100 results found for "degree-condition" in Class 10.
यदि अशून्य बहुपद (p(x)) की घात (6) और (q(x)) की घात (3) है, तो (p(x)q(x)) की घात क्या होगी?
If non-zero polynomial (p(x)) has degree (6) and (q(x)) has degree (3), what will be the degree of (p(x)q(x))?
#degree
#product
#polynomial
A (3)
B (6)
C (9)
D (18)
Explanation opens after your attempt
Step 1
Concept
In the product of two non-zero polynomials, degrees add, so (6+3=9). In multiplication, look at the highest-power terms.
Step 2
Why this answer is correct
The correct answer is C. (9). In the product of two non-zero polynomials, degrees add, so (6+3=9). In multiplication, look at the highest-power terms.
Step 3
Exam Tip
दो अशून्य बहुपदों के गुणन में घातें जुड़ती हैं, इसलिए (6+3=9)। गुणन में उच्चतम घातों का गुणन देखें।
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यदि (p(x)) की घात (5) और (q(x)) की घात (2) है, तो अशून्य (p(x)q(x)) की घात क्या होगी?
If the degree of (p(x)) is (5) and the degree of (q(x)) is (2), what is the degree of non-zero (p(x)q(x))?
#degree
#product
#polynomial
A (3)
B (5)
C (7)
D (10)
Explanation opens after your attempt
Step 1
Concept
In the product of two non-zero polynomials, degrees add, so (5+2=7). Remember degree addition in multiplication.
Step 2
Why this answer is correct
The correct answer is C. (7). In the product of two non-zero polynomials, degrees add, so (5+2=7). Remember degree addition in multiplication.
Step 3
Exam Tip
दो अशून्य बहुपदों के गुणन में घातें जुड़ती हैं, इसलिए (5+2=7)। गुणन में घातों का योग याद रखें।
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यदि (p(x)) की घात (4) और (q(x)) की घात (3) है, तो सामान्यतः (p(x)q(x)) की घात क्या होगी?
If the degree of (p(x)) is (4) and the degree of (q(x)) is (3), what will generally be the degree of (p(x)q(x))?
#degree
#product
#polynomial
A (1)
B (7)
C (12)
D (4)
Explanation opens after your attempt
Step 1
Concept
In the product of two non-zero polynomials, degrees add, so (4+3=7). Remember degree addition in multiplication.
Step 2
Why this answer is correct
The correct answer is B. (7). In the product of two non-zero polynomials, degrees add, so (4+3=7). Remember degree addition in multiplication.
Step 3
Exam Tip
दो अशून्य बहुपदों के गुणन में घातें जुड़ती हैं, इसलिए (4+3=7)। गुणन में घातों का योग याद रखें।
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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)=(k-3)x-5 +2x-3 -x+9) की घात (3) है, तो (k) क्या है?
If (p(x)=(k-3)x-5 +2x-3 -x+9) has degree (3), what is (k)?
#degree
#parameter
#polynomial
A (3)
B (0)
C (2)
D (5)
Explanation opens after your attempt
Step 1
Concept
For degree (3), the coefficient of \(x^5\) must be (0). Thus (k-3=0) and (k=3).
Step 2
Why this answer is correct
The correct answer is A. (3). For degree (3), the coefficient of \(x^5\) must be (0). Thus (k-3=0) and (k=3).
Step 3
Exam Tip
घात (3) होने के लिए \(x^5\) का गुणांक (0) होना चाहिए। इसलिए (k-3=0) और (k=3)।
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यदि (p(x)=mx-5 +(m-4 )x-4 +3x-2 +1) की घात (4) है, तो (m) क्या है?
If the degree of (p(x)=mx-5 +(m-4 )x-4 +3x-2 +1) is (4), what is (m)?
#degree
#parameter
#conditions
A (0)
B (2)
C (4)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For degree (4), the coefficient of \(x^5\) must be (0) and the coefficient of \(x^4\) must be non-zero. For (m=0), (m-4 =-4).
Step 2
Why this answer is correct
The correct answer is A. (0). For degree (4), the coefficient of \(x^5\) must be (0) and the coefficient of \(x^4\) must be non-zero. For (m=0), (m-4 =-4).
Step 3
Exam Tip
घात (4) के लिए \(x^5\) का गुणांक (0) और \(x^4\) का गुणांक अशून्य चाहिए। (m=0) पर (m-4 =-4) है।
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यदि (p(x)=ax-5 +bx-4 +cx-3 +d) में (a=0), \(b\ne0\) और \(c\ne0\), तो (p(x)) की घात क्या होगी?
If (a=0), \(b\ne0\), and \(c\ne0\) in (p(x)=ax-5 +bx-4 +cx-3 +d), what will be the degree of (p(x))?
#degree
#general polynomial
#conditions
A (3)
B (4)
C (5)
D निर्भर नहीं / Not dependent
Explanation opens after your attempt
Step 1
Concept
Since (a=0), the \(x^5\)-term vanishes, and since \(b\ne0\), the \(x^4\)-term remains. So the degree is (4).
Step 2
Why this answer is correct
The correct answer is B. (4). Since (a=0), the \(x^5\)-term vanishes, and since \(b\ne0\), the \(x^4\)-term remains. So the degree is (4).
Step 3
Exam Tip
(a=0) से \(x^5\) पद हट जाता है और \(b\ne0\) से \(x^4\) पद बचता है। इसलिए घात (4) है।
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(p(x)=6x-5 -4x-2 +1) और (q(x)=-6x-5 +3x-4 +x-9) के योग की घात क्या है?
What is the degree of the sum of (p(x)=6x-5 -4x-2 +1) and (q(x)=-6x-5 +3x-4 +x-9)?
#degree
#cancellation
#addition
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The \(x^5\)-terms cancel and the highest remaining power is (4). Recheck the degree of the polynomial after addition.
Step 2
Why this answer is correct
The correct answer is C. (4). The \(x^5\)-terms cancel and the highest remaining power is (4). Recheck the degree of the polynomial after addition.
Step 3
Exam Tip
\(x^5\) के पद कट जाते हैं और सबसे बड़ी बची घात (4) है। जोड़ के बाद बहुपद की घात फिर से जांचें।
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यदि (p(x)=(a-1)x-6 +(a+2)x-4 -5x+7) की घात (4) है, तो (a) क्या होगा?
If the degree of (p(x)=(a-1)x-6 +(a+2)x-4 -5x+7) is (4), what will (a) be?
#degree
#parameter
#polynomial
A (-2)
B (1)
C (2)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For degree (4), the coefficient of \(x^6\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (a=1).
Step 2
Why this answer is correct
The correct answer is B. (1). For degree (4), the coefficient of \(x^6\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (a=1).
Step 3
Exam Tip
घात (4) के लिए \(x^6\) का गुणांक (0) और \(x^4\) का गुणांक अशून्य चाहिए। (a=1) पर दोनों शर्तें पूरी होती हैं।
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किस मान के लिए (p(x)=(m-2 )x-4 +3x-2 +x+1) की घात (2) से अधिक नहीं होगी?
For which value will (p(x)=(m-2 )x-4 +3x-2 +x+1) have degree not more than (2)?
#degree
#parameter
#polynomial
A (m=2)
B (m=0)
C (m=1)
D (m=-2)
Explanation opens after your attempt
Step 1
Concept
To make the degree not more than (2), the coefficient of \(x^4\) must be (0), so (m-2 =0). Degree reduces only when the highest term vanishes.
Step 2
Why this answer is correct
The correct answer is A. (m=2). To make the degree not more than (2), the coefficient of \(x^4\) must be (0), so (m-2 =0). Degree reduces only when the highest term vanishes.
Step 3
Exam Tip
घात (2) से अधिक न हो इसके लिए \(x^4\) का गुणांक (0) चाहिए, अतः (m-2 =0)। उच्चतम पद हटाकर ही घात घटती है।
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यदि (p(x)=x-4 -5x-2 +4) है, तो (p(x)) का घात कितना है?
If (p(x)=x-4 -5x-2 +4), what is the degree of (p(x))?
#degree
#polynomial
#one-variable
A (4)
B (2)
C (5)
D (0)
Explanation opens after your attempt
Step 1
Concept
The highest power is \(x^4\), so the degree is (4). Terms with zero coefficients do not affect the degree.
Step 2
Why this answer is correct
The correct answer is A. (4). The highest power is \(x^4\), so the degree is (4). Terms with zero coefficients do not affect the degree.
Step 3
Exam Tip
सबसे बड़ी घात \(x^4\) है, इसलिए घात (4) है। शून्य गुणांक वाले पदों को घात तय करने में नहीं गिनते।
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यदि (p(x)=mx-4 +(m+2)x-3 +5x+1) की घात (3) है, तो (m) क्या है?
If the degree of (p(x)=mx-4 +(m+2)x-3 +5x+1) is (3), what is (m)?
#degree
#parameter
#conditions
A (-2)
B (0)
C (2)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For degree (3), the coefficient of \(x^4\) must be (0) and the coefficient of \(x^3\) must be non-zero. For (m=0), (m+2=2).
Step 2
Why this answer is correct
The correct answer is B. (0). For degree (3), the coefficient of \(x^4\) must be (0) and the coefficient of \(x^3\) must be non-zero. For (m=0), (m+2=2).
Step 3
Exam Tip
घात (3) के लिए \(x^4\) का गुणांक (0) चाहिए और \(x^3\) का गुणांक अशून्य चाहिए। (m=0) पर (m+2=2) है।
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यदि (p(x)=ax-4 +bx-3 +cx-2 +d) में (a=0), (b=0) और \(c\ne0\), तो (p(x)) की घात क्या होगी?
If (a=0), (b=0), and \(c\ne0\) in (p(x)=ax-4 +bx-3 +cx-2 +d), what will be the degree of (p(x))?
#degree
#general polynomial
#conditions
A (0)
B (1)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
The \(x^4\)- and \(x^3\)-terms vanish, but \(c\ne0\) keeps the \(x^2\)-term. So the degree is (2).
Step 2
Why this answer is correct
The correct answer is C. (2). The \(x^4\)- and \(x^3\)-terms vanish, but \(c\ne0\) keeps the \(x^2\)-term. So the degree is (2).
Step 3
Exam Tip
\(x^4\) और \(x^3\) के पद हट जाते हैं, लेकिन \(c\ne0\) से \(x^2\) पद बचता है। इसलिए घात (2) है।
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(p(x)=5x-4 -2x-2 +1) और (q(x)=-5x-4 +3x-3 +x-6) के योग की घात क्या है?
What is the degree of the sum of (p(x)=5x-4 -2x-2 +1) and (q(x)=-5x-4 +3x-3 +x-6)?
#degree
#cancellation
#addition
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The \(x^4\)-terms cancel and the highest remaining power is (3). Recheck the degree after addition.
Step 2
Why this answer is correct
The correct answer is C. (3). The \(x^4\)-terms cancel and the highest remaining power is (3). Recheck the degree after addition.
Step 3
Exam Tip
\(x^4\) के पद कट जाते हैं और सबसे बड़ी बची घात (3) है। जोड़ के बाद घात दोबारा जांचना जरूरी है।
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यदि (p(x)=(m+2)x-5 +(m-3 )x-4 +6x-1) की घात (4) है, तो (m) क्या होगा?
If the degree of (p(x)=(m+2)x-5 +(m-3 )x-4 +6x-1) is (4), what is (m)?
#degree
#parameter
#polynomial
A (-2)
B (2)
C (3)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For degree (4), the coefficient of \(x^5\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (m=-2).
Step 2
Why this answer is correct
The correct answer is A. (-2). For degree (4), the coefficient of \(x^5\) must be (0) and the coefficient of \(x^4\) must be non-zero. Both conditions hold for (m=-2).
Step 3
Exam Tip
घात (4) के लिए \(x^5\) का गुणांक (0) और \(x^4\) का गुणांक अशून्य चाहिए। (m=-2) पर दोनों शर्तें पूरी होती हैं।
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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 (p(x)=mx-3 +(m-1 )x-2 +2x+1) की घात (2) है, तो (m) क्या है?
If the degree of (p(x)=mx-3 +(m-1 )x-2 +2x+1) is (2), what is (m)?
#degree
#parameter
#conditions
A (0)
B (1)
C (2)
D कोई मान नहीं / No value
Explanation opens after your attempt
Step 1
Concept
For degree (2), the coefficient of \(x^3\) must be (0) and the coefficient of \(x^2\) must be non-zero. Both conditions hold when (m=0).
Step 2
Why this answer is correct
The correct answer is A. (0). For degree (2), the coefficient of \(x^3\) must be (0) and the coefficient of \(x^2\) must be non-zero. Both conditions hold when (m=0).
Step 3
Exam Tip
घात (2) के लिए \(x^3\) का गुणांक (0) चाहिए और \(x^2\) का गुणांक अशून्य चाहिए। (m=0) पर ये दोनों शर्तें पूरी होती हैं।
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यदि (p(x)=ax-3 +bx-2 +cx+d) में (a=0) और \(b\ne0\), तो (p(x)) की घात क्या होगी?
If (a=0) and \(b\ne0\) in (p(x)=ax-3 +bx-2 +cx+d), what will be the degree of (p(x))?
#degree
#general polynomial
#conditions
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
Since (a=0), the \(x^3\)-term vanishes, and since \(b\ne0\), the \(x^2\)-term remains. So the degree is (2).
Step 2
Why this answer is correct
The correct answer is C. (2). Since (a=0), the \(x^3\)-term vanishes, and since \(b\ne0\), the \(x^2\)-term remains. So the degree is (2).
Step 3
Exam Tip
(a=0) होने से \(x^3\) पद हट जाता है और \(b\ne0\) होने से \(x^2\) पद बचता है। इसलिए घात (2) है।
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(p(x)=4x-4 -3x-2 +2) और (q(x)=-4x-4 +5x-3 +x-8) के योग की घात क्या है?
What is the degree of the sum of (p(x)=4x-4 -3x-2 +2) and (q(x)=-4x-4 +5x-3 +x-8)?
#degree
#cancellation
#addition
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The \(x^4\)-terms cancel and the highest remaining power is (3). Recheck the degree after addition.
Step 2
Why this answer is correct
The correct answer is C. (3). The \(x^4\)-terms cancel and the highest remaining power is (3). Recheck the degree after addition.
Step 3
Exam Tip
\(x^4\) के पद कट जाते हैं और सबसे बड़ी बची घात (3) है। जोड़ के बाद घात फिर से जांचें।
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यदि (p(x)=(a-5)x-5 +2x-3 -7x+4) की घात (3) है, तो (a) क्या होगा?
If the degree of (p(x)=(a-5)x-5 +2x-3 -7x+4) is (3), what is (a)?
#degree
#parameter
#polynomial
A (0)
B (3)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
For the degree to be (3), the coefficient of \(x^5\) must be (0), so (a-5=0). First make the highest-degree term vanish.
Step 2
Why this answer is correct
The correct answer is C. (5). For the degree to be (3), the coefficient of \(x^5\) must be (0), so (a-5=0). First make the highest-degree term vanish.
Step 3
Exam Tip
घात (3) होने के लिए \(x^5\) का गुणांक (0) होना चाहिए, इसलिए (a-5=0)। उच्चतम घात वाले पद को पहले शून्य करें।
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यदि (p(x)=(k-4)x-4 +3x-2 -5x+2) की घात (2) है, तो (k) का मान क्या होगा?
If the degree of (p(x)=(k-4)x-4 +3x-2 -5x+2) is (2), what will be the value of (k)?
#degree
#parameter
#polynomial
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
For the degree to be (2), the coefficient of \(x^4\) must be (0), so (k-4=0) and (k=4). Check the coefficient of the highest power first.
Step 2
Why this answer is correct
The correct answer is C. (4). For the degree to be (2), the coefficient of \(x^4\) must be (0), so (k-4=0) and (k=4). Check the coefficient of the highest power first.
Step 3
Exam Tip
घात (2) होने के लिए \(x^4\) का गुणांक (0) होना चाहिए, इसलिए (k-4=0) और (k=4)। सबसे बड़ी घात वाले पद का गुणांक पहले जांचें।
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किसी रैखिक बहुपद (mx+n) में \(m\ne0\) हो तो उसकी घात क्या है?
If \(m\ne0\) in a linear polynomial (mx+n), what is its degree?
#linear polynomial
#degree
#general form
A (0)
B (1)
C (2)
D परिभाषित नहीं / Undefined
Explanation opens after your attempt
Step 1
Concept
When \(m\ne0\), the term (mx) exists and the highest power is (1). So the degree is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). When \(m\ne0\), the term (mx) exists and the highest power is (1). So the degree is (1).
Step 3
Exam Tip
\(m\ne0\) होने पर (mx) पद मौजूद रहता है और सबसे बड़ी घात (1) होती है। इसलिए घात (1) है।
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(p(x)=0x-5 +7x-3 -2x+1) की घात क्या है?
What is the degree of (p(x)=0x-5 +7x-3 -2x+1)?
#degree
#zero coefficient
#polynomial
A (1)
B (3)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
The coefficient of \(0x^5\) is (0), so that term is not counted. The highest effective power is (3).
Step 2
Why this answer is correct
The correct answer is B. (3). The coefficient of \(0x^5\) is (0), so that term is not counted. The highest effective power is (3).
Step 3
Exam Tip
\(0x^5\) का गुणांक (0) है इसलिए वह पद नहीं गिना जाएगा। सबसे बड़ी प्रभावी घात (3) है।
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अशून्य अचर बहुपद (p(x)=-18) की घात क्या है?
What is the degree of the non-zero constant polynomial (p(x)=-18)?
#constant polynomial
#degree
#definition
A (0)
B (1)
C (18)
D परिभाषित नहीं / Undefined
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). A constant number is linked with degree (0).
Step 2
Why this answer is correct
The correct answer is A. (0). A non-zero constant polynomial has degree (0). A constant number is linked with degree (0).
Step 3
Exam Tip
अशून्य अचर बहुपद की घात (0) होती है। अचर संख्या का अर्थ घात (0) से जुड़ा है।
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बहुपद (p(x)=11x-6 -4x-3 +x-9) की घात क्या है?
What is the degree of the polynomial (p(x)=11x-6 -4x-3 +x-9)?
#degree
#highest power
#polynomial
A (1)
B (3)
C (6)
D (11)
Explanation opens after your attempt
Step 1
Concept
The highest power is (6), so the degree is (6). Look at the highest power of the variable, not the coefficient.
Step 2
Why this answer is correct
The correct answer is C. (6). The highest power is (6), so the degree is (6). Look at the highest power of the variable, not the coefficient.
Step 3
Exam Tip
सबसे बड़ी घात (6) है इसलिए घात (6) होगी। गुणांक नहीं बल्कि चर की सबसे ऊंची घात देखें।
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कौन सा विकल्प \(2x^3-5x^2+x-4\) की घात और नियत पद को सही बताता है?
Which option correctly gives the degree and constant term of \(2x^3-5x^2+x-4\)?
#degree
#constant-term
#cubic-polynomial
A घात (3), नियत पद (-4) / Degree (3), constant term (-4)
B घात (2), नियत पद (1) / Degree (2), constant term (1)
C घात (1), नियत पद (-5) / Degree (1), constant term (-5)
D घात (4), नियत पद (2) / Degree (4), constant term (2)
Explanation opens after your attempt
Correct Answer
A. घात (3), नियत पद (-4) / Degree (3), constant term (-4)
Step 1
Concept
The highest power is (3) and the term without (x) is (-4). So the correct pair is degree (3), constant term (-4).
Step 2
Why this answer is correct
The correct answer is A. घात (3), नियत पद (-4) / Degree (3), constant term (-4). The highest power is (3) and the term without (x) is (-4). So the correct pair is degree (3), constant term (-4).
Step 3
Exam Tip
सबसे बड़ी घात (3) है और बिना (x) वाला पद (-4) है। इसलिए सही जोड़ी घात (3), नियत पद (-4) है।
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\(x^2+1\), \(x^3+x\), (5x-2) में सबसे कम घात वाला बहुपद कौन सा है?
Among \(x^2+1\), \(x^3+x\), and (5x-2), which polynomial has the least degree?
#compare-degree
#linear-polynomial
#classification
A \(x^2+1\)
B \(x^3+x\)
C (5x-2)
D तीनों की घात समान है / All three have the same degree
Explanation opens after your attempt
Step 1
Concept
Their degrees are (2), (3), and (1) respectively. The least degree is (1).
Step 2
Why this answer is correct
The correct answer is C. (5x-2). Their degrees are (2), (3), and (1) respectively. The least degree is (1).
Step 3
Exam Tip
इनकी घातें क्रमशः (2), (3) और (1) हैं। सबसे कम घात (1) है।
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यदि किसी गैर-शून्य नियत बहुपद की घात पूछी जाए, तो सही उत्तर क्या होगा?
If the degree of a non-zero constant polynomial is asked, what will be the correct answer?
#constant-polynomial
#degree
#concept
A (0)
B (1)
C परिभाषित नहीं / Not defined
D बहुपद नहीं / Not a polynomial
Explanation opens after your attempt
Step 1
Concept
The degree of a non-zero constant polynomial is (0). Keep it separate from the zero polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). The degree of a non-zero constant polynomial is (0). Keep it separate from the zero polynomial.
Step 3
Exam Tip
गैर-शून्य नियत बहुपद की घात (0) होती है। इसे शून्य बहुपद से अलग रखें।
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किस मान के लिए (p(x)=(a-2)x-3 +4x-2 +1) की घात (2) हो जाएगी?
For which value will (p(x)=(a-2)x-3 +4x-2 +1) have degree (2)?
#degree
#parameter
#highest-power
A (a=0)
B (a=1)
C (a=2)
D (a=4)
Explanation opens after your attempt
Step 1
Concept
For degree (2), the coefficient of \(x^3\) must be (0). From (a-2=0), we get (a=2).
Step 2
Why this answer is correct
The correct answer is C. (a=2). For degree (2), the coefficient of \(x^3\) must be (0). From (a-2=0), we get (a=2).
Step 3
Exam Tip
घात (2) के लिए \(x^3\) का गुणांक (0) होना चाहिए। (a-2=0) से (a=2) मिलता है।
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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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यदि (p(x)=(m-2 )x-3 +4x-2 -7) की घात (2) है, तो (m) का मान क्या होगा?
If the degree of (p(x)=(m-2 )x-3 +4x-2 -7) is (2), what will be the value of (m)?
#degree
#parameter
#polynomial
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
For the degree to be (2), the coefficient of \(x^3\) must be (0), so (m-2 =0) and (m=2). In exams, check the coefficient of the highest power first.
Step 2
Why this answer is correct
The correct answer is B. (2). For the degree to be (2), the coefficient of \(x^3\) must be (0), so (m-2 =0) and (m=2). In exams, check the coefficient of the highest power first.
Step 3
Exam Tip
घात (2) होने के लिए \(x^3\) का गुणांक (0) होना चाहिए, इसलिए (m-2 =0) और (m=2)। परीक्षा में सबसे ऊंची घात के गुणांक को पहले देखें।
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निम्न में से कौन सा (x) में बहुपद है जिसकी घात (4) है?
Which of the following is a polynomial in (x) with degree (4)?
#degree
#highest-power
#polynomial
A \(x^4-2x+7\)
B \(x^3+4\)
C \(5x^2-1\)
D (9x+6)
Explanation opens after your attempt
Correct Answer
A. \(x^4-2x+7\)
Step 1
Concept
In \(x^4-2x+7\), the highest power is (4). To identify degree, check the greatest power.
Step 2
Why this answer is correct
The correct answer is A. \(x^4-2x+7\). In \(x^4-2x+7\), the highest power is (4). To identify degree, check the greatest power.
Step 3
Exam Tip
\(x^4-2x+7\) में सबसे बड़ी घात (4) है। घात पहचानने के लिए सबसे बड़ी शक्ति देखें।
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किसी रैखिक बहुपद (ax+b) में \(a\ne0\) हो तो उसकी घात क्या है?
If \(a\ne0\) in a linear polynomial (ax+b), what is its degree?
#linear polynomial
#degree
#general form
A (0)
B (1)
C (2)
D परिभाषित नहीं / Undefined
Explanation opens after your attempt
Step 1
Concept
When \(a\ne0\) in (ax+b), the highest power of (x) is (1). So the degree is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). When \(a\ne0\) in (ax+b), the highest power of (x) is (1). So the degree is (1).
Step 3
Exam Tip
(ax+b) में \(a\ne0\) होने पर (x) की सबसे बड़ी घात (1) है। इसलिए घात (1) होगी।
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\(3x^4+0x^3-2x+5\) की घात क्या है?
What is the degree of \(3x^4+0x^3-2x+5\)?
#degree
#zero coefficient
#polynomial
A (1)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The term \(0x^3\) is ineffective, and the highest non-zero power is (4). Ignore terms with zero coefficient.
Step 2
Why this answer is correct
The correct answer is C. (4). The term \(0x^3\) is ineffective, and the highest non-zero power is (4). Ignore terms with zero coefficient.
Step 3
Exam Tip
\(0x^3\) पद प्रभावी नहीं है और सबसे बड़ी अशून्य घात (4) है। शून्य गुणांक वाले पद को नजरअंदाज करें।
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अशून्य अचर बहुपद (p(x)=12) की घात क्या होती है?
What is the degree of the non-zero constant polynomial (p(x)=12)?
#constant polynomial
#degree
#definition
A (0)
B (1)
C (12)
D परिभाषित नहीं / Undefined
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). Keep it separate from the zero polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). A non-zero constant polynomial has degree (0). Keep it separate from the zero polynomial.
Step 3
Exam Tip
अशून्य अचर बहुपद की घात (0) होती है। शून्य बहुपद से इसे अलग रखें।
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बहुपद (p(x)=4x-5 -3x-2 +9) की घात क्या है?
What is the degree of the polynomial (p(x)=4x-5 -3x-2 +9)?
#degree
#polynomial
#powers
A (2)
B (3)
C (5)
D (9)
Explanation opens after your attempt
Step 1
Concept
The highest power is (5), so the degree is (5). Always check the highest exponent.
Step 2
Why this answer is correct
The correct answer is C. (5). The highest power is (5), so the degree is (5). Always check the highest exponent.
Step 3
Exam Tip
सबसे बड़ी घात (5) है इसलिए बहुपद की घात (5) है। हमेशा सबसे ऊंची घात देखें।
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\(x^5+1\) की घात क्या है?
What is the degree of \(x^5+1\)?
#degree
#highest-power
A (1)
B (2)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
The highest power is (5), so the degree is (5). The constant term does not increase the degree.
Step 2
Why this answer is correct
The correct answer is C. (5). The highest power is (5), so the degree is (5). The constant term does not increase the degree.
Step 3
Exam Tip
सबसे बड़ी घात (5) है इसलिए बहुपद की घात (5) है। नियत पद घात को नहीं बढ़ाता।
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निम्न में से किस बहुपद की घात (2) है?
Which polynomial has degree (2)?
#degree-two
#quadratic
A \(x^2+4x\)
B \(x^4+1\)
C (6x+5)
D (3)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x\)
Step 1
Concept
The highest power in \(x^2+4x\) is (2). Therefore its degree is (2).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x\). The highest power in \(x^2+4x\) is (2). Therefore its degree is (2).
Step 3
Exam Tip
\(x^2+4x\) में सबसे बड़ी घात (2) है। इसलिए इसकी घात (2) है।
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निम्न में से किस बहुपद की घात (1) है?
Which polynomial has degree (1)?
#degree-one
#linear
A \(4x^2+1\)
B (9x-3)
C \(x^3+2\)
D (11)
Explanation opens after your attempt
Step 1
Concept
In (9x-3), the highest power of (x) is (1). So it is a polynomial of degree (1).
Step 2
Why this answer is correct
The correct answer is B. (9x-3). In (9x-3), the highest power of (x) is (1). So it is a polynomial of degree (1).
Step 3
Exam Tip
(9x-3) में (x) की सबसे बड़ी घात (1) है। इसलिए यह घात (1) का बहुपद है।
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शून्य बहुपद (0) की घात के बारे में सही कथन कौन सा है?
Which statement about the degree of the zero polynomial (0) is correct?
#zero-polynomial
#degree
A घात (0) है / Degree is (0)
B घात (1) है / Degree is (1)
C घात परिभाषित नहीं है / Degree is not defined
D घात (2) है / Degree is (2)
Explanation opens after your attempt
Correct Answer
C. घात परिभाषित नहीं है / Degree is not defined
Step 1
Concept
The degree of the zero polynomial is not defined. Remember it separately from a non-zero constant polynomial.
Step 2
Why this answer is correct
The correct answer is C. घात परिभाषित नहीं है / Degree is not defined. The degree of the zero polynomial is not defined. Remember it separately from a non-zero constant polynomial.
Step 3
Exam Tip
शून्य बहुपद की घात परिभाषित नहीं होती। इसे गैर-शून्य नियत बहुपद से अलग याद रखें।
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\(6x^4-2x^2+x-8\) की घात क्या है?
What is the degree of \(6x^4-2x^2+x-8\)?
#degree
#highest-power
A (1)
B (2)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
The highest power is (4), so the degree is (4). The degree depends on the highest power, not on the number of terms.
Step 2
Why this answer is correct
The correct answer is C. (4). The highest power is (4), so the degree is (4). The degree depends on the highest power, not on the number of terms.
Step 3
Exam Tip
सबसे बड़ी घात (4) है इसलिए घात (4) है। पदों की संख्या नहीं, सबसे बड़ी घात महत्वपूर्ण 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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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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(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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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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बहुपद (5) की घात क्या है?
What is the degree of the polynomial (5)?
#polynomials
#constant-polynomial
#easy
#degree
A (0)
B (1)
C (5)
D परिभाषित नहीं / Not defined
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). Remember \(5=5x^0\) may be considered.
Step 2
Why this answer is correct
The correct answer is A. (0). A non-zero constant polynomial has degree (0). Remember \(5=5x^0\) may be considered.
Step 3
Exam Tip
अशून्य नियत बहुपद की घात (0) होती है। याद रखें \(5=5x^0\) माना जा सकता है।
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बहुपद \(7x^3-2x+9\) की घात क्या है?
What is the degree of the polynomial \(7x^3-2x+9\)?
#polynomials
#degree
#easy
#level48
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). In exams identify the greatest exponent.
Step 2
Why this answer is correct
The correct answer is C. (3). The highest power is (3), so the degree is (3). In exams identify the greatest exponent.
Step 3
Exam Tip
सबसे बड़ी घात (3) है इसलिए बहुपद की घात (3) होगी। परीक्षा में सबसे बड़े घातांक को पहचानें।
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यदि (p(x)=ax+b) और \(a\neq0\), तो (p(x)) की घात क्या है?
If (p(x)=ax+b) and \(a\neq0\), what is the degree of (p(x))?
#linear_form
#degree
#polynomials
A (0)
B (1)
C (2)
D परिभाषित नहीं / Undefined
Explanation opens after your attempt
Step 1
Concept
Since \(a\neq0\), the (x)-term is present. Therefore the degree of the polynomial is (1).
Step 2
Why this answer is correct
The correct answer is B. (1). Since \(a\neq0\), the (x)-term is present. Therefore the degree of the polynomial is (1).
Step 3
Exam Tip
\(a\neq0\) होने से (x) वाला पद मौजूद है। इसलिए बहुपद की घात (1) है।
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बहुपद \(4x^3-2x^3+x+5\) को सरल करने पर घात क्या होगी?
After simplifying \(4x^3-2x^3+x+5\), what is its degree?
#like_terms
#degree
#simplification
A (1)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
Combining like terms gives \(2x^3+x+5\). The highest power is (3).
Step 2
Why this answer is correct
The correct answer is C. (3). Combining like terms gives \(2x^3+x+5\). The highest power is (3).
Step 3
Exam Tip
समान पद मिलाकर \(2x^3+x+5\) मिलता है। सबसे बड़ी घात (3) है।
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बहुपद \(3x^3+0x^2-2x+5\) की घात क्या है?
What is the degree of \(3x^3+0x^2-2x+5\)?
#degree
#zero_coefficient
#polynomials
A (1)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
The highest non-zero power term is \(3x^3\). So the degree is (3).
Step 2
Why this answer is correct
The correct answer is C. (3). The highest non-zero power term is \(3x^3\). So the degree is (3).
Step 3
Exam Tip
सबसे बड़ी शून्य से भिन्न घात वाला पद \(3x^3\) है। इसलिए घात (3) है।
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शून्य बहुपद (p(x)=0) की घात के बारे में सही कथन कौन-सा है?
Which statement is correct about the degree of the zero polynomial (p(x)=0)?
#zero_polynomial
#degree
#concept
A घात (0) है / Degree is (0)
B घात (1) है / Degree is (1)
C घात परिभाषित नहीं है / Degree is undefined
D घात (2) है / Degree is (2)
Explanation opens after your attempt
Correct Answer
C. घात परिभाषित नहीं है / Degree is undefined
Step 1
Concept
The degree of the zero polynomial is undefined. In exams, keep it separate from a non-zero constant polynomial.
Step 2
Why this answer is correct
The correct answer is C. घात परिभाषित नहीं है / Degree is undefined. The degree of the zero polynomial is undefined. In exams, keep it separate from a non-zero constant polynomial.
Step 3
Exam Tip
शून्य बहुपद की घात परिभाषित नहीं होती। परीक्षा में इसे स्थिर शून्य से भिन्न बहुपद से अलग रखें।
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स्थिर बहुपद (p(x)=9) की घात क्या है?
What is the degree of the constant polynomial (p(x)=9)?
#constant_polynomial
#degree
#basics
A (0)
B (1)
C (9)
D परिभाषित नहीं / Undefined
Explanation opens after your attempt
Step 1
Concept
A non-zero constant polynomial has degree (0). The number (9) may be written as \(9x^0\).
Step 2
Why this answer is correct
The correct answer is A. (0). A non-zero constant polynomial has degree (0). The number (9) may be written as \(9x^0\).
Step 3
Exam Tip
शून्य से भिन्न स्थिर बहुपद की घात (0) होती है। (9) को \(9x^0\) माना जा सकता है।
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बहुपद (p(x)=4x-3 -2x+9) की घात क्या है?
What is the degree of the polynomial (p(x)=4x-3 -2x+9)?
#degree
#polynomials
#one_variable
A (3)
B (2)
C (1)
D (9)
Explanation opens after your attempt
Step 1
Concept
The highest power is (3), so the degree of the polynomial is (3). In exams, look at the highest power of the variable.
Step 2
Why this answer is correct
The correct answer is A. (3). The highest power is (3), so the degree of the polynomial is (3). In exams, look at the highest power of the variable.
Step 3
Exam Tip
सबसे बड़ी घात (3) है इसलिए बहुपद की घात (3) है। परीक्षा में सबसे बड़ी चर घात देखें।
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समीकरण \(x^2+1=0\) की घात क्या है?
What is the degree of \(x^2+1=0\)?
#quadratic-equations
#degree
#constant-term
A (1)
B (2)
C (0)
D (4)
Explanation opens after your attempt
Step 1
Concept
The highest power of (x) is (2). The constant term does not change the degree.
Step 2
Why this answer is correct
The correct answer is B. (2). The highest power of (x) is (2). The constant term does not change the degree.
Step 3
Exam Tip
इसमें (x) की सबसे बड़ी घात (2) है। स्थिर पद घात को नहीं बदलता।
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समीकरण \(7x^2-4x+9=0\) की घात क्या है?
What is the degree of the equation \(7x^2-4x+9=0\)?
#quadratic-equations
#degree
#easy
A (1)
B (2)
C (3)
D (0)
Explanation opens after your attempt
Step 1
Concept
The highest power of (x) in this equation is (2). Degree is decided by the greatest power of the variable.
Step 2
Why this answer is correct
The correct answer is B. (2). The highest power of (x) in this equation is (2). Degree is decided by the greatest power of the variable.
Step 3
Exam Tip
इस समीकरण में (x) की सबसे बड़ी घात (2) है। घात हमेशा चर की सबसे बड़ी शक्ति से तय होती है।
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\(6x^2-5x+2=0\) की घात क्या है?
What is the degree of \(6x^2-5x+2=0\)?
#quadratic equations
#degree
#identification
A (0)
B (1)
C (2)
D (6)
Explanation opens after your attempt
Step 1
Concept
The highest power is (2). Therefore it is a quadratic equation.
Step 2
Why this answer is correct
The correct answer is C. (2). The highest power is (2). Therefore it is a quadratic equation.
Step 3
Exam Tip
सबसे बड़ी घात (2) है। इसलिए यह द्विघात समीकरण है।
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\(5x^2+2x-1=0\) की घात क्या है?
What is the degree of \(5x^2+2x-1=0\)?
#quadratic equations
#degree
#identification
A (0)
B (1)
C (2)
D (5)
Explanation opens after your attempt
Step 1
Concept
The highest power is (2). Therefore the equation is quadratic.
Step 2
Why this answer is correct
The correct answer is C. (2). The highest power is (2). Therefore the equation is quadratic.
Step 3
Exam Tip
सबसे बड़ी घात (2) है। इसलिए समीकरण द्विघात है।
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यदि किसी समीकरण की घात (2) है और वह (x) में है तो उसे क्या कहते हैं?
If an equation in (x) has degree (2), what is it called?
#quadratic equations
#definition
#degree
A रैखिक समीकरण / Linear equation
B द्विघात समीकरण / Quadratic equation
C घन समीकरण / Cubic equation
D स्थिर समीकरण / Constant equation
Explanation opens after your attempt
Correct Answer
B. द्विघात समीकरण / Quadratic equation
Step 1
Concept
An equation of degree (2) is called a quadratic equation. Remember that quadratic means degree (2).
Step 2
Why this answer is correct
The correct answer is B. द्विघात समीकरण / Quadratic equation. An equation of degree (2) is called a quadratic equation. Remember that quadratic means degree (2).
Step 3
Exam Tip
घात (2) वाले समीकरण को द्विघात समीकरण कहते हैं। नाम याद रखने के लिए द्वि का अर्थ (2) समझें।
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एक ग्राफ (x)-अक्ष को तीन बार काटता है। उस बहुपद की न्यूनतम संभावित डिग्री क्या हो सकती है?
A graph cuts the (x)-axis three times. What can be the minimum possible degree of that polynomial?
#degree
#maximum-zeroes
#graph
A (3)
B (2)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
The number of real zeroes cannot exceed the degree of the polynomial. Three crossings need minimum degree (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The number of real zeroes cannot exceed the degree of the polynomial. Three crossings need minimum degree (3).
Step 3
Exam Tip
किसी बहुपद के वास्तविक शून्यकों की संख्या उसकी डिग्री से अधिक नहीं हो सकती। तीन कटान के लिए न्यूनतम डिग्री (3) है।
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यदि कोई बहुपद (x)-अक्ष को छह अलग बिंदुओं पर काटता है तो न्यूनतम संभावित घात क्या होगी?
If a polynomial cuts the (x)-axis at six distinct points, what is the minimum possible degree?
#minimum degree
#distinct zeroes
#graph
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
For six distinct real zeroes, the degree must be at least (6). Tip: the number of distinct zeroes cannot exceed the degree.
Step 2
Why this answer is correct
The correct answer is C. (6). For six distinct real zeroes, the degree must be at least (6). Tip: the number of distinct zeroes cannot exceed the degree.
Step 3
Exam Tip
छह अलग वास्तविक शून्यकों के लिए घात कम से कम (6) होनी चाहिए। टिप: अलग शून्यकों की संख्या घात से अधिक नहीं हो सकती।
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यदि किसी बहुपद का ग्राफ (x)-अक्ष को तीन अलग बिंदुओं पर काटता है, तो बहुपद की न्यूनतम संभावित घात क्या हो सकती है?
If a polynomial graph cuts the (x)-axis at three distinct points, what can be the minimum possible degree of the polynomial?
#degree
#minimum degree
#zeroes
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
For three distinct real zeroes, the degree must be at least (3). Tip: the number of distinct zeroes cannot exceed the degree.
Step 2
Why this answer is correct
The correct answer is C. (3). For three distinct real zeroes, the degree must be at least (3). Tip: the number of distinct zeroes cannot exceed the degree.
Step 3
Exam Tip
तीन अलग वास्तविक शून्यकों के लिए घात कम से कम (3) होनी चाहिए। टिप: अलग शून्यकों की संख्या घात से अधिक नहीं हो सकती।
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विश्व धरोहर स्थल के लिए अखंडता की शर्त किस बात से संबंधित है?
The condition of integrity for a World Heritage Site is related to what?
#integrity
#heritage-condition
#site-management
A स्थल की पूर्णता और उसके मूल्य को बनाए रखने वाली स्थिति / Wholeness of the site and condition supporting its value
B केवल टिकट खिड़की की संख्या / Only number of ticket counters
C केवल स्थानीय भोजन सूची / Only local food list
D स्थल के नाम की लंबाई / Length of the site's name
Explanation opens after your attempt
Correct Answer
A. स्थल की पूर्णता और उसके मूल्य को बनाए रखने वाली स्थिति / Wholeness of the site and condition supporting its value
Step 1
Concept
Integrity shows whether the site's value is sufficiently represented and protected. For exams keep integrity and authenticity separate.
Step 2
Why this answer is correct
The correct answer is A. स्थल की पूर्णता और उसके मूल्य को बनाए रखने वाली स्थिति / Wholeness of the site and condition supporting its value. Integrity shows whether the site's value is sufficiently represented and protected. For exams keep integrity and authenticity separate.
Step 3
Exam Tip
अखंडता बताती है कि स्थल का मूल्य सुरक्षित और पर्याप्त रूप से प्रतिनिधित है या नहीं। परीक्षा में अखंडता और प्रामाणिकता अलग रखें।
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यदि (5x+8y=37) और (15x+24y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (5x+8y=37) and (15x+24y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#expert
#inconsistent
#condition
A (m=111)
B \(m\ne111\)
C (m=37)
D (m=74)
Explanation opens after your attempt
Correct Answer
B. \(m\ne111\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different.
Step 2
Why this answer is correct
The correct answer is B. \(m\ne111\). The first two ratios are equal. For inconsistency, the constant ratio must be different.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए।
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यदि (7x+3y=25) और (14x+6y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (7x+3y=25) and (14x+6y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=50)
B \(m \ne 50\)
C (m=25)
D (m=75)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 50\)
Step 1
Concept
The first two ratios are equal. For inconsistency, the constant ratio must be different so \(m \ne 50\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 50\). The first two ratios are equal. For inconsistency, the constant ratio must be different so \(m \ne 50\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं। असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए इसलिए \(m \ne 50\)।
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यदि (3x+8y=25) और (9x+24y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (3x+8y=25) and (9x+24y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=75)
B \(m \ne 75\)
C (m=25)
D (m=50)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 75\)
Step 1
Concept
The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 75\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 75\). The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 75\) is correct.
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 75\) सही है।
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यदि (2x+5y=17) और (4x+10y=m) असंगत युग्म हों, तो (m) के लिए सही शर्त क्या है?
If (2x+5y=17) and (4x+10y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#hard
#inconsistent
#condition
A (m=34)
B \(m \ne 34\)
C (m=17)
D (m=68)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 34\)
Step 1
Concept
The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 34\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 34\). The first two ratios are equal, so the constant ratio must be different for inconsistency. Hence, \(m \ne 34\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 34\) होगा।
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यदि (5x+2y=13) और (10x+4y=m) असंगत युग्म हैं तो (m) के लिए सही शर्त क्या है?
If (5x+2y=13) and (10x+4y=m) form an inconsistent pair then what is the correct condition for (m)?
#linear equations
#inconsistent
#condition
A (m=26)
B (m=13)
C \(m \ne 26\)
D (m=39)
Explanation opens after your attempt
Correct Answer
C. \(m \ne 26\)
Step 1
Concept
The first two ratios are equal so the constant ratio must differ for inconsistency. Hence \(m \ne 26\).
Step 2
Why this answer is correct
The correct answer is C. \(m \ne 26\). The first two ratios are equal so the constant ratio must differ for inconsistency. Hence \(m \ne 26\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 26\)।
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यदि (4x+5y=16) और (8x+10y=m) असंगत युग्म हैं, तो (m) के लिए सही शर्त क्या है?
If (4x+5y=16) and (8x+10y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#inconsistent
#condition
A (m=32)
B \(m \ne 32\)
C (m=16)
D (m=24)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 32\)
Step 1
Concept
The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence, \(m \ne 32\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 32\). The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence, \(m \ne 32\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 32\)।
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यदि (2x+3y=7) और (4x+6y=m) असंगत युग्म हैं, तो (m) के लिए सही शर्त क्या है?
If (2x+3y=7) and (4x+6y=m) form an inconsistent pair, what is the correct condition for (m)?
#linear equations
#inconsistent pair
#condition
A (m=14)
B \(m \ne 14\)
C (m=7)
D (m=21)
Explanation opens after your attempt
Correct Answer
B. \(m \ne 14\)
Step 1
Concept
The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence \(m \ne 14\).
Step 2
Why this answer is correct
The correct answer is B. \(m \ne 14\). The first two ratios are equal, so for inconsistency the constant ratio must differ. Hence \(m \ne 14\).
Step 3
Exam Tip
पहले दो अनुपात बराबर हैं, इसलिए असंगत होने के लिए स्थिर पद का अनुपात अलग होना चाहिए। अतः \(m \ne 14\)।
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किस स्थिति में दो रैखिक समीकरणों का युग्म संगत और आश्रित कहलाता है?
In which condition is a pair of two linear equations called consistent and dependent?
#linear equations
#consistent dependent
#condition
A जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
B जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
C जब (a_1 / a_2=b_1 / b_2 \ne c_1 / c_2) हो / When \(a_1 / c_2\)
D जब रेखाएं कटती हों / When lines intersect
Explanation opens after your attempt
Correct Answer
A. जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
Step 1
Concept
If all three ratios are equal both equations represent the same line. This is a consistent and dependent pair.
Step 2
Why this answer is correct
The correct answer is A. जब \(a_1 / a_2=b_1 / b_2=c_1 / c_2\) हो / When \(a_1 / c_2\). If all three ratios are equal both equations represent the same line. This is a consistent and dependent pair.
Step 3
Exam Tip
तीनों अनुपात बराबर हों तो दोनों समीकरण समान रेखा दर्शाते हैं। यही संगत और आश्रित युग्म है।
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किस स्थिति में दो रैखिक समीकरणों का युग्म संगत और स्वतंत्र कहलाता है?
In which condition is a pair of two linear equations called consistent and independent?
#linear equations
#consistent independent
#condition
A जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
B जब (a_1 / a_2=b_1 / b_2 \ne c_1 / c_2) हो / When \(a_1 / c_2\)
C जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
D जब कोई हल न हो / When there is no solution
Explanation opens after your attempt
Correct Answer
C. जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
Step 1
Concept
A consistent and independent pair has one unique solution. For this the ratios of (a) and (b) must be different.
Step 2
Why this answer is correct
The correct answer is C. जब \(a_1 / a_2 \ne b_1 / b_2\) हो / When \(a_1 / b_2\). A consistent and independent pair has one unique solution. For this the ratios of (a) and (b) must be different.
Step 3
Exam Tip
संगत और स्वतंत्र युग्म में एक अद्वितीय हल होता है। इसके लिए (a) और (b) के अनुपात अलग होने चाहिए।
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यदि \(a_1x+b_1y+c_1=0\) और \(a_2x+b_2y+c_2=0\) के ग्राफ प्रतिच्छेदी हैं, तो कौन सी शर्त सही है?
If the graphs of \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) are intersecting, which condition is correct?
#linear equations
#graphical method
#intersecting lines
#ratio condition
A \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\)
B \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
C \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
D \(\frac{c_1}{c_2}=0\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
Step 1
Concept
For intersecting lines, the coefficient ratios of (x) and (y) are not equal. This is the condition for a unique solution.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\). For intersecting lines, the coefficient ratios of (x) and (y) are not equal. This is the condition for a unique solution.
Step 3
Exam Tip
प्रतिच्छेदी रेखाओं के लिए (x) और (y) के गुणांक अनुपात बराबर नहीं होते। यही अद्वितीय समाधान की शर्त है।
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किस स्थिति में दो रेखाओं का ग्राफ अनंत समाधान दिखाता है?
In which condition does the graph of two lines show infinitely many solutions?
#linear equations
#graphical method
#ratio condition
#infinite solutions
A \(\frac{a_1}{a_2}\neq\frac{b_1}{b_2}\)
B \(\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq\frac{c_1}{c_2}\)
C \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
D \(\frac{a_1}{a_2}=0\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\)
Step 1
Concept
Infinite solutions occur when both lines are the same line. For this, all three ratios are equal.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\). Infinite solutions occur when both lines are the same line. For this, all three ratios are equal.
Step 3
Exam Tip
अनंत समाधान तब होते हैं जब दोनों रेखाएं एक ही रेखा हों। इसके लिए तीनों अनुपात बराबर होते हैं।
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समीकरण (x-2 +2(k+1)x+k-2 +6k+9=0) के वास्तविक मूल न होने के लिए (k) पर क्या शर्त है?
What condition on (k) is needed for (x-2 +2(k+1)x+k-2 +6k+9=0) to have no real roots?
#quadratic equations
#no real roots
#parameter condition
A (k>-2)
B (k<-2)
C (k=-2)
D सभी वास्तविक (k) / All real (k)
Explanation opens after your attempt
Step 1
Concept
For no real roots, (D<0) is needed. Here (D=-16(k+2)), so (k>-2).
Step 2
Why this answer is correct
The correct answer is A. (k>-2). For no real roots, (D<0) is needed. Here (D=-16(k+2)), so (k>-2).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (D=-16(k+2)), इसलिए (k>-2)।
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यदि \(x^2+2gx+g^2-6g+11=0\) के वास्तविक मूल हैं, तो (g) पर क्या शर्त है?
If \(x^2+2gx+g^2-6g+11=0\) has real roots, what condition on (g) is required?
#quadratic equations
#real roots
#fraction condition
A \(g\ge\frac{11}{6}\)
B \(g<\frac{11}{6}\)
C (g=0)
D सभी वास्तविक (g) / All real (g)
Explanation opens after your attempt
Correct Answer
A. \(g\ge\frac{11}{6}\)
Step 1
Concept
Here (D=4g-2 -4\(g^2-6g+11\)=24g-44). From \(D\ge0\), \(g\ge\frac{11}{6}\).
Step 2
Why this answer is correct
The correct answer is A. \(g\ge\frac{11}{6}\). Here (D=4g-2 -4\(g^2-6g+11\)=24g-44). From \(D\ge0\), \(g\ge\frac{11}{6}\).
Step 3
Exam Tip
यहाँ (D=4g-2 -4\(g^2-6g+11\)=24g-44) है। \(D\ge0\) से \(g\ge\frac{11}{6}\) मिलता है।
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यदि \(x^2+2px+2p+9=0\) के मूल वास्तविक हैं, तो (p) पर सही शर्त कौन सी है?
If \(x^2+2px+2p+9=0\) has real roots, which condition on (p) is correct?
#quadratic equations
#real roots
#interval condition
A \(p\le -2\) या \(p\ge \frac{9}{2}\) / \(p\le -2\) or \(p\ge \frac{9}{2}\)
B \(-2<p<\frac{9}{2}\)
C (p=-2) केवल / (p=-2) only
D \(p=\frac{9}{2}\) केवल / \(p=\frac{9}{2}\) only
Explanation opens after your attempt
Correct Answer
A. \(p\le -2\) या \(p\ge \frac{9}{2}\) / \(p\le -2\) or \(p\ge \frac{9}{2}\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=4(p+2)(2p-9)), so \(p\le -2\) or \(p\ge \frac{9}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(p\le -2\) या \(p\ge \frac{9}{2}\) / \(p\le -2\) or \(p\ge \frac{9}{2}\). For real roots, \(D\ge0\) is required. Here (D=4(p+2)(2p-9)), so \(p\le -2\) or \(p\ge \frac{9}{2}\).
Step 3
Exam Tip
वास्तविक मूलों के लिए \(D\ge0\) चाहिए। यहाँ (D=4(p+2)(2p-9)), इसलिए \(p\le -2\) या \(p\ge \frac{9}{2}\)।
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यदि \(x^2+2kx+k^2-4k+8=0\) के वास्तविक मूल हैं, तो (k) पर क्या शर्त है?
If \(x^2+2kx+k^2-4k+8=0\) has real roots, what is the condition on (k)?
#quadratic equations
#real roots
#parameter condition
A \(k\ge2\)
B \(k\le2\)
C (k>4)
D (k<0)
Explanation opens after your attempt
Correct Answer
A. \(k\ge2\)
Step 1
Concept
Here (D=4k-2 -4\(k^2-4k+8\)=16(k-2)). For real roots \(D\ge0\), so \(k\ge2\).
Step 2
Why this answer is correct
The correct answer is A. \(k\ge2\). Here (D=4k-2 -4\(k^2-4k+8\)=16(k-2)). For real roots \(D\ge0\), so \(k\ge2\).
Step 3
Exam Tip
यहाँ (D=4k-2 -4\(k^2-4k+8\)=16(k-2)) है। वास्तविक मूलों के लिए \(D\ge0\), इसलिए \(k\ge2\)।
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किस शर्त पर \(x^2-2sx+s+2=0\) के मूल वास्तविक और भिन्न होंगे?
Under which condition will \(x^2-2sx+s+2=0\) have real and distinct roots?
#quadratic equations
#interval condition
#real distinct roots
A (s<-1) या (s>2) / (s<-1) or (s>2)
B (-1<s<2)
C (s=-1) या (s=2) / (s=-1) or (s=2)
D (0<s<1)
Explanation opens after your attempt
Correct Answer
A. (s<-1) या (s>2) / (s<-1) or (s>2)
Step 1
Concept
Here (D=4s-2 -4(s+2)=4(s-2 )(s+1)). From (D>0), (s<-1) or (s>2).
Step 2
Why this answer is correct
The correct answer is A. (s<-1) या (s>2) / (s<-1) or (s>2). Here (D=4s-2 -4(s+2)=4(s-2 )(s+1)). From (D>0), (s<-1) or (s>2).
Step 3
Exam Tip
यहाँ (D=4s-2 -4(s+2)=4(s-2 )(s+1)) है। (D>0) से (s<-1) या (s>2) मिलता है।
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समीकरण (x-2 +2(m-1 )x+(m+5)=0) के वास्तविक मूल न होने की शर्त क्या है?
What is the condition for (x-2 +2(m-1 )x+(m+5)=0) to have no real roots?
#quadratic equations
#no real roots
#parameter condition
A \(m^2-3m-4<0\)
B \(m^2-3m-4>0\)
C \(m^2-3m-4=0\)
D \(m^2+3m+4<0\)
Explanation opens after your attempt
Correct Answer
A. \(m^2-3m-4<0\)
Step 1
Concept
For no real roots, (D<0) is needed. Here (D=4[(m-1 )2 -(m+5)]=4\(m^2-3m-4\)).
Step 2
Why this answer is correct
The correct answer is A. \(m^2-3m-4<0\). For no real roots, (D<0) is needed. Here (D=4[(m-1 )2 -(m+5)]=4\(m^2-3m-4\)).
Step 3
Exam Tip
वास्तविक मूल न होने के लिए (D<0) चाहिए। यहाँ (D=4[(m-1 )2 -(m+5)]=4\(m^2-3m-4\)) है।
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यदि \(x^2-6x+c=0\) की दोनों जड़ें वास्तविक और धनात्मक हैं, तो (c) पर सही शर्त क्या है?
If both roots of \(x^2-6x+c=0\) are real and positive, what is the correct condition on (c)?
#quadratic-roots
#positive-roots
#condition
A \(0<c\le9\)
B (c>9)
C (c<0)
D (c=0)
Explanation opens after your attempt
Correct Answer
A. \(0<c\le9\)
Step 1
Concept
The sum (6) is positive and (c>0) is needed for both positive roots. For real roots, \(36-4c\ge0\), so \(0<c\le9\).
Step 2
Why this answer is correct
The correct answer is A. \(0<c\le9\). The sum (6) is positive and (c>0) is needed for both positive roots. For real roots, \(36-4c\ge0\), so \(0<c\le9\).
Step 3
Exam Tip
योग (6) धनात्मक है और दोनों धनात्मक जड़ों के लिए (c>0) चाहिए। वास्तविक जड़ों के लिए \(36-4c\ge0\), इसलिए \(0<c\le9\)।
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(9x-2 -6(a-1)x+a-2 -4a-5=0) की जड़ें वास्तविक हों, तो सही शर्त क्या है?
What is the correct condition for (9x-2 -6(a-1)x+a-2 -4a-5=0) to have real roots?
#quadratic-roots
#real-roots
#parameter-condition
A \(a\ge-3\)
B \(a\le-3\)
C (a>3)
D (a< -3)
Explanation opens after your attempt
Correct Answer
A. \(a\ge-3\)
Step 1
Concept
Here (D=36(a-1)2 -36\(a^2-4a-5\)=72(a+3)). For real roots, \(D\ge0\), so \(a\ge-3\).
Step 2
Why this answer is correct
The correct answer is A. \(a\ge-3\). Here (D=36(a-1)2 -36\(a^2-4a-5\)=72(a+3)). For real roots, \(D\ge0\), so \(a\ge-3\).
Step 3
Exam Tip
यहाँ (D=36(a-1)2 -36\(a^2-4a-5\)=72(a+3)) है। वास्तविक जड़ों के लिए \(D\ge0\), इसलिए \(a\ge-3\)।
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यदि ((m-1 )x-2 +2(m+1)x+(m-1 )=0) की जड़ें वास्तविक और व्युत्क्रम हों, तो (m) पर सही शर्त क्या है?
If ((m-1 )x-2 +2(m+1)x+(m-1 )=0) has real reciprocal roots, what is the correct condition on (m)?
#quadratic-roots
#reciprocal-roots
#parameter-condition
A \(m\ge0\) और \(m\neq1\) / \(m\ge0\) and \(m\neq1\)
B (m<0)
C (m=1)
D \(m\le0\)
Explanation opens after your attempt
Correct Answer
A. \(m\ge0\) और \(m\neq1\) / \(m\ge0\) and \(m\neq1\)
Step 1
Concept
The product of roots is \(\frac{m-1}{m-1}=1\), so \(m\neq1\) is needed. For real roots, \(D=16m\ge0\), hence \(m\ge0\) and \(m\neq1\).
Step 2
Why this answer is correct
The correct answer is A. \(m\ge0\) और \(m\neq1\) / \(m\ge0\) and \(m\neq1\). The product of roots is \(\frac{m-1}{m-1}=1\), so \(m\neq1\) is needed. For real roots, \(D=16m\ge0\), hence \(m\ge0\) and \(m\neq1\).
Step 3
Exam Tip
जड़ों का गुणनफल \(\frac{m-1}{m-1}=1\) है, इसलिए \(m\neq1\) चाहिए। वास्तविक जड़ों के लिए \(D=16m\ge0\), अतः \(m\ge0\) और \(m\neq1\)।
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यदि (x-2 -2mx+\(m^2-m\)=0) की जड़ें वास्तविक हों, तो (m) पर सही शर्त क्या है?
If (x-2 -2mx+\(m^2-m\)=0) has real roots, what is the correct condition on (m)?
#quadratic-roots
#real-roots
#parameter-condition
A (m>0)
B (m<0)
C \(m\ge0\)
D \(m\le0\)
Explanation opens after your attempt
Correct Answer
C. \(m\ge0\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=4m), so \(m\ge0\).
Step 2
Why this answer is correct
The correct answer is C. \(m\ge0\). For real roots, \(D\ge0\) is required. Here (D=4m), so \(m\ge0\).
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D\ge0\) चाहिए। यहाँ (D=4m), इसलिए \(m\ge0\)।
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यदि \(x^2-sx+1=0\) की जड़ें \(\tan\theta\) और \(\cot\theta\) हो सकती हैं, तो वास्तविक \(\theta\) के लिए (s) पर सही शर्त क्या है?
If the roots of \(x^2-sx+1=0\) can be \(\tan\theta\) and \(\cot\theta\), what is the correct condition on (s) for real \(\theta\)?
#quadratic-roots
#trigonometric-roots
#condition
A (-2<s<2)
B (s=0)
C \(s^2\ge4\)
D \(s^2<4\)
Explanation opens after your attempt
Correct Answer
C. \(s^2\ge4\)
Step 1
Concept
We have \(\tan\theta\cdot\cot\theta=1\) and \(\tan\theta+\cot\theta=s\). For real values, \(s^2-4\ge0\), so \(s^2\ge4\).
Step 2
Why this answer is correct
The correct answer is C. \(s^2\ge4\). We have \(\tan\theta\cdot\cot\theta=1\) and \(\tan\theta+\cot\theta=s\). For real values, \(s^2-4\ge0\), so \(s^2\ge4\).
Step 3
Exam Tip
\(\tan\theta\cdot\cot\theta=1\) और \(\tan\theta+\cot\theta=s\) है। वास्तविक मानों के लिए \(s^2-4\ge0\), इसलिए \(s^2\ge4\)।
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यदि \(x^2-5x+c=0\) की दोनों जड़ें वास्तविक और धनात्मक हैं, तो (c) पर सही शर्त क्या है?
If both roots of \(x^2-5x+c=0\) are real and positive, what is the correct condition on (c)?
#quadratic-roots
#positive-roots
#condition
A (c<0)
B \(0<c\le\frac{25}{4}\)
C \(c>\frac{25}{4}\)
D (c=0)
Explanation opens after your attempt
Correct Answer
B. \(0<c\le\frac{25}{4}\)
Step 1
Concept
The sum (5) is positive and product (c>0) is needed for both roots. For real roots, \(25-4c\ge0\), so \(0<c\le\frac{25}{4}\).
Step 2
Why this answer is correct
The correct answer is B. \(0<c\le\frac{25}{4}\). The sum (5) is positive and product (c>0) is needed for both roots. For real roots, \(25-4c\ge0\), so \(0<c\le\frac{25}{4}\).
Step 3
Exam Tip
योग (5) धनात्मक है और दोनों जड़ों के लिए गुणनफल (c>0) चाहिए। वास्तविक जड़ों के लिए \(25-4c\ge0\), इसलिए \(0<c\le\frac{25}{4}\)।
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(9x-2 -6(a+1)x+a-2 -3a=0) की जड़ें वास्तविक हों, तो (a) पर सही शर्त क्या है?
For (9x-2 -6(a+1)x+a-2 -3a=0) to have real roots, what is the correct condition on (a)?
#quadratic-roots
#real-roots
#discriminant-condition
A \(a\ge-\frac{1}{5}\)
B \(a\le-\frac{1}{5}\)
C (a>5)
D \(a<-\frac{1}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(a\ge-\frac{1}{5}\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=36(5a+1)), so \(a\ge-\frac{1}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(a\ge-\frac{1}{5}\). For real roots, \(D\ge0\) is required. Here (D=36(5a+1)), so \(a\ge-\frac{1}{5}\).
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D\ge0\) चाहिए। यहाँ (D=36(5a+1)), इसलिए \(a\ge-\frac{1}{5}\)।
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यदि \(x^2+4x+c=0\) की दोनों जड़ें वास्तविक और ऋणात्मक हैं, तो कौन-सी शर्त पर्याप्त और आवश्यक है?
If both roots of \(x^2+4x+c=0\) are real and negative, which condition is necessary and sufficient?
#quadratic-roots
#negative-roots
#condition
A \(0<c\le4\)
B (c>4)
C (c<0)
D (c=0)
Explanation opens after your attempt
Correct Answer
A. \(0<c\le4\)
Step 1
Concept
The sum (-4) is already negative and the product must be positive, so (c>0). For real roots, \(16-4c\ge0\), hence \(0<c\le4\).
Step 2
Why this answer is correct
The correct answer is A. \(0<c\le4\). The sum (-4) is already negative and the product must be positive, so (c>0). For real roots, \(16-4c\ge0\), hence \(0<c\le4\).
Step 3
Exam Tip
योग (-4) पहले से ऋणात्मक है और गुणनफल धनात्मक चाहिए, इसलिए (c>0)। वास्तविक जड़ों के लिए \(16-4c\ge0\), अतः \(0<c\le4\)।
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(4x-2 -4(a-1)x+a-2 -4a=0) की जड़ें वास्तविक हों, तो (a) पर सही शर्त क्या है?
For (4x-2 -4(a-1)x+a-2 -4a=0) to have real roots, what is the correct condition on (a)?
#quadratic-roots
#real-roots
#discriminant-condition
A \(a\le1\)
B \(a\ge1\)
C (a<0)
D (a>4)
Explanation opens after your attempt
Correct Answer
A. \(a\le1\)
Step 1
Concept
For real roots, \(D\ge0\) is required. Here (D=16(1-a)), so \(a\le1\).
Step 2
Why this answer is correct
The correct answer is A. \(a\le1\). For real roots, \(D\ge0\) is required. Here (D=16(1-a)), so \(a\le1\).
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D\ge0\) चाहिए। यहाँ (D=16(1-a)), इसलिए \(a\le1\) है।
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\(kx^2+6x+9=0\) की वास्तविक जड़ें हों और \(k\ne0\), तो (k) पर सही शर्त कौन-सी है?
For \(kx^2+6x+9=0\) to have real roots with \(k\ne0\), which condition on (k) is correct?
#quadratic-roots
#real-roots
#parameter-condition
A \(k\le 1,\ k\ne0\)
B (k>1)
C \(k\ge 1\)
D (k<0) केवल / (k<0) only
Explanation opens after your attempt
Correct Answer
A. \(k\le 1,\ k\ne0\)
Step 1
Concept
For real roots, \(D=36-36k\ge0\) is required. Thus \(k\le1\), and \(k\ne0\) is also needed for a quadratic equation.
Step 2
Why this answer is correct
The correct answer is A. \(k\le 1,\ k\ne0\). For real roots, \(D=36-36k\ge0\) is required. Thus \(k\le1\), and \(k\ne0\) is also needed for a quadratic equation.
Step 3
Exam Tip
वास्तविक जड़ों के लिए \(D=36-36k\ge0\) होना चाहिए। इसलिए \(k\le1\) और द्विघात के लिए \(k\ne0\) भी जरूरी है।
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किस स्थिति में द्विघात समीकरण के कोई वास्तविक मूल नहीं होते?
In which condition does a quadratic equation have no real roots?
#roots
#discriminant
#condition
A (D>0)
B (D=0)
C (D<0)
D \(D\ge0\)
Explanation opens after your attempt
Step 1
Concept
When (D<0), there are no real roots. This is a direct rule for the nature of roots.
Step 2
Why this answer is correct
The correct answer is C. (D<0). When (D<0), there are no real roots. This is a direct rule for the nature of roots.
Step 3
Exam Tip
जब (D<0) होता है तब वास्तविक मूल नहीं होते। यह मूलों की प्रकृति का सीधा नियम है।
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किस शर्त पर (0) समीकरण \(ax^2+bx+c=0\) का मूल होगा?
Under which condition will (0) be a root of \(ax^2+bx+c=0\)?
#roots
#zero_root
#condition
A (c=0)
B (a=0)
C (b=0)
D (a=b)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0) makes the equation (c=0). So for a zero root the constant term must be zero.
Step 2
Why this answer is correct
The correct answer is A. (c=0). Putting (x=0) makes the equation (c=0). So for a zero root the constant term must be zero.
Step 3
Exam Tip
(x=0) रखने पर समीकरण (c=0) बनता है। इसलिए शून्य मूल के लिए अचर पद शून्य होना चाहिए।
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यदि (\(t^2-64\)x-2 +(t-8)x+5=0) द्विघात समीकरण है, तो (t) पर सही शर्त क्या है?
If (\(t^2-64\)x-2 +(t-8)x+5=0) is a quadratic equation, what is the correct condition on (t)?
#quadratic-equations
#parameter
#condition
#expert
A \(t\neq 8\)
B \(t\neq -8\)
C \(t\neq \pm8\)
D \(t=\pm8\)
Explanation opens after your attempt
Correct Answer
C. \(t\neq \pm8\)
Step 1
Concept
For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(t^2-64\neq0\), so \(t\neq\pm8\).
Step 2
Why this answer is correct
The correct answer is C. \(t\neq \pm8\). For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(t^2-64\neq0\), so \(t\neq\pm8\).
Step 3
Exam Tip
द्विघात होने के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। यहाँ \(t^2-64\neq0\), इसलिए \(t\neq\pm8\)।
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यदि (\(r^2-49\)x-2 +(r+7)x+2=0) द्विघात समीकरण है, तो (r) पर सही शर्त क्या है?
If (\(r^2-49\)x-2 +(r+7)x+2=0) is a quadratic equation, what is the correct condition on (r)?
#quadratic-equations
#parameter
#condition
#expert
A \(r\neq 7\)
B \(r\neq -7\)
C \(r\neq \pm7\)
D \(r=\pm7\)
Explanation opens after your attempt
Correct Answer
C. \(r\neq \pm7\)
Step 1
Concept
For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(r^2-49\neq0\), so \(r\neq\pm7\).
Step 2
Why this answer is correct
The correct answer is C. \(r\neq \pm7\). For the equation to be quadratic, the coefficient of \(x^2\) must not be (0). Here \(r^2-49\neq0\), so \(r\neq\pm7\).
Step 3
Exam Tip
द्विघात होने के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। यहाँ \(r^2-49\neq0\), इसलिए \(r\neq\pm7\)।
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यदि (\(k^2-25\)x-2 +(k-5)x+1=0) द्विघात समीकरण है, तो (k) पर सही शर्त क्या है?
If (\(k^2-25\)x-2 +(k-5)x+1=0) is a quadratic equation, what is the correct condition on (k)?
#quadratic-equations
#parameter
#condition
#expert
A \(k\neq5\)
B \(k\neq -5\)
C \(k\neq \pm5\)
D \(k=\pm5\)
Explanation opens after your attempt
Correct Answer
C. \(k\neq \pm5\)
Step 1
Concept
For the equation to be quadratic, \(k^2-25\neq0\) is required. So both \(k\neq5\) and \(k\neq-5\) are necessary.
Step 2
Why this answer is correct
The correct answer is C. \(k\neq \pm5\). For the equation to be quadratic, \(k^2-25\neq0\) is required. So both \(k\neq5\) and \(k\neq-5\) are necessary.
Step 3
Exam Tip
द्विघात होने के लिए \(k^2-25\neq0\) होना चाहिए। इसलिए \(k\neq5\) और \(k\neq-5\) दोनों शर्तें जरूरी हैं।
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यदि (\(n^2-16\)x-2 -3x+7=0) द्विघात समीकरण है, तो (n) पर सही शर्त क्या है?
If (\(n^2-16\)x-2 -3x+7=0) is a quadratic equation, what is the correct condition on (n)?
#quadratic-equations
#parameter
#condition
#hard
A \(n\neq 4\)
B \(n\neq -4\)
C \(n\neq \pm4\)
D \(n=\pm4\)
Explanation opens after your attempt
Correct Answer
C. \(n\neq \pm4\)
Step 1
Concept
For the equation to be quadratic, \(n^2-16\neq0\) is needed. Hence both \(n\neq4\) and \(n\neq-4\) are necessary.
Step 2
Why this answer is correct
The correct answer is C. \(n\neq \pm4\). For the equation to be quadratic, \(n^2-16\neq0\) is needed. Hence both \(n\neq4\) and \(n\neq-4\) are necessary.
Step 3
Exam Tip
द्विघात होने के लिए \(n^2-16\neq0\) होना चाहिए। इसलिए \(n\neq4\) और \(n\neq-4\) दोनों जरूरी हैं।
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यदि (\(m^2-9\)x-2 +4x-5=0) द्विघात समीकरण है, तो (m) पर सही शर्त क्या है?
If (\(m^2-9\)x-2 +4x-5=0) is a quadratic equation, what is the correct condition on (m)?
#quadratic-equations
#parameter
#condition
#hard
A \(m\neq 3\)
B \(m\neq -3\)
C \(m\neq \pm3\)
D \(m=\pm3\)
Explanation opens after your attempt
Correct Answer
C. \(m\neq \pm3\)
Step 1
Concept
For the equation to be quadratic, \(m^2-9\neq0\) is needed. Hence both \(m\neq3\) and \(m\neq-3\) are necessary.
Step 2
Why this answer is correct
The correct answer is C. \(m\neq \pm3\). For the equation to be quadratic, \(m^2-9\neq0\) is needed. Hence both \(m\neq3\) and \(m\neq-3\) are necessary.
Step 3
Exam Tip
द्विघात होने के लिए \(m^2-9\neq0\) होना चाहिए। इसलिए \(m\neq3\) और \(m\neq-3\) दोनों जरूरी हैं।
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यदि ((5-p)x-2 +2x+9=0) द्विघात समीकरण है, तो (p) के लिए सही शर्त क्या है?
If ((5-p)x-2 +2x+9=0) is a quadratic equation, what is the correct condition for (p)?
#quadratic-equations
#parameter
#condition
#medium
A (p=5)
B \(p\neq 5\)
C (p=0)
D \(p\neq -5\)
Explanation opens after your attempt
Correct Answer
B. \(p\neq 5\)
Step 1
Concept
For a quadratic equation, the coefficient of \(x^2\) must not be (0). Thus \(5-p\neq0\), so \(p\neq5\).
Step 2
Why this answer is correct
The correct answer is B. \(p\neq 5\). For a quadratic equation, the coefficient of \(x^2\) must not be (0). Thus \(5-p\neq0\), so \(p\neq5\).
Step 3
Exam Tip
द्विघात समीकरण के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। इसलिए \(5-p\neq0\), अर्थात \(p\neq5\)।
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यदि ((2m-3)x-2 +7x-1=0) द्विघात समीकरण है, तो (m) के लिए सही शर्त क्या है?
If ((2m-3)x-2 +7x-1=0) is a quadratic equation, what is the correct condition for (m)?
#quadratic-equations
#parameter
#condition
#medium
A \(m=\frac{3}{2}\)
B \(m\neq \frac{3}{2}\)
C \(m\neq -\frac{3}{2}\)
D (m=0)
Explanation opens after your attempt
Correct Answer
B. \(m\neq \frac{3}{2}\)
Step 1
Concept
For a quadratic equation, the coefficient of \(x^2\) must not be (0). Thus \(2m-3\neq 0\), so \(m\neq \frac{3}{2}\).
Step 2
Why this answer is correct
The correct answer is B. \(m\neq \frac{3}{2}\). For a quadratic equation, the coefficient of \(x^2\) must not be (0). Thus \(2m-3\neq 0\), so \(m\neq \frac{3}{2}\).
Step 3
Exam Tip
द्विघात होने के लिए \(x^2\) का गुणांक (0) नहीं होना चाहिए। इसलिए \(2m-3\neq 0\), अर्थात \(m\neq \frac{3}{2}\)।
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