Class 9 Mathematics - Sequences and Progressions - Recursive rule Hard Quiz

Mathematics Sequences and Progressions Recursive rule Hard Class 9 Level 25

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Question 1/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक (7(2x-3)-4(3x+5)) का सरल रूप क्या है?

What is the simplified form of (7(2x-3)-4(3x+5))?

Explanation opens after your attempt
Correct Answer

A. (2x-41)

Step 1

Concept

Expanding gives (14x-21-12x-20=2x-41). Expand first and then combine like terms.

Step 2

Why this answer is correct

The correct answer is A. (2x-41). Expanding gives (14x-21-12x-20=2x-41). Expand first and then combine like terms.

Step 3

Exam Tip

कोष्ठक खोलने पर (14x-21-12x-20=2x-41) मिलता है। पहले विस्तार करें फिर समान पद जोड़ें।

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Question 2/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

यदि (x=-4), तो \(3x^2+2x-7\) का मान क्या होगा?

If (x=-4), what is the value of \(3x^2+2x-7\)?

Explanation opens after your attempt
Correct Answer

B. (33)

Step 1

Concept

Substitution gives (3(16)-8-7=33). The square of a negative number is positive.

Step 2

Why this answer is correct

The correct answer is B. (33). Substitution gives (3(16)-8-7=33). The square of a negative number is positive.

Step 3

Exam Tip

मान रखने पर (3(16)-8-7=33) मिलता है। ऋणात्मक संख्या का वर्ग धनात्मक होता है।

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Question 3/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक \(9a^2-6a+11-4a^2+13a-8\) का सरल रूप क्या है?

What is the simplified form of \(9a^2-6a+11-4a^2+13a-8\)?

Explanation opens after your attempt
Correct Answer

C. \(5a^2+7a+3\)

Step 1

Concept

Combining like terms gives \(9a^2-4a^2=5a^2\), (-6a+13a=7a), and (11-8=3). Group terms by powers.

Step 2

Why this answer is correct

The correct answer is C. \(5a^2+7a+3\). Combining like terms gives \(9a^2-4a^2=5a^2\), (-6a+13a=7a), and (11-8=3). Group terms by powers.

Step 3

Exam Tip

समान पद जोड़ने पर \(9a^2-4a^2=5a^2\), (-6a+13a=7a), और (11-8=3) मिलता है। घात के अनुसार पदों को समूहित करें।

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Question 4/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

(11x-9) में से (4x-15) घटाने पर क्या मिलेगा?

What is obtained by subtracting (4x-15) from (11x-9)?

Explanation opens after your attempt
Correct Answer

D. (7x+6)

Step 1

Concept

((11x-9)-(4x-15)=11x-9-4x+15=7x+6). Change all signs of the subtracted expression.

Step 2

Why this answer is correct

The correct answer is D. (7x+6). ((11x-9)-(4x-15)=11x-9-4x+15=7x+6). Change all signs of the subtracted expression.

Step 3

Exam Tip

((11x-9)-(4x-15)=11x-9-4x+15=7x+6)। घटाए गए व्यंजक के सभी चिह्न बदलें।

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Question 5/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

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

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

Explanation opens after your attempt
Correct Answer

A. (-44)

Step 1

Concept

Substitution gives (9(-2)-2(3)(4)-2=-44). \(q^2\) will be positive but (q) remains negative.

Step 2

Why this answer is correct

The correct answer is A. (-44). Substitution gives (9(-2)-2(3)(4)-2=-44). \(q^2\) will be positive but (q) remains negative.

Step 3

Exam Tip

मान रखने पर (9(-2)-2(3)(4)-2=-44) मिलता है। \(q^2\) धनात्मक होगा लेकिन (q) ऋणात्मक रहेगा।

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Question 6/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक (6(3m-2n)-5(m-4n)) का सरल रूप क्या है?

What is the simplified form of (6(3m-2n)-5(m-4n))?

Explanation opens after your attempt
Correct Answer

B. (13m+8n)

Step 1

Concept

Expanding gives (18m-12n-5m+20n=13m+8n). Combine (m) and (n) terms separately.

Step 2

Why this answer is correct

The correct answer is B. (13m+8n). Expanding gives (18m-12n-5m+20n=13m+8n). Combine (m) and (n) terms separately.

Step 3

Exam Tip

खोलने पर (18m-12n-5m+20n=13m+8n) मिलता है। (m) और (n) वाले पद अलग-अलग जोड़ें।

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Question 7/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

कौन सा व्यंजक (x) और (5) के अंतर के (3) गुने में (2x) जोड़ने को दर्शाता है?

Which expression represents adding (2x) to (3) times the difference of (x) and (5)?

Explanation opens after your attempt
Correct Answer

C. (3(x-5)+2x)

Step 1

Concept

The difference is (x-5), and three times it is (3(x-5)). Adding (2x) gives (3(x-5)+2x).

Step 2

Why this answer is correct

The correct answer is C. (3(x-5)+2x). The difference is (x-5), and three times it is (3(x-5)). Adding (2x) gives (3(x-5)+2x).

Step 3

Exam Tip

अंतर (x-5) है और उसका (3) गुना (3(x-5)) है। उसमें (2x) जोड़ने पर (3(x-5)+2x) मिलता है।

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Question 8/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

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

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

Explanation opens after your attempt
Correct Answer

A. (3)

Step 1

Concept

Substitution gives (2(-27)+5(9)+12=3). In an odd power, the negative sign remains.

Step 2

Why this answer is correct

The correct answer is A. (3). Substitution gives (2(-27)+5(9)+12=3). In an odd power, the negative sign remains.

Step 3

Exam Tip

मान रखने पर (2(-27)+5(9)+12=3) मिलता है। विषम घात में ऋणात्मक चिह्न बना रहता है।

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

व्यंजक (5x-[3x-{2x+7}]) का सरल रूप क्या है?

What is the simplified form of (5x-[3x-{2x+7}])?

Explanation opens after your attempt
Correct Answer

A. (4x+7)

Step 1

Concept

Inside (3x-(2x+7)=x-7), so (5x-(x-7)=4x+7). Solve the inner bracket first.

Step 2

Why this answer is correct

The correct answer is A. (4x+7). Inside (3x-(2x+7)=x-7), so (5x-(x-7)=4x+7). Solve the inner bracket first.

Step 3

Exam Tip

अंदर (3x-(2x+7)=x-7), इसलिए (5x-(x-7)=4x+7)। अंदरूनी कोष्ठक पहले हल करें।

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Question 10/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

किस विकल्प में (8ab-5a+6ab-9a) का सही सरल रूप है?

Which option gives the correct simplified form of (8ab-5a+6ab-9a)?

Explanation opens after your attempt
Correct Answer

B. (14ab-14a)

Step 1

Concept

(8ab+6ab=14ab) and (-5a-9a=-14a). (ab) and (a) are unlike terms.

Step 2

Why this answer is correct

The correct answer is B. (14ab-14a). (8ab+6ab=14ab) and (-5a-9a=-14a). (ab) and (a) are unlike terms.

Step 3

Exam Tip

(8ab+6ab=14ab) और (-5a-9a=-14a)। (ab) और (a) असमान पद हैं।

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Question 11/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

यदि (a+b=12) और (ab=20), तो (4(a+b)-3ab) का मान क्या होगा?

If (a+b=12) and (ab=20), what is the value of (4(a+b)-3ab)?

Explanation opens after your attempt
Correct Answer

A. (-12)

Step 1

Concept

Using the given values gives (4(12)-3(20)=48-60=-12). Treat the whole (a+b) as one value.

Step 2

Why this answer is correct

The correct answer is A. (-12). Using the given values gives (4(12)-3(20)=48-60=-12). Treat the whole (a+b) as one value.

Step 3

Exam Tip

दिए गए मान रखने पर (4(12)-3(20)=48-60=-12) मिलता है। पूरे (a+b) को एक मान की तरह लें।

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Question 12/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक (3x(4x-5)-2x(5x+1)) का सरल रूप क्या है?

What is the simplified form of (3x(4x-5)-2x(5x+1))?

Explanation opens after your attempt
Correct Answer

B. \(2x^2-17x\)

Step 1

Concept

Expanding gives \(12x^2-15x-10x^2-2x=2x^2-17x\). Do each multiplication separately.

Step 2

Why this answer is correct

The correct answer is B. \(2x^2-17x\). Expanding gives \(12x^2-15x-10x^2-2x=2x^2-17x\). Do each multiplication separately.

Step 3

Exam Tip

खोलने पर \(12x^2-15x-10x^2-2x=2x^2-17x\) मिलता है। हर गुणन को अलग से करें।

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Question 13/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

किस विकल्प में \(4x^2\) और \(-11x^2\) का योग सही है?

Which option gives the correct sum of \(4x^2\) and \(-11x^2\)?

Explanation opens after your attempt
Correct Answer

C. \(-7x^2\)

Step 1

Concept

The coefficients are (4+(-11)=-7), and the variable part \(x^2\) remains the same. So the sum is \(-7x^2\).

Step 2

Why this answer is correct

The correct answer is C. \(-7x^2\). The coefficients are (4+(-11)=-7), and the variable part \(x^2\) remains the same. So the sum is \(-7x^2\).

Step 3

Exam Tip

गुणांक (4+(-11)=-7) हैं और चर भाग \(x^2\) वही रहता है। इसलिए योग \(-7x^2\) है।

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Question 14/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

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

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

Explanation opens after your attempt
Correct Answer

B. (8)

Step 1

Concept

Substitution gives \(\frac{36-18+6}{3}=\frac{24}{3}=8\). Simplify the whole numerator first.

Step 2

Why this answer is correct

The correct answer is B. (8). Substitution gives \(\frac{36-18+6}{3}=\frac{24}{3}=8\). Simplify the whole numerator first.

Step 3

Exam Tip

मान रखने पर \(\frac{36-18+6}{3}=\frac{24}{3}=8\) मिलता है। पूरा अंश पहले सरल करें।

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Question 15/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक (12-(4x-7)+3(x-5)) का सरल रूप क्या है?

What is the simplified form of (12-(4x-7)+3(x-5))?

Explanation opens after your attempt
Correct Answer

B. (-x+4)

Step 1

Concept

Expanding gives (12-4x+7+3x-15=-x+4). Change signs if a minus is before a bracket.

Step 2

Why this answer is correct

The correct answer is B. (-x+4). Expanding gives (12-4x+7+3x-15=-x+4). Change signs if a minus is before a bracket.

Step 3

Exam Tip

खोलने पर (12-4x+7+3x-15=-x+4) मिलता है। कोष्ठक से पहले ऋण हो तो चिह्न बदलें।

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Question 16/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

एक त्रिभुज की भुजाएं (3x+2), (2x-7) और (x+9) हैं। परिमाप का व्यंजक क्या होगा?

The sides of a triangle are (3x+2), (2x-7), and (x+9). What is the expression for its perimeter?

Explanation opens after your attempt
Correct Answer

C. (6x+4)

Step 1

Concept

Perimeter is the sum of all sides. ((3x+2)+(2x-7)+(x+9)=6x+4).

Step 2

Why this answer is correct

The correct answer is C. (6x+4). Perimeter is the sum of all sides. ((3x+2)+(2x-7)+(x+9)=6x+4).

Step 3

Exam Tip

परिमाप सभी भुजाओं का योग है। ((3x+2)+(2x-7)+(x+9)=6x+4)।

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Question 17/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक (6p-[3p-{4p-(p+6)}]) का सरल रूप क्या है?

What is the simplified form of (6p-[3p-{4p-(p+6)}])?

Explanation opens after your attempt
Correct Answer

B. (6p-6)

Step 1

Concept

Inside (4p-(p+6)=3p-6), then (3p-(3p-6)=6), so (6p-6). Simplify from inside to outside.

Step 2

Why this answer is correct

The correct answer is B. (6p-6). Inside (4p-(p+6)=3p-6), then (3p-(3p-6)=6), so (6p-6). Simplify from inside to outside.

Step 3

Exam Tip

अंदर (4p-(p+6)=3p-6), फिर (3p-(3p-6)=6), इसलिए (6p-6)। अंदर से बाहर की ओर सरल करें।

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Question 18/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

यदि (u=2) और (v=-5), तो \(u^2v+uv^2-3u\) का मान क्या होगा?

If (u=2) and (v=-5), what is the value of \(u^2v+uv^2-3u\)?

Explanation opens after your attempt
Correct Answer

B. (24)

Step 1

Concept

Substitution gives (4(-5)+2(25)-6=24). \(v^2\) will be positive.

Step 2

Why this answer is correct

The correct answer is B. (24). Substitution gives (4(-5)+2(25)-6=24). \(v^2\) will be positive.

Step 3

Exam Tip

मान रखने पर (4(-5)+2(25)-6=24) मिलता है। \(v^2\) धनात्मक होगा।

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Question 19/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

कौन सा व्यंजक (y) से (6) अधिक संख्या के वर्ग को दर्शाता है?

Which expression represents the square of the number (6) more than (y)?

Explanation opens after your attempt
Correct Answer

C. ((y+6)2)

Step 1

Concept

The number (6) more than (y) is (y+6). To square the whole sum, write ((y+6)2).

Step 2

Why this answer is correct

The correct answer is C. ((y+6)2). The number (6) more than (y) is (y+6). To square the whole sum, write ((y+6)2).

Step 3

Exam Tip

(6) अधिक संख्या (y+6) है। पूरे योग के वर्ग के लिए ((y+6)2) लिखते हैं।

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Question 20/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक \(8x^2-7xy+4xy-5x^2\) का सरल रूप क्या है?

What is the simplified form of \(8x^2-7xy+4xy-5x^2\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

\(8x^2-5x^2=3x^2\) and (-7xy+4xy=-3xy). \(x^2\) and (xy) are different variable parts.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2-3xy\). \(8x^2-5x^2=3x^2\) and (-7xy+4xy=-3xy). \(x^2\) and (xy) are different variable parts.

Step 3

Exam Tip

\(8x^2-5x^2=3x^2\) और (-7xy+4xy=-3xy)। \(x^2\) और (xy) अलग चर भाग हैं।

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Question 21/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

यदि (m-n=9), तो (2m-2n+11) का मान क्या होगा?

If (m-n=9), what is the value of (2m-2n+11)?

Explanation opens after your attempt
Correct Answer

C. (29)

Step 1

Concept

(2m-2n+11=2(m-n)+11=18+11=29). If the same coefficient appears, take the common factor.

Step 2

Why this answer is correct

The correct answer is C. (29). (2m-2n+11=2(m-n)+11=18+11=29). If the same coefficient appears, take the common factor.

Step 3

Exam Tip

(2m-2n+11=2(m-n)+11=18+11=29)। समान गुणांक दिखे तो सामान्य गुणक निकालें।

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Question 22/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक (4(3x-2y)-3(x-4y)+5y) का सरल रूप क्या है?

What is the simplified form of (4(3x-2y)-3(x-4y)+5y)?

Explanation opens after your attempt
Correct Answer

A. (9x+9y)

Step 1

Concept

Expanding gives (12x-8y-3x+12y+5y=9x+9y). Combine terms with the same variable.

Step 2

Why this answer is correct

The correct answer is A. (9x+9y). Expanding gives (12x-8y-3x+12y+5y=9x+9y). Combine terms with the same variable.

Step 3

Exam Tip

खोलने पर (12x-8y-3x+12y+5y=9x+9y) मिलता है। समान चर वाले पद जोड़ें।

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Question 23/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

किस विकल्प में \(2x^2+5x-6\) और \(3x^2-7x+10\) का योग सही है?

Which option gives the correct sum of \(2x^2+5x-6\) and \(3x^2-7x+10\)?

Explanation opens after your attempt
Correct Answer

C. \(5x^2-2x+4\)

Step 1

Concept

In the sum, \(2x^2+3x^2=5x^2\), (5x-7x=-2x), and (-6+10=4). Add like terms separately.

Step 2

Why this answer is correct

The correct answer is C. \(5x^2-2x+4\). In the sum, \(2x^2+3x^2=5x^2\), (5x-7x=-2x), and (-6+10=4). Add like terms separately.

Step 3

Exam Tip

योग में \(2x^2+3x^2=5x^2\), (5x-7x=-2x), और (-6+10=4) है। समान पद अलग-अलग जोड़ें।

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

यदि (x=0), तो \(-4x^3+9x^2-5x+13\) का मान क्या होगा?

If (x=0), what is the value of \(-4x^3+9x^2-5x+13\)?

Explanation opens after your attempt
Correct Answer

C. (13)

Step 1

Concept

Putting (x=0) makes all variable terms (0). Therefore the value is (13).

Step 2

Why this answer is correct

The correct answer is C. (13). Putting (x=0) makes all variable terms (0). Therefore the value is (13).

Step 3

Exam Tip

(x=0) रखने पर सभी चर वाले पद (0) हो जाते हैं। इसलिए मान (13) है।

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

व्यंजक (5a-2[3a-4(a-2)]) का सरल रूप क्या है?

What is the simplified form of (5a-2[3a-4(a-2)])?

Explanation opens after your attempt
Correct Answer

A. (7a-16)

Step 1

Concept

Inside (3a-4a+8=-a+8), so (5a-2(-a+8)=7a-16). Simplify the inside part first.

Step 2

Why this answer is correct

The correct answer is A. (7a-16). Inside (3a-4a+8=-a+8), so (5a-2(-a+8)=7a-16). Simplify the inside part first.

Step 3

Exam Tip

अंदर (3a-4a+8=-a+8), इसलिए (5a-2(-a+8)=7a-16)। अंदर का भाग पहले सरल करें।

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Question 26/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

यदि (s=2) और (t=-1), तो \(s^3t-st^3+2t\) का मान क्या होगा?

If (s=2) and (t=-1), what is the value of \(s^3t-st^3+2t\)?

Explanation opens after your attempt
Correct Answer

A. (-8)

Step 1

Concept

Substitution gives (8(-1)-2(-1)-2=-8). An odd power of a negative value remains negative.

Step 2

Why this answer is correct

The correct answer is A. (-8). Substitution gives (8(-1)-2(-1)-2=-8). An odd power of a negative value remains negative.

Step 3

Exam Tip

मान रखने पर (8(-1)-2(-1)-2=-8) मिलता है। ऋणात्मक मान की विषम घात ऋणात्मक रहती है।

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Question 27/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

किस विकल्प में (6(x-2)-[4x-{3x+1}]) का सही सरल रूप है?

Which option gives the correct simplified form of (6(x-2)-[4x-{3x+1}])?

Explanation opens after your attempt
Correct Answer

A. (5x-13)

Step 1

Concept

Inside (4x-(3x+1)=x-1), so (6x-12-(x-1)=5x-11). Add the final constants carefully.

Step 2

Why this answer is correct

The correct answer is A. (5x-13). Inside (4x-(3x+1)=x-1), so (6x-12-(x-1)=5x-11). Add the final constants carefully.

Step 3

Exam Tip

अंदर (4x-(3x+1)=x-1), इसलिए (6x-12-(x-1)=5x-11) नहीं बल्कि (5x-11) है। गणना में अंतिम नियतांक ध्यान से जोड़ें।

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Question 28/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक (6(x-2)-[4x-{3x+1}]) का सही सरल रूप कौन सा है?

Which is the correct simplified form of (6(x-2)-[4x-{3x+1}])?

Explanation opens after your attempt
Correct Answer

B. (5x-11)

Step 1

Concept

Inside (4x-{3x+1}=x-1). Therefore (6x-12-(x-1)=5x-11).

Step 2

Why this answer is correct

The correct answer is B. (5x-11). Inside (4x-{3x+1}=x-1). Therefore (6x-12-(x-1)=5x-11).

Step 3

Exam Tip

अंदर (4x-{3x+1}=x-1) है। इसलिए (6x-12-(x-1)=5x-11)।

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Question 29/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

(x) से (7) कम संख्या और (x) से (4) अधिक संख्या के योग का व्यंजक क्या होगा?

What is the expression for the sum of the number (7) less than (x) and the number (4) more than (x)?

Explanation opens after your attempt
Correct Answer

A. (2x-3)

Step 1

Concept

The two numbers are (x-7) and (x+4). Their sum is (2x-3).

Step 2

Why this answer is correct

The correct answer is A. (2x-3). The two numbers are (x-7) and (x+4). Their sum is (2x-3).

Step 3

Exam Tip

दो संख्याएं (x-7) और (x+4) हैं। उनका योग (2x-3) है।

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Question 30/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक \(\frac{7x}{10}-\frac{x}{5}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{7x}{10}-\frac{x}{5}\)?

Explanation opens after your attempt
Correct Answer

A. \(\frac{x}{2}\)

Step 1

Concept

\(\frac{x}{5}=\frac{2x}{10}\), so \(\frac{7x}{10}-\frac{2x}{10}=\frac{x}{2}\). Make a common denominator for fraction terms.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{x}{2}\). \(\frac{x}{5}=\frac{2x}{10}\), so \(\frac{7x}{10}-\frac{2x}{10}=\frac{x}{2}\). Make a common denominator for fraction terms.

Step 3

Exam Tip

\(\frac{x}{5}=\frac{2x}{10}\), इसलिए \(\frac{7x}{10}-\frac{2x}{10}=\frac{x}{2}\)। भिन्न पदों में समान हर बनाएं।

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Question 31/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

यदि (x+y=8) और (x-y=2), तो (4(x+y)-5(x-y)) का मान क्या होगा?

If (x+y=8) and (x-y=2), what is the value of (4(x+y)-5(x-y))?

Explanation opens after your attempt
Correct Answer

A. (22)

Step 1

Concept

Using the given values gives (4(8)-5(2)=22). Use the whole bracket as one value.

Step 2

Why this answer is correct

The correct answer is A. (22). Using the given values gives (4(8)-5(2)=22). Use the whole bracket as one value.

Step 3

Exam Tip

दिए गए मान रखने पर (4(8)-5(2)=22) मिलता है। पूरे कोष्ठक को एक मान की तरह उपयोग करें।

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Question 32/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक \(5x^2-6xy+3y^2-2x^2+11xy-8y^2\) का सरल रूप क्या है?

What is the simplified form of \(5x^2-6xy+3y^2-2x^2+11xy-8y^2\)?

Explanation opens after your attempt
Correct Answer

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

Step 1

Concept

Combining \(x^2\), (xy), and \(y^2\) terms separately gives \(3x^2+5xy-5y^2\). Do not mix different variable parts.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2+5xy-5y^2\). Combining \(x^2\), (xy), and \(y^2\) terms separately gives \(3x^2+5xy-5y^2\). Do not mix different variable parts.

Step 3

Exam Tip

\(x^2\), (xy), और \(y^2\) पदों को अलग जोड़ने पर \(3x^2+5xy-5y^2\) मिलता है। अलग चर भागों को न मिलाएं।

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Question 33/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक (15-[4x-3(2-x)]) का सरल रूप क्या है?

What is the simplified form of (15-[4x-3(2-x)])?

Explanation opens after your attempt
Correct Answer

B. (21-7x)

Step 1

Concept

Inside (4x-6+3x=7x-6), so (15-(7x-6)=21-7x). Apply the outside minus sign to the whole bracket.

Step 2

Why this answer is correct

The correct answer is B. (21-7x). Inside (4x-6+3x=7x-6), so (15-(7x-6)=21-7x). Apply the outside minus sign to the whole bracket.

Step 3

Exam Tip

अंदर (4x-6+3x=7x-6), इसलिए (15-(7x-6)=21-7x)। बाहर का ऋण चिह्न पूरे कोष्ठक पर लागू करें।

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Question 34/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

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

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

Explanation opens after your attempt
Correct Answer

C. (36)

Step 1

Concept

Substitution gives (2(81)-5(27)+9=36). Evaluate higher powers first.

Step 2

Why this answer is correct

The correct answer is C. (36). Substitution gives (2(81)-5(27)+9=36). Evaluate higher powers first.

Step 3

Exam Tip

मान रखने पर (2(81)-5(27)+9=36) मिलता है। बड़ी घातों का मान पहले निकालें।

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Question 35/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

कौन सा व्यंजक (a) और (b) के योग के (5) गुने में उनके अंतर को घटाता है?

Which expression subtracts the difference of (a) and (b) from (5) times their sum?

Explanation opens after your attempt
Correct Answer

C. (5(a+b)-(a-b))

Step 1

Concept

The sum is (a+b), and five times it is (5(a+b)). Subtracting the difference (a-b) gives (5(a+b)-(a-b)).

Step 2

Why this answer is correct

The correct answer is C. (5(a+b)-(a-b)). The sum is (a+b), and five times it is (5(a+b)). Subtracting the difference (a-b) gives (5(a+b)-(a-b)).

Step 3

Exam Tip

योग (a+b) है और उसका (5) गुना (5(a+b)) है। इसमें से अंतर (a-b) घटाने पर (5(a+b)-(a-b)) बनता है।

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Question 36/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक ((3x-4)+(2x+9)-(5x-7)) का सरल रूप क्या है?

What is the simplified form of ((3x-4)+(2x+9)-(5x-7))?

Explanation opens after your attempt
Correct Answer

A. (12)

Step 1

Concept

Removing brackets gives (3x-4+2x+9-5x+7=12). The (x)-terms cancel out.

Step 2

Why this answer is correct

The correct answer is A. (12). Removing brackets gives (3x-4+2x+9-5x+7=12). The (x)-terms cancel out.

Step 3

Exam Tip

कोष्ठक हटाने पर (3x-4+2x+9-5x+7=12) मिलता है। (x) वाले पद कट जाते हैं।

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Question 37/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

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

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

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

Substitution gives (2+3+4-5=4). Even powers of (-1) are (1), and odd powers are (-1).

Step 2

Why this answer is correct

The correct answer is B. (4). Substitution gives (2+3+4-5=4). Even powers of (-1) are (1), and odd powers are (-1).

Step 3

Exam Tip

मान रखने पर (2+3+4-5=4) मिलता है। (-1) की सम घात (1) और विषम घात (-1) होती है।

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Question 38/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

किस विकल्प में (6x-3y) में से (2x+8y) घटाने का सही परिणाम है?

Which option gives the correct result of subtracting (2x+8y) from (6x-3y)?

Explanation opens after your attempt
Correct Answer

A. (4x-11y)

Step 1

Concept

((6x-3y)-(2x+8y)=6x-3y-2x-8y=4x-11y). Change all signs of the second expression while subtracting.

Step 2

Why this answer is correct

The correct answer is A. (4x-11y). ((6x-3y)-(2x+8y)=6x-3y-2x-8y=4x-11y). Change all signs of the second expression while subtracting.

Step 3

Exam Tip

((6x-3y)-(2x+8y)=6x-3y-2x-8y=4x-11y)। घटाते समय दूसरे व्यंजक के सभी चिह्न बदलें।

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Question 39/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक \(4x^2y-9xy^2+5x^2y+6xy^2\) का सरल रूप क्या है?

What is the simplified form of \(4x^2y-9xy^2+5x^2y+6xy^2\)?

Explanation opens after your attempt
Correct Answer

A. \(9x^2y-3xy^2\)

Step 1

Concept

\(4x^2y+5x^2y=9x^2y\) and \(-9xy^2+6xy^2=-3xy^2\). Terms are like only when powers match.

Step 2

Why this answer is correct

The correct answer is A. \(9x^2y-3xy^2\). \(4x^2y+5x^2y=9x^2y\) and \(-9xy^2+6xy^2=-3xy^2\). Terms are like only when powers match.

Step 3

Exam Tip

\(4x^2y+5x^2y=9x^2y\) और \(-9xy^2+6xy^2=-3xy^2\)। घातें समान हों तभी पद समान होते हैं।

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Question 40/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

यदि (q=4), तो \(\frac{q^3-2q}{4}\) का मान क्या होगा?

If (q=4), what is the value of \(\frac{q^3-2q}{4}\)?

Explanation opens after your attempt
Correct Answer

B. (14)

Step 1

Concept

Putting (q=4) gives \(\frac{64-8}{4}=14\). Simplify the numerator completely first.

Step 2

Why this answer is correct

The correct answer is B. (14). Putting (q=4) gives \(\frac{64-8}{4}=14\). Simplify the numerator completely first.

Step 3

Exam Tip

(q=4) रखने पर \(\frac{64-8}{4}=14\) मिलता है। अंश को पहले पूरा सरल करें।

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Question 41/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

(n) से शुरू होने वाली चार लगातार विषम संख्याओं का योग क्या होगा?

What is the sum of four consecutive odd numbers starting from (n)?

Explanation opens after your attempt
Correct Answer

B. (4n+12)

Step 1

Concept

The four odd numbers are (n), (n+2), (n+4), and (n+6). Their sum is (4n+12).

Step 2

Why this answer is correct

The correct answer is B. (4n+12). The four odd numbers are (n), (n+2), (n+4), and (n+6). Their sum is (4n+12).

Step 3

Exam Tip

चार विषम संख्याएं (n), (n+2), (n+4), और (n+6) होंगी। उनका योग (4n+12) है।

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Question 42/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक (3(4x-5)-[2x-3(1-x)]) का सरल रूप क्या है?

What is the simplified form of (3(4x-5)-[2x-3(1-x)])?

Explanation opens after your attempt
Correct Answer

A. (7x-12)

Step 1

Concept

Inside (2x-3+3x=5x-3), so (12x-15-(5x-3)=7x-12). Simplify inside the square bracket first.

Step 2

Why this answer is correct

The correct answer is A. (7x-12). Inside (2x-3+3x=5x-3), so (12x-15-(5x-3)=7x-12). Simplify inside the square bracket first.

Step 3

Exam Tip

अंदर (2x-3+3x=5x-3), इसलिए (12x-15-(5x-3)=7x-12)। वर्ग कोष्ठक के अंदर पहले सरल करें।

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Question 43/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

यदि (x=1) और (y=3), तो (3(x+y)2-4xy) का मान क्या होगा?

If (x=1) and (y=3), what is the value of (3(x+y)2-4xy)?

Explanation opens after your attempt
Correct Answer

A. (36)

Step 1

Concept

Substitution gives (3(4)2-4(1)(3)=48-12=36). Evaluate brackets and squares first.

Step 2

Why this answer is correct

The correct answer is A. (36). Substitution gives (3(4)2-4(1)(3)=48-12=36). Evaluate brackets and squares first.

Step 3

Exam Tip

मान रखने पर (3(4)2-4(1)(3)=48-12=36) मिलता है। कोष्ठक और वर्ग पहले निकालें।

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Question 44/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

किस विकल्प में (4a-5b+9a-2b-6a) का सही सरल रूप है?

Which option gives the correct simplified form of (4a-5b+9a-2b-6a)?

Explanation opens after your attempt
Correct Answer

A. (7a-7b)

Step 1

Concept

(4a+9a-6a=7a) and (-5b-2b=-7b). Combine only terms with the same variable.

Step 2

Why this answer is correct

The correct answer is A. (7a-7b). (4a+9a-6a=7a) and (-5b-2b=-7b). Combine only terms with the same variable.

Step 3

Exam Tip

(4a+9a-6a=7a) और (-5b-2b=-7b)। समान चर वाले पद ही जोड़ें।

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Question 45/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

एक आयत की लंबाई (4x-7) और चौड़ाई (3x+2) है। परिमाप का व्यंजक क्या होगा?

A rectangle has length (4x-7) and breadth (3x+2). What is the expression for its perimeter?

Explanation opens after your attempt
Correct Answer

A. (14x-10)

Step 1

Concept

The perimeter is (2[(4x-7)+(3x+2)]=2(7x-5)=14x-10). Add length and breadth first.

Step 2

Why this answer is correct

The correct answer is A. (14x-10). The perimeter is (2[(4x-7)+(3x+2)]=2(7x-5)=14x-10). Add length and breadth first.

Step 3

Exam Tip

परिमाप (2[(4x-7)+(3x+2)]=2(7x-5)=14x-10) है। पहले लंबाई और चौड़ाई जोड़ें।

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Question 46/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

यदि (x=1), तो \(6x^3-9x^2+4x-8\) का मान क्या होगा?

If (x=1), what is the value of \(6x^3-9x^2+4x-8\)?

Explanation opens after your attempt
Correct Answer

A. (-7)

Step 1

Concept

Putting (x=1) gives (6-9+4-8=-7). Every positive power of (1) is (1).

Step 2

Why this answer is correct

The correct answer is A. (-7). Putting (x=1) gives (6-9+4-8=-7). Every positive power of (1) is (1).

Step 3

Exam Tip

(x=1) रखने पर (6-9+4-8=-7) मिलता है। (1) की हर धनात्मक घात (1) होती है।

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Question 47/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

व्यंजक (7x-3[2x-{x-6}]) का सरल रूप क्या है?

What is the simplified form of (7x-3[2x-{x-6}])?

Explanation opens after your attempt
Correct Answer

A. (4x-18)

Step 1

Concept

Inside (2x-(x-6)=x+6), so (7x-3(x+6)=4x-18). Remove inner brackets first.

Step 2

Why this answer is correct

The correct answer is A. (4x-18). Inside (2x-(x-6)=x+6), so (7x-3(x+6)=4x-18). Remove inner brackets first.

Step 3

Exam Tip

अंदर (2x-(x-6)=x+6), इसलिए (7x-3(x+6)=4x-18)। अंदरूनी कोष्ठक पहले हटाएं।

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Question 48/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

किस विकल्प में \(5x^2-3x+8\) में से \(2x^2-7x-6\) घटाने का सही परिणाम है?

Which option gives the correct result of subtracting \(2x^2-7x-6\) from \(5x^2-3x+8\)?

Explanation opens after your attempt
Correct Answer

A. \(3x^2+4x+14\)

Step 1

Concept

(\(5x^2-3x+8\)-\(2x^2-7x-6\)=3x-2+4x+14). Change all signs of the second expression while subtracting.

Step 2

Why this answer is correct

The correct answer is A. \(3x^2+4x+14\). (\(5x^2-3x+8\)-\(2x^2-7x-6\)=3x-2+4x+14). Change all signs of the second expression while subtracting.

Step 3

Exam Tip

(\(5x^2-3x+8\)-\(2x^2-7x-6\)=3x-2+4x+14)। घटाते समय दूसरे व्यंजक के सभी चिह्न बदलें।

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Question 49/50 Hard Mathematics Introduction to Polynomials Algebraic expressions Class 9 Level 25

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

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

Explanation opens after your attempt
Correct Answer

A. (11)

Step 1

Concept

Substitution gives (2(7)-3(1)=11). Evaluate the brackets first.

Step 2

Why this answer is correct

The correct answer is A. (11). Substitution gives (2(7)-3(1)=11). Evaluate the brackets first.

Step 3

Exam Tip

मान रखने पर (2(7)-3(1)=11) मिलता है। पहले कोष्ठक का मान निकालें।

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

व्यंजक (2(5x-3)-4[2x-{x-2}]) का सरल रूप क्या है?

What is the simplified form of (2(5x-3)-4[2x-{x-2}])?

Explanation opens after your attempt
Correct Answer

B. (6x-14)

Step 1

Concept

Inside (2x-(x-2)=x+2), so (10x-6-4(x+2)=6x-14). Solve brackets from inside to outside.

Step 2

Why this answer is correct

The correct answer is B. (6x-14). Inside (2x-(x-2)=x+2), so (10x-6-4(x+2)=6x-14). Solve brackets from inside to outside.

Step 3

Exam Tip

अंदर (2x-(x-2)=x+2), इसलिए (10x-6-4(x+2)=6x-14)। कोष्ठकों को अंदर से बाहर हल करें।

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