100 results found for "polynomials" in Class 10.
निम्न में से कौन सा बहुपद मानक रूप में व्यवस्थित है?
Which of the following polynomials is arranged in standard form?
#polynomials
#standard-form
#easy
#arrangement
A \(2x^3+x^2+5x+1\)
B \(5x+2x^3+1+x^2\)
C \(1+5x+x^2+2x^3\)
D \(x^2+2x^3+5x+1\)
Explanation opens after your attempt
Correct Answer
A. \(2x^3+x^2+5x+1\)
Step 1
Concept
In standard form, powers are written in descending order. \(2x^3+x^2+5x+1\) follows this order.
Step 2
Why this answer is correct
The correct answer is A. \(2x^3+x^2+5x+1\). In standard form, powers are written in descending order. \(2x^3+x^2+5x+1\) follows this order.
Step 3
Exam Tip
मानक रूप में घातें घटते क्रम में लिखी जाती हैं। \(2x^3+x^2+5x+1\) में यही क्रम है।
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निम्न में से किस बहुपद में प्रमुख गुणांक (1) नहीं है?
Which of the following polynomials does not have leading coefficient (1)?
#leading-coefficient
#monic-polynomial
#classification
A \(x^3+2x+5\)
B \(x^2-4\)
C \(3x^2+x+1\)
D \(x^5-x\)
Explanation opens after your attempt
Correct Answer
C. \(3x^2+x+1\)
Step 1
Concept
The leading term of \(3x^2+x+1\) is \(3x^2\). Its leading coefficient is (3), not (1).
Step 2
Why this answer is correct
The correct answer is C. \(3x^2+x+1\). The leading term of \(3x^2+x+1\) is \(3x^2\). Its leading coefficient is (3), not (1).
Step 3
Exam Tip
\(3x^2+x+1\) का प्रमुख पद \(3x^2\) है। इसका प्रमुख गुणांक (3) है, (1) नहीं।
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निम्न में से किस बहुपद में (x) का गुणांक (0) है?
In which of the following polynomials is the coefficient of (x) equal to (0)?
#coefficient
#missing-x-term
#polynomial
A \(x^2+5x+6\)
B \(3x^2-4\)
C \(2x^3+x-1\)
D (7x-9)
Explanation opens after your attempt
Correct Answer
B. \(3x^2-4\)
Step 1
Concept
In \(3x^2-4\), there is no (x)-term. So the coefficient of (x) is (0).
Step 2
Why this answer is correct
The correct answer is B. \(3x^2-4\). In \(3x^2-4\), there is no (x)-term. So the coefficient of (x) is (0).
Step 3
Exam Tip
\(3x^2-4\) में (x) का पद नहीं है। इसलिए (x) का गुणांक (0) है।
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यदि (p(x)=x-3 -5x-2 +ax+12) में (x-3) गुणनखंड है, तो (a) का मान क्या है?
If (x-3) is a factor of (p(x)=x-3 -5x-2 +ax+12), what is the value of (a)?
#factor-theorem
#polynomials
#parameter
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
By the factor theorem (p(3)=0), so (27-45+3a+12=0) and (a=2). In exams, substitute the zero from the given factor directly.
Step 2
Why this answer is correct
The correct answer is A. (2). By the factor theorem (p(3)=0), so (27-45+3a+12=0) and (a=2). In exams, substitute the zero from the given factor directly.
Step 3
Exam Tip
गुणनखंड प्रमेय से (p(3)=0), इसलिए (27-45+3a+12=0) और (a=2)। परीक्षा में दिए गए गुणनखंड से मूल तुरंत रखिए।
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यदि (p(x)=x-2 -7x+10) और (q(x)=p(x+1)) है, तो (q(x)) के शून्यक कौन-से हैं?
If (p(x)=x-2 -7x+10) and (q(x)=p(x+1)), what are the zeroes of (q(x))?
#polynomials
#transformed-zeroes
#expert
A (1,4)
B (2,5)
C (3,6)
D (0,3)
Explanation opens after your attempt
Step 1
Concept
The zeroes of (p(x)) are (2) and (5), so for (p(x+1)=0), (x+1=2) or (x+1=5). Hence the zeroes of (q(x)) are (1) and (4).
Step 2
Why this answer is correct
The correct answer is A. (1,4). The zeroes of (p(x)) are (2) and (5), so for (p(x+1)=0), (x+1=2) or (x+1=5). Hence the zeroes of (q(x)) are (1) and (4).
Step 3
Exam Tip
(p(x)) के शून्यक (2) और (5) हैं, इसलिए (p(x+1)=0) के लिए (x+1=2) या (x+1=5)। अतः (q(x)) के शून्यक (1) और (4) हैं।
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यदि (p(x)=2x-3 -5x-2 +mx+6) को (x+1) से भाग देने पर शेष (0) है, तो (m) क्या है?
If (p(x)=2x-3 -5x-2 +mx+6) leaves remainder (0) when divided by (x+1), what is (m)?
#remainder-theorem
#signs
#polynomials
A (-13)
B (13)
C (-9)
D (9)
Explanation opens after your attempt
Step 1
Concept
By remainder theorem (p(-1)=0), so (-2-5-m+6=0), giving (-1-m=0) and (m=-1). Always check signs carefully.
Step 2
Why this answer is correct
The correct answer is A. (-13). By remainder theorem (p(-1)=0), so (-2-5-m+6=0), giving (-1-m=0) and (m=-1). Always check signs carefully.
Step 3
Exam Tip
शेष प्रमेय से (p(-1)=0), इसलिए (-2-5-m+6=0) और (m=-1) नहीं, सही समीकरण (-1-m=0) देता है (m=-1)।
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यदि (x-2) बहुपद (p(x)=x-3 +kx-2 -4x-4) का गुणनखंड है, तो (k) का मान क्या है?
If (x-2) is a factor of (p(x)=x-3 +kx-2 -4x-4), what is the value of (k)?
#factor-theorem
#polynomials
#expert
A (1)
B (2)
C (-1)
D (-2)
Explanation opens after your attempt
Step 1
Concept
By factor theorem (p(2)=0), so (8+4k-8-4=0) and (k=1). In exams, substitute the given zero directly.
Step 2
Why this answer is correct
The correct answer is A. (1). By factor theorem (p(2)=0), so (8+4k-8-4=0) and (k=1). In exams, substitute the given zero directly.
Step 3
Exam Tip
गुणनखंड प्रमेय से (p(2)=0), इसलिए (8+4k-8-4=0) और (k=1)। परीक्षा में पहले दिए गए मूल को सीधे रखिए।
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यदि (p(x)=ax-2 +bx+c) में \(a\neq0\) है और (p(1)=p(-1)=0) है, तो (b) का मान क्या होगा?
If (p(x)=ax-2 +bx+c) with \(a\neq0\) and (p(1)=p(-1)=0), what is the value of (b)?
#polynomials
#one-variable
#values
A (0)
B (a)
C (c)
D (-a)
Explanation opens after your attempt
Step 1
Concept
(p(1)=a+b+c) and (p(-1)=a-b+c); subtracting gives (2b=0). In exams, use addition or subtraction for symmetric inputs.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(1)=a+b+c) and (p(-1)=a-b+c); subtracting gives (2b=0). In exams, use addition or subtraction for symmetric inputs.
Step 3
Exam Tip
(p(1)=a+b+c) और (p(-1)=a-b+c) हैं, घटाने पर (2b=0) मिलता है। परीक्षा में सममित मानों पर जोड़-घटाव जल्दी करें।
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यदि द्विघात बहुपद \(x^2-6x+k\) के शून्यक \(\alpha\) और \(\beta\) हैं तथा \(\alpha^2+\beta^2=20\) है, तो (k) का मान क्या होगा?
If \(\alpha\) and \(\beta\) are zeroes of the quadratic polynomial \(x^2-6x+k\) and \(\alpha^2+\beta^2=20\), what is the value of (k)?
#polynomials
#zeroes
#identity
#hard
A (8)
B (6)
C (10)
D (16)
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=6\) and (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta). So (20=36-2k), giving (k=8).
Step 2
Why this answer is correct
The correct answer is A. (8). Here \(\alpha+\beta=6\) and (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta). So (20=36-2k), giving (k=8).
Step 3
Exam Tip
\(\alpha+\beta=6\) और (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta) होता है। इसलिए (20=36-2k) से (k=8) मिलता है।
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यदि (p(x)=x-3 +mx-2 -4x-4) में (x+2) एक गुणनखंड है, तो (m) का मान क्या होगा?
If (x+2) is a factor of (p(x)=x-3 +mx-2 -4x-4), what is (m)?
#polynomials
#factor_parameter
#hard
A (1)
B (-1)
C (2)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Putting (p(-2)=0) gives (-8+4m+8-4=0). Thus (4m-4=0), so (m=1).
Step 2
Why this answer is correct
The correct answer is A. (1). Putting (p(-2)=0) gives (-8+4m+8-4=0). Thus (4m-4=0), so (m=1).
Step 3
Exam Tip
(p(-2)=0) रखने पर (-8+4m+8-4=0) मिलता है। इससे (4m-4=0) और (m=1) है।
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\(x^3-7x+6\) के लिए कौन सा कथन सही है?
Which statement is correct for \(x^3-7x+6\)?
#polynomials
#factor_theorem
#two_factors
#hard
A (x-1) और (x-2) दोनों गुणनखंड हैं / Both (x-1) and (x-2) are factors
B केवल (x-1) गुणनखंड है / Only (x-1) is a factor
C केवल (x-2) गुणनखंड है / Only (x-2) is a factor
D दोनों गुणनखंड नहीं हैं / Neither is a factor
Explanation opens after your attempt
Correct Answer
A. (x-1) और (x-2) दोनों गुणनखंड हैं / Both (x-1) and (x-2) are factors
Step 1
Concept
Both (p(1)=0) and (p(2)=0). Hence (x-1) and (x-2) are both factors.
Step 2
Why this answer is correct
The correct answer is A. (x-1) और (x-2) दोनों गुणनखंड हैं / Both (x-1) and (x-2) are factors. Both (p(1)=0) and (p(2)=0). Hence (x-1) and (x-2) are both factors.
Step 3
Exam Tip
(p(1)=0) और (p(2)=0) दोनों हैं। इसलिए (x-1) और (x-2) दोनों गुणनखंड हैं।
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यदि (p(x)=4x-2 -12x+9), तो इसके शून्यकों के बारे में कौन सा कथन सही है?
If (p(x)=4x-2 -12x+9), which statement about its zeroes is correct?
#polynomials
#perfect_square
#zeroes
#hard
A दोनों शून्यक \(\frac{3}{2}\) हैं / Both zeroes are \(\frac{3}{2}\)
B दोनों शून्यक \(-\frac{3}{2}\) हैं / Both zeroes are \(-\frac{3}{2}\)
C शून्यक \(\frac{2}{3}\) और \(\frac{3}{2}\) हैं / Zeroes are \(\frac{2}{3}\) and \(\frac{3}{2}\)
D कोई शून्यक नहीं है / There is no zero
Explanation opens after your attempt
Correct Answer
A. दोनों शून्यक \(\frac{3}{2}\) हैं / Both zeroes are \(\frac{3}{2}\)
Step 1
Concept
(4x-2 -12x+9=(2x-3)2 ). Therefore, both zeroes are \(\frac{3}{2}\).
Step 2
Why this answer is correct
The correct answer is A. दोनों शून्यक \(\frac{3}{2}\) हैं / Both zeroes are \(\frac{3}{2}\). (4x-2 -12x+9=(2x-3)2 ). Therefore, both zeroes are \(\frac{3}{2}\).
Step 3
Exam Tip
(4x-2 -12x+9=(2x-3)2 ) है। इसलिए दोनों शून्यक \(\frac{3}{2}\) हैं।
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यदि \(x^2-11x+30\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो (\(\alpha-\beta\)2 ) क्या है?
If \(\alpha\) and \(\beta\) are zeroes of \(x^2-11x+30\), what is (\(\alpha-\beta\)2 )?
#polynomials
#zeroes
#difference_square
#hard
A (1)
B (121)
C (60)
D (49)
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-\beta\)2 =\(\alpha+\beta\)2 -4\alpha\beta). We get (121-120=1).
Step 2
Why this answer is correct
The correct answer is A. (1). (\(\alpha-\beta\)2 =\(\alpha+\beta\)2 -4\alpha\beta). We get (121-120=1).
Step 3
Exam Tip
(\(\alpha-\beta\)2 =\(\alpha+\beta\)2 -4\alpha\beta) है। (121-120=1) मिलता है।
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यदि \(x^2+mx+n\) का एक शून्यक (0) है और दूसरा शून्यक (5) है, तो (m+n) क्या होगा?
If one zero of \(x^2+mx+n\) is (0) and the other zero is (5), what is (m+n)?
#polynomials
#zeroes
#constant_term
#hard
A (-5)
B (5)
C (0)
D (10)
Explanation opens after your attempt
Step 1
Concept
The sum is (5), so (m=-5), and the product is (0), so (n=0). Hence (m+n=-5).
Step 2
Why this answer is correct
The correct answer is A. (-5). The sum is (5), so (m=-5), and the product is (0), so (n=0). Hence (m+n=-5).
Step 3
Exam Tip
योग (5) है इसलिए (m=-5), और गुणनफल (0) है इसलिए (n=0)। अतः (m+n=-5)।
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यदि (p(x)=x-4 -5x-2 +4), तो कौन सा मान (p(x)) का शून्यक नहीं है?
If (p(x)=x-4 -5x-2 +4), which value is not a zero of (p(x))?
#polynomials
#quartic
#zero_check
#hard
A (1)
B (-1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(3)=81-45+4=40), so (3) is not a zero. The values (1), (-1), and (2) make the polynomial (0).
Step 2
Why this answer is correct
The correct answer is D. (3). (p(3)=81-45+4=40), so (3) is not a zero. The values (1), (-1), and (2) make the polynomial (0).
Step 3
Exam Tip
(p(3)=81-45+4=40) है, इसलिए (3) शून्यक नहीं है। शेष (1), (-1) और (2) पर मान (0) मिलता है।
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किस बहुपद के शून्यक (0), (2) और (-3) हैं?
Which polynomial has zeroes (0), (2), and (-3)?
#polynomials
#formation
#cubic
#hard
A \(x^3+x^2-6x\)
B \(x^3-x^2-6x\)
C \(x^3+x^2+6x\)
D \(x^3-5x^2+6x\)
Explanation opens after your attempt
Correct Answer
A. \(x^3+x^2-6x\)
Step 1
Concept
From the zeroes, the polynomial is (x(x-2)(x+3)). Expanding gives \(x^3+x^2-6x\).
Step 2
Why this answer is correct
The correct answer is A. \(x^3+x^2-6x\). From the zeroes, the polynomial is (x(x-2)(x+3)). Expanding gives \(x^3+x^2-6x\).
Step 3
Exam Tip
शून्यकों से बहुपद (x(x-2)(x+3)) बनेगा। इसे फैलाने पर \(x^3+x^2-6x\) मिलता है।
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यदि \(2x^2+5x-3\) को (\(x-\alpha\)\(x-\beta\)) के रूप में लिखा जाए, तो \(\alpha+\beta\) क्या होगा?
If \(2x^2+5x-3\) is considered with factors involving (\(x-\alpha\)\(x-\beta\)), what is \(\alpha+\beta\)?
#polynomials
#sum_zeroes
#hard
A \(-\frac{5}{2}\)
B \(\frac{5}{2}\)
C (-3)
D (3)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{5}{2}\)
Step 1
Concept
For \(ax^2+bx+c\), the sum of zeroes is \(-\frac{b}{a}\). Hence \(\alpha+\beta=-\frac{5}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{5}{2}\). For \(ax^2+bx+c\), the sum of zeroes is \(-\frac{b}{a}\). Hence \(\alpha+\beta=-\frac{5}{2}\).
Step 3
Exam Tip
द्विघात \(ax^2+bx+c\) के लिए शून्यकों का योग \(-\frac{b}{a}\) होता है। इसलिए \(\alpha+\beta=-\frac{5}{2}\)।
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यदि \(x^2-3x-10\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो \(\alpha^2\beta+\alpha\beta^2\) क्या है?
If \(\alpha\) and \(\beta\) are zeroes of \(x^2-3x-10\), what is \(\alpha^2\beta+\alpha\beta^2\)?
#polynomials
#zeroes
#symmetric_expression
#hard
A (-30)
B (30)
C (-13)
D (13)
Explanation opens after your attempt
Step 1
Concept
(\alpha-2 \beta+\alpha\beta-2 =\alpha\beta\(\alpha+\beta\)). Here \(\alpha\beta=-10\) and \(\alpha+\beta=3\), so the value is (-30).
Step 2
Why this answer is correct
The correct answer is A. (-30). (\alpha-2 \beta+\alpha\beta-2 =\alpha\beta\(\alpha+\beta\)). Here \(\alpha\beta=-10\) and \(\alpha+\beta=3\), so the value is (-30).
Step 3
Exam Tip
(\alpha-2 \beta+\alpha\beta-2 =\alpha\beta\(\alpha+\beta\)) होता है। यहां \(\alpha\beta=-10\) और \(\alpha+\beta=3\), इसलिए मान (-30) है।
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यदि (p(x)=x-3 +ax-2 +bx+8) के शून्यक (-1), (-2) और (-4) हैं, तो (a+b) क्या है?
If the zeroes of (p(x)=x-3 +ax-2 +bx+8) are (-1), (-2), and (-4), what is (a+b)?
#polynomials
#cubic_zeroes
#coefficients
#hard
A (21)
B (7)
C (14)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The polynomial is ((x+1)(x+2)(x+4)=x-3 +7x-2 +14x+8). Hence (a+b=21).
Step 2
Why this answer is correct
The correct answer is A. (21). The polynomial is ((x+1)(x+2)(x+4)=x-3 +7x-2 +14x+8). Hence (a+b=21).
Step 3
Exam Tip
बहुपद ((x+1)(x+2)(x+4)=x-3 +7x-2 +14x+8) है। इसलिए (a+b=21)।
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यदि \(x^2-10x+q\) के शून्यक (2r) और (3r) हैं, तो (q) का मान क्या है?
If the zeroes of \(x^2-10x+q\) are (2r) and (3r), what is (q)?
#polynomials
#ratio_zeroes
#product
#hard
A (24)
B (20)
C (12)
D (30)
Explanation opens after your attempt
Step 1
Concept
From the sum (5r=10), (r=2). The product is \(2r\cdot3r=6r^2=24\).
Step 2
Why this answer is correct
The correct answer is A. (24). From the sum (5r=10), (r=2). The product is \(2r\cdot3r=6r^2=24\).
Step 3
Exam Tip
योग (5r=10) से (r=2) है। गुणनफल \(2r\cdot3r=6r^2=24\) है।
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द्विघात बहुपद \(kx^2+6x+4\) के शून्यकों का योग (-3) है। (k) का मान क्या है?
The sum of zeroes of the quadratic polynomial \(kx^2+6x+4\) is (-3). What is (k)?
#polynomials
#parameter
#sum_zeroes
#hard
A (2)
B (-2)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The sum is \(-\frac{6}{k}\), and it equals (-3). Therefore, (k=2).
Step 2
Why this answer is correct
The correct answer is A. (2). The sum is \(-\frac{6}{k}\), and it equals (-3). Therefore, (k=2).
Step 3
Exam Tip
योग \(-\frac{6}{k}\) है और यह (-3) है। इसलिए (k=2) होगा।
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यदि \(x^2-8x+k\) के शून्यक \(\alpha\) और \(\beta\) हैं तथा \(\alpha-\beta=2\), तो (k) क्या है?
If \(\alpha\) and \(\beta\) are zeroes of \(x^2-8x+k\) and \(\alpha-\beta=2\), what is (k)?
#polynomials
#zeroes
#difference
#hard
A (15)
B (16)
C (12)
D (10)
Explanation opens after your attempt
Step 1
Concept
From sum (8) and difference (2), the zeroes are (5) and (3). Their product is (15), so (k=15).
Step 2
Why this answer is correct
The correct answer is A. (15). From sum (8) and difference (2), the zeroes are (5) and (3). Their product is (15), so (k=15).
Step 3
Exam Tip
योग (8) और अंतर (2) से शून्यक (5) और (3) हैं। गुणनफल (15) है इसलिए (k=15)।
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किस (k) के लिए \(x^2+kx+9\) का एक शून्यक दूसरे का तीन गुना है और दोनों धनात्मक हैं?
For which (k) does \(x^2+kx+9\) have one zero three times the other and both positive?
#polynomials
#zeroes
#ratio
#hard
A \(-4\sqrt{3}\)
B \(4\sqrt{3}\)
C (-6)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(-4\sqrt{3}\)
Step 1
Concept
Let the zeroes be (t) and (3t), so \(3t^2=9\) gives \(t=\sqrt{3}\). The sum is \(4\sqrt{3}\), hence \(k=-4\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is A. \(-4\sqrt{3}\). Let the zeroes be (t) and (3t), so \(3t^2=9\) gives \(t=\sqrt{3}\). The sum is \(4\sqrt{3}\), hence \(k=-4\sqrt{3}\).
Step 3
Exam Tip
शून्यक (t) और (3t) मानें, तो \(3t^2=9\) से \(t=\sqrt{3}\) है। योग \(4\sqrt{3}\) है इसलिए \(k=-4\sqrt{3}\)।
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यदि \(x^2-4x+1\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो \(\alpha^3+\beta^3\) का मान क्या है?
If \(\alpha\) and \(\beta\) are zeroes of \(x^2-4x+1\), what is \(\alpha^3+\beta^3\)?
#polynomials
#zeroes
#cube_identity
#hard
A (52)
B (64)
C (40)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(\alpha+\beta=4\) and \(\alpha\beta=1\). (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)=64-12=52).
Step 2
Why this answer is correct
The correct answer is A. (52). \(\alpha+\beta=4\) and \(\alpha\beta=1\). (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)=64-12=52).
Step 3
Exam Tip
\(\alpha+\beta=4\) और \(\alpha\beta=1\) है। (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)=64-12=52)।
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यदि \(x^2+5x+6\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो नया बहुपद जिसके शून्यक \(\alpha+1\) और \(\beta+1\) हैं, क्या है?
If \(\alpha\) and \(\beta\) are zeroes of \(x^2+5x+6\), what is the new polynomial whose zeroes are \(\alpha+1\) and \(\beta+1\)?
#polynomials
#transformed_zeroes
#hard
A \(x^2+3x+2\)
B \(x^2+5x+6\)
C \(x^2+7x+12\)
D \(x^2-3x+2\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+2\)
Step 1
Concept
The original zeroes are (-2) and (-3), so the new zeroes are (-1) and (-2). The new polynomial is \(x^2+3x+2\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x+2\). The original zeroes are (-2) and (-3), so the new zeroes are (-1) and (-2). The new polynomial is \(x^2+3x+2\).
Step 3
Exam Tip
मूल शून्यक (-2) और (-3) हैं, इसलिए नए शून्यक (-1) और (-2) हैं। नया बहुपद \(x^2+3x+2\) है।
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यदि (p(x)=x-3 -2x-2 -5x+6), तो निम्न में से कौन सा शून्यक नहीं है?
If (p(x)=x-3 -2x-2 -5x+6), which of the following is not a zero?
#polynomials
#not_zero
#hard
A (1)
B (2)
C (3)
D (-2)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8-8-10+6=-4), so (2) is not a zero. The other options can be checked by substitution.
Step 2
Why this answer is correct
The correct answer is B. (2). (p(2)=8-8-10+6=-4), so (2) is not a zero. The other options can be checked by substitution.
Step 3
Exam Tip
(p(2)=8-8-10+6=-4) है इसलिए (2) शून्यक नहीं है। बाकी विकल्पों को भी प्रतिस्थापन से जांच सकते हैं।
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बहुपद \(2x^3-9x^2+13x-6\) का एक गुणनखंड कौन सा है?
Which is a factor of \(2x^3-9x^2+13x-6\)?
#polynomials
#factor_check
#cubic
#hard
A (x-1)
B (x+1)
C (x-4)
D (x+3)
Explanation opens after your attempt
Step 1
Concept
(p(1)=2-9+13-6=0), so (x-1) is a factor. In option checking, try small values first.
Step 2
Why this answer is correct
The correct answer is A. (x-1). (p(1)=2-9+13-6=0), so (x-1) is a factor. In option checking, try small values first.
Step 3
Exam Tip
(p(1)=2-9+13-6=0) है इसलिए (x-1) गुणनखंड है। विकल्प जांच में छोटे मान पहले लगाएं।
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यदि (p(x)=x-2 -4x+k) और (p(1)=p(3)), तो (k) के बारे में क्या कहा जा सकता है?
If (p(x)=x-2 -4x+k) and (p(1)=p(3)), what can be said about (k)?
#polynomials
#evaluation
#parameter
#hard
A (k=1)
B (k=3)
C कोई भी वास्तविक मान / Any real value
D कोई मान संभव नहीं / No value possible
Explanation opens after your attempt
Correct Answer
C. कोई भी वास्तविक मान / Any real value
Step 1
Concept
(p(1)=k-3) and (p(3)=k-3), so they are equal. Hence (k) can be any real value.
Step 2
Why this answer is correct
The correct answer is C. कोई भी वास्तविक मान / Any real value. (p(1)=k-3) and (p(3)=k-3), so they are equal. Hence (k) can be any real value.
Step 3
Exam Tip
(p(1)=k-3) और (p(3)=k-3) दोनों बराबर हैं। इसलिए (k) कोई भी वास्तविक मान हो सकता है।
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यदि \(x^2+px+16\) के शून्यक परस्पर बराबर और ऋणात्मक हैं, तो (p) का मान क्या है?
If the zeroes of \(x^2+px+16\) are equal and negative, what is (p)?
#polynomials
#equal_negative_zeroes
#hard
A (8)
B (-8)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
The equal negative zeroes are (-4) and (-4) because the product is (16). The sum is (-8), so (p=8).
Step 2
Why this answer is correct
The correct answer is A. (8). The equal negative zeroes are (-4) and (-4) because the product is (16). The sum is (-8), so (p=8).
Step 3
Exam Tip
बराबर ऋणात्मक शून्यक (-4) और (-4) होंगे क्योंकि गुणनफल (16) है। योग (-8) है इसलिए (p=8)।
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यदि \(3x^2+2x-1\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो (\(\alpha+\beta\)2 ) का मान क्या है?
If \(\alpha\) and \(\beta\) are zeroes of \(3x^2+2x-1\), what is (\(\alpha+\beta\)2 )?
#polynomials
#sum_zeroes
#square
#hard
A \(\frac{4}{9}\)
B \(-\frac{4}{9}\)
C \(\frac{1}{9}\)
D \(\frac{2}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{4}{9}\)
Step 1
Concept
\(\alpha+\beta=-\frac{2}{3}\). Therefore, (\(\alpha+\beta\)2 =\frac{4}{9}).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{4}{9}\). \(\alpha+\beta=-\frac{2}{3}\). Therefore, (\(\alpha+\beta\)2 =\frac{4}{9}).
Step 3
Exam Tip
\(\alpha+\beta=-\frac{2}{3}\) है। इसलिए (\(\alpha+\beta\)2 =\frac{4}{9}) होगा।
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यदि \(x^2-7x+10\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो \(\alpha^2+\beta^2\) क्या है?
If \(\alpha\) and \(\beta\) are zeroes of \(x^2-7x+10\), what is \(\alpha^2+\beta^2\)?
#polynomials
#zeroes
#identity
#hard
A (29)
B (49)
C (20)
D (39)
Explanation opens after your attempt
Step 1
Concept
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta). Thus (72 -2(10)=29).
Step 2
Why this answer is correct
The correct answer is A. (29). (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta). Thus (72 -2(10)=29).
Step 3
Exam Tip
(\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta) होता है। (72 -2(10)=29) है।
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यदि \(2x^2-3x-5\) के शून्यक \(\alpha\) और \(\beta\) हैं, तो \(\frac{1}{\alpha}+\frac{1}{\beta}\) क्या होगा?
If \(\alpha\) and \(\beta\) are zeroes of \(2x^2-3x-5\), what is \(\frac{1}{\alpha}+\frac{1}{\beta}\)?
#polynomials
#zeroes
#reciprocal
#hard
A \(-\frac{3}{5}\)
B \(\frac{3}{5}\)
C \(-\frac{5}{3}\)
D \(\frac{5}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{3}{5}\)
Step 1
Concept
\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here \(\frac{3}{2}\div-\frac{5}{2}=-\frac{3}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{3}{5}\). \(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\). Here \(\frac{3}{2}\div-\frac{5}{2}=-\frac{3}{5}\).
Step 3
Exam Tip
\(\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha\beta}\) है। यहां \(\frac{3}{2}\div-\frac{5}{2}=-\frac{3}{5}\)।
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यदि द्विघात बहुपद के शून्यक \(\alpha\) और \(\beta\) हैं तथा \(\alpha+\beta=5\), \(\alpha\beta=6\), तो मोनिक बहुपद क्या है?
If a quadratic polynomial has zeroes \(\alpha\) and \(\beta\), with \(\alpha+\beta=5\) and \(\alpha\beta=6\), what is the monic polynomial?
#polynomials
#monic
#formation
#hard
A \(x^2-5x+6\)
B \(x^2+5x+6\)
C \(x^2-6x+5\)
D \(x^2+6x+5\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-5x+6\)
Step 1
Concept
The monic polynomial is (x-2 -\(\alpha+\beta\)x+\alpha\beta). Hence \(x^2-5x+6\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-5x+6\). The monic polynomial is (x-2 -\(\alpha+\beta\)x+\alpha\beta). Hence \(x^2-5x+6\) is correct.
Step 3
Exam Tip
मोनिक बहुपद (x-2 -\(\alpha+\beta\)x+\alpha\beta) होता है। इसलिए \(x^2-5x+6\) सही है।
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यदि (p(x)=x-2 -2x+5), तो (p(1)) का मान क्या है और क्या (1) शून्यक है?
If (p(x)=x-2 -2x+5), what is (p(1)), and is (1) a zero?
#polynomials
#evaluation
#zero_check
#hard
A (4), नहीं / (4), no
B (0), हां / (0), yes
C (2), नहीं / (2), no
D (5), नहीं / (5), no
Explanation opens after your attempt
Correct Answer
A. (4), नहीं / (4), no
Step 1
Concept
(p(1)=1-2+5=4), so (1) is not a zero. A zero must make the value (0).
Step 2
Why this answer is correct
The correct answer is A. (4), नहीं / (4), no. (p(1)=1-2+5=4), so (1) is not a zero. A zero must make the value (0).
Step 3
Exam Tip
(p(1)=1-2+5=4) है इसलिए (1) शून्यक नहीं है। शून्यक तभी होगा जब मान (0) हो।
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\(x^4-1\) के रैखिक गुणनखंडों में से कौन सा गलत है?
Which one is not a linear factor of \(x^4-1\)?
#polynomials
#factors
#degree
#hard
A (x-1)
B (x+1)
C \(x^2+1\)
D (x-i)
Explanation opens after your attempt
Correct Answer
C. \(x^2+1\)
Step 1
Concept
\(x^2+1\) is not linear because its degree is (2). Over real numbers, it is not a linear factor.
Step 2
Why this answer is correct
The correct answer is C. \(x^2+1\). \(x^2+1\) is not linear because its degree is (2). Over real numbers, it is not a linear factor.
Step 3
Exam Tip
\(x^2+1\) रैखिक नहीं है क्योंकि उसकी घात (2) है। वास्तविक संख्याओं में इसे रैखिक गुणनखंड नहीं माना जाता।
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यदि (p(x)) को (x-4) से भाग देने पर शेषफल (7) है, तो (p(4)) क्या होगा?
If the remainder when (p(x)) is divided by (x-4) is (7), what is (p(4))?
#polynomials
#remainder_theorem
#concept
#hard
A (4)
B (7)
C (-7)
D (0)
Explanation opens after your attempt
Step 1
Concept
By the remainder theorem, the remainder on division by (x-4) is (p(4)). Therefore, (p(4)=7).
Step 2
Why this answer is correct
The correct answer is B. (7). By the remainder theorem, the remainder on division by (x-4) is (p(4)). Therefore, (p(4)=7).
Step 3
Exam Tip
शेषफल प्रमेय के अनुसार (x-4) से भाग देने पर शेषफल (p(4)) होता है। इसलिए (p(4)=7)।
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\(3x^3-2x^2+x+7\) को (x+2) से भाग देने पर शेषफल क्या है?
What is the remainder when \(3x^3-2x^2+x+7\) is divided by (x+2)?
#polynomials
#remainder
#substitution
#hard
A (-27)
B (-25)
C (25)
D (27)
Explanation opens after your attempt
Step 1
Concept
The remainder is (p(-2)). (3(-8)-2(4)-2+7=-27).
Step 2
Why this answer is correct
The correct answer is A. (-27). The remainder is (p(-2)). (3(-8)-2(4)-2+7=-27).
Step 3
Exam Tip
शेषफल (p(-2)) होगा। (3(-8)-2(4)-2+7=-27) है।
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\(x^3-5x^2+8x-4\) को (x-1) से भाग देने पर शेषफल क्या होगा?
What is the remainder when \(x^3-5x^2+8x-4\) is divided by (x-1)?
#polynomials
#remainder_theorem
#hard
A (0)
B (1)
C (-1)
D (4)
Explanation opens after your attempt
Step 1
Concept
By the remainder theorem, the remainder is (p(1)). We get (1-5+8-4=0).
Step 2
Why this answer is correct
The correct answer is A. (0). By the remainder theorem, the remainder is (p(1)). We get (1-5+8-4=0).
Step 3
Exam Tip
शेषफल प्रमेय से शेषफल (p(1)) है। (1-5+8-4=0) मिलता है।
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यदि (x+1) बहुपद \(2x^3+kx^2-5x+2\) का गुणनखंड है, तो (k) का सही मान क्या है?
If (x+1) is a factor of \(2x^3+kx^2-5x+2\), what is the correct value of (k)?
#polynomials
#factor_theorem
#parameter
#hard
A (-5)
B (5)
C (-1)
D (1)
Explanation opens after your attempt
Step 1
Concept
Putting (p(-1)=0) gives (-2+k+5+2=0). Therefore, (k=-5) is correct.
Step 2
Why this answer is correct
The correct answer is A. (-5). Putting (p(-1)=0) gives (-2+k+5+2=0). Therefore, (k=-5) is correct.
Step 3
Exam Tip
(p(-1)=0) रखने पर (-2+k+5+2=0) मिलता है। इसलिए (k=-5) सही है।
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यदि (x+1) बहुपद \(2x^3+kx^2-5x+2\) का गुणनखंड है, तो (k) का मान क्या है?
If (x+1) is a factor of \(2x^3+kx^2-5x+2\), what is (k)?
#polynomials
#factor_theorem
#parameter
#hard
A (5)
B (-5)
C (1)
D (-1)
Explanation opens after your attempt
Step 1
Concept
If (x+1) is a factor, then (p(-1)=0). From (-2+k+5+2=0), we get (k=-5).
Step 2
Why this answer is correct
The correct answer is A. (5). If (x+1) is a factor, then (p(-1)=0). From (-2+k+5+2=0), we get (k=-5).
Step 3
Exam Tip
(x+1) गुणनखंड होने पर (p(-1)=0) होगा। (-2+k+5+2=0) से (k=-5) नहीं बल्कि (k=-5) मिलता है।
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यदि (p(x)=x-3 -3x-2 -4x+12) है, तो कौन सा (p(x)) का गुणनखंड है?
If (p(x)=x-3 -3x-2 -4x+12), which is a factor of (p(x))?
#polynomials
#factor_theorem
#hard
A (x-2)
B (x+2)
C (x-3)
D (x+3)
Explanation opens after your attempt
Step 1
Concept
Since (p(2)=8-12-8+12=0), (x-2) is a factor. Use the factor theorem.
Step 2
Why this answer is correct
The correct answer is A. (x-2). Since (p(2)=8-12-8+12=0), (x-2) is a factor. Use the factor theorem.
Step 3
Exam Tip
(p(2)=8-12-8+12=0) है इसलिए (x-2) गुणनखंड है। गुणनखंड प्रमेय का प्रयोग करें।
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बहुपद \(x^3-6x^2+11x-6\) के शून्यक कौन से हैं?
What are the zeroes of \(x^3-6x^2+11x-6\)?
#polynomials
#cubic_zeroes
#hard
A (1,2,3)
B (-1,-2,-3)
C (1,1,6)
D (2,2,2)
Explanation opens after your attempt
Correct Answer
A. (1,2,3)
Step 1
Concept
It equals ((x-1)(x-2)(x-3)). Therefore, the zeroes are (1), (2), and (3).
Step 2
Why this answer is correct
The correct answer is A. (1,2,3). It equals ((x-1)(x-2)(x-3)). Therefore, the zeroes are (1), (2), and (3).
Step 3
Exam Tip
यह ((x-1)(x-2)(x-3)) के बराबर है। अतः शून्यक (1), (2) और (3) हैं।
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यदि (x-a), (x-b) और (x-c) किसी घन बहुपद के गुणनखंड हैं, तो उसका एक संभावित बहुपद कौन सा है?
If (x-a), (x-b), and (x-c) are factors of a cubic polynomial, which is a possible polynomial?
#polynomials
#cubic
#factors
#hard
A (x-3 -(a+b+c)x-2 +(ab+bc+ca)x-abc)
B (x-3 +(a+b+c)x-2 +(ab+bc+ca)x+abc)
C (x-3 -(ab+bc+ca)x-2 +(a+b+c)x-abc)
D (x-3 +abcx-2 -(a+b+c)x+ab+bc+ca)
Explanation opens after your attempt
Correct Answer
A. (x-3 -(a+b+c)x-2 +(ab+bc+ca)x-abc)
Step 1
Concept
Expanding ((x-a)(x-b)(x-c)) gives the first form. Remember the link between zeroes and factors.
Step 2
Why this answer is correct
The correct answer is A. (x-3 -(a+b+c)x-2 +(ab+bc+ca)x-abc). Expanding ((x-a)(x-b)(x-c)) gives the first form. Remember the link between zeroes and factors.
Step 3
Exam Tip
((x-a)(x-b)(x-c)) फैलाने पर पहला रूप मिलता है। शून्यकों और गुणनखंडों का संबंध याद रखें।
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बहुपद \(x^2-6x+9\) के शून्यकों के बारे में सही कथन कौन सा है?
Which statement about the zeroes of \(x^2-6x+9\) is correct?
#polynomials
#equal_zeroes
#factorisation
#hard
A दोनों शून्यक अलग हैं / Both zeroes are distinct
B दोनों शून्यक बराबर हैं / Both zeroes are equal
C कोई वास्तविक शून्यक नहीं है / There is no real zero
D शून्यकों का गुणनफल (6) है / Product of zeroes is (6)
Explanation opens after your attempt
Correct Answer
B. दोनों शून्यक बराबर हैं / Both zeroes are equal
Step 1
Concept
(x-2 -6x+9=(x-3)2 ), so both zeroes are (3). Recognizing square form is a fast exam method.
Step 2
Why this answer is correct
The correct answer is B. दोनों शून्यक बराबर हैं / Both zeroes are equal. (x-2 -6x+9=(x-3)2 ), so both zeroes are (3). Recognizing square form is a fast exam method.
Step 3
Exam Tip
(x-2 -6x+9=(x-3)2 ) है इसलिए दोनों शून्यक (3) हैं। वर्ग रूप को पहचानना परीक्षा में तेज तरीका है।
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यदि (p(x)=3x-2 -10x+m) के शून्यकों का गुणनफल \(\frac{4}{3}\) है, तो (m) का मान क्या है?
If the product of zeroes of (p(x)=3x-2 -10x+m) is \(\frac{4}{3}\), what is (m)?
#polynomials
#product_zeroes
#hard
A (4)
B (3)
C \(\frac{4}{9}\)
D (12)
Explanation opens after your attempt
Step 1
Concept
The product is \(\frac{m}{3}\). From \(\frac{m}{3}=\frac{4}{3}\), we get (m=4).
Step 2
Why this answer is correct
The correct answer is A. (4). The product is \(\frac{m}{3}\). From \(\frac{m}{3}=\frac{4}{3}\), we get (m=4).
Step 3
Exam Tip
गुणनफल \(\frac{m}{3}\) है। \(\frac{m}{3}=\frac{4}{3}\) से (m=4) मिलता है।
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यदि (p(x)=2x-2 +kx+8) के शून्यकों का योग (3) है, तो (k) क्या होगा?
If the sum of zeroes of (p(x)=2x-2 +kx+8) is (3), what is (k)?
#polynomials
#sum_zeroes
#hard
A (6)
B (-6)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The sum is \(-\frac{k}{2}\), and it equals (3). Hence (k=-6).
Step 2
Why this answer is correct
The correct answer is B. (-6). The sum is \(-\frac{k}{2}\), and it equals (3). Hence (k=-6).
Step 3
Exam Tip
योग \(-\frac{k}{2}\) होता है और यह (3) है। इसलिए (k=-6) है।
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यदि (p(x)=x-2 -5x+6) है, तो (p(3)-p(2)) का मान क्या है?
If (p(x)=x-2 -5x+6), what is the value of (p(3)-p(2))?
#polynomials
#evaluation
#zeroes
#hard
A (0)
B (1)
C (-1)
D (6)
Explanation opens after your attempt
Step 1
Concept
Both (2) and (3) are zeroes, so (p(3)=0) and (p(2)=0). Therefore, the difference is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). Both (2) and (3) are zeroes, so (p(3)=0) and (p(2)=0). Therefore, the difference is (0).
Step 3
Exam Tip
(2) और (3) दोनों शून्यक हैं, इसलिए (p(3)=0) और (p(2)=0)। अतः अंतर (0) है।
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किस बहुपद की घात (4) है?
Which polynomial has degree (4)?
#polynomials
#degree
#zero_coefficient
#hard
A \(7x^4+0x^5-3x+1\)
B \(0x^6+5x^3-2\)
C \(x^2+x+1\)
D (9)
Explanation opens after your attempt
Correct Answer
A. \(7x^4+0x^5-3x+1\)
Step 1
Concept
The term \(0x^5\) does not affect degree because its coefficient is (0). The highest non-zero power is (4).
Step 2
Why this answer is correct
The correct answer is A. \(7x^4+0x^5-3x+1\). The term \(0x^5\) does not affect degree because its coefficient is (0). The highest non-zero power is (4).
Step 3
Exam Tip
\(0x^5\) पद घात नहीं बढ़ाता क्योंकि उसका गुणांक (0) है। सबसे बड़ा शून्येतर घात (4) है।
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यदि \(x^2+ax+b\) के शून्यक (4) और (-7) हैं, तो (a-b) क्या होगा?
If the zeroes of \(x^2+ax+b\) are (4) and (-7), what is (a-b)?
#polynomials
#zeroes
#coefficient_relation
#hard
A (25)
B (31)
C (-25)
D (-31)
Explanation opens after your attempt
Step 1
Concept
The sum is (-3), so (a=3), and the product is (-28), so (b=-28). Hence (a-b=31).
Step 2
Why this answer is correct
The correct answer is B. (31). The sum is (-3), so (a=3), and the product is (-28), so (b=-28). Hence (a-b=31).
Step 3
Exam Tip
योग (-3) है इसलिए (a=3) और गुणनफल (-28) है इसलिए (b=-28)। अतः (a-b=31) है।
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द्विघात बहुपद जिसके शून्यक \(\frac{2}{3}\) और \(-\frac{5}{4}\) हैं, कौन सा हो सकता है?
Which can be a quadratic polynomial whose zeroes are \(\frac{2}{3}\) and \(-\frac{5}{4}\)?
#polynomials
#formation
#zeroes
#hard
A \(12x^2+7x-10\)
B \(12x^2-7x-10\)
C \(12x^2+7x+10\)
D \(12x^2-7x+10\)
Explanation opens after your attempt
Correct Answer
A. \(12x^2+7x-10\)
Step 1
Concept
The sum is \(-\frac{7}{12}\) and the product is \(-\frac{5}{6}\). So \(12x^2+7x-10\) is correct.
Step 2
Why this answer is correct
The correct answer is A. \(12x^2+7x-10\). The sum is \(-\frac{7}{12}\) and the product is \(-\frac{5}{6}\). So \(12x^2+7x-10\) is correct.
Step 3
Exam Tip
शून्यकों का योग \(-\frac{7}{12}\) और गुणनफल \(-\frac{5}{6}\) है। इसलिए \(12x^2+7x-10\) सही है।
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यदि (p(x)=x-3 +px-2 +qx-6) के शून्यक (1), (2) और (3) हैं, तो (p+q) का सही मान क्या है?
If the zeroes of (p(x)=x-3 +px-2 +qx-6) are (1), (2), and (3), what is the correct value of (p+q)?
#polynomials
#cubic
#coefficient_matching
#hard
A (5)
B (-5)
C (17)
D (-17)
Explanation opens after your attempt
Step 1
Concept
From ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6), (p=-6) and (q=11). Hence (p+q=5).
Step 2
Why this answer is correct
The correct answer is A. (5). From ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6), (p=-6) and (q=11). Hence (p+q=5).
Step 3
Exam Tip
((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6) से (p=-6) और (q=11)। अतः (p+q=5) है।
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यदि (p(x)=x-3 +px-2 +qx-6) के शून्यक (1), (2) और (3) हैं, तो (p+q) का मान क्या है?
If the zeroes of (p(x)=x-3 +px-2 +qx-6) are (1), (2), and (3), what is (p+q)?
#polynomials
#cubic
#coefficients
#hard
A (-5)
B (5)
C (11)
D (0)
Explanation opens after your attempt
Step 1
Concept
The polynomial is ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6). Hence (p=-6), (q=11), so (p+q=5).
Step 2
Why this answer is correct
The correct answer is A. (-5). The polynomial is ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6). Hence (p=-6), (q=11), so (p+q=5).
Step 3
Exam Tip
बहुपद ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6) है। इसलिए (p=-6), (q=11) और (p+q=5) नहीं बल्कि (5) है।
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बहुपद \(x^3-4x^2+x+6\) में (x=2) रखने पर क्या निष्कर्ष निकलेगा?
What conclusion follows when (x=2) is substituted in \(x^3-4x^2+x+6\)?
#polynomials
#zero
#substitution
#hard
A (2) शून्यक है / (2) is a zero
B (2) शून्यक नहीं है / (2) is not a zero
C बहुपद रैखिक है / The polynomial is linear
D बहुपद स्थिर है / The polynomial is constant
Explanation opens after your attempt
Correct Answer
A. (2) शून्यक है / (2) is a zero
Step 1
Concept
(p(2)=8-16+2+6=0), so (2) is a zero. Direct substitution is the quickest check.
Step 2
Why this answer is correct
The correct answer is A. (2) शून्यक है / (2) is a zero. (p(2)=8-16+2+6=0), so (2) is a zero. Direct substitution is the quickest check.
Step 3
Exam Tip
(p(2)=8-16+2+6=0) है इसलिए (2) शून्यक है। सीधे प्रतिस्थापन से जल्दी जांच होती है।
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यदि \(x^2-9x+k\) के शून्यक बराबर हैं, तो (k) का मान क्या है?
If the zeroes of \(x^2-9x+k\) are equal, what is the value of (k)?
#polynomials
#equal_zeroes
#discriminant
#hard
A (18)
B (81)
C \(\frac{81}{4}\)
D \(\frac{9}{4}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{81}{4}\)
Step 1
Concept
For equal zeroes, the discriminant \(b^2-4ac=0\). Thus (81-4k=0), giving \(k=\frac{81}{4}\).
Step 2
Why this answer is correct
The correct answer is C. \(\frac{81}{4}\). For equal zeroes, the discriminant \(b^2-4ac=0\). Thus (81-4k=0), giving \(k=\frac{81}{4}\).
Step 3
Exam Tip
बराबर शून्यकों के लिए विविक्तकर \(b^2-4ac=0\) होता है। इसलिए (81-4k=0) से \(k=\frac{81}{4}\) मिलता है।
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द्विघात बहुपद \(2x^2-7x+3\) के शून्यकों का गुणनफल क्या है?
What is the product of the zeroes of the quadratic polynomial \(2x^2-7x+3\)?
#polynomials
#zeroes
#product
#hard
A (3)
B \(\frac{3}{2}\)
C \(-\frac{7}{2}\)
D (2)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3}{2}\)
Step 1
Concept
For \(ax^2+bx+c\), the product is \(\frac{c}{a}\). Here, \(\frac{3}{2}\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{2}\). For \(ax^2+bx+c\), the product is \(\frac{c}{a}\). Here, \(\frac{3}{2}\) is correct.
Step 3
Exam Tip
द्विघात \(ax^2+bx+c\) में गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{3}{2}\) सही है।
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यदि (p(x)=x-2 -(m+3)x+12) के शून्यक (3) और (4) हैं, तो (m) का मान क्या है?
If the zeroes of (p(x)=x-2 -(m+3)x+12) are (3) and (4), what is (m)?
#polynomials
#zeroes
#sum
#hard
A (3)
B (4)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
The sum of zeroes is (7), which equals (m+3). Therefore, (m=4).
Step 2
Why this answer is correct
The correct answer is B. (4). The sum of zeroes is (7), which equals (m+3). Therefore, (m=4).
Step 3
Exam Tip
शून्यकों का योग (7) है और यह (m+3) के बराबर है। इसलिए (m=4) मिलेगा।
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यदि (p(x)=kx-2 -5x+6) का एक शून्यक (2) है, तो (k) का मान क्या होगा?
If (2) is a zero of (p(x)=kx-2 -5x+6), what is the value of (k)?
#polynomials
#zero
#value
#hard
A (1)
B (2)
C (-1)
D (-2)
Explanation opens after your attempt
Step 1
Concept
Putting (p(2)=0) gives (4k-10+6=0), so (k=1). For a zero, use (p\(\alpha\)=0).
Step 2
Why this answer is correct
The correct answer is A. (1). Putting (p(2)=0) gives (4k-10+6=0), so (k=1). For a zero, use (p\(\alpha\)=0).
Step 3
Exam Tip
(p(2)=0) रखने पर (4k-10+6=0) से (k=1) मिलता है। शून्यक के लिए (p\(\alpha\)=0) लगाएं।
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बहुपद (p(x)=ax-3 +bx-2 +cx+d) में \(a\ne0\) है। यदि (p(x)) को रैखिक बहुपद कहा जाए, तो यह कथन क्यों गलत है?
In the polynomial (p(x)=ax-3 +bx-2 +cx+d), \(a\ne0\). Why is it wrong to call (p(x)) a linear polynomial?
#polynomials
#degree
#cubic
#hard
A क्योंकि घात (1) है / Because degree is (1)
B क्योंकि घात (2) है / Because degree is (2)
C क्योंकि घात (3) है / Because degree is (3)
D क्योंकि स्थिर पद (d) है / Because constant term is (d)
Explanation opens after your attempt
Correct Answer
C. क्योंकि घात (3) है / Because degree is (3)
Step 1
Concept
The highest power is (3), so the polynomial is cubic. In exams, always check the highest non-zero exponent.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि घात (3) है / Because degree is (3). The highest power is (3), so the polynomial is cubic. In exams, always check the highest non-zero exponent.
Step 3
Exam Tip
सबसे बड़ी घात (3) है इसलिए बहुपद घन है। परीक्षा में हमेशा सबसे बड़े शून्येतर घातांक को देखें।
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\(5x^2-6x+2\) और \(2x^2+9x-1\) में (x) के गुणांकों का योग क्या है?
What is the sum of the coefficients of (x) in \(5x^2-6x+2\) and \(2x^2+9x-1\)?
#coefficients
#like terms
#polynomials
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (-6) in the first polynomial and (9) in the second, so the sum is (3). Add coefficients of like powers only.
Step 2
Why this answer is correct
The correct answer is C. (3). The coefficient of (x) is (-6) in the first polynomial and (9) in the second, so the sum is (3). Add coefficients of like powers only.
Step 3
Exam Tip
पहले बहुपद में (x) का गुणांक (-6) और दूसरे में (9) है, योग (3) है। समान घात के गुणांक ही जोड़ें।
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(p(x)=6x-2 -x+3) से (r(x)=2x-2 +5x-8) घटाने पर क्या मिलेगा?
What is obtained when (r(x)=2x-2 +5x-8) is subtracted from (p(x)=6x-2 -x+3)?
#subtraction
#like terms
#polynomials
A \(4x^2-6x+11\)
B \(8x^2+4x-5\)
C \(4x^2+6x+11\)
D \(8x^2-6x-11\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-6x+11\)
Step 1
Concept
(p(x)-r(x)=6x-2 -x+3-\(2x^2+5x-8\)=4x-2 -6x+11). Change all signs inside the bracket while subtracting.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-6x+11\). (p(x)-r(x)=6x-2 -x+3-\(2x^2+5x-8\)=4x-2 -6x+11). Change all signs inside the bracket while subtracting.
Step 3
Exam Tip
(p(x)-r(x)=6x-2 -x+3-\(2x^2+5x-8\)=4x-2 -6x+11)। घटाते समय कोष्ठक के सभी संकेत बदलें।
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(p(x)=4x-2 -9x+2) और (q(x)=3x-2 +x-7) का योग क्या है?
What is the sum of (p(x)=4x-2 -9x+2) and (q(x)=3x-2 +x-7)?
#addition
#like terms
#polynomials
A \(7x^2-8x-5\)
B \(x^2-10x+9\)
C \(7x^2+8x-5\)
D \(12x^4-9x-14\)
Explanation opens after your attempt
Correct Answer
A. \(7x^2-8x-5\)
Step 1
Concept
Adding like terms gives \(7x^2-8x-5\). Add only like terms.
Step 2
Why this answer is correct
The correct answer is A. \(7x^2-8x-5\). Adding like terms gives \(7x^2-8x-5\). Add only like terms.
Step 3
Exam Tip
समान घात वाले पद जोड़ने पर \(7x^2-8x-5\) मिलता है। केवल समान पदों को ही जोड़ें।
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यदि (p(x)=ax-2 +3x+5) की घात (1) है, तो (a) का मान क्या होगा?
If (p(x)=ax-2 +3x+5) has degree (1), what will be the value of (a)?
#polynomials
#degree
#parameter
A (0)
B (1)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
For degree (1), the coefficient of \(x^2\) must be (0). Therefore (a=0).
Step 2
Why this answer is correct
The correct answer is A. (0). For degree (1), the coefficient of \(x^2\) must be (0). Therefore (a=0).
Step 3
Exam Tip
घात (1) होने के लिए \(x^2\) का गुणांक (0) होना चाहिए। इसलिए (a=0) है।
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बहुपद (p(x)=2x-2 +3) में (p(0)) का मान क्या है?
For the polynomial (p(x)=2x-2 +3), what is the value of (p(0))?
#polynomials
#substitution
#constant-term
A (0)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
(p(0)=2(0)2 +3=3). When (x=0), the constant term remains.
Step 2
Why this answer is correct
The correct answer is C. (3). (p(0)=2(0)2 +3=3). When (x=0), the constant term remains.
Step 3
Exam Tip
(p(0)=2(0)2 +3=3) है। (x=0) रखने पर नियत पद बचता है।
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\(3x^2-2x+1\) और \(x^2+4x+7\) में (x) के गुणांकों का योग क्या है?
What is the sum of the coefficients of (x) in \(3x^2-2x+1\) and \(x^2+4x+7\)?
#coefficients
#like terms
#polynomials
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (-2) in the first polynomial and (4) in the second, so the sum is (2). Add coefficients of like powers only.
Step 2
Why this answer is correct
The correct answer is A. (2). The coefficient of (x) is (-2) in the first polynomial and (4) in the second, so the sum is (2). Add coefficients of like powers only.
Step 3
Exam Tip
पहले बहुपद में (x) का गुणांक (-2) और दूसरे में (4) है, योग (2) है। समान घात के गुणांक ही जोड़ें।
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(p(x)=5x-2 +3x-2) से (r(x)=2x-2 -x+4) घटाने पर क्या मिलेगा?
What is obtained when (r(x)=2x-2 -x+4) is subtracted from (p(x)=5x-2 +3x-2)?
#subtraction
#polynomials
#like terms
A \(3x^2+4x-6\)
B \(7x^2+2x+2\)
C \(3x^2+2x+2\)
D \(7x^2+4x-6\)
Explanation opens after your attempt
Correct Answer
A. \(3x^2+4x-6\)
Step 1
Concept
(p(x)-r(x)=5x-2 +3x-2-\(2x^2-x+4\)=3x-2 +4x-6). Change all signs while subtracting.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2+4x-6\). (p(x)-r(x)=5x-2 +3x-2-\(2x^2-x+4\)=3x-2 +4x-6). Change all signs while subtracting.
Step 3
Exam Tip
(p(x)-r(x)=5x-2 +3x-2-\(2x^2-x+4\)=3x-2 +4x-6)। घटाते समय सभी संकेत बदलें।
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(p(x)=3x-2 -4x+1) और (q(x)=x-2 +2x-5) का योग क्या है?
What is the sum of (p(x)=3x-2 -4x+1) and (q(x)=x-2 +2x-5)?
#addition
#like terms
#polynomials
A \(4x^2-2x-4\)
B \(2x^2-6x+6\)
C \(4x^2+6x-4\)
D \(3x^4-8x^2-5\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-2x-4\)
Step 1
Concept
Adding like terms gives \(4x^2-2x-4\). Combine only like terms.
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-2x-4\). Adding like terms gives \(4x^2-2x-4\). Combine only like terms.
Step 3
Exam Tip
समान घात वाले पद जोड़ने पर \(4x^2-2x-4\) मिलता है। केवल समान पदों को मिलाएं।
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बहुपद \(2x^2+3x-11\) में नियत पद कौन सा है?
Which is the constant term in \(2x^2+3x-11\)?
#constant-term
#polynomials
A (2)
B (3)
C (-11)
D (11x)
Explanation opens after your attempt
Step 1
Concept
The term without (x) is the constant term. Here the constant term is (-11).
Step 2
Why this answer is correct
The correct answer is C. (-11). The term without (x) is the constant term. Here the constant term is (-11).
Step 3
Exam Tip
जिस पद में (x) नहीं होता वह नियत पद होता है। यहाँ नियत पद (-11) है।
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बहुपद \(7x^3-4x+9\) की घात क्या है?
What is the degree of the polynomial \(7x^3-4x+9\)?
#degree
#polynomials
#class10
A (1)
B (2)
C (3)
D (9)
Explanation opens after your attempt
Step 1
Concept
The highest power is (3), so the degree is (3). Always check the highest power of the variable.
Step 2
Why this answer is correct
The correct answer is C. (3). The highest power is (3), so the degree is (3). Always check the highest power of the variable.
Step 3
Exam Tip
सबसे बड़ी घात (3) है इसलिए बहुपद की घात (3) है। हमेशा चर की सबसे बड़ी घात देखें।
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(p(x)=x-2 +3x+2) के लिए (p(1)) का मान क्या है?
For (p(x)=x-2 +3x+2), what is the value of (p(1))?
#polynomials
#one-variable
#value
#substitution
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(p(1)=12 +3\cdot1+2=6). While evaluating, replace every (x) with the given number.
Step 2
Why this answer is correct
The correct answer is C. (6). (p(1)=12 +3\cdot1+2=6). While evaluating, replace every (x) with the given number.
Step 3
Exam Tip
(p(1)=12 +3\cdot1+2=6) है। मान निकालते समय हर (x) की जगह दी गई संख्या रखें।
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यदि (p(x)=2x-3 -5x+9) है, तो इसमें \(x^2\) का गुणांक क्या है?
If (p(x)=2x-3 -5x+9), what is the coefficient of \(x^2\)?
#polynomials
#one-variable
#coefficient
#missing-term
A (2)
B (-5)
C (9)
D (0)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^2\)-term in this polynomial, so its coefficient is (0). The coefficient of a missing term is always taken as (0).
Step 2
Why this answer is correct
The correct answer is D. (0). There is no \(x^2\)-term in this polynomial, so its coefficient is (0). The coefficient of a missing term is always taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^2\) पद नहीं है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद का गुणांक हमेशा (0) माना जाता है।
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एक छात्र \(x^2+2x+1\) की घात (3) बताता है क्योंकि इसमें (3) पद हैं। सही घात क्या है?
A student says the degree of \(x^2+2x+1\) is (3) because it has (3) terms. What is the correct degree?
#polynomials
#common-mistake
#degree
#easy
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Degree is decided by the highest power (2), not by the number of terms. Avoid this common exam mistake.
Step 2
Why this answer is correct
The correct answer is B. (2). Degree is decided by the highest power (2), not by the number of terms. Avoid this common exam mistake.
Step 3
Exam Tip
घात पदों की संख्या से नहीं, सबसे बड़ी घात (2) से तय होती है। यह सामान्य गलती परीक्षा में न करें।
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यदि (p(x)=x-2 +4x+4) है, तो (p(-2)) कितना है?
If (p(x)=x-2 +4x+4), what is (p(-2))?
#polynomials
#value
#zero
#easy
A (0)
B (2)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=(-2)2 +4(-2)+4=4-8+4=0). Be careful with signs when substituting a negative value.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(-2)=(-2)2 +4(-2)+4=4-8+4=0). Be careful with signs when substituting a negative value.
Step 3
Exam Tip
(p(-2)=(-2)2 +4(-2)+4=4-8+4=0) है। ऋणात्मक मान रखते समय चिह्न सावधानी से लिखें।
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(p(x)=7x-2 ) में नियत पद क्या है?
What is the constant term in (p(x)=7x-2 )?
#polynomials
#constant-term
#easy
#missing-term
A (7)
B (2)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
There is no separate constant term, so the constant term is (0). Do not treat a term containing (x) as constant.
Step 2
Why this answer is correct
The correct answer is C. (0). There is no separate constant term, so the constant term is (0). Do not treat a term containing (x) as constant.
Step 3
Exam Tip
कोई अलग नियत पद नहीं है, इसलिए नियत पद (0) है। केवल (x) वाले पद को नियत पद न मानें।
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\(x^4+3x^2+2\) में कौन सा पद अनुपस्थित है?
Which term is missing in \(x^4+3x^2+2\)?
#polynomials
#missing-term
#easy
#standard-form
A \(x^4\)
B \(x^3\)
C \(3x^2\)
D (2)
Explanation opens after your attempt
Correct Answer
B. \(x^3\)
Step 1
Concept
The \(x^3\)-term is not present in this polynomial. Its coefficient may be taken as (0).
Step 2
Why this answer is correct
The correct answer is B. \(x^3\). The \(x^3\)-term is not present in this polynomial. Its coefficient may be taken as (0).
Step 3
Exam Tip
इस बहुपद में \(x^3\) पद नहीं है। अनुपस्थित पद का गुणांक (0) माना जा सकता है।
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(p(x)=x-2 -1) के लिए (p(-1)) क्या है?
For (p(x)=x-2 -1), what is (p(-1))?
#polynomials
#value
#zero
#easy
A (0)
B (-2)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=(-1)2 -1=1-1=0). Use brackets when substituting a negative value.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(-1)=(-1)2 -1=1-1=0). Use brackets when substituting a negative value.
Step 3
Exam Tip
(p(-1)=(-1)2 -1=1-1=0) है। कोष्ठक लगाकर ऋणात्मक मान रखें।
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बहुपद \(2x^2+3x+4\) में (x) का गुणांक और नियत पद क्रमशः क्या हैं?
In \(2x^2+3x+4\), what are the coefficient of (x) and the constant term respectively?
#polynomials
#coefficient
#constant-term
#easy
A (3,4)
B (2,3)
C (4,3)
D (2,4)
Explanation opens after your attempt
Step 1
Concept
The coefficient of (x) is (3), and the constant term is (4). Keep the asked order in mind.
Step 2
Why this answer is correct
The correct answer is A. (3,4). The coefficient of (x) is (3), and the constant term is (4). Keep the asked order in mind.
Step 3
Exam Tip
(x) का गुणांक (3) और नियत पद (4) है। क्रमशः पूछे गए क्रम का ध्यान रखें।
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यदि किसी बहुपद की घात (3) है, तो उसे क्या कहते हैं?
If a polynomial has degree (3), what is it called?
#polynomials
#cubic
#easy
#degree
A घन बहुपद / Cubic polynomial
B द्विघात बहुपद / Quadratic polynomial
C रैखिक बहुपद / Linear polynomial
D नियत बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
A. घन बहुपद / Cubic polynomial
Step 1
Concept
A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.
Step 2
Why this answer is correct
The correct answer is A. घन बहुपद / Cubic polynomial. A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.
Step 3
Exam Tip
घात (3) वाला बहुपद घन बहुपद कहलाता है। सबसे बड़ी घात ही नाम तय करती है।
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यदि किसी बहुपद की घात (2) है, तो उसे क्या कहते हैं?
If a polynomial has degree (2), what is it called?
#polynomials
#quadratic
#easy
#degree
A रैखिक बहुपद / Linear polynomial
B द्विघात बहुपद / Quadratic polynomial
C घन बहुपद / Cubic polynomial
D शून्य बहुपद / Zero polynomial
Explanation opens after your attempt
Correct Answer
B. द्विघात बहुपद / Quadratic polynomial
Step 1
Concept
A degree (2) polynomial is called quadratic. A non-zero \(x^2\)-term must be present.
Step 2
Why this answer is correct
The correct answer is B. द्विघात बहुपद / Quadratic polynomial. A degree (2) polynomial is called quadratic. A non-zero \(x^2\)-term must be present.
Step 3
Exam Tip
घात (2) वाला बहुपद द्विघात कहलाता है। \(x^2\) का अशून्य पद होना जरूरी है।
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यदि किसी बहुपद की घात (1) है, तो उसे क्या कहते हैं?
If a polynomial has degree (1), what is it called?
#polynomials
#degree
#type
#easy
A नियत बहुपद / Constant polynomial
B रैखिक बहुपद / Linear polynomial
C द्विघात बहुपद / Quadratic polynomial
D घन बहुपद / Cubic polynomial
Explanation opens after your attempt
Correct Answer
B. रैखिक बहुपद / Linear polynomial
Step 1
Concept
A polynomial of degree (1) is called a linear polynomial. Link the name with the degree.
Step 2
Why this answer is correct
The correct answer is B. रैखिक बहुपद / Linear polynomial. A polynomial of degree (1) is called a linear polynomial. Link the name with the degree.
Step 3
Exam Tip
घात (1) वाले बहुपद को रैखिक बहुपद कहते हैं। नाम हमेशा घात से जोड़कर याद करें।
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\(3x^2+2x+1\) में (x=0) रखने पर किस पद का मान बचता है?
When (x=0) is put in \(3x^2+2x+1\), which term remains?
#polynomials
#value
#constant-term
#easy
A \(3x^2\)
B (2x)
C (1)
D \(3x^2+2x\)
Explanation opens after your attempt
Step 1
Concept
At (x=0), \(3x^2\) and (2x) become zero. Only the constant term (1) remains.
Step 2
Why this answer is correct
The correct answer is C. (1). At (x=0), \(3x^2\) and (2x) become zero. Only the constant term (1) remains.
Step 3
Exam Tip
(x=0) पर \(3x^2\) और (2x) शून्य हो जाते हैं। केवल नियत पद (1) बचता है।
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किस विकल्प में (x) की घात बहुपद के लिए स्वीकार्य है?
In which option is the power of (x) acceptable for a polynomial?
#polynomials
#powers
#easy
#concept
A \(x^{-1}\)
B \(x^{\frac{1}{2}}\)
C \(x^0\)
D \(x^{-3}\)
Explanation opens after your attempt
Correct Answer
C. \(x^0\)
Step 1
Concept
In a polynomial, powers of (x) must be \(0,1,2,\ldots\). \(x^0\) is acceptable.
Step 2
Why this answer is correct
The correct answer is C. \(x^0\). In a polynomial, powers of (x) must be \(0,1,2,\ldots\). \(x^0\) is acceptable.
Step 3
Exam Tip
बहुपद में (x) की घात \(0,1,2,\ldots\) जैसी होनी चाहिए। \(x^0\) स्वीकार्य है।
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(p(x)=4x-8) में (x=2) रखने पर क्या निष्कर्ष निकलेगा?
What conclusion follows when (x=2) is substituted in (p(x)=4x-8)?
#polynomials
#zero
#reasoning
#easy
A (2) शून्यक है / (2) is a zero
B (2) घात है / (2) is the degree
C (2) गुणांक है / (2) is the coefficient
D (2) नियत पद है / (2) is the constant term
Explanation opens after your attempt
Correct Answer
A. (2) शून्यक है / (2) is a zero
Step 1
Concept
(p(2)=4\cdot2-8=0), so (2) is a zero. To test a zero, the value must be (0).
Step 2
Why this answer is correct
The correct answer is A. (2) शून्यक है / (2) is a zero. (p(2)=4\cdot2-8=0), so (2) is a zero. To test a zero, the value must be (0).
Step 3
Exam Tip
(p(2)=4\cdot2-8=0), इसलिए (2) शून्यक है। शून्यक जांचने के लिए मान (0) आना चाहिए।
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(p(x)=x-3 +2x-2 +x) में अग्र पद कौन सा है?
What is the leading term of (p(x)=x-3 +2x-2 +x)?
#polynomials
#leading-term
#easy
A \(x^3\)
B \(2x^2\)
C (x)
D (0)
Explanation opens after your attempt
Correct Answer
A. \(x^3\)
Step 1
Concept
The term with the highest power is \(x^3\). To identify the leading term, look for the highest power.
Step 2
Why this answer is correct
The correct answer is A. \(x^3\). The term with the highest power is \(x^3\). To identify the leading term, look for the highest power.
Step 3
Exam Tip
सबसे बड़ी घात वाला पद \(x^3\) है। अग्र पद पहचानने के लिए सबसे बड़ी घात देखें।
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(p(x)=ax-2 +bx+c) में यदि \(a\ne0\) है, तो यह किस प्रकार का बहुपद है?
In (p(x)=ax-2 +bx+c), if \(a\ne0\), what type of polynomial is it?
#polynomials
#quadratic-form
#easy
#degree
A रैखिक / Linear
B द्विघात / Quadratic
C घन / Cubic
D नियत / Constant
Explanation opens after your attempt
Correct Answer
B. द्विघात / Quadratic
Step 1
Concept
Since \(a\ne0\), the \(x^2\)-term remains, so the degree is (2). A degree (2) polynomial is quadratic.
Step 2
Why this answer is correct
The correct answer is B. द्विघात / Quadratic. Since \(a\ne0\), the \(x^2\)-term remains, so the degree is (2). A degree (2) polynomial is quadratic.
Step 3
Exam Tip
\(a\ne0\) होने से \(x^2\) पद रहता है, इसलिए घात (2) है। घात (2) वाला बहुपद द्विघात होता है।
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(p(x)=ax+b) में यदि \(a\ne0\) है, तो इसकी घात क्या होती है?
In (p(x)=ax+b), if \(a\ne0\), what is its degree?
#polynomials
#linear-form
#easy
#degree
A (0)
B (1)
C (2)
D परिभाषित नहीं / Not defined
Explanation opens after your attempt
Step 1
Concept
When \(a\ne0\), the (x)-term exists, so the degree is (1). This is the form of a linear polynomial.
Step 2
Why this answer is correct
The correct answer is B. (1). When \(a\ne0\), the (x)-term exists, so the degree is (1). This is the form of a linear polynomial.
Step 3
Exam Tip
\(a\ne0\) होने पर (x) वाला पद मौजूद है, इसलिए घात (1) है। यही रैखिक बहुपद का रूप है।
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कौन सा बहुपद नियत बहुपद है?
Which is a constant polynomial?
#polynomials
#constant-polynomial
#easy
A (6)
B (x+6)
C (6x)
D \(x^2+6\)
Explanation opens after your attempt
Step 1
Concept
A polynomial with no variable is a constant polynomial. (6) has no (x).
Step 2
Why this answer is correct
The correct answer is A. (6). A polynomial with no variable is a constant polynomial. (6) has no (x).
Step 3
Exam Tip
जिस बहुपद में चर नहीं होता वह नियत बहुपद है। (6) में (x) नहीं है।
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बहुपद \(x^2-5x+6\) में पदों की संख्या कितनी है?
How many terms are in the polynomial \(x^2-5x+6\)?
#polynomials
#terms
#easy
#trinomial
A (1)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
It has three terms: \(x^2\), (-5x), and (6). Count terms with their signs.
Step 2
Why this answer is correct
The correct answer is C. (3). It has three terms: \(x^2\), (-5x), and (6). Count terms with their signs.
Step 3
Exam Tip
इसमें \(x^2\), (-5x) और (6) तीन पद हैं। चिह्न सहित पद गिनें।
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(p(x)=2x-2 -8) के लिए (p(2)) का मान क्या है?
For (p(x)=2x-2 -8), what is the value of (p(2))?
#polynomials
#value
#easy
#substitution
A (0)
B (2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(2)=2\cdot22 -8=8-8=0). Square first, then multiply.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(2)=2\cdot22 -8=8-8=0). Square first, then multiply.
Step 3
Exam Tip
(p(2)=2\cdot22 -8=8-8=0) है। पहले वर्ग करें फिर गुणा करें।
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यदि (p(x)=x-2 +x) है, तो (p(-1)) क्या होगा?
If (p(x)=x-2 +x), what is (p(-1))?
#polynomials
#value
#negative-input
#easy
A (0)
B (-1)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=(-1)2 +(-1)=1-1=0). The square of a negative number is positive.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(-1)=(-1)2 +(-1)=1-1=0). The square of a negative number is positive.
Step 3
Exam Tip
(p(-1)=(-1)2 +(-1)=1-1=0) है। ऋणात्मक संख्या का वर्ग धनात्मक होता है।
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बहुपद \(x^3-1\) में (x=1) रखने पर मान क्या है?
What is the value of \(x^3-1\) when (x=1)?
#polynomials
#value
#zero
#easy
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(1^3-1=0\). So (1) is also a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). \(1^3-1=0\). So (1) is also a zero of this polynomial.
Step 3
Exam Tip
\(1^3-1=0\) है। इसलिए (1) इस बहुपद का शून्यक भी है।
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बहुपद \(11x^5-3x^2+8\) की घात क्या है?
What is the degree of \(11x^5-3x^2+8\)?
#polynomials
#degree
#easy
#highest-power
A (2)
B (3)
C (5)
D (8)
Explanation opens after your attempt
Step 1
Concept
The highest power is (5), so the degree is (5). Look at the greatest power, not the number of terms.
Step 2
Why this answer is correct
The correct answer is C. (5). The highest power is (5), so the degree is (5). Look at the greatest power, not the number of terms.
Step 3
Exam Tip
सबसे बड़ी घात (5) है इसलिए घात (5) होगी। पदों की संख्या नहीं बल्कि सबसे बड़ी घात देखें।
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कौन सा बहुपद एक चर (x) में है?
Which polynomial is in one variable (x)?
#polynomials
#one-variable
#easy
#concept
A \(x^2+2x+1\)
B (x+y+1)
C \(a^2+b^2\)
D (xy+3)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2x+1\)
Step 1
Concept
A polynomial in one variable (x) contains only the variable (x). The other options have more than one variable.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2x+1\). A polynomial in one variable (x) contains only the variable (x). The other options have more than one variable.
Step 3
Exam Tip
एक चर (x) में बहुपद में केवल (x) चर होता है। अन्य विकल्पों में एक से अधिक चर हैं।
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\(4x^3+x+2\) में \(x^2\) का गुणांक क्या है?
What is the coefficient of \(x^2\) in \(4x^3+x+2\)?
#polynomials
#missing-term
#easy
#coefficient
A (4)
B (1)
C (2)
D (0)
Explanation opens after your attempt
Step 1
Concept
There is no \(x^2\)-term, so its coefficient is (0). The coefficient of a missing term is taken as zero.
Step 2
Why this answer is correct
The correct answer is D. (0). There is no \(x^2\)-term, so its coefficient is (0). The coefficient of a missing term is taken as zero.
Step 3
Exam Tip
इस बहुपद में \(x^2\) पद नहीं है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद का गुणांक शून्य माना जाता है।
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बहुपद \(2x^2-7x+1\) में अग्र गुणांक क्या है?
What is the leading coefficient of \(2x^2-7x+1\)?
#polynomials
#leading-coefficient
#easy
A (2)
B (-7)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the highest-degree term \(2x^2\) is (2). This is called the leading coefficient.
Step 2
Why this answer is correct
The correct answer is A. (2). The coefficient of the highest-degree term \(2x^2\) is (2). This is called the leading coefficient.
Step 3
Exam Tip
सबसे बड़ी घात वाले पद \(2x^2\) का गुणांक (2) है। इसी को अग्र गुणांक कहते हैं।
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\(x^2+1\) में (x=1) रखने पर क्या मान मिलेगा?
What value is obtained by putting (x=1) in \(x^2+1\)?
#polynomials
#value
#easy
#substitution
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
\(1^2+1=2\). Even for small values, calculate in the correct order.
Step 2
Why this answer is correct
The correct answer is C. (2). \(1^2+1=2\). Even for small values, calculate in the correct order.
Step 3
Exam Tip
\(1^2+1=2\) होता है। छोटे मानों पर भी सही क्रम से गणना करें।
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बहुपद \(x^2-9\) का कौन सा मान शून्यक है?
Which value is a zero of the polynomial \(x^2-9\)?
#polynomials
#zero
#quadratic
#easy
A (2)
B (3)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(3^2-9=0\), so (3) is a zero. Substituting options is an easy method.
Step 2
Why this answer is correct
The correct answer is B. (3). \(3^2-9=0\), so (3) is a zero. Substituting options is an easy method.
Step 3
Exam Tip
\(3^2-9=0\), इसलिए (3) शून्यक है। विकल्पों को रखकर जांचना आसान तरीका है।
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(p(x)=5x+10) का शून्यक कौन सा है?
Which is the zero of (p(x)=5x+10)?
#polynomials
#zero
#linear
#easy
A (2)
B (-2)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
From (5x+10=0), we get (x=-2). Do not forget the sign change.
Step 2
Why this answer is correct
The correct answer is B. (-2). From (5x+10=0), we get (x=-2). Do not forget the sign change.
Step 3
Exam Tip
(5x+10=0) से (x=-2) मिलता है। चिह्न बदलना न भूलें।
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यदि (p(x)=3x-12) है, तो इसका शून्यक क्या है?
If (p(x)=3x-12), what is its zero?
#polynomials
#zero
#linear
#easy
A (3)
B (4)
C (-4)
D (12)
Explanation opens after your attempt
Step 1
Concept
From (3x-12=0), we get (x=4). For a linear polynomial, form a simple equation.
Step 2
Why this answer is correct
The correct answer is B. (4). From (3x-12=0), we get (x=4). For a linear polynomial, form a simple equation.
Step 3
Exam Tip
(3x-12=0) से (x=4) मिलता है। रैखिक बहुपद में सीधे समीकरण बनाएं।
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(p(x)=x-2 +2x+1) में (p(0)) का मान क्या है?
For (p(x)=x-2 +2x+1), what is (p(0))?
#polynomials
#value
#easy
#zero-input
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(0)=02 +2\cdot0+1=1). When (x=0), only the constant term remains.
Step 2
Why this answer is correct
The correct answer is B. (1). (p(0)=02 +2\cdot0+1=1). When (x=0), only the constant term remains.
Step 3
Exam Tip
(p(0)=02 +2\cdot0+1=1) है। (x=0) रखने पर केवल नियत पद बचता है।
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निम्न में से कौन सा त्रिपदी है?
Which of the following is a trinomial?
#polynomials
#trinomial
#easy
#classification
A (4x)
B \(x^2-2x+1\)
C \(x^3+1\)
D (9)
Explanation opens after your attempt
Correct Answer
B. \(x^2-2x+1\)
Step 1
Concept
A polynomial with three terms is a trinomial. \(x^2-2x+1\) has three terms.
Step 2
Why this answer is correct
The correct answer is B. \(x^2-2x+1\). A polynomial with three terms is a trinomial. \(x^2-2x+1\) has three terms.
Step 3
Exam Tip
तीन पदों वाला बहुपद त्रिपदी कहलाता है। \(x^2-2x+1\) में तीन पद हैं।
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