व्यंजक \(4x^2-3x+7\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in the expression \(4x^2-3x+7\)?
#algebraic_expressions
#coefficient
#polynomials
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A (4)
B (-3)
C (7)
D (1)
Explanation opens after your attempt
Step 1
Concept
The number multiplied with \(x^2\) is (4). Check both sign and number in a coefficient.
Step 2
Why this answer is correct
The correct answer is A. (4). The number multiplied with \(x^2\) is (4). Check both sign and number in a coefficient.
Step 3
Exam Tip
\(x^2\) के साथ गुणा हुई संख्या (4) है। गुणांक में चिह्न और संख्या दोनों देखें।
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व्यंजक (6a-5b+9) में कौन सा पद नियतांक है?
Which term is constant in the expression (6a-5b+9)?
#algebraic_expressions
#constant_term
#medium
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A (6a)
B (-5b)
C (9)
D (a)
Explanation opens after your attempt
Step 1
Concept
A constant term has no variable. Here (9) is the term without a variable.
Step 2
Why this answer is correct
The correct answer is C. (9). A constant term has no variable. Here (9) is the term without a variable.
Step 3
Exam Tip
नियतांक पद में कोई चर नहीं होता। यहां (9) बिना चर वाला पद है।
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व्यंजक \(3p^2+2p-8\) में कुल कितने पद हैं?
How many terms are there in \(3p^2+2p-8\)?
#algebraic_expressions
#terms
#counting
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The terms are \(3p^2\), (2p), and (-8). So there are (3) terms.
Step 2
Why this answer is correct
The correct answer is B. (3). The terms are \(3p^2\), (2p), and (-8). So there are (3) terms.
Step 3
Exam Tip
पद \(3p^2\), (2p), और (-8) हैं। इसलिए कुल (3) पद हैं।
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कौन सा युग्म समान पदों का है?
Which pair is a pair of like terms?
#algebraic_expressions
#like_terms
#medium
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A (5xy) और (7x) / (5xy) and (7x)
B \(2m^2\) और (3m) / \(2m^2\) and (3m)
C (-4ab) और (9ab) / (-4ab) and (9ab)
D (6p) और (6q) / (6p) and (6q)
Explanation opens after your attempt
Correct Answer
C. (-4ab) और (9ab) / (-4ab) and (9ab)
Step 1
Concept
Like terms have the same variable part. In (-4ab) and (9ab), the variable part (ab) is the same.
Step 2
Why this answer is correct
The correct answer is C. (-4ab) और (9ab) / (-4ab) and (9ab). Like terms have the same variable part. In (-4ab) and (9ab), the variable part (ab) is the same.
Step 3
Exam Tip
समान पदों में चर वाला भाग समान होता है। (-4ab) और (9ab) में चर वाला भाग (ab) समान है।
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व्यंजक (7x+4-2x+9) का सरल रूप क्या है?
What is the simplified form of (7x+4-2x+9)?
#algebraic_expressions
#simplification
#like_terms
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A (5x+13)
B (9x+13)
C (5x-5)
D (9x+5)
Explanation opens after your attempt
Correct Answer
A. (5x+13)
Step 1
Concept
Combining like terms gives (7x-2x=5x) and (4+9=13). So the simplified form is (5x+13).
Step 2
Why this answer is correct
The correct answer is A. (5x+13). Combining like terms gives (7x-2x=5x) and (4+9=13). So the simplified form is (5x+13).
Step 3
Exam Tip
समान पद जोड़ने पर (7x-2x=5x) और (4+9=13)। इसलिए सरल रूप (5x+13) है।
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व्यंजक (2(3y-5)) को खोलने पर क्या मिलेगा?
What is obtained by expanding (2(3y-5))?
#algebraic_expressions
#expansion
#distributive_property
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A (6y-5)
B (6y-10)
C (3y-10)
D (5y-7)
Explanation opens after your attempt
Correct Answer
B. (6y-10)
Step 1
Concept
Multiply (2) by both (3y) and (-5). Therefore (2(3y-5)=6y-10).
Step 2
Why this answer is correct
The correct answer is B. (6y-10). Multiply (2) by both (3y) and (-5). Therefore (2(3y-5)=6y-10).
Step 3
Exam Tip
(2) को (3y) और (-5) दोनों से गुणा करें। इसलिए (2(3y-5)=6y-10)।
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यदि (a=3), तो \(2a^2-a+1\) का मान क्या होगा?
If (a=3), what is the value of \(2a^2-a+1\)?
#algebraic_expressions
#evaluation
#medium
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A (13)
B (14)
C (16)
D (18)
Explanation opens after your attempt
Step 1
Concept
Substituting gives (2a-2 -a+1=2\(3^2\)-3+1=16). Evaluate powers before multiplication.
Step 2
Why this answer is correct
The correct answer is C. (16). Substituting gives (2a-2 -a+1=2\(3^2\)-3+1=16). Evaluate powers before multiplication.
Step 3
Exam Tip
मान रखने पर (2a-2 -a+1=2\(3^2\)-3+1=16)। पहले घात फिर गुणा करें।
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यदि (x=2) और (y=5), तो (3x+y) का मान क्या होगा?
If (x=2) and (y=5), what is the value of (3x+y)?
#algebraic_expressions
#two_variable_evaluation
#medium
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A (7)
B (9)
C (10)
D (11)
Explanation opens after your attempt
Step 1
Concept
(3x+y=3(2)+5=11). In two-variable questions, substitute both values in the correct places.
Step 2
Why this answer is correct
The correct answer is D. (11). (3x+y=3(2)+5=11). In two-variable questions, substitute both values in the correct places.
Step 3
Exam Tip
(3x+y=3(2)+5=11)। दो चर वाले प्रश्न में दोनों मान सही जगह रखें।
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(n) के वर्ग के तीन गुने में (4) जोड़ने का व्यंजक कौन सा है?
Which expression represents adding (4) to three times the square of (n)?
#algebraic_expressions
#word_to_expression
#medium
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A \(3n^2+4\)
B (3(n+4)2 )
C \(n^2+12\)
D \(3n+4^2\)
Explanation opens after your attempt
Correct Answer
A. \(3n^2+4\)
Step 1
Concept
The square of (n) is \(n^2\), and three times it is \(3n^2\). Adding (4) gives \(3n^2+4\).
Step 2
Why this answer is correct
The correct answer is A. \(3n^2+4\). The square of (n) is \(n^2\), and three times it is \(3n^2\). Adding (4) gives \(3n^2+4\).
Step 3
Exam Tip
(n) का वर्ग \(n^2\) है और उसका तीन गुना \(3n^2\) है। उसमें (4) जोड़ने पर \(3n^2+4\) मिलता है।
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व्यंजक \(5r^2-2r^2+6r\) का सरल रूप क्या है?
What is the simplified form of \(5r^2-2r^2+6r\)?
#algebraic_expressions
#combine_like_terms
#medium
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A \(3r+6r^2\)
B \(3r^2+6r\)
C \(9r^2\)
D \(3r^2-6r\)
Explanation opens after your attempt
Correct Answer
B. \(3r^2+6r\)
Step 1
Concept
\(5r^2\) and \(-2r^2\) are like terms. Their sum is \(3r^2\), and (6r) remains separate.
Step 2
Why this answer is correct
The correct answer is B. \(3r^2+6r\). \(5r^2\) and \(-2r^2\) are like terms. Their sum is \(3r^2\), and (6r) remains separate.
Step 3
Exam Tip
\(5r^2\) और \(-2r^2\) समान पद हैं। उनका योग \(3r^2\) है और (6r) अलग रहता है।
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निम्न में से कौन सा व्यंजक द्विपदी है?
Which of the following expressions is a binomial?
#algebraic_expressions
#binomial
#medium
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A \(4x^2-7\)
B \(x^2+x+1\)
C (9x)
D (5)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-7\)
Step 1
Concept
A binomial has two terms. \(4x^2-7\) has the two terms \(4x^2\) and (-7).
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-7\). A binomial has two terms. \(4x^2-7\) has the two terms \(4x^2\) and (-7).
Step 3
Exam Tip
द्विपदी में दो पद होते हैं। \(4x^2-7\) में \(4x^2\) और (-7) दो पद हैं।
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व्यंजक (-3xy+8xy-2) का सरल रूप क्या है?
What is the simplified form of (-3xy+8xy-2)?
#algebraic_expressions
#simplify_multivariable
#medium
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A (11xy-2)
B (5xy-2)
C (5x-y-2)
D (5xy+2)
Explanation opens after your attempt
Correct Answer
B. (5xy-2)
Step 1
Concept
(-3xy+8xy=5xy), and (-2) remains separate. So the correct form is (5xy-2).
Step 2
Why this answer is correct
The correct answer is B. (5xy-2). (-3xy+8xy=5xy), and (-2) remains separate. So the correct form is (5xy-2).
Step 3
Exam Tip
(-3xy+8xy=5xy) और (-2) अलग रहता है। इसलिए सही रूप (5xy-2) है।
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यदि (p=-2), तो \(p^2+3p\) का मान क्या होगा?
If (p=-2), what is the value of \(p^2+3p\)?
#algebraic_expressions
#negative_substitution
#medium
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A (-2)
B (2)
C (-10)
D (10)
Explanation opens after your attempt
Step 1
Concept
Putting (p=-2), \(p^2+3p=4-6=-2\). The square of a negative value is positive.
Step 2
Why this answer is correct
The correct answer is A. (-2). Putting (p=-2), \(p^2+3p=4-6=-2\). The square of a negative value is positive.
Step 3
Exam Tip
(p=-2) रखने पर \(p^2+3p=4-6=-2\)। ऋणात्मक मान का वर्ग धनात्मक होता है।
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व्यंजक (9m-4n+2m-6n) का सरल रूप क्या है?
What is the simplified form of (9m-4n+2m-6n)?
#algebraic_expressions
#two_variable_simplification
#medium
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A (11m+10n)
B (7m-10n)
C (11m-10n)
D (7m+2n)
Explanation opens after your attempt
Correct Answer
C. (11m-10n)
Step 1
Concept
(9m+2m=11m) and (-4n-6n=-10n). So the simplified form is (11m-10n).
Step 2
Why this answer is correct
The correct answer is C. (11m-10n). (9m+2m=11m) and (-4n-6n=-10n). So the simplified form is (11m-10n).
Step 3
Exam Tip
(9m+2m=11m) और (-4n-6n=-10n)। इसलिए सरल रूप (11m-10n) है।
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(5) कम है (2x) और (3) के योग से। इसका सही व्यंजक कौन सा है?
(5) less than the sum of (2x) and (3). Which is the correct expression?
#algebraic_expressions
#phrase_translation
#medium
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A (2x+3+5)
B (2x-3-5)
C (5-(2x+3))
D (2x+3-5)
Explanation opens after your attempt
Correct Answer
D. (2x+3-5)
Step 1
Concept
First the sum is (2x+3), and then (5) is subtracted from it. So the expression is (2x+3-5).
Step 2
Why this answer is correct
The correct answer is D. (2x+3-5). First the sum is (2x+3), and then (5) is subtracted from it. So the expression is (2x+3-5).
Step 3
Exam Tip
पहले योग (2x+3) है और फिर उसमें से (5) घटता है। इसलिए व्यंजक (2x+3-5) है।
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व्यंजक (3(x+2)+4x) का सरल रूप क्या है?
What is the simplified form of (3(x+2)+4x)?
#algebraic_expressions
#expansion_simplification
#medium
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A (7x+6)
B (3x+6)
C (7x+2)
D (12x+6)
Explanation opens after your attempt
Step 1
Concept
First expand (3(x+2)=3x+6). Then combine (3x+4x=7x) to get (7x+6).
Step 2
Why this answer is correct
The correct answer is A. (7x+6). First expand (3(x+2)=3x+6). Then combine (3x+4x=7x) to get (7x+6).
Step 3
Exam Tip
पहले (3(x+2)=3x+6) करें। फिर (3x+4x=7x) जोड़कर (7x+6) मिलेगा।
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कौन सा व्यंजक (a) और (b) के अंतर के (4) गुने को दर्शाता है?
Which expression represents (4) times the difference of (a) and (b)?
#algebraic_expressions
#brackets
#medium
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A (4a-b)
B (a-4b)
C (4(a-b))
D (a+b-4)
Explanation opens after your attempt
Correct Answer
C. (4(a-b))
Step 1
Concept
The difference of (a) and (b) is (a-b). For (4) times it, keep the whole difference in brackets.
Step 2
Why this answer is correct
The correct answer is C. (4(a-b)). The difference of (a) and (b) is (a-b). For (4) times it, keep the whole difference in brackets.
Step 3
Exam Tip
(a) और (b) का अंतर (a-b) है। उसके (4) गुने के लिए पूरा अंतर कोष्ठक में रखें।
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यदि (u=1) और (v=-3), तो (u-2v) का मान क्या होगा?
If (u=1) and (v=-3), what is the value of (u-2v)?
#algebraic_expressions
#signed_evaluation
#medium
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A (-5)
B (4)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
(u-2v=1-2(-3)=1+6=7). Pay attention to signs while multiplying a negative number.
Step 2
Why this answer is correct
The correct answer is D. (7). (u-2v=1-2(-3)=1+6=7). Pay attention to signs while multiplying a negative number.
Step 3
Exam Tip
(u-2v=1-2(-3)=1+6=7)। ऋणात्मक संख्या से गुणा करते समय चिह्न पर ध्यान दें।
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व्यंजक \(12c^2-5c+3c^2-2c\) का सरल रूप क्या है?
What is the simplified form of \(12c^2-5c+3c^2-2c\)?
#algebraic_expressions
#polynomial_simplification
#medium
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A \(15c^2-7c\)
B \(9c^2-3c\)
C \(15c^2+7c\)
D \(12c^2-7c\)
Explanation opens after your attempt
Correct Answer
A. \(15c^2-7c\)
Step 1
Concept
\(12c^2+3c^2=15c^2\) and (-5c-2c=-7c). Combine like terms separately.
Step 2
Why this answer is correct
The correct answer is A. \(15c^2-7c\). \(12c^2+3c^2=15c^2\) and (-5c-2c=-7c). Combine like terms separately.
Step 3
Exam Tip
\(12c^2+3c^2=15c^2\) और (-5c-2c=-7c)। समान पद अलग-अलग जोड़ें।
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व्यंजक \(4x^2y\) में चर वाला भाग कौन सा है?
What is the variable part in \(4x^2y\)?
#algebraic_expressions
#variable_part
#medium
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A (4)
B \(x^2y\)
C (4x)
D (2y)
Explanation opens after your attempt
Correct Answer
B. \(x^2y\)
Step 1
Concept
After removing the numerical coefficient (4), the variable part \(x^2y\) remains. View a term as coefficient and variable part.
Step 2
Why this answer is correct
The correct answer is B. \(x^2y\). After removing the numerical coefficient (4), the variable part \(x^2y\) remains. View a term as coefficient and variable part.
Step 3
Exam Tip
संख्यात्मक गुणांक (4) को हटाने पर चर वाला भाग \(x^2y\) बचता है। पद को गुणांक और चर भाग में बांटकर देखें।
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किस विकल्प में \(2x^2\) और \(-5x^2\) के योग का सही परिणाम है?
Which option gives the correct sum of \(2x^2\) and \(-5x^2\)?
#algebraic_expressions
#add_like_terms
#medium
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A \(-7x^2\)
B \(3x^2\)
C \(-3x^2\)
D \(-3x^4\)
Explanation opens after your attempt
Correct Answer
C. \(-3x^2\)
Step 1
Concept
The coefficients are (2+(-5)=-3), and the variable part \(x^2\) stays the same. So the sum is \(-3x^2\).
Step 2
Why this answer is correct
The correct answer is C. \(-3x^2\). The coefficients are (2+(-5)=-3), and the variable part \(x^2\) stays the same. So the sum is \(-3x^2\).
Step 3
Exam Tip
गुणांक (2+(-5)=-3) हैं और चर भाग \(x^2\) वही रहता है। इसलिए योग \(-3x^2\) है।
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व्यंजक (5(a-2)-2(a+1)) का सरल रूप क्या है?
What is the simplified form of (5(a-2)-2(a+1))?
#algebraic_expressions
#bracket_simplification
#medium
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A (3a-12)
B (7a-8)
C (3a-8)
D (5a-12)
Explanation opens after your attempt
Correct Answer
A. (3a-12)
Step 1
Concept
On expanding, (5a-10-2a-2=3a-12). Apply the negative sign to the whole bracket.
Step 2
Why this answer is correct
The correct answer is A. (3a-12). On expanding, (5a-10-2a-2=3a-12). Apply the negative sign to the whole bracket.
Step 3
Exam Tip
खोलने पर (5a-10-2a-2=3a-12) मिलता है। ऋण चिह्न को पूरे कोष्ठक पर लागू करें।
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यदि (x=-1), तो \(x^2-4x+3\) का मान क्या होगा?
If (x=-1), what is the value of \(x^2-4x+3\)?
#algebraic_expressions
#evaluate_quadratic
#medium
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A (0)
B (4)
C (8)
D (12)
Explanation opens after your attempt
Step 1
Concept
Putting (x=-1) gives (1+4+3=8). The value of (-4(-1)) is (4).
Step 2
Why this answer is correct
The correct answer is C. (8). Putting (x=-1) gives (1+4+3=8). The value of (-4(-1)) is (4).
Step 3
Exam Tip
(x=-1) रखने पर (1+4+3=8) मिलता है। (-4(-1)) का मान (4) होगा।
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किस व्यंजक में (x) का गुणांक (0) है?
In which expression is the coefficient of (x) equal to (0)?
#algebraic_expressions
#missing_term
#medium
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A (5+x)
B \(x^2+6\)
C (3x-1)
D (2x+4)
Explanation opens after your attempt
Correct Answer
B. \(x^2+6\)
Step 1
Concept
In \(x^2+6\), there is no first-power (x) term. So the coefficient of (x) is taken as (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^2+6\). In \(x^2+6\), there is no first-power (x) term. So the coefficient of (x) is taken as (0).
Step 3
Exam Tip
\(x^2+6\) में (x) का प्रथम घात वाला पद नहीं है। इसलिए (x) का गुणांक (0) माना जाता है।
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व्यंजक (8k-3(2k-1)) का सरल रूप क्या है?
What is the simplified form of (8k-3(2k-1))?
#algebraic_expressions
#distributive_property
#medium
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A (2k-3)
B (2k+3)
C (14k-3)
D (14k+3)
Explanation opens after your attempt
Step 1
Concept
(8k-3(2k-1)=8k-6k+3=2k+3). Handle negative multiplication before brackets carefully.
Step 2
Why this answer is correct
The correct answer is B. (2k+3). (8k-3(2k-1)=8k-6k+3=2k+3). Handle negative multiplication before brackets carefully.
Step 3
Exam Tip
(8k-3(2k-1)=8k-6k+3=2k+3)। कोष्ठक से पहले ऋणात्मक गुणन ध्यान से करें।
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यदि आयत की लंबाई (x+4) और चौड़ाई (x-1) है, तो परिमाप का व्यंजक क्या होगा?
If the length of a rectangle is (x+4) and breadth is (x-1), what is the expression for its perimeter?
#algebraic_expressions
#perimeter_expression
#medium
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A (2x+3)
B (4x+6)
C (2x+6)
D (4x+3)
Explanation opens after your attempt
Step 1
Concept
The perimeter is (2[(x+4)+(x-1)]=2(2x+3)=4x+6). Add length and breadth first.
Step 2
Why this answer is correct
The correct answer is B. (4x+6). The perimeter is (2[(x+4)+(x-1)]=2(2x+3)=4x+6). Add length and breadth first.
Step 3
Exam Tip
परिमाप (2[(x+4)+(x-1)]=2(2x+3)=4x+6) है। पहले लंबाई और चौड़ाई जोड़ें।
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व्यंजक (x(x+3)) को खोलने पर क्या मिलेगा?
What is obtained by expanding (x(x+3))?
#algebraic_expressions
#expanding_brackets
#medium
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A \(x^2+3x\)
B (2x+3)
C \(x^2+3\)
D \(3x^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x\)
Step 1
Concept
Multiply (x) by both (x) and (3). This gives \(x^2+3x\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x\). Multiply (x) by both (x) and (3). This gives \(x^2+3x\).
Step 3
Exam Tip
(x) को (x) और (3) दोनों से गुणा करें। इससे \(x^2+3x\) मिलता है।
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यदि (m=2) और (n=4), तो \(mn+m^2\) का मान क्या होगा?
If (m=2) and (n=4), what is the value of \(mn+m^2\)?
#algebraic_expressions
#multivariable_evaluation
#medium
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A (8)
B (10)
C (12)
D (16)
Explanation opens after your attempt
Step 1
Concept
(mn+m-2 =2(4)+22 =8+4=12). Do multiplication and powers in the correct order.
Step 2
Why this answer is correct
The correct answer is C. (12). (mn+m-2 =2(4)+22 =8+4=12). Do multiplication and powers in the correct order.
Step 3
Exam Tip
(mn+m-2 =2(4)+22 =8+4=12)। गुणन और घात दोनों सही क्रम में करें।
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कौन सा कथन (xy) और (x+y) के बारे में सही है?
Which statement about (xy) and (x+y) is correct?
#algebraic_expressions
#product_sum
#medium
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A दोनों हमेशा बराबर होते हैं / Both are always equal
B (xy) गुणन है और (x+y) योग है / (xy) is product and (x+y) is sum
C (xy) योग है और (x+y) गुणन है / (xy) is sum and (x+y) is product
D दोनों में कोई चर नहीं है / Both have no variable
Explanation opens after your attempt
Correct Answer
B. (xy) गुणन है और (x+y) योग है / (xy) is product and (x+y) is sum
Step 1
Concept
Variables written together show multiplication and the (+) sign shows addition. So (xy) and (x+y) are different expressions.
Step 2
Why this answer is correct
The correct answer is B. (xy) गुणन है और (x+y) योग है / (xy) is product and (x+y) is sum. Variables written together show multiplication and the (+) sign shows addition. So (xy) and (x+y) are different expressions.
Step 3
Exam Tip
साथ लिखे गए चर गुणन दर्शाते हैं और (+) चिह्न योग दर्शाता है। इसलिए (xy) और (x+y) अलग व्यंजक हैं।
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व्यंजक (6x-2(3x-5)) का सरल रूप क्या है?
What is the simplified form of (6x-2(3x-5))?
#algebraic_expressions
#cancellation
#medium
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A (10)
B (12x-10)
C (0x-10)
D (-10)
Explanation opens after your attempt
Step 1
Concept
(6x-2(3x-5)=6x-6x+10=10). Like terms can cancel, so the final answer may be a constant.
Step 2
Why this answer is correct
The correct answer is A. (10). (6x-2(3x-5)=6x-6x+10=10). Like terms can cancel, so the final answer may be a constant.
Step 3
Exam Tip
(6x-2(3x-5)=6x-6x+10=10)। समान पद कट सकते हैं इसलिए अंतिम उत्तर नियतांक हो सकता है।
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(3) लगातार पूर्णांकों में पहला (n) है। उनका योग किस व्यंजक से दर्शेगा?
The first of (3) consecutive integers is (n). Which expression represents their sum?
#algebraic_expressions
#consecutive_integers
#medium
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A (3n+1)
B (3n+3)
C (n+3)
D \(n^3\)
Explanation opens after your attempt
Step 1
Concept
The three integers are (n), (n+1), and (n+2). Their sum is (3n+3).
Step 2
Why this answer is correct
The correct answer is B. (3n+3). The three integers are (n), (n+1), and (n+2). Their sum is (3n+3).
Step 3
Exam Tip
तीन पूर्णांक (n), (n+1), और (n+2) होंगे। उनका योग (3n+3) है।
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व्यंजक \(2x^2+5x-3x^2+x\) का सरल रूप क्या है?
What is the simplified form of \(2x^2+5x-3x^2+x\)?
#algebraic_expressions
#powers_simplification
#medium
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A \(-x^2+6x\)
B \(5x^2+6x\)
C \(-x^2+4x\)
D \(x^2+6x\)
Explanation opens after your attempt
Correct Answer
A. \(-x^2+6x\)
Step 1
Concept
\(2x^2-3x^2=-x^2\) and (5x+x=6x). Combine terms with different powers separately.
Step 2
Why this answer is correct
The correct answer is A. \(-x^2+6x\). \(2x^2-3x^2=-x^2\) and (5x+x=6x). Combine terms with different powers separately.
Step 3
Exam Tip
\(2x^2-3x^2=-x^2\) और (5x+x=6x)। अलग घात वाले पदों को अलग जोड़ें।
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किस विकल्प में \(4a^2b\) और \(-7a^2b\) का अंतर (4a-2 b-\(-7a^2b\)) सही है?
Which option correctly gives the difference (4a-2 b-\(-7a^2b\))?
#algebraic_expressions
#subtract_negative_terms
#medium
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A \(-3a^2b\)
B \(11a^2b\)
C \(3a^2b\)
D \(11a^4b^2\)
Explanation opens after your attempt
Correct Answer
B. \(11a^2b\)
Step 1
Concept
Subtracting a negative term means addition. So \(4a^2b+7a^2b=11a^2b\).
Step 2
Why this answer is correct
The correct answer is B. \(11a^2b\). Subtracting a negative term means addition. So \(4a^2b+7a^2b=11a^2b\).
Step 3
Exam Tip
ऋणात्मक पद घटाने का अर्थ जोड़ना है। इसलिए \(4a^2b+7a^2b=11a^2b\)।
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यदि (x=3), तो (2(x+4)-x-2 ) का मान क्या होगा?
If (x=3), what is the value of (2(x+4)-x-2 )?
#algebraic_expressions
#evaluate_with_brackets
#medium
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A (5)
B (7)
C (9)
D (11)
Explanation opens after your attempt
Step 1
Concept
(2(3+4)-32 =14-9=5). Evaluate brackets and powers first.
Step 2
Why this answer is correct
The correct answer is A. (5). (2(3+4)-32 =14-9=5). Evaluate brackets and powers first.
Step 3
Exam Tip
(2(3+4)-32 =14-9=5)। पहले कोष्ठक और घात का मान निकालें।
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कौन सा व्यंजक (x) के तीन गुने और (y) के दोगुने के योग को दर्शाता है?
Which expression represents the sum of three times (x) and twice (y)?
#algebraic_expressions
#word_translation
#medium
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A (3(x+2y))
B (3x+2y)
C (2x+3y)
D (5xy)
Explanation opens after your attempt
Correct Answer
B. (3x+2y)
Step 1
Concept
Three times (x) is (3x) and twice (y) is (2y). Their sum is (3x+2y).
Step 2
Why this answer is correct
The correct answer is B. (3x+2y). Three times (x) is (3x) and twice (y) is (2y). Their sum is (3x+2y).
Step 3
Exam Tip
(x) का तीन गुना (3x) और (y) का दोगुना (2y) है। उनका योग (3x+2y) है।
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व्यंजक (10-3(2-z)) का सरल रूप क्या है?
What is the simplified form of (10-3(2-z))?
#algebraic_expressions
#signs_brackets
#medium
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A (4-3z)
B (16-3z)
C (4+3z)
D (16+3z)
Explanation opens after your attempt
Step 1
Concept
(10-3(2-z)=10-6+3z=4+3z). Apply the negative sign to every term in the bracket.
Step 2
Why this answer is correct
The correct answer is C. (4+3z). (10-3(2-z)=10-6+3z=4+3z). Apply the negative sign to every term in the bracket.
Step 3
Exam Tip
(10-3(2-z)=10-6+3z=4+3z)। ऋण चिह्न को कोष्ठक के हर पद पर लागू करें।
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व्यंजक \(3x^2y-2xy^2\) में पद \(3x^2y\) और \(-2xy^2\) कैसे पद हैं?
In the expression \(3x^2y-2xy^2\), what type of terms are \(3x^2y\) and \(-2xy^2\)?
#algebraic_expressions
#unlike_terms
#powers
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A समान पद / Like terms
B असमान पद / Unlike terms
C नियतांक पद / Constant terms
D शून्य पद / Zero terms
Explanation opens after your attempt
Correct Answer
B. असमान पद / Unlike terms
Step 1
Concept
Both have variables, but their powers are different. Therefore they are unlike terms.
Step 2
Why this answer is correct
The correct answer is B. असमान पद / Unlike terms. Both have variables, but their powers are different. Therefore they are unlike terms.
Step 3
Exam Tip
दोनों में चर हैं पर घातों का क्रम अलग है। इसलिए वे असमान पद हैं।
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यदि एक संख्या (x) है और दूसरी संख्या उससे (6) अधिक है, तो दोनों का योग क्या होगा?
If one number is (x) and another number is (6) more than it, what is their sum?
#algebraic_expressions
#number_expression
#medium
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A (2x+6)
B (x+6)
C (2x-6)
D (6x)
Explanation opens after your attempt
Step 1
Concept
The second number is (x+6). The sum is (x+(x+6)=2x+6).
Step 2
Why this answer is correct
The correct answer is A. (2x+6). The second number is (x+6). The sum is (x+(x+6)=2x+6).
Step 3
Exam Tip
दूसरी संख्या (x+6) है। योग (x+(x+6)=2x+6) होगा।
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व्यंजक (2x+3y-5x+y) का सरल रूप क्या है?
What is the simplified form of (2x+3y-5x+y)?
#algebraic_expressions
#linear_simplification
#medium
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A (-3x+4y)
B (7x+4y)
C (-3x+2y)
D (3x-4y)
Explanation opens after your attempt
Correct Answer
A. (-3x+4y)
Step 1
Concept
(2x-5x=-3x) and (3y+y=4y). So the simplified form is (-3x+4y).
Step 2
Why this answer is correct
The correct answer is A. (-3x+4y). (2x-5x=-3x) and (3y+y=4y). So the simplified form is (-3x+4y).
Step 3
Exam Tip
(2x-5x=-3x) और (3y+y=4y)। इसलिए सरल रूप (-3x+4y) है।
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कौन सा व्यंजक (x) को (3) से घटाकर परिणाम को (5) से गुणा करता है?
Which expression subtracts (3) from (x) and then multiplies the result by (5)?
#algebraic_expressions
#ordered_operations
#medium
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A (5x-3)
B (x-15)
C (5(x-3))
D (3(x-5))
Explanation opens after your attempt
Correct Answer
C. (5(x-3))
Step 1
Concept
First (x-3) is formed, and then the whole result is multiplied by (5). So (5(x-3)) is correct.
Step 2
Why this answer is correct
The correct answer is C. (5(x-3)). First (x-3) is formed, and then the whole result is multiplied by (5). So (5(x-3)) is correct.
Step 3
Exam Tip
पहले (x-3) बनता है और फिर पूरे परिणाम को (5) से गुणा किया जाता है। इसलिए (5(x-3)) सही है।
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यदि (a=4) और (b=2), तो \(a^2-b^2\) का मान क्या होगा?
If (a=4) and (b=2), what is the value of \(a^2-b^2\)?
#algebraic_expressions
#evaluate_difference_squares
#medium
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A (8)
B (10)
C (12)
D (14)
Explanation opens after your attempt
Step 1
Concept
\(a^2-b^2=4^2-2^2=16-4=12\). Find both squares separately.
Step 2
Why this answer is correct
The correct answer is C. (12). \(a^2-b^2=4^2-2^2=16-4=12\). Find both squares separately.
Step 3
Exam Tip
\(a^2-b^2=4^2-2^2=16-4=12\)। दोनों वर्ग अलग-अलग निकालें।
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व्यंजक \(\frac{x}{2}+x\) का सरल रूप क्या है?
What is the simplified form of \(\frac{x}{2}+x\)?
#algebraic_expressions
#fraction_terms
#medium
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A \(\frac{x}{3}\)
B \(\frac{3x}{2}\)
C \(\frac{2x}{3}\)
D (2x)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3x}{2}\)
Step 1
Concept
We can write (x) as \(\frac{2x}{2}\). Thus \(\frac{x}{2}+x=\frac{3x}{2}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3x}{2}\). We can write (x) as \(\frac{2x}{2}\). Thus \(\frac{x}{2}+x=\frac{3x}{2}\).
Step 3
Exam Tip
(x) को \(\frac{2x}{2}\) लिख सकते हैं। इसलिए \(\frac{x}{2}+x=\frac{3x}{2}\)।
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व्यंजक (4(2x-1)+3) का सरल रूप क्या है?
What is the simplified form of (4(2x-1)+3)?
#algebraic_expressions
#expand_and_add
#medium
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A (8x-1)
B (8x-7)
C (8x+2)
D (6x-1)
Explanation opens after your attempt
Step 1
Concept
(4(2x-1)=8x-4) and (8x-4+3=8x-1). Expand the bracket first.
Step 2
Why this answer is correct
The correct answer is A. (8x-1). (4(2x-1)=8x-4) and (8x-4+3=8x-1). Expand the bracket first.
Step 3
Exam Tip
(4(2x-1)=8x-4) और (8x-4+3=8x-1)। पहले कोष्ठक खोलें।
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किस विकल्प में (3x+2) और (x-5) का योग सही है?
Which option gives the correct sum of (3x+2) and (x-5)?
#algebraic_expressions
#addition_expressions
#medium
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A (2x-3)
B (4x-3)
C (4x+7)
D \(3x^2-3\)
Explanation opens after your attempt
Step 1
Concept
The sum is ((3x+2)+(x-5)=4x-3). Combine like terms and constants separately.
Step 2
Why this answer is correct
The correct answer is B. (4x-3). The sum is ((3x+2)+(x-5)=4x-3). Combine like terms and constants separately.
Step 3
Exam Tip
योग ((3x+2)+(x-5)=4x-3) है। समान पदों को जोड़ें और नियतांक अलग जोड़ें।
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व्यंजक (7x-4) में से (2x+3) घटाने पर क्या मिलेगा?
What is obtained by subtracting (2x+3) from (7x-4)?
#algebraic_expressions
#subtract_expressions
#medium
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A (5x-1)
B (9x-1)
C (5x-7)
D (9x-7)
Explanation opens after your attempt
Step 1
Concept
((7x-4)-(2x+3)=7x-4-2x-3=5x-7). Change the signs of both terms of the subtracted expression.
Step 2
Why this answer is correct
The correct answer is C. (5x-7). ((7x-4)-(2x+3)=7x-4-2x-3=5x-7). Change the signs of both terms of the subtracted expression.
Step 3
Exam Tip
((7x-4)-(2x+3)=7x-4-2x-3=5x-7)। घटाए गए व्यंजक के दोनों पदों का चिह्न बदलें।
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यदि (x=2), तो \(x^3+x\) का मान क्या होगा?
If (x=2), what is the value of \(x^3+x\)?
#algebraic_expressions
#cubic_evaluation
#medium
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A (6)
B (8)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(x^3+x=2^3+2=8+2=10\). The power should be evaluated first.
Step 2
Why this answer is correct
The correct answer is C. (10). \(x^3+x=2^3+2=8+2=10\). The power should be evaluated first.
Step 3
Exam Tip
\(x^3+x=2^3+2=8+2=10\)। घात का मान पहले निकालना चाहिए।
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किस विकल्प में (-2x(3x-4)) का सही विस्तार है?
Which option gives the correct expansion of (-2x(3x-4))?
#algebraic_expressions
#negative_expansion
#medium
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A \(-6x^2+8x\)
B \(6x^2-8x\)
C \(-6x^2-8x\)
D \(-5x^2+6x\)
Explanation opens after your attempt
Correct Answer
A. \(-6x^2+8x\)
Step 1
Concept
Multiply (-2x) by both (3x) and (-4). This gives \(-6x^2+8x\).
Step 2
Why this answer is correct
The correct answer is A. \(-6x^2+8x\). Multiply (-2x) by both (3x) and (-4). This gives \(-6x^2+8x\).
Step 3
Exam Tip
(-2x) को (3x) और (-4) दोनों से गुणा करें। इससे \(-6x^2+8x\) मिलेगा।
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(x) और (4) के योग का वर्ग सीधे कौन सा व्यंजक दिखाता है?
Which expression directly shows the square of the sum of (x) and (4)?
#algebraic_expressions
#square_of_sum
#medium
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A \(x^2+4\)
B \(x+4^2\)
C (2(x+4))
D ((x+4)2 )
Explanation opens after your attempt
Correct Answer
D. ((x+4)2 )
Step 1
Concept
First the sum (x+4) is taken. To square the whole sum, we write ((x+4)2 ).
Step 2
Why this answer is correct
The correct answer is D. ((x+4)2 ). First the sum (x+4) is taken. To square the whole sum, we write ((x+4)2 ).
Step 3
Exam Tip
पहले योग (x+4) लिया जाता है। फिर पूरे योग का वर्ग करने के लिए ((x+4)2 ) लिखते हैं।
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व्यंजक (2x+3y+4z) में (y) का गुणांक क्या है?
What is the coefficient of (y) in (2x+3y+4z)?
#algebraic_expressions
#coefficient_identification
#medium
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A (2)
B (3)
C (4)
D (9)
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Step 1
Concept
The number multiplied with (y) is (3). Therefore the coefficient of (y) is (3).
Step 2
Why this answer is correct
The correct answer is B. (3). The number multiplied with (y) is (3). Therefore the coefficient of (y) is (3).
Step 3
Exam Tip
(y) के साथ गुणा हुई संख्या (3) है। इसलिए (y) का गुणांक (3) है।
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यदि (r=5), तो \(\frac{r+7}{2}\) का मान क्या होगा?
If (r=5), what is the value of \(\frac{r+7}{2}\)?
#algebraic_expressions
#fraction_evaluation
#medium
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
Putting (r=5), \(\frac{r+7}{2}=\frac{12}{2}=6\). In a fraction, identify numerator and denominator correctly.
Step 2
Why this answer is correct
The correct answer is C. (6). Putting (r=5), \(\frac{r+7}{2}=\frac{12}{2}=6\). In a fraction, identify numerator and denominator correctly.
Step 3
Exam Tip
(r=5) रखने पर \(\frac{r+7}{2}=\frac{12}{2}=6\)। भिन्न में पहले हर और अंश को सही पहचानें।
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