यदि (2x-2 -3x+5-\(x^2+4x-7\)) को सरल किया जाए, तो परिणाम क्या होगा?
If (2x-2 -3x+5-\(x^2+4x-7\)) is simplified, what is the result?
#algebraic-expressions
#brackets
#simplification
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A \(x^2-7x+12\)
B \(3x^2+x-2\)
C \(x^2+x-2\)
D \(x^2-7x-2\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-7x+12\)
Step 1
Concept
Signs change when the bracket is subtracted. Thus \(2x^2-3x+5-x^2-4x+7=x^2-7x+12\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-7x+12\). Signs change when the bracket is subtracted. Thus \(2x^2-3x+5-x^2-4x+7=x^2-7x+12\).
Step 3
Exam Tip
कोष्ठक हटाते समय अंदर के चिन्ह बदलेंगे। इसलिए \(2x^2-3x+5-x^2-4x+7=x^2-7x+12\)।
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यदि (x=-2) हो, तो \(3x^3-2x^2+5x-1\) का मान क्या होगा?
If (x=-2), what is the value of \(3x^3-2x^2+5x-1\)?
#algebraic-expressions
#evaluation
#cubic
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A (-43)
B (-35)
C (21)
D (-17)
Explanation opens after your attempt
Step 1
Concept
((-2)3 ) is negative and ((-2)2 ) is positive. The value is (3(-8)-2(4)+5(-2)-1=-43).
Step 2
Why this answer is correct
The correct answer is A. (-43). ((-2)3 ) is negative and ((-2)2 ) is positive. The value is (3(-8)-2(4)+5(-2)-1=-43).
Step 3
Exam Tip
((-2)3 ) ऋणात्मक और ((-2)2 ) धनात्मक होगा। मान (3(-8)-2(4)+5(-2)-1=-43) है।
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\(4a^2b-3ab^2+5a^2b+7ab^2\) को सरल करने पर क्या मिलेगा?
What is obtained after simplifying \(4a^2b-3ab^2+5a^2b+7ab^2\)?
#algebraic-expressions
#like-terms
#multiple-variables
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A \(9a^2b+4ab^2\)
B \(9a^2b-10ab^2\)
C \(16a^3b^3\)
D \(a^2b+12ab^2\)
Explanation opens after your attempt
Correct Answer
A. \(9a^2b+4ab^2\)
Step 1
Concept
Terms with \(a^2b\) and \(ab^2\) combine separately. Therefore the answer is \(9a^2b+4ab^2\).
Step 2
Why this answer is correct
The correct answer is A. \(9a^2b+4ab^2\). Terms with \(a^2b\) and \(ab^2\) combine separately. Therefore the answer is \(9a^2b+4ab^2\).
Step 3
Exam Tip
\(a^2b\) वाले पद और \(ab^2\) वाले पद अलग-अलग मिलेंगे। इसलिए उत्तर \(9a^2b+4ab^2\) है।
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किस व्यंजक का सरल रूप (5p-18) है?
Which expression has the simplified form (5p-18)?
#algebraic-expressions
#equivalent-expression
#expansion
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A (3(2p-5)-(p+3))
B (2(3p-9)+p)
C (5(p-18))
D (6p-5(p-18))
Explanation opens after your attempt
Correct Answer
A. (3(2p-5)-(p+3))
Step 1
Concept
(3(2p-5)-(p+3)=6p-15-p-3=5p-18). Open brackets first to check options.
Step 2
Why this answer is correct
The correct answer is A. (3(2p-5)-(p+3)). (3(2p-5)-(p+3)=6p-15-p-3=5p-18). Open brackets first to check options.
Step 3
Exam Tip
(3(2p-5)-(p+3)=6p-15-p-3=5p-18)। विकल्प जाँचने के लिए पहले कोष्ठक खोलें।
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यदि (m=3) और (n=-2), तो \(m^2n-2mn^2\) का मान क्या होगा?
If (m=3) and (n=-2), what is the value of \(m^2n-2mn^2\)?
#algebraic-expressions
#substitution
#two-variables
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A (-42)
B (6)
C (-18)
D (42)
Explanation opens after your attempt
Step 1
Concept
(m-2 n=9(-2)=-18) and (2mn-2 =2(3)(4)=24). So the total value is (-18-24=-42).
Step 2
Why this answer is correct
The correct answer is A. (-42). (m-2 n=9(-2)=-18) and (2mn-2 =2(3)(4)=24). So the total value is (-18-24=-42).
Step 3
Exam Tip
(m-2 n=9(-2)=-18) और (2mn-2 =2(3)(4)=24)। इसलिए कुल मान (-18-24=-42) है।
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(2(x+3y)-3(2x-y)+4x) को सरल करने पर क्या मिलेगा?
What is obtained after simplifying (2(x+3y)-3(2x-y)+4x)?
#algebraic-expressions
#brackets
#cancellation
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A (12y)
B (9y)
C (12x+9y)
D (9x+3y)
Explanation opens after your attempt
Step 1
Concept
Expanding gives (2x+6y-6x+3y+4x). The (x)-terms cancel and (9y) remains.
Step 2
Why this answer is correct
The correct answer is B. (9y). Expanding gives (2x+6y-6x+3y+4x). The (x)-terms cancel and (9y) remains.
Step 3
Exam Tip
खोलने पर (2x+6y-6x+3y+4x) मिलता है। (x) पद कट जाते हैं और (9y) बचता है।
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किस स्थिति में (kx+6x) का सरल रूप (11x) होगा?
For which value of (k) will (kx+6x) simplify to (11x)?
#algebraic-expressions
#unknown-coefficient
#like-terms
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A (17)
B (5)
C (6)
D (-5)
Explanation opens after your attempt
Step 1
Concept
Combining like terms gives (kx+6x=(k+6)x). From (k+6=11), (k=5).
Step 2
Why this answer is correct
The correct answer is B. (5). Combining like terms gives (kx+6x=(k+6)x). From (k+6=11), (k=5).
Step 3
Exam Tip
समान पद मिलाने पर (kx+6x=(k+6)x)। (k+6=11) से (k=5) मिलेगा।
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\(7u^2v-4uv^2+3u^2v-9uv^2\) में \(uv^2\) का गुणांक सरल करने के बाद क्या होगा?
After simplifying \(7u^2v-4uv^2+3u^2v-9uv^2\), what will be the coefficient of \(uv^2\)?
#algebraic-expressions
#coefficient
#like-terms
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A (-4)
B (-13)
C (10)
D (13)
Explanation opens after your attempt
Step 1
Concept
The \(uv^2\) terms are \(-4uv^2\) and \(-9uv^2\). Their sum is \(-13uv^2\).
Step 2
Why this answer is correct
The correct answer is B. (-13). The \(uv^2\) terms are \(-4uv^2\) and \(-9uv^2\). Their sum is \(-13uv^2\).
Step 3
Exam Tip
\(uv^2\) वाले पद \(-4uv^2\) और \(-9uv^2\) हैं। इनका योग \(-13uv^2\) है।
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कौन-सा व्यंजक (x) के वर्ग और (y) के वर्ग के योग में (2xy) घटाने को दर्शाता है?
Which expression represents subtracting (2xy) from the sum of the squares of (x) and (y)?
#algebraic-expressions
#word-to-expression
#squares
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A \(x^2-y^2-2xy\)
B \(x^2+y^2+2xy\)
C \(x^2+y^2-2xy\)
D \(2xy-x^2-y^2\)
Explanation opens after your attempt
Correct Answer
C. \(x^2+y^2-2xy\)
Step 1
Concept
First the sum of squares is \(x^2+y^2\), and (2xy) is subtracted from it. So \(x^2+y^2-2xy\) is correct.
Step 2
Why this answer is correct
The correct answer is C. \(x^2+y^2-2xy\). First the sum of squares is \(x^2+y^2\), and (2xy) is subtracted from it. So \(x^2+y^2-2xy\) is correct.
Step 3
Exam Tip
पहले वर्गों का योग \(x^2+y^2\) है और उसमें से (2xy) घटाना है। इसलिए \(x^2+y^2-2xy\) सही है।
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यदि (x=1) और (y=-3), तो \(2x^2-xy+y^2\) का मान क्या होगा?
If (x=1) and (y=-3), what is the value of \(2x^2-xy+y^2\)?
#algebraic-expressions
#evaluation
#quadratic-two-variables
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A (8)
B (11)
C (14)
D (-4)
Explanation opens after your attempt
Step 1
Concept
(2(1)2 -(1)(-3)+(-3)2 =2+3+9=14). Watch negative multiplication and squares carefully.
Step 2
Why this answer is correct
The correct answer is C. (14). (2(1)2 -(1)(-3)+(-3)2 =2+3+9=14). Watch negative multiplication and squares carefully.
Step 3
Exam Tip
(2(1)2 -(1)(-3)+(-3)2 =2+3+9=14)। ऋणात्मक गुणन और वर्ग पर ध्यान दें।
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(5x-2 -\(2x^2-3x\)+(4x-7)) को सरल करने पर (x) का गुणांक क्या होगा?
After simplifying (5x-2 -\(2x^2-3x\)+(4x-7)), what is the coefficient of (x)?
#algebraic-expressions
#coefficient
#brackets
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A (3)
B (4)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The expression becomes \(5x^2-2x^2+3x+4x-7=3x^2+7x-7\). So the coefficient of (x) is (7).
Step 2
Why this answer is correct
The correct answer is C. (7). The expression becomes \(5x^2-2x^2+3x+4x-7=3x^2+7x-7\). So the coefficient of (x) is (7).
Step 3
Exam Tip
व्यंजक \(5x^2-2x^2+3x+4x-7=3x^2+7x-7\) बनेगा। इसलिए (x) का गुणांक (7) है।
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किस विकल्प में \(a^2b\) के समान पदों का पूरा समूह है?
Which option is a complete group of like terms of \(a^2b\)?
#algebraic-expressions
#like-terms
#classification
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A \(3a^2b\), \(-5a^2b\), \(8a^2b\)
B \(a^2b\), \(ab^2\), \(a^2\)
C (2ab), \(4a^2b\), \(6b^2a\)
D \(a^2b\), \(a^3b\), \(a^2b^2\)
Explanation opens after your attempt
Correct Answer
A. \(3a^2b\), \(-5a^2b\), \(8a^2b\)
Step 1
Concept
Like terms have exactly the same variables and powers. In the first option, every variable part is \(a^2b\).
Step 2
Why this answer is correct
The correct answer is A. \(3a^2b\), \(-5a^2b\), \(8a^2b\). Like terms have exactly the same variables and powers. In the first option, every variable part is \(a^2b\).
Step 3
Exam Tip
समान पदों में चर और उनकी घातें बिल्कुल समान होती हैं। पहले विकल्प में सभी का चर भाग \(a^2b\) है।
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(3(2a-b)-2(a+3b)+5b) को सरल करने पर क्या मिलेगा?
What is obtained after simplifying (3(2a-b)-2(a+3b)+5b)?
#algebraic-expressions
#expansion
#two-variables
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A (4a-4b)
B (4a+4b)
C (8a-4b)
D (4a-14b)
Explanation opens after your attempt
Correct Answer
A. (4a-4b)
Step 1
Concept
Expanding gives (6a-3b-2a-6b+5b). Combining like terms gives (4a-4b).
Step 2
Why this answer is correct
The correct answer is A. (4a-4b). Expanding gives (6a-3b-2a-6b+5b). Combining like terms gives (4a-4b).
Step 3
Exam Tip
खोलने पर (6a-3b-2a-6b+5b) मिलता है। समान पद मिलाकर (4a-4b) मिलता है।
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यदि \(2x^2+kx-15\) में (x=3) रखने पर मान (0) मिलता है, तो (k) क्या होगा?
If substituting (x=3) in \(2x^2+kx-15\) gives (0), what is (k)?
#algebraic-expressions
#substitution
#parameter
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A (-1)
B (1)
C (-3)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (2(3)2 +3k-15=0), (18+3k-15=0). Hence (3k=-3) and (k=-1).
Step 2
Why this answer is correct
The correct answer is A. (-1). From (2(3)2 +3k-15=0), (18+3k-15=0). Hence (3k=-3) and (k=-1).
Step 3
Exam Tip
(2(3)2 +3k-15=0) से (18+3k-15=0)। इसलिए (3k=-3) और (k=-1)।
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\(4x^2y-6xy+2x^2y+9xy-5\) में कितने अलग-अलग प्रकार के पद सरल रूप में रहेंगे?
How many different types of terms remain in the simplified form of \(4x^2y-6xy+2x^2y+9xy-5\)?
#algebraic-expressions
#terms
#simplification
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The simplified form is \(6x^2y+3xy-5\). It has three types: \(x^2y\), (xy), and a constant term.
Step 2
Why this answer is correct
The correct answer is C. (3). The simplified form is \(6x^2y+3xy-5\). It has three types: \(x^2y\), (xy), and a constant term.
Step 3
Exam Tip
सरल रूप \(6x^2y+3xy-5\) है। इसमें \(x^2y\), (xy) और स्थिर पद तीन प्रकार हैं।
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किस व्यंजक में स्थिर पद नहीं है लेकिन दो अलग-अलग चर-पद हैं?
Which expression has no constant term but has two different variable terms?
#algebraic-expressions
#constant-term
#term-types
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A \(7x^2-3x\)
B (5x+8)
C \(x^2+4x+6\)
D (9)
Explanation opens after your attempt
Correct Answer
A. \(7x^2-3x\)
Step 1
Concept
In \(7x^2-3x\), both terms contain variables and there is no constant term. It has two terms with different powers.
Step 2
Why this answer is correct
The correct answer is A. \(7x^2-3x\). In \(7x^2-3x\), both terms contain variables and there is no constant term. It has two terms with different powers.
Step 3
Exam Tip
\(7x^2-3x\) में दोनों पद चर वाले हैं और कोई स्थिर पद नहीं है। यह दो अलग-अलग घातों वाले पद रखता है।
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(2p(p-3)+4(p+1)) को सरल करने पर क्या मिलेगा?
What is obtained after simplifying (2p(p-3)+4(p+1))?
#algebraic-expressions
#expansion
#polynomial
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A \(2p^2-2p+4\)
B \(2p^2+10p+4\)
C \(2p^2-6p+4\)
D \(2p^2+4p-3\)
Explanation opens after your attempt
Correct Answer
A. \(2p^2-2p+4\)
Step 1
Concept
(2p(p-3)=2p-2 -6p) and (4(p+1)=4p+4). Combining gives \(2p^2-2p+4\).
Step 2
Why this answer is correct
The correct answer is A. \(2p^2-2p+4\). (2p(p-3)=2p-2 -6p) and (4(p+1)=4p+4). Combining gives \(2p^2-2p+4\).
Step 3
Exam Tip
(2p(p-3)=2p-2 -6p) और (4(p+1)=4p+4)। मिलाने पर \(2p^2-2p+4\) मिलेगा।
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यदि (x+y=5) हो, तो (2(x+y)-3) का मान क्या होगा?
If (x+y=5), what is the value of (2(x+y)-3)?
#algebraic-expressions
#substitution
#group-value
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A (7)
B (10)
C (2)
D (13)
Explanation opens after your attempt
Step 1
Concept
Replace the whole (x+y) by (5). Then (2(5)-3=7).
Step 2
Why this answer is correct
The correct answer is A. (7). Replace the whole (x+y) by (5). Then (2(5)-3=7).
Step 3
Exam Tip
पूरे (x+y) को (5) से बदलें। तब (2(5)-3=7) होगा।
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\(9r^2s-4rs+rs-5r^2s\) को सरल करने पर \(r^2s\) का गुणांक क्या होगा?
After simplifying \(9r^2s-4rs+rs-5r^2s\), what will be the coefficient of \(r^2s\)?
#algebraic-expressions
#coefficient
#multiple-variables
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A (14)
B (4)
C (-3)
D (3)
Explanation opens after your attempt
Step 1
Concept
The \(r^2s\) terms are \(9r^2s\) and \(-5r^2s\). Their sum is \(4r^2s\).
Step 2
Why this answer is correct
The correct answer is B. (4). The \(r^2s\) terms are \(9r^2s\) and \(-5r^2s\). Their sum is \(4r^2s\).
Step 3
Exam Tip
\(r^2s\) वाले पद \(9r^2s\) और \(-5r^2s\) हैं। उनका योग \(4r^2s\) है।
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कौन-सा व्यंजक (3x-2y) के (4) गुने में (x+y) जोड़ने को दर्शाता है?
Which expression represents adding (x+y) to four times (3x-2y)?
#algebraic-expressions
#word-to-expression
#brackets
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A (4(3x-2y)+x+y)
B (4(3x-2y+x+y))
C (3x-2y+4(x+y))
D (4(3x)+2y+x+y)
Explanation opens after your attempt
Correct Answer
A. (4(3x-2y)+x+y)
Step 1
Concept
First take four times (3x-2y), then add (x+y). Therefore (4(3x-2y)+x+y) is correct.
Step 2
Why this answer is correct
The correct answer is A. (4(3x-2y)+x+y). First take four times (3x-2y), then add (x+y). Therefore (4(3x-2y)+x+y) is correct.
Step 3
Exam Tip
पहले (3x-2y) का (4) गुना लेना है और फिर (x+y) जोड़ना है। इसलिए (4(3x-2y)+x+y) सही है।
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\(x^2+2x-3\) और \(2x^2-x+4\) का योग क्या होगा?
What is the sum of \(x^2+2x-3\) and \(2x^2-x+4\)?
#algebraic-expressions
#addition
#polynomials
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A \(3x^2+x+1\)
B \(3x^2+3x+7\)
C \(x^2+3x-7\)
D \(3x^4+x+1\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+x+1\)
Step 1
Concept
Adding like terms gives \(x^2+2x^2=3x^2\), (2x-x=x), and (-3+4=1).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2+x+1\). Adding like terms gives \(x^2+2x^2=3x^2\), (2x-x=x), and (-3+4=1).
Step 3
Exam Tip
समान पद जोड़ने पर \(x^2+2x^2=3x^2\), (2x-x=x) और (-3+4=1)।
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\(5x^2-3x+8\) में से \(2x^2+4x-1\) घटाने पर क्या मिलेगा?
What is obtained by subtracting \(2x^2+4x-1\) from \(5x^2-3x+8\)?
#algebraic-expressions
#subtraction
#polynomials
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A \(7x^2+x+7\)
B \(3x^2-7x+9\)
C \(3x^2+x+9\)
D \(7x^2-7x+7\)
Explanation opens after your attempt
Correct Answer
B. \(3x^2-7x+9\)
Step 1
Concept
Subtraction gives (5x-2 -3x+8-\(2x^2+4x-1\)). The simplified form is \(3x^2-7x+9\).
Step 2
Why this answer is correct
The correct answer is B. \(3x^2-7x+9\). Subtraction gives (5x-2 -3x+8-\(2x^2+4x-1\)). The simplified form is \(3x^2-7x+9\).
Step 3
Exam Tip
घटाने पर (5x-2 -3x+8-\(2x^2+4x-1\)) मिलेगा। सरल रूप \(3x^2-7x+9\) है।
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यदि (a-b=4) और (b=3), तो (2a-b) का मान क्या होगा?
If (a-b=4) and (b=3), what is the value of (2a-b)?
#algebraic-expressions
#value
#linear-relation
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A (8)
B (11)
C (14)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (a-b=4) and (b=3), (a=7). Therefore (2a-b=14-3=11).
Step 2
Why this answer is correct
The correct answer is B. (11). From (a-b=4) and (b=3), (a=7). Therefore (2a-b=14-3=11).
Step 3
Exam Tip
(a-b=4) और (b=3) से (a=7)। इसलिए (2a-b=14-3=11)।
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(3xy-2x+4xy+7x-5y) को सरल करने पर कौन-सा पद नहीं रहेगा?
After simplifying (3xy-2x+4xy+7x-5y), which term will not remain?
#algebraic-expressions
#simplification
#term-identification
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A (7xy)
B (5x)
C (-5y)
D (9x)
Explanation opens after your attempt
Step 1
Concept
The simplified form is (7xy+5x-5y). There is no term like (9x).
Step 2
Why this answer is correct
The correct answer is D. (9x). The simplified form is (7xy+5x-5y). There is no term like (9x).
Step 3
Exam Tip
सरल रूप (7xy+5x-5y) है। इसमें (9x) जैसा कोई पद नहीं है।
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किस विकल्प में (2x(x-4)+3x) का सही सरल रूप है?
Which option gives the correct simplified form of (2x(x-4)+3x)?
#algebraic-expressions
#expansion
#simplification
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A \(2x^2-5x\)
B \(2x^2-8x+3\)
C \(2x^2-11x\)
D \(2x^2+x\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-5x\)
Step 1
Concept
(2x(x-4)=2x-2 -8x). Adding (3x) gives \(2x^2-5x\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-5x\). (2x(x-4)=2x-2 -8x). Adding (3x) gives \(2x^2-5x\).
Step 3
Exam Tip
(2x(x-4)=2x-2 -8x) है। इसमें (3x) जोड़ने पर \(2x^2-5x\) मिलता है।
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यदि (x=2) पर \(x^2+kx+6\) का मान (16) है, तो (k) क्या होगा?
If the value of \(x^2+kx+6\) at (x=2) is (16), what is (k)?
#algebraic-expressions
#parameter
#evaluation
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From \(2^2+2k+6=16\), (10+2k=16). Hence (k=3).
Step 2
Why this answer is correct
The correct answer is B. (3). From \(2^2+2k+6=16\), (10+2k=16). Hence (k=3).
Step 3
Exam Tip
\(2^2+2k+6=16\) से (10+2k=16)। इसलिए (k=3) है।
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\(2a^2-3ab+4b^2+a^2+5ab-b^2\) को सरल करने पर क्या मिलेगा?
What is obtained after simplifying \(2a^2-3ab+4b^2+a^2+5ab-b^2\)?
#algebraic-expressions
#like-terms
#three-term-form
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A \(3a^2+2ab+3b^2\)
B \(3a^2-8ab+5b^2\)
C \(a^2+2ab+3b^2\)
D \(3a^2+8ab+3b^2\)
Explanation opens after your attempt
Correct Answer
A. \(3a^2+2ab+3b^2\)
Step 1
Concept
Combine \(a^2\), (ab), and \(b^2\) terms separately. The simplified form is \(3a^2+2ab+3b^2\).
Step 2
Why this answer is correct
The correct answer is A. \(3a^2+2ab+3b^2\). Combine \(a^2\), (ab), and \(b^2\) terms separately. The simplified form is \(3a^2+2ab+3b^2\).
Step 3
Exam Tip
\(a^2\), (ab) और \(b^2\) वाले पद अलग-अलग मिलाएँ। सरल रूप \(3a^2+2ab+3b^2\) है।
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\(6x^3-4x^2+x-9\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(6x^3-4x^2+x-9\)?
#algebraic-expressions
#coefficient
#powers
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A (6)
B (-4)
C (1)
D (-9)
Explanation opens after your attempt
Step 1
Concept
The term containing \(x^2\) is \(-4x^2\). Therefore, the coefficient is (-4).
Step 2
Why this answer is correct
The correct answer is B. (-4). The term containing \(x^2\) is \(-4x^2\). Therefore, the coefficient is (-4).
Step 3
Exam Tip
\(x^2\) वाला पद \(-4x^2\) है। इसलिए गुणांक (-4) है।
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किस व्यंजक में (x) और (y) दोनों की कुल घात (5) है?
In which expression is the total power of (x) and (y) equal to (5)?
#algebraic-expressions
#total-degree
#variables
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A \(x^2y^3\)
B \(x^3y^3\)
C \(x^4y^2\)
D \(xy^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^2y^3\)
Step 1
Concept
In \(x^2y^3\), the total power is (2+3=5). In a multivariable term, add the powers to get the total power.
Step 2
Why this answer is correct
The correct answer is A. \(x^2y^3\). In \(x^2y^3\), the total power is (2+3=5). In a multivariable term, add the powers to get the total power.
Step 3
Exam Tip
\(x^2y^3\) में कुल घात (2+3=5) है। बहु-चर पद में घातें जोड़कर कुल घात मिलती है।
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यदि (x-y=6) और (x+y=10), तो (2x) का मान क्या होगा?
If (x-y=6) and (x+y=10), what is the value of (2x)?
#algebraic-expressions
#expression-value
#linear-relations
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A (16)
B (10)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
Adding the two equations gives (2x=16). In such questions, try adding the given expressions.
Step 2
Why this answer is correct
The correct answer is A. (16). Adding the two equations gives (2x=16). In such questions, try adding the given expressions.
Step 3
Exam Tip
दोनों समीकरणों को जोड़ने पर (2x=16) मिलता है। ऐसे प्रश्नों में दिए गए पूरे व्यंजकों को जोड़कर देखें।
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(4(2x-y)-3(x+2y)+5y) को सरल करने पर क्या मिलेगा?
What is obtained after simplifying (4(2x-y)-3(x+2y)+5y)?
#algebraic-expressions
#expansion
#two-variables
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A (5x-5y)
B (11x-5y)
C (5x+5y)
D (11x+5y)
Explanation opens after your attempt
Correct Answer
A. (5x-5y)
Step 1
Concept
Expanding gives (8x-4y-3x-6y+5y). Combining like terms gives (5x-5y).
Step 2
Why this answer is correct
The correct answer is A. (5x-5y). Expanding gives (8x-4y-3x-6y+5y). Combining like terms gives (5x-5y).
Step 3
Exam Tip
खोलने पर (8x-4y-3x-6y+5y) मिलता है। समान पद मिलाकर (5x-5y) बनेगा।
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\(x^2+px+12\) में यदि (x) का गुणांक (-7) है, तो (p) क्या है?
In \(x^2+px+12\), if the coefficient of (x) is (-7), what is (p)?
#algebraic-expressions
#coefficient
#parameter
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A (7)
B (-7)
C (12)
D (-12)
Explanation opens after your attempt
Step 1
Concept
In (px), the coefficient of (x) is (p). Therefore, (p=-7).
Step 2
Why this answer is correct
The correct answer is B. (-7). In (px), the coefficient of (x) is (p). Therefore, (p=-7).
Step 3
Exam Tip
(px) में (x) का गुणांक (p) है। इसलिए (p=-7) होगा।
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कौन-सा व्यंजक \(2x^2-3x+1\) में \(x^2+x-4\) जोड़ने पर मिलता है?
Which expression is obtained by adding \(x^2+x-4\) to \(2x^2-3x+1\)?
#algebraic-expressions
#addition
#like-terms
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A \(3x^2-2x-3\)
B \(x^2-4x+5\)
C \(3x^2-4x-3\)
D \(3x^2-2x+5\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-2x-3\)
Step 1
Concept
Add like terms: \(2x^2+x^2=3x^2\), (-3x+x=-2x), and (1-4=-3).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-2x-3\). Add like terms: \(2x^2+x^2=3x^2\), (-3x+x=-2x), and (1-4=-3).
Step 3
Exam Tip
समान पद जोड़ें: \(2x^2+x^2=3x^2\), (-3x+x=-2x), (1-4=-3)।
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यदि (a=2), (b=-1), तो \(a^3+3a^2b+2b^3\) का मान क्या होगा?
If (a=2), (b=-1), what is the value of \(a^3+3a^2b+2b^3\)?
#algebraic-expressions
#evaluation
#cubic-two-variables
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A (-6)
B (-2)
C (18)
D (6)
Explanation opens after your attempt
Step 1
Concept
Substitution gives (8+3(4)(-1)+2(-1)=-6). Handle powers and signs carefully.
Step 2
Why this answer is correct
The correct answer is A. (-6). Substitution gives (8+3(4)(-1)+2(-1)=-6). Handle powers and signs carefully.
Step 3
Exam Tip
मान रखने पर (8+3(4)(-1)+2(-1)=-6) मिलता है। घात और चिन्ह दोनों ध्यान से लें।
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(5x-(2x-(3x-4))) को सरल करने पर क्या मिलेगा?
What is obtained after simplifying (5x-(2x-(3x-4)))?
#algebraic-expressions
#nested-brackets
#simplification
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A (6x-4)
B (4x-4)
C (6x+4)
D (4x+4)
Explanation opens after your attempt
Step 1
Concept
Inside, (2x-(3x-4)=-x+4). Hence (5x-(-x+4)=6x-4).
Step 2
Why this answer is correct
The correct answer is A. (6x-4). Inside, (2x-(3x-4)=-x+4). Hence (5x-(-x+4)=6x-4).
Step 3
Exam Tip
अंदर से (2x-(3x-4)=-x+4) है। इसलिए (5x-(-x+4)=6x-4)।
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कौन-सा पद \(6x^2yz\) का समान पद है?
Which term is a like term of \(6x^2yz\)?
#algebraic-expressions
#like-terms
#three-variables
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A \(9x^2yz\)
B \(9xy^2z\)
C \(9x^2y^2z\)
D (9xyz)
Explanation opens after your attempt
Correct Answer
A. \(9x^2yz\)
Step 1
Concept
A like term must keep the variable part \(x^2yz\). \(9x^2yz\) has the same variable part.
Step 2
Why this answer is correct
The correct answer is A. \(9x^2yz\). A like term must keep the variable part \(x^2yz\). \(9x^2yz\) has the same variable part.
Step 3
Exam Tip
समान पद में चर भाग \(x^2yz\) ही रहना चाहिए। \(9x^2yz\) का चर भाग समान है।
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\(3x^2-5xy+2y^2-7x^2+xy-y^2\) को सरल करने पर क्या मिलेगा?
What is obtained after simplifying \(3x^2-5xy+2y^2-7x^2+xy-y^2\)?
#algebraic-expressions
#combine-like-terms
#three-groups
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A \(-4x^2-4xy+y^2\)
B \(10x^2-6xy+3y^2\)
C \(-4x^2-6xy+y^2\)
D \(-4x^2-4xy+3y^2\)
Explanation opens after your attempt
Correct Answer
A. \(-4x^2-4xy+y^2\)
Step 1
Concept
\(3x^2-7x^2=-4x^2\), (-5xy+xy=-4xy), and \(2y^2-y^2=y^2\).
Step 2
Why this answer is correct
The correct answer is A. \(-4x^2-4xy+y^2\). \(3x^2-7x^2=-4x^2\), (-5xy+xy=-4xy), and \(2y^2-y^2=y^2\).
Step 3
Exam Tip
\(3x^2-7x^2=-4x^2\), (-5xy+xy=-4xy), और \(2y^2-y^2=y^2\)।
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यदि (x=3), तो \(\frac{x^2+2x-3}{x}\) का मान क्या होगा?
If (x=3), what is the value of \(\frac{x^2+2x-3}{x}\)?
#algebraic-expressions
#evaluation
#fraction
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A (4)
B (3)
C (6)
D (12)
Explanation opens after your attempt
Step 1
Concept
The numerator is (32 +2(3)-3=12). Then \(\frac{12}{3}=4\).
Step 2
Why this answer is correct
The correct answer is A. (4). The numerator is (32 +2(3)-3=12). Then \(\frac{12}{3}=4\).
Step 3
Exam Tip
अंश (32 +2(3)-3=12) है। फिर \(\frac{12}{3}=4\) मिलेगा।
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किस व्यंजक का मान (x=0) पर स्थिर पद के बराबर होता है?
For which expression is the value at (x=0) equal to its constant term?
#algebraic-expressions
#constant-term
#evaluation
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A \(7x^2-2x+9\)
B केवल \(x^2\) वाले व्यंजक / Only expressions with \(x^2\)
C केवल (x) वाले व्यंजक / Only expressions with (x)
D कोई भी नहीं / None
Explanation opens after your attempt
Correct Answer
A. \(7x^2-2x+9\)
Step 1
Concept
When (x=0), variable terms become zero. The value of \(7x^2-2x+9\) is (9), the constant term.
Step 2
Why this answer is correct
The correct answer is A. \(7x^2-2x+9\). When (x=0), variable terms become zero. The value of \(7x^2-2x+9\) is (9), the constant term.
Step 3
Exam Tip
(x=0) रखने पर चर वाले पद शून्य हो जाते हैं। \(7x^2-2x+9\) का मान (9) यानी स्थिर पद है।
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(2(3a-2b)+5(a+b)-4a) को सरल करने पर (b) का गुणांक क्या होगा?
After simplifying (2(3a-2b)+5(a+b)-4a), what will be the coefficient of (b)?
#algebraic-expressions
#coefficient
#expansion
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A (1)
B (-1)
C (9)
D (5)
Explanation opens after your attempt
Step 1
Concept
The simplified form is (6a-4b+5a+5b-4a=7a+b). So the coefficient of (b) is (1).
Step 2
Why this answer is correct
The correct answer is A. (1). The simplified form is (6a-4b+5a+5b-4a=7a+b). So the coefficient of (b) is (1).
Step 3
Exam Tip
सरल रूप (6a-4b+5a+5b-4a=7a+b) है। इसलिए (b) का गुणांक (1) है।
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यदि \(x^2=9\) और (x=3), तो \(4x^2-5x+2\) का मान क्या होगा?
If \(x^2=9\) and (x=3), what is the value of \(4x^2-5x+2\)?
#algebraic-expressions
#evaluation
#given-values
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A (23)
B (53)
C (17)
D (-7)
Explanation opens after your attempt
Step 1
Concept
Substitute \(x^2=9\) and (x=3) directly. (4(9)-5(3)+2=23).
Step 2
Why this answer is correct
The correct answer is A. (23). Substitute \(x^2=9\) and (x=3) directly. (4(9)-5(3)+2=23).
Step 3
Exam Tip
सीधे \(x^2=9\) और (x=3) रखें। (4(9)-5(3)+2=23)।
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कौन-सा व्यंजक \(2x^2-3xy+y^2\) में \(-x^2+5xy-4y^2\) जोड़ने पर मिलता है?
Which expression is obtained by adding \(-x^2+5xy-4y^2\) to \(2x^2-3xy+y^2\)?
#algebraic-expressions
#addition
#two-variable-polynomial
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A \(x^2+2xy-3y^2\)
B \(3x^2-8xy+5y^2\)
C \(x^2-8xy-3y^2\)
D \(x^2+2xy+5y^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2xy-3y^2\)
Step 1
Concept
Adding like terms gives \(2x^2-x^2=x^2\), (-3xy+5xy=2xy), and \(y^2-4y^2=-3y^2\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2xy-3y^2\). Adding like terms gives \(2x^2-x^2=x^2\), (-3xy+5xy=2xy), and \(y^2-4y^2=-3y^2\).
Step 3
Exam Tip
समान पद जोड़ने पर \(2x^2-x^2=x^2\), (-3xy+5xy=2xy), और \(y^2-4y^2=-3y^2\)।
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यदि (3x-2=10), तो \(x^2+x\) का मान क्या होगा?
If (3x-2=10), what is the value of \(x^2+x\)?
#algebraic-expressions
#evaluation
#linear-condition
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A (12)
B (20)
C (16)
D (8)
Explanation opens after your attempt
Step 1
Concept
From (3x=12), (x=4). Therefore \(x^2+x=16+4=20\).
Step 2
Why this answer is correct
The correct answer is B. (20). From (3x=12), (x=4). Therefore \(x^2+x=16+4=20\).
Step 3
Exam Tip
(3x=12) से (x=4) है। इसलिए \(x^2+x=16+4=20\)।
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(10x-2 -3x+1-\(4x^2-8x+6\)) को सरल करने पर क्या मिलेगा?
What is obtained after simplifying (10x-2 -3x+1-\(4x^2-8x+6\))?
#algebraic-expressions
#subtraction
#brackets
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A \(6x^2+5x-5\)
B \(14x^2-11x+7\)
C \(6x^2-11x-5\)
D \(6x^2+5x+7\)
Explanation opens after your attempt
Correct Answer
A. \(6x^2+5x-5\)
Step 1
Concept
Subtraction gives \(10x^2-3x+1-4x^2+8x-6\). The simplified form is \(6x^2+5x-5\).
Step 2
Why this answer is correct
The correct answer is A. \(6x^2+5x-5\). Subtraction gives \(10x^2-3x+1-4x^2+8x-6\). The simplified form is \(6x^2+5x-5\).
Step 3
Exam Tip
घटाने पर \(10x^2-3x+1-4x^2+8x-6\) बनेगा। सरल रूप \(6x^2+5x-5\) है।
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किस विकल्प में \(x^2y\) और \(xy^2\) को समान पद मानने की गलती सही तरह से पकड़ी गई है?
Which option correctly identifies the mistake in treating \(x^2y\) and \(xy^2\) as like terms?
#algebraic-expressions
#error-analysis
#like-terms
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A दोनों में गुणांक नहीं है इसलिए समान हैं / They are like because both have no coefficient
B दोनों में (x) और (y) हैं इसलिए समान हैं / They are like because both have (x) and (y)
C घातें अलग हैं इसलिए असमान हैं / They are unlike because powers are different
D दोनों स्थिर पद हैं इसलिए समान हैं / They are like because both are constants
Explanation opens after your attempt
Correct Answer
C. घातें अलग हैं इसलिए असमान हैं / They are unlike because powers are different
Step 1
Concept
For like terms, the power of each variable must be the same. In \(x^2y\) and \(xy^2\), the powers are different.
Step 2
Why this answer is correct
The correct answer is C. घातें अलग हैं इसलिए असमान हैं / They are unlike because powers are different. For like terms, the power of each variable must be the same. In \(x^2y\) and \(xy^2\), the powers are different.
Step 3
Exam Tip
समान पदों के लिए प्रत्येक चर की घात समान होनी चाहिए। \(x^2y\) और \(xy^2\) में घातें अलग हैं।
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यदि (a+b=7) और (ab=10), तो (3(a+b)-2ab) का मान क्या होगा?
If (a+b=7) and (ab=10), what is the value of (3(a+b)-2ab)?
#algebraic-expressions
#expression-value
#substitution
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A (1)
B (31)
C (-1)
D (11)
Explanation opens after your attempt
Step 1
Concept
Substitute the given whole expressions directly. (3(7)-2(10)=21-20=1).
Step 2
Why this answer is correct
The correct answer is A. (1). Substitute the given whole expressions directly. (3(7)-2(10)=21-20=1).
Step 3
Exam Tip
दिए हुए पूरे व्यंजकों को सीधे रखें। (3(7)-2(10)=21-20=1)।
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(4x(x+2)-2\(3x^2-x\)) को सरल करने पर क्या मिलेगा?
What is obtained after simplifying (4x(x+2)-2\(3x^2-x\))?
#algebraic-expressions
#expansion
#quadratic
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A \(-2x^2+10x\)
B \(10x^2+6x\)
C \(-2x^2+6x\)
D \(2x^2+10x\)
Explanation opens after your attempt
Correct Answer
A. \(-2x^2+10x\)
Step 1
Concept
(4x(x+2)=4x-2 +8x) and (-2\(3x^2-x\)=-6x-2 +2x). The total is \(-2x^2+10x\).
Step 2
Why this answer is correct
The correct answer is A. \(-2x^2+10x\). (4x(x+2)=4x-2 +8x) and (-2\(3x^2-x\)=-6x-2 +2x). The total is \(-2x^2+10x\).
Step 3
Exam Tip
(4x(x+2)=4x-2 +8x) और (-2\(3x^2-x\)=-6x-2 +2x)। कुल \(-2x^2+10x\) है।
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\(2x^2+3x+5\) में से कौन-सा पद हटाने पर व्यंजक में स्थिर पद नहीं रहेगा?
Which term should be removed from \(2x^2+3x+5\) so that the expression has no constant term?
#algebraic-expressions
#constant-term
#identification
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A \(2x^2\)
B (3x)
C (5)
D \(2x^2+3x\)
Explanation opens after your attempt
Step 1
Concept
The constant term has no variable. Removing (5) leaves only variable terms.
Step 2
Why this answer is correct
The correct answer is C. (5). The constant term has no variable. Removing (5) leaves only variable terms.
Step 3
Exam Tip
स्थिर पद वह है जिसमें कोई चर नहीं होता। (5) हटाने पर केवल चर वाले पद बचते हैं।
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यदि (x=2), (y=3), तो \(x^2y+xy^2\) और (xy(x+y)) के बारे में सही कथन कौन-सा है?
If (x=2), (y=3), which statement is correct about \(x^2y+xy^2\) and (xy(x+y))?
#algebraic-expressions
#equivalent-expression
#factor-form
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A पहला बड़ा है / The first is greater
B दूसरा बड़ा है / The second is greater
C दोनों बराबर हैं / Both are equal
D दोनों शून्य हैं / Both are zero
Explanation opens after your attempt
Correct Answer
C. दोनों बराबर हैं / Both are equal
Step 1
Concept
(x-2 y+xy-2 =xy(x+y)) are equivalent forms. Substitution gives (30) for both.
Step 2
Why this answer is correct
The correct answer is C. दोनों बराबर हैं / Both are equal. (x-2 y+xy-2 =xy(x+y)) are equivalent forms. Substitution gives (30) for both.
Step 3
Exam Tip
(x-2 y+xy-2 =xy(x+y)) समान रूप हैं। दिए मान रखने पर दोनों (30) देते हैं।
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\(7x^2-2xy+3y^2-4x^2+6xy-8y^2\) को सरल करने पर क्या मिलेगा?
What is obtained after simplifying \(7x^2-2xy+3y^2-4x^2+6xy-8y^2\)?
#algebraic-expressions
#simplification
#three-groups
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A \(3x^2+4xy-5y^2\)
B \(11x^2+4xy-11y^2\)
C \(3x^2-8xy-5y^2\)
D \(3x^2+4xy+5y^2\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+4xy-5y^2\)
Step 1
Concept
\(7x^2-4x^2=3x^2\), (-2xy+6xy=4xy), and \(3y^2-8y^2=-5y^2\).
Step 2
Why this answer is correct
The correct answer is A. \(3x^2+4xy-5y^2\). \(7x^2-4x^2=3x^2\), (-2xy+6xy=4xy), and \(3y^2-8y^2=-5y^2\).
Step 3
Exam Tip
\(7x^2-4x^2=3x^2\), (-2xy+6xy=4xy), और \(3y^2-8y^2=-5y^2\)।
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