बहुपद (p(z)=-6z-5 +4z-4 -z+8) का अग्र गुणांक क्या है?
What is the leading coefficient of (p(z)=-6z-5 +4z-4 -z+8)?
#leading coefficient
#degree
#polynomial
A (-6)
B (4)
C (-1)
D (8)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the highest power term \(z^5\) is (-6). The leading coefficient is written with its sign.
Step 2
Why this answer is correct
The correct answer is A. (-6). The coefficient of the highest power term \(z^5\) is (-6). The leading coefficient is written with its sign.
Step 3
Exam Tip
सबसे बड़ी घात \(z^5\) के पद का गुणांक (-6) है। अग्र गुणांक संकेत सहित लिखा जाता है।
Login to save your score, XP, coins and progress. Login
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।
Login to save your score, XP, coins and progress. Login
बहुपद \(3x^4-5x^2+2x-8\) का प्रमुख गुणांक क्या है?
What is the leading coefficient of \(3x^4-5x^2+2x-8\)?
#leading-coefficient
#degree-four
#polynomial
A (3)
B (-5)
C (2)
D (-8)
Explanation opens after your attempt
Step 1
Concept
The leading term is \(3x^4\). Therefore the leading coefficient is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The leading term is \(3x^4\). Therefore the leading coefficient is (3).
Step 3
Exam Tip
प्रमुख पद \(3x^4\) है। इसलिए प्रमुख गुणांक (3) है।
Login to save your score, XP, coins and progress. Login
निम्न में से किस बहुपद का प्रमुख गुणांक (-2) है?
Which polynomial has leading coefficient (-2)?
#leading-coefficient
#cubic-polynomial
#easy
A \(5x^2-2x+1\)
B \(-2x^3+4x+7\)
C \(x^2-2\)
D (3x-2)
Explanation opens after your attempt
Correct Answer
B. \(-2x^3+4x+7\)
Step 1
Concept
The leading term of \(-2x^3+4x+7\) is \(-2x^3\). So the leading coefficient is (-2).
Step 2
Why this answer is correct
The correct answer is B. \(-2x^3+4x+7\). The leading term of \(-2x^3+4x+7\) is \(-2x^3\). So the leading coefficient is (-2).
Step 3
Exam Tip
\(-2x^3+4x+7\) का प्रमुख पद \(-2x^3\) है। इसलिए प्रमुख गुणांक (-2) है।
Login to save your score, XP, coins and progress. Login
बहुपद (p(y)=9y-4 -y-2 +5y-6) का अग्र गुणांक क्या है?
What is the leading coefficient of (p(y)=9y-4 -y-2 +5y-6)?
#leading coefficient
#degree
#polynomial
A (9)
B (-1)
C (5)
D (-6)
Explanation opens after your attempt
Step 1
Concept
The coefficient of the highest power term \(y^4\) is (9). That is the leading coefficient.
Step 2
Why this answer is correct
The correct answer is A. (9). The coefficient of the highest power term \(y^4\) is (9). That is the leading coefficient.
Step 3
Exam Tip
सबसे बड़ी घात \(y^4\) के पद का गुणांक (9) है। अग्र गुणांक वही होता है।
Login to save your score, XP, coins and progress. Login
\(3x^2-5x+7\) में प्रमुख गुणांक क्या है?
What is the leading coefficient of \(3x^2-5x+7\)?
#leading-coefficient
#polynomial
A (3)
B (-5)
C (7)
D (2)
Explanation opens after your attempt
Step 1
Concept
The leading term is \(3x^2\), so the leading coefficient is (3). The coefficient of the highest degree term is the leading coefficient.
Step 2
Why this answer is correct
The correct answer is A. (3). The leading term is \(3x^2\), so the leading coefficient is (3). The coefficient of the highest degree term is the leading coefficient.
Step 3
Exam Tip
प्रमुख पद \(3x^2\) है इसलिए प्रमुख गुणांक (3) है। सबसे बड़ी घात वाले पद का गुणांक प्रमुख गुणांक कहलाता है।
Login to save your score, XP, coins and progress. Login
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।
Login to save your score, XP, coins and progress. Login
बहुपद \(6x^5+x^2-4\) का अग्र गुणांक क्या है?
What is the leading coefficient of \(6x^5+x^2-4\)?
#leading_coefficient
#polynomials
#degree
A (6)
B (1)
C \(-4\)
D (5)
Explanation opens after your attempt
Step 1
Concept
The term with the highest power is \(6x^5\). So the leading coefficient is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). The term with the highest power is \(6x^5\). So the leading coefficient is (6).
Step 3
Exam Tip
सबसे बड़ी घात वाला पद \(6x^5\) है। इसलिए अग्र गुणांक (6) है।
Login to save your score, XP, coins and progress. Login
समीकरण \(kx^2-6x+k=0\) के वास्तविक और भिन्न मूलों के लिए सही शर्त क्या है?
What is the correct condition for real and distinct roots of \(kx^2-6x+k=0\)?
#quadratic equations
#real distinct roots
#leading coefficient
A \(k^2<9\) और \(k\neq0\) / \(k^2<9\) and \(k\neq0\)
B \(k^2>9\)
C \(k^2=9\)
D (k=0)
Explanation opens after your attempt
Correct Answer
A. \(k^2<9\) और \(k\neq0\) / \(k^2<9\) and \(k\neq0\)
Step 1
Concept
Here \(D=36-4k^2\). For real and distinct roots (D>0) and \(k\neq0\), hence \(k^2<9\).
Step 2
Why this answer is correct
The correct answer is A. \(k^2<9\) और \(k\neq0\) / \(k^2<9\) and \(k\neq0\). Here \(D=36-4k^2\). For real and distinct roots (D>0) and \(k\neq0\), hence \(k^2<9\).
Step 3
Exam Tip
यहाँ \(D=36-4k^2\) है। वास्तविक और भिन्न मूलों के लिए (D>0) और \(k\neq0\), अतः \(k^2<9\)।
Login to save your score, XP, coins and progress. Login
यदि किसी द्विघात समीकरण की जड़ें (3) और (-2) हैं और \(x^2\) का गुणांक (2) है, तो समीकरण कौन-सा है?
If the roots of a quadratic equation are (3) and (-2), and the coefficient of \(x^2\) is (2), which is the equation?
#quadratic-roots
#forming-equation
#leading-coefficient
A \(2x^2-2x-12=0\)
B \(2x^2+2x-12=0\)
C \(2x^2-2x+12=0\)
D \(x^2-x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-2x-12=0\)
Step 1
Concept
The monic equation is \(x^2-x-6=0\). Since the coefficient of \(x^2\) must be (2), multiply the whole equation by (2).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-2x-12=0\). The monic equation is \(x^2-x-6=0\). Since the coefficient of \(x^2\) must be (2), multiply the whole equation by (2).
Step 3
Exam Tip
मॉनिक समीकरण \(x^2-x-6=0\) है। \(x^2\) का गुणांक (2) चाहिए, इसलिए पूरे समीकरण को (2) से गुणा करें।
Login to save your score, XP, coins and progress. Login
यदि (x=4) समीकरण \(ax^2-10x+8=0\) का मूल है तो (a) का मान क्या है?
If (x=4) is a root of \(ax^2-10x+8=0\), what is the value of (a)?
#roots
#parameter
#leading_coefficient
A (2)
B (1)
C (-2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
Putting (x=4) gives (16a-40+8=0), so (16a=32) and (a=2). Substitute when a coefficient is unknown.
Step 2
Why this answer is correct
The correct answer is A. (2). Putting (x=4) gives (16a-40+8=0), so (16a=32) and (a=2). Substitute when a coefficient is unknown.
Step 3
Exam Tip
(x=4) रखने पर (16a-40+8=0) इसलिए (16a=32) और (a=2)। अज्ञात गुणांक में प्रतिस्थापन करें।
Login to save your score, XP, coins and progress. Login
यदि (x=3) समीकरण \(ax^2-8x+6=0\) का मूल है तो (a) का मान क्या है?
If (x=3) is a root of \(ax^2-8x+6=0\), what is the value of (a)?
#roots
#parameter
#leading_coefficient
A (2)
B (1)
C (-2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
Putting (x=3) gives (9a-24+6=0), so (9a=18) and (a=2). Substitute in questions with an unknown coefficient.
Step 2
Why this answer is correct
The correct answer is A. (2). Putting (x=3) gives (9a-24+6=0), so (9a=18) and (a=2). Substitute in questions with an unknown coefficient.
Step 3
Exam Tip
(x=3) रखने पर (9a-24+6=0) इसलिए (9a=18) और (a=2)। अज्ञात गुणांक वाले प्रश्न में प्रतिस्थापन करें।
Login to save your score, XP, coins and progress. Login
यदि (x=2) समीकरण \(ax^2-5x+2=0\) का मूल है तो (a) का मान क्या है?
If (x=2) is a root of \(ax^2-5x+2=0\), what is the value of (a)?
#roots
#parameter
#leading_coefficient
A (2)
B (1)
C (-2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
Putting (x=2) gives (4a-10+2=0), so (4a=8) and (a=2). Substitute in questions with an unknown coefficient.
Step 2
Why this answer is correct
The correct answer is A. (2). Putting (x=2) gives (4a-10+2=0), so (4a=8) and (a=2). Substitute in questions with an unknown coefficient.
Step 3
Exam Tip
(x=2) रखने पर (4a-10+2=0) इसलिए (4a=8) और (a=2)। अज्ञात गुणांक वाले प्रश्न में प्रतिस्थापन करें।
Login to save your score, XP, coins and progress. Login
समीकरण ((k-1)x-2 +3x+2=0) द्विघात रहे इसके लिए कौन सी शर्त सही है?
Which condition is correct for ((k-1)x-2 +3x+2=0) to remain quadratic?
#quadratic equations
#parameter
#leading coefficient
A (k=1)
B \(k\neq1\)
C (k=0)
D (k=-1)
Explanation opens after your attempt
Correct Answer
B. \(k\neq1\)
Step 1
Concept
The coefficient of the quadratic term is ((k-1)), which must not be (0). Hence \(k\neq1\) is necessary.
Step 2
Why this answer is correct
The correct answer is B. \(k\neq1\). The coefficient of the quadratic term is ((k-1)), which must not be (0). Hence \(k\neq1\) is necessary.
Step 3
Exam Tip
द्विघात पद का गुणांक ((k-1)) है जो (0) नहीं होना चाहिए। इसलिए \(k\neq1\) होना जरूरी है।
Login to save your score, XP, coins and progress. Login
किस शर्त पर \(px^2+qx+r=0\) द्विघात समीकरण होगा?
Under which condition will \(px^2+qx+r=0\) be a quadratic equation?
#quadratic equations
#condition
#leading coefficient
A (p=0)
B \(p\neq0\)
C (q=0)
D (r=0)
Explanation opens after your attempt
Correct Answer
B. \(p\neq0\)
Step 1
Concept
The quadratic term \(px^2\) must remain, so \(p\neq0\). If (p=0), degree (2) will not remain.
Step 2
Why this answer is correct
The correct answer is B. \(p\neq0\). The quadratic term \(px^2\) must remain, so \(p\neq0\). If (p=0), degree (2) will not remain.
Step 3
Exam Tip
द्विघात पद \(px^2\) बना रहे इसलिए \(p\neq0\) होना चाहिए। यदि (p=0) हो तो घात (2) नहीं रहेगी।
Login to save your score, XP, coins and progress. Login
