व्यंजक (7(2x-3)-4(3x+5)) का सरल रूप क्या है?
What is the simplified form of (7(2x-3)-4(3x+5))?
#algebraic_expressions
#expansion
#hard
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A (2x-41)
B (26x-1)
C (2x-1)
D (26x-41)
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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यदि (x=-4), तो \(3x^2+2x-7\) का मान क्या होगा?
If (x=-4), what is the value of \(3x^2+2x-7\)?
#algebraic_expressions
#evaluation
#negative_value
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A (25)
B (33)
C (49)
D (57)
Explanation opens after your attempt
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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व्यंजक \(9a^2-6a+11-4a^2+13a-8\) का सरल रूप क्या है?
What is the simplified form of \(9a^2-6a+11-4a^2+13a-8\)?
#algebraic_expressions
#like_terms
#quadratic
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A \(13a^2+7a+3\)
B \(5a^2-19a+19\)
C \(5a^2+7a+3\)
D \(13a^2-19a+3\)
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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(11x-9) में से (4x-15) घटाने पर क्या मिलेगा?
What is obtained by subtracting (4x-15) from (11x-9)?
#algebraic_expressions
#subtraction
#signs
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A (7x-24)
B (15x-24)
C (15x+6)
D (7x+6)
Explanation opens after your attempt
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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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 \(p^2q-2pq^2+q\)?
#algebraic_expressions
#two_variable_evaluation
#hard
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A (-44)
B (-40)
C (4)
D (8)
Explanation opens after your attempt
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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व्यंजक (6(3m-2n)-5(m-4n)) का सरल रूप क्या है?
What is the simplified form of (6(3m-2n)-5(m-4n))?
#algebraic_expressions
#two_variable
#expansion
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A (23m+8n)
B (13m+8n)
C (13m-32n)
D (23m-32n)
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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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)?
#algebraic_expressions
#word_expression
#brackets
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A (3x-5+2x)
B (3(x+5)+2x)
C (3(x-5)+2x)
D (2x-3(x-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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यदि (r=-3), तो \(2r^3+5r^2-4r\) का मान क्या होगा?
If (r=-3), what is the value of \(2r^3+5r^2-4r\)?
#algebraic_expressions
#cubic_evaluation
#hard
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A (3)
B (9)
C (15)
D (21)
Explanation opens after your attempt
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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व्यंजक (5x-[3x-{2x+7}]) का सरल रूप क्या है?
What is the simplified form of (5x-[3x-{2x+7}])?
#algebraic_expressions
#nested_brackets
#hard
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A (4x+7)
B (4x-7)
C (6x+7)
D (6x-7)
Explanation opens after your attempt
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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किस विकल्प में (8ab-5a+6ab-9a) का सही सरल रूप है?
Which option gives the correct simplified form of (8ab-5a+6ab-9a)?
#algebraic_expressions
#multivariable_terms
#hard
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A (14ab+4a)
B (14ab-14a)
C (2ab-14a)
D \(14a^2b-14a\)
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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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)?
#algebraic_expressions
#given_values
#hard
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A (-12)
B (8)
C (28)
D (108)
Explanation opens after your attempt
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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व्यंजक (3x(4x-5)-2x(5x+1)) का सरल रूप क्या है?
What is the simplified form of (3x(4x-5)-2x(5x+1))?
#algebraic_expressions
#product_expansion
#hard
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A \(22x^2-13x\)
B \(2x^2-17x\)
C \(22x^2-17x\)
D \(2x^2-13x\)
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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किस विकल्प में \(4x^2\) और \(-11x^2\) का योग सही है?
Which option gives the correct sum of \(4x^2\) and \(-11x^2\)?
#algebraic_expressions
#add_like_terms
#powers
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A \(15x^2\)
B \(7x^2\)
C \(-7x^2\)
D \(-7x^4\)
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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यदि (x=6), तो \(\frac{x^2-3x+6}{3}\) का मान क्या होगा?
If (x=6), what is the value of \(\frac{x^2-3x+6}{3}\)?
#algebraic_expressions
#fraction_evaluation
#hard
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A (6)
B (8)
C (10)
D (12)
Explanation opens after your attempt
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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व्यंजक (12-(4x-7)+3(x-5)) का सरल रूप क्या है?
What is the simplified form of (12-(4x-7)+3(x-5))?
#algebraic_expressions
#signs
#simplification
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A (x+4)
B (-x+4)
C (-x+34)
D (7x-10)
Explanation opens after your attempt
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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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?
#algebraic_expressions
#geometry
#perimeter
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A (5x+4)
B (6x+18)
C (6x+4)
D (5x+18)
Explanation opens after your attempt
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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व्यंजक (6p-[3p-{4p-(p+6)}]) का सरल रूप क्या है?
What is the simplified form of (6p-[3p-{4p-(p+6)}])?
#algebraic_expressions
#nested_simplification
#hard
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A (6p+6)
B (6p-6)
C (2p+6)
D (2p-6)
Explanation opens after your attempt
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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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 \(u^2v+uv^2-3u\)?
#algebraic_expressions
#two_variable_power
#hard
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A (18)
B (24)
C (30)
D (34)
Explanation opens after your attempt
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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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)?
#algebraic_expressions
#word_to_expression
#square
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A \(y^2+6\)
B (y+36)
C ((y+6)2 )
D \(6-y^2\)
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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व्यंजक \(8x^2-7xy+4xy-5x^2\) का सरल रूप क्या है?
What is the simplified form of \(8x^2-7xy+4xy-5x^2\)?
#algebraic_expressions
#combine_terms
#multivariable
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A \(3x^2-3xy\)
B \(13x^2-3xy\)
C \(3x^2-11xy\)
D \(13x^2-11xy\)
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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यदि (m-n=9), तो (2m-2n+11) का मान क्या होगा?
If (m-n=9), what is the value of (2m-2n+11)?
#algebraic_expressions
#given_difference
#hard
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A (18)
B (20)
C (29)
D (31)
Explanation opens after your attempt
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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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)?
#algebraic_expressions
#linear_combination
#hard
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A (9x+9y)
B (9x-15y)
C (15x+9y)
D (15x-15y)
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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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 \(3x^2-7x+10\)?
#algebraic_expressions
#polynomial_addition
#hard
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A \(5x^2+12x+4\)
B \(x^2-2x+4\)
C \(5x^2-2x+4\)
D \(5x^2-12x-16\)
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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यदि (x=0), तो \(-4x^3+9x^2-5x+13\) का मान क्या होगा?
If (x=0), what is the value of \(-4x^3+9x^2-5x+13\)?
#algebraic_expressions
#zero_substitution
#hard
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A (0)
B (9)
C (13)
D (-13)
Explanation opens after your attempt
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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व्यंजक (5a-2[3a-4(a-2)]) का सरल रूप क्या है?
What is the simplified form of (5a-2[3a-4(a-2)])?
#algebraic_expressions
#bracket_simplification
#hard
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A (7a-16)
B (7a+16)
C (3a-16)
D (3a+16)
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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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 \(s^3t-st^3+2t\)?
#algebraic_expressions
#signed_evaluation
#hard
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A (-8)
B (-6)
C (-4)
D (0)
Explanation opens after your attempt
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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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}])?
#algebraic_expressions
#braces
#hard
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A (5x-13)
B (5x-11)
C (7x-13)
D (7x-11)
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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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}])?
#algebraic_expressions
#correct_simplification
#hard
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A (5x-13)
B (5x-11)
C (7x-13)
D (7x-11)
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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(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)?
#algebraic_expressions
#word_problem
#hard
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A (2x-3)
B (2x+11)
C (x-3)
D (x+11)
Explanation opens after your attempt
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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व्यंजक \(\frac{7x}{10}-\frac{x}{5}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{7x}{10}-\frac{x}{5}\)?
#algebraic_expressions
#fraction_terms
#hard
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A \(\frac{x}{2}\)
B \(\frac{9x}{10}\)
C \(\frac{3x}{5}\)
D \(\frac{7x^2}{50}\)
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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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))?
#algebraic_expressions
#substitution_given
#hard
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A (22)
B (24)
C (26)
D (30)
Explanation opens after your attempt
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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व्यंजक \(5x^2-6xy+3y^2-2x^2+11xy-8y^2\) का सरल रूप क्या है?
What is the simplified form of \(5x^2-6xy+3y^2-2x^2+11xy-8y^2\)?
#algebraic_expressions
#quadratic_two_variables
#hard
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A \(3x^2+5xy-5y^2\)
B \(7x^2+5xy-5y^2\)
C \(3x^2-17xy+11y^2\)
D \(7x^2-17xy-5y^2\)
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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व्यंजक (15-[4x-3(2-x)]) का सरल रूप क्या है?
What is the simplified form of (15-[4x-3(2-x)])?
#algebraic_expressions
#square_brackets
#hard
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A (21-x)
B (21-7x)
C (9+7x)
D (9+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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यदि (t=3), तो \(2t^4-5t^3+t^2\) का मान क्या होगा?
If (t=3), what is the value of \(2t^4-5t^3+t^2\)?
#algebraic_expressions
#power_evaluation
#hard
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A (0)
B (18)
C (36)
D (54)
Explanation opens after your attempt
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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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?
#algebraic_expressions
#phrase_expression
#hard
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A (5(a-b)-(a+b))
B (5(a+b)+(a-b))
C (5(a+b)-(a-b))
D (a-b-5(a+b))
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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व्यंजक ((3x-4)+(2x+9)-(5x-7)) का सरल रूप क्या है?
What is the simplified form of ((3x-4)+(2x+9)-(5x-7))?
#algebraic_expressions
#cancellation
#hard
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A (12)
B (10x+12)
C (12-0x)
D (0)
Explanation opens after your attempt
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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यदि (p=-1), तो \(2p^4-3p^3+4p^2-5\) का मान क्या होगा?
If (p=-1), what is the value of \(2p^4-3p^3+4p^2-5\)?
#algebraic_expressions
#negative_one_power
#hard
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
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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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)?
#algebraic_expressions
#two_variable_subtraction
#hard
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A (4x-11y)
B (8x+5y)
C (4x+5y)
D (8x-11y)
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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व्यंजक \(4x^2y-9xy^2+5x^2y+6xy^2\) का सरल रूप क्या है?
What is the simplified form of \(4x^2y-9xy^2+5x^2y+6xy^2\)?
#algebraic_expressions
#multivariable_powers
#hard
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A \(9x^2y-3xy^2\)
B \(9x^2y+15xy^2\)
C \(-x^2y-3xy^2\)
D \(9x^3y^3-3xy^2\)
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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यदि (q=4), तो \(\frac{q^3-2q}{4}\) का मान क्या होगा?
If (q=4), what is the value of \(\frac{q^3-2q}{4}\)?
#algebraic_expressions
#cubic_fraction
#hard
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A (12)
B (14)
C (16)
D (18)
Explanation opens after your attempt
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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(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)?
#algebraic_expressions
#consecutive_odd_numbers
#hard
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A (4n+8)
B (4n+12)
C (n+12)
D (4n+6)
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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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)])?
#algebraic_expressions
#complex_brackets
#hard
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A (7x-12)
B (7x-18)
C (17x-12)
D (17x-18)
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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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)?
#algebraic_expressions
#two_variable_square
#hard
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A (36)
B (38)
C (40)
D (42)
Explanation opens after your attempt
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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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)?
#algebraic_expressions
#linear_terms
#hard
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A (7a-7b)
B (19a-7b)
C (7a-3b)
D (19a+3b)
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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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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?
#algebraic_expressions
#rectangle_perimeter
#hard
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A (14x-10)
B (7x-5)
C (14x-5)
D (7x-10)
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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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यदि (x=1), तो \(6x^3-9x^2+4x-8\) का मान क्या होगा?
If (x=1), what is the value of \(6x^3-9x^2+4x-8\)?
#algebraic_expressions
#value_at_one
#hard
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A (-7)
B (-5)
C (5)
D (7)
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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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व्यंजक (7x-3[2x-{x-6}]) का सरल रूप क्या है?
What is the simplified form of (7x-3[2x-{x-6}])?
#algebraic_expressions
#braces_simplification
#hard
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A (4x-18)
B (4x+18)
C (10x-18)
D (10x+18)
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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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 \(5x^2-3x+8\)?
#algebraic_expressions
#polynomial_subtraction
#hard
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A \(3x^2+4x+14\)
B \(7x^2-10x+2\)
C \(3x^2-10x+2\)
D \(7x^2+4x+14\)
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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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))?
#algebraic_expressions
#bracket_evaluation
#hard
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A (11)
B (13)
C (15)
D (17)
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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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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}])?
#algebraic_expressions
#nested_brackets_final
#hard
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A (6x+2)
B (6x-14)
C (14x+2)
D (14x-14)
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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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