correct Answer

C. \(2a^2b+11ab^2\)

Step 1

Concept

Terms with \(a^2b\) and \(ab^2\) combine separately. Therefore, the result is \(2a^2b+11ab^2\).

Step 2

Why this answer is correct

The correct answer is C. \(2a^2b+11ab^2\). Terms with \(a^2b\) and \(ab^2\) combine separately. Therefore, the result is \(2a^2b+11ab^2\).

Step 3

Exam Tip

\(a^2b\) वाले पद और \(ab^2\) वाले पद अलग-अलग मिलते हैं। इसलिए परिणाम \(2a^2b+11ab^2\) है।

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Question 4/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि ((k-2)x+5x) का सरल रूप (9x) है, तो (k) का मान क्या होगा?

If the simplified form of ((k-2)x+5x) is (9x), what is the value of (k)?

Explanation opens after your attempt
Correct Answer

B. (6)

Step 1

Concept

Combining like terms gives ((k-2+5)x=(k+3)x). From (k+3=9), (k=6).

Step 2

Why this answer is correct

The correct answer is B. (6). Combining like terms gives ((k-2+5)x=(k+3)x). From (k+3=9), (k=6).

Step 3

Exam Tip

समान पद मिलाने पर ((k-2+5)x=(k+3)x) मिलता है। (k+3=9) से (k=6) होगा।

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Question 5/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (x-y=8) और (x+y=14), तो (x) का मान क्या होगा?

If (x-y=8) and (x+y=14), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

C. (11)

Step 1

Concept

Adding the two given expressions gives (2x=22). Therefore, (x=11).

Step 2

Why this answer is correct

The correct answer is C. (11). Adding the two given expressions gives (2x=22). Therefore, (x=11).

Step 3

Exam Tip

दोनों दिए हुए व्यंजकों को जोड़ने पर (2x=22) मिलता है। इसलिए (x=11) है।

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Question 6/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

(4(3p-2q)-2(5p+q)+7q) को सरल करने पर क्या मिलेगा?

What is obtained after simplifying (4(3p-2q)-2(5p+q)+7q)?

Explanation opens after your attempt
Correct Answer

A. (2p-3q)

Step 1

Concept

Expanding gives (12p-8q-10p-2q+7q). Combining like terms gives (2p-3q).

Step 2

Why this answer is correct

The correct answer is A. (2p-3q). Expanding gives (12p-8q-10p-2q+7q). Combining like terms gives (2p-3q).

Step 3

Exam Tip

खोलने पर (12p-8q-10p-2q+7q) मिलता है। समान पद मिलाकर (2p-3q) बनेगा।

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Question 7/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (m=2) और (n=-3), तो \(2m^2n+mn^2\) का मान क्या होगा?

If (m=2) and (n=-3), what is the value of \(2m^2n+mn^2\)?

Explanation opens after your attempt
Correct Answer

B. (-6)

Step 1

Concept

(2m-2n=2(4)(-3)=-24) and (mn-2=2(9)=18). The total value is (-6).

Step 2

Why this answer is correct

The correct answer is B. (-6). (2m-2n=2(4)(-3)=-24) and (mn-2=2(9)=18). The total value is (-6).

Step 3

Exam Tip

(2m-2n=2(4)(-3)=-24) और (mn-2=2(9)=18) है। कुल मान (-6) है।

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Question 8/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

कौन-सा व्यंजक (a) और (b) के योग के वर्ग में से (ab) का (3) गुना घटाने को दर्शाता है?

Which expression represents subtracting (3) times (ab) from the square of the sum of (a) and (b)?

Explanation opens after your attempt
Correct Answer

C. ((a+b)2-3ab)

Step 1

Concept

First square the sum (a+b), then subtract (3ab). Therefore, ((a+b)2-3ab) is correct.

Step 2

Why this answer is correct

The correct answer is C. ((a+b)2-3ab). First square the sum (a+b), then subtract (3ab). Therefore, ((a+b)2-3ab) is correct.

Step 3

Exam Tip

पहले योग (a+b) का वर्ग लिया जाएगा और फिर (3ab) घटेगा। इसलिए ((a+b)2-3ab) सही है।

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Question 9/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(8x^2y-5xy^2-3x^2y+7xy^2\) में \(xy^2\) का गुणांक सरल करने के बाद क्या होगा?

After simplifying \(8x^2y-5xy^2-3x^2y+7xy^2\), what will be the coefficient of \(xy^2\)?

Explanation opens after your attempt
Correct Answer

A. (2)

Step 1

Concept

The \(xy^2\) terms are \(-5xy^2\) and \(7xy^2\). Their sum is \(2xy^2\).

Step 2

Why this answer is correct

The correct answer is A. (2). The \(xy^2\) terms are \(-5xy^2\) and \(7xy^2\). Their sum is \(2xy^2\).

Step 3

Exam Tip

\(xy^2\) वाले पद \(-5xy^2\) और \(7xy^2\) हैं। इनका योग \(2xy^2\) है।

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Question 10/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

(5x-(2x-(4x+3))) को सरल करने पर क्या मिलेगा?

What is obtained after simplifying (5x-(2x-(4x+3)))?

Explanation opens after your attempt
Correct Answer

C. (7x+3)

Step 1

Concept

Inside, (2x-(4x+3)=-2x-3). Hence (5x-(-2x-3)=7x+3).

Step 2

Why this answer is correct

The correct answer is C. (7x+3). Inside, (2x-(4x+3)=-2x-3). Hence (5x-(-2x-3)=7x+3).

Step 3

Exam Tip

अंदर (2x-(4x+3)=-2x-3) है। इसलिए (5x-(-2x-3)=7x+3)।

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Question 11/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (x=2) पर \(kx^2-5x+3\) का मान (9) है, तो (k) क्या होगा?

If the value of \(kx^2-5x+3\) at (x=2) is (9), what is (k)?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

Substitution gives (4k-10+3=9). Thus (4k=16) and (k=4).

Step 2

Why this answer is correct

The correct answer is C. (4). Substitution gives (4k-10+3=9). Thus (4k=16) and (k=4).

Step 3

Exam Tip

मान रखने पर (4k-10+3=9) मिलता है। इससे (4k=16) और (k=4) होगा।

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Question 12/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

किस विकल्प में \(x^2yz\) के समान पदों का सही समूह है?

Which option gives the correct group of like terms of \(x^2yz\)?

Explanation opens after your attempt
Correct Answer

A. \(3x^2yz\), \(-7x^2yz\), \(11x^2yz\)

Step 1

Concept

Like terms have exactly the same variables and powers. In the first option, every term has variable part \(x^2yz\).

Step 2

Why this answer is correct

The correct answer is A. \(3x^2yz\), \(-7x^2yz\), \(11x^2yz\). Like terms have exactly the same variables and powers. In the first option, every term has variable part \(x^2yz\).

Step 3

Exam Tip

समान पदों में चर और उनकी घातें बिल्कुल समान होती हैं। पहले विकल्प में सभी पदों का चर भाग \(x^2yz\) है।

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Question 13/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

(2a-2+3ab-b-2-\(a^2-4ab+2b^2\)) को सरल करने पर क्या मिलेगा?

What is obtained after simplifying (2a-2+3ab-b-2-\(a^2-4ab+2b^2\))?

Explanation opens after your attempt
Correct Answer

B. \(a^2+7ab-3b^2\)

Step 1

Concept

Signs change in the subtracted bracket. The simplified form is \(2a^2+3ab-b^2-a^2+4ab-2b^2=a^2+7ab-3b^2\).

Step 2

Why this answer is correct

The correct answer is B. \(a^2+7ab-3b^2\). Signs change in the subtracted bracket. The simplified form is \(2a^2+3ab-b^2-a^2+4ab-2b^2=a^2+7ab-3b^2\).

Step 3

Exam Tip

घटाने वाले कोष्ठक के चिन्ह बदलेंगे। सरल रूप \(2a^2+3ab-b^2-a^2+4ab-2b^2=a^2+7ab-3b^2\) है।

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Question 14/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (x+y=9) और (xy=14), तो (2(x+y)+3xy) का मान क्या होगा?

If (x+y=9) and (xy=14), what is the value of (2(x+y)+3xy)?

Explanation opens after your attempt
Correct Answer

C. (60)

Step 1

Concept

Substitute the given whole expressions directly. (2(9)+3(14)=18+42=60).

Step 2

Why this answer is correct

The correct answer is C. (60). Substitute the given whole expressions directly. (2(9)+3(14)=18+42=60).

Step 3

Exam Tip

दिए हुए पूरे व्यंजकों को सीधे रखें। (2(9)+3(14)=18+42=60)।

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Question 15/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

(3r(r+2)-2r(4-r)) को सरल करने पर क्या मिलेगा?

What is obtained after simplifying (3r(r+2)-2r(4-r))?

Explanation opens after your attempt
Correct Answer

A. \(5r^2-2r\)

Step 1

Concept

(3r(r+2)=3r-2+6r) and (-2r(4-r)=-8r+2r-2). The total is \(5r^2-2r\).

Step 2

Why this answer is correct

The correct answer is A. \(5r^2-2r\). (3r(r+2)=3r-2+6r) and (-2r(4-r)=-8r+2r-2). The total is \(5r^2-2r\).

Step 3

Exam Tip

(3r(r+2)=3r-2+6r) और (-2r(4-r)=-8r+2r-2) है। कुल \(5r^2-2r\) मिलेगा।

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Question 16/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(7p^2q-2pq+5pq-4p^2q+9\) को सरल करने पर कितने पद रहेंगे?

How many terms remain after simplifying \(7p^2q-2pq+5pq-4p^2q+9\)?

Explanation opens after your attempt
Correct Answer

B. (3)

Step 1

Concept

The simplified form is \(3p^2q+3pq+9\). It has three terms.

Step 2

Why this answer is correct

The correct answer is B. (3). The simplified form is \(3p^2q+3pq+9\). It has three terms.

Step 3

Exam Tip

सरल रूप \(3p^2q+3pq+9\) है। इसमें तीन पद रहेंगे।

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Question 17/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

किस व्यंजक में (m) की घात (2) और (n) की घात (3) है?

In which expression is the power of (m) equal to (2) and the power of (n) equal to (3)?

Explanation opens after your attempt
Correct Answer

B. \(m^2n^3\)

Step 1

Concept

In \(m^2n^3\), the power of (m) is (2) and the power of (n) is (3). Check each variable's power separately.

Step 2

Why this answer is correct

The correct answer is B. \(m^2n^3\). In \(m^2n^3\), the power of (m) is (2) and the power of (n) is (3). Check each variable's power separately.

Step 3

Exam Tip

\(m^2n^3\) में (m) की घात (2) और (n) की घात (3) है। हर चर की घात अलग देखें।

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Question 18/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (x=-2) और (y=4), तो \(x^2y-xy^2\) का मान क्या होगा?

If (x=-2) and (y=4), what is the value of \(x^2y-xy^2\)?

Explanation opens after your attempt
Correct Answer

A. (48)

Step 1

Concept

(x-2y=4(4)=16) and (xy-2=(-2)(16)=-32). Therefore, (16-(-32)=48).

Step 2

Why this answer is correct

The correct answer is A. (48). (x-2y=4(4)=16) and (xy-2=(-2)(16)=-32). Therefore, (16-(-32)=48).

Step 3

Exam Tip

(x-2y=4(4)=16) और (xy-2=(-2)(16)=-32) है। इसलिए (16-(-32)=48)।

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Question 19/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(6x^2-3x+2\) और \(-2x^2+7x-9\) का योग क्या होगा?

What is the sum of \(6x^2-3x+2\) and \(-2x^2+7x-9\)?

Explanation opens after your attempt
Correct Answer

A. \(4x^2+4x-7\)

Step 1

Concept

Adding like terms gives \(6x^2-2x^2=4x^2\), (-3x+7x=4x), and (2-9=-7).

Step 2

Why this answer is correct

The correct answer is A. \(4x^2+4x-7\). Adding like terms gives \(6x^2-2x^2=4x^2\), (-3x+7x=4x), and (2-9=-7).

Step 3

Exam Tip

समान पद जोड़ने पर \(6x^2-2x^2=4x^2\), (-3x+7x=4x), और (2-9=-7)।

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Question 20/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (3x+2=17), तो \(x^2-1\) का मान क्या होगा?

If (3x+2=17), what is the value of \(x^2-1\)?

Explanation opens after your attempt
Correct Answer

B. (24)

Step 1

Concept

From (3x=15), (x=5). Therefore, \(x^2-1=25-1=24\).

Step 2

Why this answer is correct

The correct answer is B. (24). From (3x=15), (x=5). Therefore, \(x^2-1=25-1=24\).

Step 3

Exam Tip

(3x=15) से (x=5) है। इसलिए \(x^2-1=25-1=24\)।

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Question 21/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

कौन-सा पद \(4a^3b^2\) का समान पद है?

Which term is a like term of \(4a^3b^2\)?

Explanation opens after your attempt
Correct Answer

B. \(-5a^3b^2\)

Step 1

Concept

A like term must have the same variable part \(a^3b^2\). \(-5a^3b^2\) has the same variable part.

Step 2

Why this answer is correct

The correct answer is B. \(-5a^3b^2\). A like term must have the same variable part \(a^3b^2\). \(-5a^3b^2\) has the same variable part.

Step 3

Exam Tip

समान पद में चर भाग \(a^3b^2\) ही होना चाहिए। \(-5a^3b^2\) का चर भाग समान है।

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Question 22/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

(4x-2-5xy+2y-2-\(x^2+3xy-6y^2\)) को सरल करने पर क्या मिलेगा?

What is obtained after simplifying (4x-2-5xy+2y-2-\(x^2+3xy-6y^2\))?

Explanation opens after your attempt
Correct Answer

A. \(3x^2-8xy+8y^2\)

Step 1

Concept

When the bracket is subtracted, all inside signs change. The simplified form is \(3x^2-8xy+8y^2\).

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-8xy+8y^2\). When the bracket is subtracted, all inside signs change. The simplified form is \(3x^2-8xy+8y^2\).

Step 3

Exam Tip

कोष्ठक घटाने पर सभी अंदरूनी चिन्ह बदलते हैं। सरल रूप \(3x^2-8xy+8y^2\) है।

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Question 23/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (a-b=5) और (a+b=13), तो (b) का मान क्या होगा?

If (a-b=5) and (a+b=13), what is the value of (b)?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

Subtracting the first expression from the second gives (2b=8). Therefore, (b=4).

Step 2

Why this answer is correct

The correct answer is A. (4). Subtracting the first expression from the second gives (2b=8). Therefore, (b=4).

Step 3

Exam Tip

दूसरे व्यंजक में से पहला घटाने पर (2b=8) मिलता है। इसलिए (b=4) है।

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Question 24/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(2x^3-5x^2+x+7\) में \(x^2\) का गुणांक क्या है?

What is the coefficient of \(x^2\) in \(2x^3-5x^2+x+7\)?

Explanation opens after your attempt
Correct Answer

B. (-5)

Step 1

Concept

The term containing \(x^2\) is \(-5x^2\). Therefore, the coefficient is (-5).

Step 2

Why this answer is correct

The correct answer is B. (-5). The term containing \(x^2\) is \(-5x^2\). Therefore, the coefficient is (-5).

Step 3

Exam Tip

\(x^2\) वाला पद \(-5x^2\) है। इसलिए गुणांक (-5) है।

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Question 25/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

(3(2x+y)-4(x-2y)+x) को सरल करने पर (y) का गुणांक क्या होगा?

After simplifying (3(2x+y)-4(x-2y)+x), what will be the coefficient of (y)?

Explanation opens after your attempt
Correct Answer

C. (11)

Step 1

Concept

The simplified form is (6x+3y-4x+8y+x=3x+11y). So the coefficient of (y) is (11).

Step 2

Why this answer is correct

The correct answer is C. (11). The simplified form is (6x+3y-4x+8y+x=3x+11y). So the coefficient of (y) is (11).

Step 3

Exam Tip

सरल रूप (6x+3y-4x+8y+x=3x+11y) है। इसलिए (y) का गुणांक (11) है।

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Question 26/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

किस व्यंजक में कुल घात (6) है?

Which expression has total degree (6)?

Explanation opens after your attempt
Correct Answer

A. \(x^2y^4\)

Step 1

Concept

In \(x^2y^4\), the total degree is (2+4=6). Add powers in a multivariable term.

Step 2

Why this answer is correct

The correct answer is A. \(x^2y^4\). In \(x^2y^4\), the total degree is (2+4=6). Add powers in a multivariable term.

Step 3

Exam Tip

\(x^2y^4\) में कुल घात (2+4=6) है। बहु-चर पद में घातों को जोड़ें।

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Question 27/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (x+y=4) और (x-y=2), तो \(x^2-y^2\) का मान क्या होगा?

If (x+y=4) and (x-y=2), what is the value of \(x^2-y^2\)?

Explanation opens after your attempt
Correct Answer

C. (8)

Step 1

Concept

(x-2-y-2=(x-y)(x+y)). Therefore, the value is \(2\cdot4=8\).

Step 2

Why this answer is correct

The correct answer is C. (8). (x-2-y-2=(x-y)(x+y)). Therefore, the value is \(2\cdot4=8\).

Step 3

Exam Tip

(x-2-y-2=(x-y)(x+y)) होता है। इसलिए मान \(2\cdot4=8\) है।

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Question 28/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(5u^2v-3uv+2u^2v+6uv-4\) को सरल करने पर क्या मिलेगा?

What is obtained after simplifying \(5u^2v-3uv+2u^2v+6uv-4\)?

Explanation opens after your attempt
Correct Answer

A. \(7u^2v+3uv-4\)

Step 1

Concept

\(5u^2v+2u^2v=7u^2v\) and (-3uv+6uv=3uv). The constant term (-4) remains separate.

Step 2

Why this answer is correct

The correct answer is A. \(7u^2v+3uv-4\). \(5u^2v+2u^2v=7u^2v\) and (-3uv+6uv=3uv). The constant term (-4) remains separate.

Step 3

Exam Tip

\(5u^2v+2u^2v=7u^2v\) और (-3uv+6uv=3uv)। स्थिर पद (-4) अलग रहेगा।

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Question 29/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (x=-3), तो \(\frac{x^3+2x^2-6}{x}\) का मान क्या होगा?

If (x=-3), what is the value of \(\frac{x^3+2x^2-6}{x}\)?

Explanation opens after your attempt
Correct Answer

A. (5)

Step 1

Concept

The numerator is ((-27)+18-6=-15). Then \(\frac{-15}{-3}=5\).

Step 2

Why this answer is correct

The correct answer is A. (5). The numerator is ((-27)+18-6=-15). Then \(\frac{-15}{-3}=5\).

Step 3

Exam Tip

अंश ((-27)+18-6=-15) है। \(\frac{-15}{-3}=5\) मिलेगा।

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Question 30/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

कौन-सा व्यंजक \(2x^2-5x+3\) में \(x^2+4x-8\) जोड़ने पर मिलता है?

Which expression is obtained by adding \(x^2+4x-8\) to \(2x^2-5x+3\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

Add like terms: \(2x^2+x^2=3x^2\), (-5x+4x=-x), and (3-8=-5).

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-x-5\). Add like terms: \(2x^2+x^2=3x^2\), (-5x+4x=-x), and (3-8=-5).

Step 3

Exam Tip

समान पद जोड़ें: \(2x^2+x^2=3x^2\), (-5x+4x=-x), और (3-8=-5)।

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Question 31/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(9x^2-4x+1\) में से \(3x^2+2x-5\) घटाने पर क्या मिलेगा?

What is obtained by subtracting \(3x^2+2x-5\) from \(9x^2-4x+1\)?

Explanation opens after your attempt
Correct Answer

C. \(6x^2-6x+6\)

Step 1

Concept

Subtraction gives \(9x^2-4x+1-3x^2-2x+5\). Its simplified form is \(6x^2-6x+6\).

Step 2

Why this answer is correct

The correct answer is C. \(6x^2-6x+6\). Subtraction gives \(9x^2-4x+1-3x^2-2x+5\). Its simplified form is \(6x^2-6x+6\).

Step 3

Exam Tip

घटाने पर \(9x^2-4x+1-3x^2-2x+5\) मिलेगा। इसका सरल रूप \(6x^2-6x+6\) है।

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Question 32/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

कौन-सा कथन \(x^2y\) और \(xy^2\) के लिए सही है?

Which statement is correct for \(x^2y\) and \(xy^2\)?

Explanation opens after your attempt
Correct Answer

B. ये असमान पद हैं क्योंकि घातें अलग हैंThey are unlike terms because powers are different

Step 1

Concept

Both contain (x) and (y), but the power of each variable is not the same. So they are unlike terms.

Step 2

Why this answer is correct

The correct answer is B. ये असमान पद हैं क्योंकि घातें अलग हैं / They are unlike terms because powers are different. Both contain (x) and (y), but the power of each variable is not the same. So they are unlike terms.

Step 3

Exam Tip

दोनों में (x) और (y) हैं पर प्रत्येक चर की घात समान नहीं है। इसलिए ये असमान पद हैं।

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Question 33/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (a=1), (b=-2), तो \(4a^2b-3ab^2+b^3\) का मान क्या होगा?

If (a=1), (b=-2), what is the value of \(4a^2b-3ab^2+b^3\)?

Explanation opens after your attempt
Correct Answer

A. (-28)

Step 1

Concept

(4(1)(-2)-3(1)(4)+(-8)=-8-12-8=-28). Handle powers and signs carefully.

Step 2

Why this answer is correct

The correct answer is A. (-28). (4(1)(-2)-3(1)(4)+(-8)=-8-12-8=-28). Handle powers and signs carefully.

Step 3

Exam Tip

(4(1)(-2)-3(1)(4)+(-8)=-8-12-8=-28)। घात और चिन्ह दोनों सावधानी से लें।

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Question 34/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

(2(4x-3y)-5(x-y)+3y) को सरल करने पर क्या मिलेगा?

What is obtained after simplifying (2(4x-3y)-5(x-y)+3y)?

Explanation opens after your attempt
Correct Answer

A. (3x+2y)

Step 1

Concept

Expanding gives (8x-6y-5x+5y+3y). Combining like terms gives (3x+2y).

Step 2

Why this answer is correct

The correct answer is A. (3x+2y). Expanding gives (8x-6y-5x+5y+3y). Combining like terms gives (3x+2y).

Step 3

Exam Tip

खोलने पर (8x-6y-5x+5y+3y) मिलता है। समान पद मिलाकर (3x+2y) बनेगा।

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Question 35/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(x^2+kx+16\) में यदि (x) का गुणांक (12) है, तो (k-5) का मान क्या होगा?

In \(x^2+kx+16\), if the coefficient of (x) is (12), what is the value of (k-5)?

Explanation opens after your attempt
Correct Answer

A. (7)

Step 1

Concept

In (kx), the coefficient of (x) is (k), so (k=12). Hence (k-5=7).

Step 2

Why this answer is correct

The correct answer is A. (7). In (kx), the coefficient of (x) is (k), so (k=12). Hence (k-5=7).

Step 3

Exam Tip

(kx) में (x) का गुणांक (k) है, इसलिए (k=12)। अतः (k-5=7)।

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Question 36/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

कौन-सा व्यंजक (x) के वर्ग के (3) गुने और (y) के दोगुने के अंतर को दर्शाता है?

Which expression represents the difference between three times the square of (x) and twice (y)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

Three times the square of (x) is \(3x^2\), and twice (y) is (2y). The difference is \(3x^2-2y\).

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-2y\). Three times the square of (x) is \(3x^2\), and twice (y) is (2y). The difference is \(3x^2-2y\).

Step 3

Exam Tip

(x) के वर्ग का (3) गुना \(3x^2\) है और (y) का दोगुना (2y) है। अंतर \(3x^2-2y\) होगा।

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Question 37/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(4x^2-3xy+2y^2+5xy-7y^2-x^2\) को सरल करने पर क्या मिलेगा?

What is obtained after simplifying \(4x^2-3xy+2y^2+5xy-7y^2-x^2\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

\(4x^2-x^2=3x^2\), (-3xy+5xy=2xy), and \(2y^2-7y^2=-5y^2\).

Step 2

Why this answer is correct

The correct answer is A. \(3x^2+2xy-5y^2\). \(4x^2-x^2=3x^2\), (-3xy+5xy=2xy), and \(2y^2-7y^2=-5y^2\).

Step 3

Exam Tip

\(4x^2-x^2=3x^2\), (-3xy+5xy=2xy), और \(2y^2-7y^2=-5y^2\)।

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Question 38/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (x=3), तो (2x(x-5)+4x-2) का मान क्या होगा?

If (x=3), what is the value of (2x(x-5)+4x-2)?

Explanation opens after your attempt
Correct Answer

B. (24)

Step 1

Concept

First simplify (2x(x-5)+4x-2=6x-2-10x). Substituting (x=3) gives (54-30=24).

Step 2

Why this answer is correct

The correct answer is B. (24). First simplify (2x(x-5)+4x-2=6x-2-10x). Substituting (x=3) gives (54-30=24).

Step 3

Exam Tip

पहले सरल करें (2x(x-5)+4x-2=6x-2-10x)। (x=3) रखने पर (54-30=24)।

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Question 39/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(3x^2y+2xy^2-5x^2y+8xy^2\) को सरल करने पर \(x^2y\) का गुणांक क्या होगा?

After simplifying \(3x^2y+2xy^2-5x^2y+8xy^2\), what will be the coefficient of \(x^2y\)?

Explanation opens after your attempt
Correct Answer

B. (-2)

Step 1

Concept

The \(x^2y\) terms are \(3x^2y\) and \(-5x^2y\). Their sum is \(-2x^2y\).

Step 2

Why this answer is correct

The correct answer is B. (-2). The \(x^2y\) terms are \(3x^2y\) and \(-5x^2y\). Their sum is \(-2x^2y\).

Step 3

Exam Tip

\(x^2y\) वाले पद \(3x^2y\) और \(-5x^2y\) हैं। इनका योग \(-2x^2y\) है।

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Question 40/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

किस व्यंजक का सरल रूप \(4x^2-9x\) है?

Which expression has the simplified form \(4x^2-9x\)?

Explanation opens after your attempt
Correct Answer

A. (x(4x-9))

Step 1

Concept

Expanding (x(4x-9)) gives \(4x^2-9x\). Use the distributive rule to check options.

Step 2

Why this answer is correct

The correct answer is A. (x(4x-9)). Expanding (x(4x-9)) gives \(4x^2-9x\). Use the distributive rule to check options.

Step 3

Exam Tip

(x(4x-9)) खोलने पर \(4x^2-9x\) मिलता है। विकल्प जाँचने के लिए वितरण नियम लगाएँ।

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Question 41/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (p+q=6) और (p-q=2), तो (3p-q) का मान क्या होगा?

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

Explanation opens after your attempt
Correct Answer

C. (10)

Step 1

Concept

The two equations give (p=4) and (q=2). Therefore, (3p-q=12-2=10).

Step 2

Why this answer is correct

The correct answer is C. (10). The two equations give (p=4) and (q=2). Therefore, (3p-q=12-2=10).

Step 3

Exam Tip

दोनों समीकरणों से (p=4) और (q=2) मिलता है। इसलिए (3p-q=12-2=10)।

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Question 42/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(5a^2-2ab+3b^2\) में से \(2a^2+5ab-b^2\) घटाने पर क्या मिलेगा?

What is obtained by subtracting \(2a^2+5ab-b^2\) from \(5a^2-2ab+3b^2\)?

Explanation opens after your attempt
Correct Answer

A. \(3a^2-7ab+4b^2\)

Step 1

Concept

Subtraction gives \(5a^2-2ab+3b^2-2a^2-5ab+b^2\). The simplified form is \(3a^2-7ab+4b^2\).

Step 2

Why this answer is correct

The correct answer is A. \(3a^2-7ab+4b^2\). Subtraction gives \(5a^2-2ab+3b^2-2a^2-5ab+b^2\). The simplified form is \(3a^2-7ab+4b^2\).

Step 3

Exam Tip

घटाने पर \(5a^2-2ab+3b^2-2a^2-5ab+b^2\) मिलता है। सरल रूप \(3a^2-7ab+4b^2\) है।

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Question 43/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(2x^2+5x+3\) में से कौन-सा पद हटाने पर केवल (2) पदों वाला व्यंजक बचेगा और स्थिर पद भी नहीं रहेगा?

Which term should be removed from \(2x^2+5x+3\) so that only (2) terms remain and no constant term remains?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

The constant term is (3). Removing it leaves \(2x^2+5x\), which has (2) variable terms.

Step 2

Why this answer is correct

The correct answer is C. (3). The constant term is (3). Removing it leaves \(2x^2+5x\), which has (2) variable terms.

Step 3

Exam Tip

स्थिर पद (3) है। उसे हटाने पर \(2x^2+5x\) बचेगा जिसमें (2) चर पद हैं।

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Question 44/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (x=-1), (y=2), तो \(x^2y^2-2xy\) का मान क्या होगा?

If (x=-1), (y=2), what is the value of \(x^2y^2-2xy\)?

Explanation opens after your attempt
Correct Answer

C. (8)

Step 1

Concept

\(x^2y^2=1\cdot4=4\) and (2xy=2(-1)(2)=-4). Therefore, (4-(-4)=8).

Step 2

Why this answer is correct

The correct answer is C. (8). \(x^2y^2=1\cdot4=4\) and (2xy=2(-1)(2)=-4). Therefore, (4-(-4)=8).

Step 3

Exam Tip

\(x^2y^2=1\cdot4=4\) और (2xy=2(-1)(2)=-4)। इसलिए (4-(-4)=8)।

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Question 45/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

कौन-सा विकल्प (2(3x-y)+4(x+2y)-5x) के बराबर है?

Which option is equal to (2(3x-y)+4(x+2y)-5x)?

Explanation opens after your attempt
Correct Answer

A. (5x+6y)

Step 1

Concept

Expanding gives (6x-2y+4x+8y-5x). Combining like terms gives (5x+6y).

Step 2

Why this answer is correct

The correct answer is A. (5x+6y). Expanding gives (6x-2y+4x+8y-5x). Combining like terms gives (5x+6y).

Step 3

Exam Tip

खोलने पर (6x-2y+4x+8y-5x) मिलता है। समान पद मिलाकर (5x+6y) बनेगा।

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Question 46/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(x^3y^2\) में कुल घात और (y) की घात का अंतर क्या है?

What is the difference between the total degree and the power of (y) in \(x^3y^2\)?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

The total degree is (3+2=5), and the power of (y) is (2). The difference is (5-2=3).

Step 2

Why this answer is correct

The correct answer is C. (3). The total degree is (3+2=5), and the power of (y) is (2). The difference is (5-2=3).

Step 3

Exam Tip

कुल घात (3+2=5) है और (y) की घात (2) है। अंतर (5-2=3) होगा।

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Question 47/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि \(x^2+x=20\), तो \(3x^2+3x-4\) का मान क्या होगा?

If \(x^2+x=20\), what is the value of \(3x^2+3x-4\)?

Explanation opens after your attempt
Correct Answer

A. (56)

Step 1

Concept

(3x-2+3x-4=3\(x^2+x\)-4). Using the given value, (3(20)-4=56).

Step 2

Why this answer is correct

The correct answer is A. (56). (3x-2+3x-4=3\(x^2+x\)-4). Using the given value, (3(20)-4=56).

Step 3

Exam Tip

(3x-2+3x-4=3\(x^2+x\)-4) है। दिए मान से (3(20)-4=56)।

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Question 48/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(7x^2y-3xy+4x^2y+2xy-6\) को सरल करने पर कौन-सा पद नहीं रहेगा?

After simplifying \(7x^2y-3xy+4x^2y+2xy-6\), which term will not remain?

Explanation opens after your attempt
Correct Answer

D. (5xy)

Step 1

Concept

The simplified form is \(11x^2y-xy-6\). It does not contain the term (5xy).

Step 2

Why this answer is correct

The correct answer is D. (5xy). The simplified form is \(11x^2y-xy-6\). It does not contain the term (5xy).

Step 3

Exam Tip

सरल रूप \(11x^2y-xy-6\) है। इसमें (5xy) पद नहीं है।

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Question 49/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

यदि (x=2) और (y=1), तो \(x^2y+xy^2\) और (xy(x+y)) के बारे में सही कथन कौन-सा है?

If (x=2) and (y=1), which statement is correct about \(x^2y+xy^2\) and (xy(x+y))?

Explanation opens after your attempt
Correct Answer

C. दोनों बराबर हैंBoth are equal

Step 1

Concept

(x-2y+xy-2=xy(x+y)) are equivalent forms. For the given values, both equal (6).

Step 2

Why this answer is correct

The correct answer is C. दोनों बराबर हैं / Both are equal. (x-2y+xy-2=xy(x+y)) are equivalent forms. For the given values, both equal (6).

Step 3

Exam Tip

(x-2y+xy-2=xy(x+y)) समान रूप हैं। दिए मानों पर दोनों का मान (6) है।

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Question 50/50 Expert Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 24

\(8x^2-6xy+y^2-3x^2+9xy-5y^2\) को सरल करने पर क्या मिलेगा?

What is obtained after simplifying \(8x^2-6xy+y^2-3x^2+9xy-5y^2\)?

Explanation opens after your attempt
Correct Answer

A. \(5x^2+3xy-4y^2\)

Step 1

Concept

\(8x^2-3x^2=5x^2\), (-6xy+9xy=3xy), and \(y^2-5y^2=-4y^2\).

Step 2

Why this answer is correct

The correct answer is A. \(5x^2+3xy-4y^2\). \(8x^2-3x^2=5x^2\), (-6xy+9xy=3xy), and \(y^2-5y^2=-4y^2\).

Step 3

Exam Tip

\(8x^2-3x^2=5x^2\), (-6xy+9xy=3xy), और \(y^2-5y^2=-4y^2\)।

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