100 results found for "slow variable" in Class 10.
एक चर के बहुपद में चर की घातें कैसी होनी चाहिए?
What should the powers of the variable be in a polynomial in one variable?
#powers
#definition
#polynomial
A ऋणात्मक पूर्णांक / Negative integers
B भिन्न संख्याएं / Fractions
C अऋणात्मक पूर्णांक / Non-negative integers
D केवल अभाज्य संख्याएं / Only prime numbers
Explanation opens after your attempt
Correct Answer
C. अऋणात्मक पूर्णांक / Non-negative integers
Step 1
Concept
In a polynomial, powers of the variable are non-negative integers like \(0,1,2,\ldots\). This is the basic identification rule.
Step 2
Why this answer is correct
The correct answer is C. अऋणात्मक पूर्णांक / Non-negative integers. In a polynomial, powers of the variable are non-negative integers like \(0,1,2,\ldots\). This is the basic identification rule.
Step 3
Exam Tip
बहुपद में चर की घातें \(0,1,2,\ldots\) जैसी अऋणात्मक पूर्णांक होती हैं। यही बहुपद की मूल पहचान है।
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बहुपद (p(u)=13u-3 -2u+9) में चर कौन सा है?
What is the variable in the polynomial (p(u)=13u-3 -2u+9)?
#variable
#one variable
#polynomial
A (p)
B (u)
C (13)
D (9)
Explanation opens after your attempt
Step 1
Concept
The letter whose values can change is the variable. Here the variable is (u).
Step 2
Why this answer is correct
The correct answer is B. (u). The letter whose values can change is the variable. Here the variable is (u).
Step 3
Exam Tip
जिस अक्षर के मान बदल सकते हैं वह चर होता है। यहां चर (u) है।
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बहुपद (p(t)=6t-2 -7t+3) में चर कौन सा है?
What is the variable in the polynomial (p(t)=6t-2 -7t+3)?
#variable
#one variable
#polynomial
A (p)
B (t)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
The letter whose value can vary is the variable. Here the variable is (t).
Step 2
Why this answer is correct
The correct answer is B. (t). The letter whose value can vary is the variable. Here the variable is (t).
Step 3
Exam Tip
जिस अक्षर का मान बदल सकता है वह चर है। यहां चर (t) है।
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लोहे पर जंग लगना किस कारण धीमे ऑक्सीकरण का उदाहरण माना जाता है?
Why is rusting of iron considered an example of slow oxidation?
#science
#class10
#hard
#rusting
#slow-oxidation
A यह ऑक्सीजन और नमी के साथ धीरे धीरे होता है / It occurs slowly with oxygen and moisture
B यह जल में तुरंत घुल जाता है / It dissolves instantly in water
C यह प्रकाश से एक पल में होता है / It happens instantly by light
D यह बिना ऑक्सीजन के होता है / It occurs without oxygen
Explanation opens after your attempt
Correct Answer
A. यह ऑक्सीजन और नमी के साथ धीरे धीरे होता है / It occurs slowly with oxygen and moisture
Step 1
Concept
Iron combines with oxygen during rusting.
Step 2
Why this answer is correct
Moisture helps this process.
Step 3
Exam Tip
Since it happens slowly it is slow oxidation. चरण 1: जंग लगने में लोहा ऑक्सीजन से जुड़ता है। चरण 2: नमी इस प्रक्रिया में मदद करती है। चरण 3: यह धीरे धीरे होने के कारण धीमा ऑक्सीकरण है।
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लोहे की जंग को धीमा ऑक्सीकरण क्यों कहा जा सकता है?
Why can rusting of iron be called slow oxidation?
#science
#class10
#medium
#rusting
#slow-oxidation
A क्योंकि यह तुरंत विस्फोट से होती है / Because it occurs by instant explosion
B क्योंकि लोहा धीरे धीरे ऑक्सीजन और नमी से अभिक्रिया करता है / Because iron slowly reacts with oxygen and moisture
C क्योंकि इसमें कोई ऑक्सीजन नहीं होती / Because oxygen is absent in it
D क्योंकि इसमें केवल जल जमता है / Because only water freezes
Explanation opens after your attempt
Correct Answer
B. क्योंकि लोहा धीरे धीरे ऑक्सीजन और नमी से अभिक्रिया करता है / Because iron slowly reacts with oxygen and moisture
Step 1
Concept
Rusting does not happen instantly.
Step 2
Why this answer is correct
Iron reacts with oxygen and moisture over time.
Step 3
Exam Tip
Therefore it is an example of slow oxidation. चरण 1: जंग लगना तुरंत नहीं होता। चरण 2: लोहा समय के साथ ऑक्सीजन और नमी से अभिक्रिया करता है। चरण 3: इसलिए यह धीमे ऑक्सीकरण का उदाहरण है।
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निम्न में से एक चर वाला बहुपद कौन सा नहीं है?
Which of the following is not a polynomial in one variable?
#one variable
#two variables
#identification
A \(2x^2+3x+1\)
B \(5t^3-t\)
C \(x^2+y+1\)
D (9z-4)
Explanation opens after your attempt
Correct Answer
C. \(x^2+y+1\)
Step 1
Concept
\(x^2+y+1\) has two variables (x) and (y). Therefore it is not a polynomial in one variable.
Step 2
Why this answer is correct
The correct answer is C. \(x^2+y+1\). \(x^2+y+1\) has two variables (x) and (y). Therefore it is not a polynomial in one variable.
Step 3
Exam Tip
\(x^2+y+1\) में दो चर (x) और (y) हैं। इसलिए यह एक चर वाला बहुपद नहीं है।
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इनमें से कौन सा एक चर में बहुपद है?
Which of the following is a polynomial in one variable?
#polynomial
#one variable
#identification
A (p(x)=3x-2 -5x+7)
B (p(x)=\frac{2}{x}+1)
C (p(x)=\sqrt{x}+4)
D (p(x)=x^{-2}+3)
Explanation opens after your attempt
Correct Answer
A. (p(x)=3x-2 -5x+7)
Step 1
Concept
In a polynomial in one variable, powers of the variable are non-negative integers. In exams, reject negative powers and roots of the variable.
Step 2
Why this answer is correct
The correct answer is A. (p(x)=3x-2 -5x+7). In a polynomial in one variable, powers of the variable are non-negative integers. In exams, reject negative powers and roots of the variable.
Step 3
Exam Tip
एक चर के बहुपद में चर की घात केवल अशून्य पूर्णांक या शून्य होती है। परीक्षा में ऋणात्मक घात और मूल से बचें।
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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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बहुपद (p(t)=8t-2 -3t+4) में चर कौन-सा है?
Which is the variable in the polynomial (p(t)=8t-2 -3t+4)?
#variable
#polynomial_notation
#basics
A (p)
B (t)
C (8)
D (4)
Explanation opens after your attempt
Step 1
Concept
In (p(t)), the changing symbol is (t). So the variable is (t).
Step 2
Why this answer is correct
The correct answer is B. (t). In (p(t)), the changing symbol is (t). So the variable is (t).
Step 3
Exam Tip
(p(t)) में बदलने वाला चिन्ह (t) है। इसलिए चर (t) है।
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कौन सा व्यंजक बहुपद नहीं है क्योंकि चर की घात भिन्न है?
Which expression is not a polynomial because the variable has a fractional power?
#not polynomial
#fractional power
#definition
A \(x^4-2x+5\)
B \(3x^2+\sqrt{2}x-7\)
C \(x^{\frac{3}{2}}+x+1\)
D \(9x^3-4x^2\)
Explanation opens after your attempt
Correct Answer
C. \(x^{\frac{3}{2}}+x+1\)
Step 1
Concept
In \(x^{\frac{3}{2}}\), the power of the variable is fractional, so it is not a polynomial. In a polynomial, powers are non-negative integers.
Step 2
Why this answer is correct
The correct answer is C. \(x^{\frac{3}{2}}+x+1\). In \(x^{\frac{3}{2}}\), the power of the variable is fractional, so it is not a polynomial. In a polynomial, powers are non-negative integers.
Step 3
Exam Tip
\(x^{\frac{3}{2}}\) में चर की घात भिन्न है, इसलिए यह बहुपद नहीं है। बहुपद में घातें अऋणात्मक पूर्णांक होती हैं।
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कौन सा विकल्प एक चर में बहुपद है लेकिन रैखिक नहीं है?
Which option is a polynomial in one variable but not linear?
#classification
#quadratic
#not linear
A (5x-8)
B \(x^2+2x+3\)
C \(x+\frac{1}{x}\)
D \(\sqrt{x}+2\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+2x+3\)
Step 1
Concept
\(x^2+2x+3\) is a polynomial and its degree is (2). Therefore it is not linear.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+2x+3\). \(x^2+2x+3\) is a polynomial and its degree is (2). Therefore it is not linear.
Step 3
Exam Tip
\(x^2+2x+3\) बहुपद है और इसकी घात (2) है। इसलिए यह रैखिक नहीं है।
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निम्न में से कौन सा बहुपद (x) में है लेकिन (y) में नहीं है?
Which of the following is a polynomial in (x) but not in (y)?
#one-variable
#variable-identification
#polynomial
A \(x^2+3x+1\)
B \(y^2+3y+1\)
C (xy+1)
D (x+y+1)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+1\)
Step 1
Concept
\(x^2+3x+1\) has only the variable (x). So it is a one-variable polynomial in (x).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x+1\). \(x^2+3x+1\) has only the variable (x). So it is a one-variable polynomial in (x).
Step 3
Exam Tip
\(x^2+3x+1\) में केवल (x) चर है। इसलिए यह (x) में एक चर वाला बहुपद है।
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कौन सा विकल्प एक चर में बहुपद है लेकिन द्विघात नहीं है?
Which option is a polynomial in one variable but not quadratic?
#classification
#cubic
#not quadratic
A \(x^2+2x+1\)
B \(4x^3+x-9\)
C \(\frac{1}{x}+2\)
D \(\sqrt{x}+3\)
Explanation opens after your attempt
Correct Answer
B. \(4x^3+x-9\)
Step 1
Concept
\(4x^3+x-9\) is a polynomial and its degree is (3). Therefore it is not quadratic.
Step 2
Why this answer is correct
The correct answer is B. \(4x^3+x-9\). \(4x^3+x-9\) is a polynomial and its degree is (3). Therefore it is not quadratic.
Step 3
Exam Tip
\(4x^3+x-9\) बहुपद है और इसकी घात (3) है। इसलिए यह द्विघात नहीं है।
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कौन-सा व्यंजक एक चर वाला बहुपद है जिसमें वास्तविक गुणांक हैं?
Which expression is a polynomial in one variable with real coefficients?
#real_coefficients
#polynomial_identification
#irrational_coefficient
A \(\sqrt{2}x^2-3x+1\)
B \(\sqrt{x}+2\)
C \(x^{-2}+1\)
D \(\frac{1}{x}+3\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{2}x^2-3x+1\)
Step 1
Concept
\(\sqrt{2}\) is a real number and the powers of (x) are whole numbers. So it is a polynomial.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{2}x^2-3x+1\). \(\sqrt{2}\) is a real number and the powers of (x) are whole numbers. So it is a polynomial.
Step 3
Exam Tip
\(\sqrt{2}\) एक वास्तविक संख्या है और (x) की घातें पूर्ण संख्याएँ हैं। इसलिए यह बहुपद है।
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कौन-सा व्यंजक बहुपद नहीं है क्योंकि चर हर में है?
Which expression is not a polynomial because the variable is in the denominator?
#variable_denominator
#not_polynomial
#negative_power
A \(x^2+2\)
B \(\frac{3}{x}+1\)
C (4x-5)
D \(8x^3\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{3}{x}+1\)
Step 1
Concept
\(\frac{3}{x}=3x^{-1}\), so the variable has a negative power. Therefore it is not a polynomial.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{x}+1\). \(\frac{3}{x}=3x^{-1}\), so the variable has a negative power. Therefore it is not a polynomial.
Step 3
Exam Tip
\(\frac{3}{x}=3x^{-1}\) है और चर की घात ऋणात्मक है। इसलिए यह बहुपद नहीं है।
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कौन-सा व्यंजक (z) में एक चर वाला बहुपद है?
Which expression is a polynomial in one variable (z)?
#one_variable
#polynomial_identification
#z_variable
A \(z^4-2z+1\)
B \(z^{-2}+3\)
C \(\frac{1}{z}+5\)
D (z+w)
Explanation opens after your attempt
Correct Answer
A. \(z^4-2z+1\)
Step 1
Concept
The expression \(z^4-2z+1\) has only (z) and no negative powers. So it is a polynomial in (z).
Step 2
Why this answer is correct
The correct answer is A. \(z^4-2z+1\). The expression \(z^4-2z+1\) has only (z) and no negative powers. So it is a polynomial in (z).
Step 3
Exam Tip
\(z^4-2z+1\) में केवल (z) है और घातें ऋणात्मक नहीं हैं। इसलिए यह (z) में बहुपद है।
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\(2x^2+3xy+1\) एक चर वाला बहुपद क्यों नहीं है?
Why is \(2x^2+3xy+1\) not a polynomial in one variable?
#one_variable
#not_polynomial
#concept
A क्योंकि इसमें दो चर हैं / Because it has two variables
B क्योंकि इसमें कोई स्थिर पद नहीं है / Because it has no constant term
C क्योंकि इसकी घात (2) है / Because its degree is (2)
D क्योंकि गुणांक वास्तविक नहीं हैं / Because coefficients are not real
Explanation opens after your attempt
Correct Answer
A. क्योंकि इसमें दो चर हैं / Because it has two variables
Step 1
Concept
It contains both (x) and (y). A polynomial in one variable should contain only one variable.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि इसमें दो चर हैं / Because it has two variables. It contains both (x) and (y). A polynomial in one variable should contain only one variable.
Step 3
Exam Tip
इसमें (x) और (y) दोनों चर हैं। एक चर वाले बहुपद में केवल एक ही चर होना चाहिए।
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कौन-सा व्यंजक (x) में एक चर वाला बहुपद है?
Which expression is a polynomial in one variable (x)?
#polynomials
#one_variable
#identification
A \(3x^2-5x+7\)
B \(\frac{2}{x}+1\)
C \(\sqrt{x}+4\)
D (x+y)
Explanation opens after your attempt
Correct Answer
A. \(3x^2-5x+7\)
Step 1
Concept
The expression \(3x^2-5x+7\) has only (x) and non-negative integer powers. In exams, the variable power must not be negative or fractional.
Step 2
Why this answer is correct
The correct answer is A. \(3x^2-5x+7\). The expression \(3x^2-5x+7\) has only (x) and non-negative integer powers. In exams, the variable power must not be negative or fractional.
Step 3
Exam Tip
\(3x^2-5x+7\) में केवल (x) है और घातें पूर्ण संख्याएँ हैं। परीक्षा में चर की घात ऋणात्मक या भिन्न नहीं होनी चाहिए।
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किस कारण से एक क्षेत्र में संसाधन होते हुए भी विकास धीमा हो सकता है?
Why can development be slow even if a region has resources?
#development
#technology
#transport
A तकनीक परिवहन या कौशल की कमी से / Due to lack of technology transport or skill
B संसाधन हमेशा विकास रोकते हैं / Resources always stop development
C विकास में मनुष्य की जरूरत नहीं / Development needs no humans
D संसाधन अपने आप बाजार पहुंच जाते हैं / Resources reach market by themselves
Explanation opens after your attempt
Correct Answer
A. तकनीक परिवहन या कौशल की कमी से / Due to lack of technology transport or skill
Step 1
Concept
Having resources alone is not enough. Exam tip: understand the difference between availability and ability to use.
Step 2
Why this answer is correct
The correct answer is A. तकनीक परिवहन या कौशल की कमी से / Due to lack of technology transport or skill. Having resources alone is not enough. Exam tip: understand the difference between availability and ability to use.
Step 3
Exam Tip
केवल संसाधन होना काफी नहीं होता। परीक्षा में उपलब्धता और उपयोग क्षमता का अंतर समझें।
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धीमी बहती रेखा किस भाव से जुड़ सकती है?
Slow flowing line can be connected with which feeling?
#flowing line
#calmness
#softness
A शांति और सौम्यता / Calmness and softness
B अचानक डर / Sudden fear
C भारी टूटन / Heavy break
D कठोर मशीन / Hard machine
Explanation opens after your attempt
Correct Answer
A. शांति और सौम्यता / Calmness and softness
Step 1
Concept
Flowing line can feel soft and calm. Exam tip: connect flowing line with gentle movement.
Step 2
Why this answer is correct
The correct answer is A. शांति और सौम्यता / Calmness and softness. Flowing line can feel soft and calm. Exam tip: connect flowing line with gentle movement.
Step 3
Exam Tip
बहती रेखा कोमल और शांत लग सकती है। परीक्षा में flowing line को gentle movement से जोड़ें।
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इटली अभियान में एन्सिओ की धीमी प्रगति ने कौन सी रणनीतिक समस्या दिखाई?
What strategic problem did slow progress at Anzio show in the Italian campaign?
#world history
#world wars
#anzio
#italian campaign
A उतराई के बाद तेज विस्तार न हो तो आश्चर्य का लाभ घट सकता है / If rapid expansion after landing does not happen the advantage of surprise can decline
B जापान ने इटली बचा लिया / Japan saved Italy
C जर्मनी ने तुरंत आत्मसमर्पण किया / Germany surrendered immediately
D राष्ट्र संघ ने रास्ता रोका / The League blocked the route
Explanation opens after your attempt
Correct Answer
A. उतराई के बाद तेज विस्तार न हो तो आश्चर्य का लाभ घट सकता है / If rapid expansion after landing does not happen the advantage of surprise can decline
Step 1
Concept
Slow movement after Anzio gave German defense time. For exams understand the relation between landing and speed of advance.
Step 2
Why this answer is correct
The correct answer is A. उतराई के बाद तेज विस्तार न हो तो आश्चर्य का लाभ घट सकता है / If rapid expansion after landing does not happen the advantage of surprise can decline. Slow movement after Anzio gave German defense time. For exams understand the relation between landing and speed of advance.
Step 3
Exam Tip
एन्सिओ में उतराई के बाद धीमी गति ने जर्मन रक्षा को समय दिया। परीक्षा में उतराई और आगे बढ़ने की गति का संबंध समझें।
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हार्मोन नियंत्रण धीमा होते हुए भी जीवों के लिए अनिवार्य क्यों है?
Why is hormonal control essential for organisms even though it is slow?
#hormonal-control
#long-term-response
#metabolism
A क्योंकि यह वृद्धि उपापचय और दीर्घकालीन शरीर क्रियाओं को नियंत्रित करता है / Because it controls growth metabolism and long term body functions
B क्योंकि यह हमेशा प्रतिवर्ती चाप से तेज है / Because it is always faster than reflex arc
C क्योंकि यह लक्ष्य अंगों तक नहीं पहुंचता / Because it does not reach target organs
D क्योंकि यह केवल स्वाद पहचानता है / Because it only detects taste
Explanation opens after your attempt
Correct Answer
A. क्योंकि यह वृद्धि उपापचय और दीर्घकालीन शरीर क्रियाओं को नियंत्रित करता है / Because it controls growth metabolism and long term body functions
Step 1
Concept
Hormones travel through blood so their effect may be slow.
Step 2
Why this answer is correct
Still they control important long term functions.
Step 3
Exam Tip
Therefore chemical coordination is essential for the body. चरण 1: हार्मोन रक्त द्वारा चलते हैं इसलिए प्रभाव धीमा हो सकता है। चरण 2: फिर भी वे लंबी अवधि की महत्वपूर्ण क्रियाएं नियंत्रित करते हैं। चरण 3: इसलिए रासायनिक समन्वय शरीर के लिए अनिवार्य है।
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सूखे की स्थिति में पौधे में वृद्धि धीमी होने और पत्तियों के मुरझाने से कौन सा हार्मोन अधिक जुड़ा है?
During drought slow growth and wilting of leaves in a plant are more related to which hormone?
#control_coordination
#abscisic_acid
#drought
A एब्सिसिक अम्ल / Abscisic acid
B जिबरेलिन / Gibberellin
C टेस्टोस्टेरॉन / Testosterone
D इंसुलिन / Insulin
Explanation opens after your attempt
Correct Answer
A. एब्सिसिक अम्ल / Abscisic acid
Step 1
Concept
During drought the plant faces water stress.
Step 2
Why this answer is correct
Abscisic acid is linked with growth inhibition and stress response.
Step 3
Exam Tip
Therefore it is important in wilting and slow growth. चरण 1: सूखे में पौधे को जल की कमी का तनाव होता है। चरण 2: एब्सिसिक अम्ल वृद्धि रोकने और तनाव प्रतिक्रिया से जुड़ा है। चरण 3: इसलिए पत्तियों के मुरझाने और धीमी वृद्धि में इसका संबंध महत्वपूर्ण है।
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पौधों में गति प्रायः धीमी क्यों होती है?
Why is movement in plants usually slow?
#plant-movement
#growth-response
#tropism
A क्योंकि कई पौध प्रतिक्रियाएं वृद्धि पर आधारित होती हैं / Because many plant responses are based on growth
B क्योंकि पौधों में कोशिकाएं नहीं होतीं / Because plants have no cells
C क्योंकि पौधे प्रकाश नहीं पहचानते / Because plants do not detect light
D क्योंकि पौधों में जल नहीं होता / Because plants have no water
Explanation opens after your attempt
Correct Answer
A. क्योंकि कई पौध प्रतिक्रियाएं वृद्धि पर आधारित होती हैं / Because many plant responses are based on growth
Step 1
Concept
Many plant movements occur through changes in cell growth.
Step 2
Why this answer is correct
Growth takes time.
Step 3
Exam Tip
Therefore responses like phototropism appear slow. चरण 1: कई पौध गति कोशिका वृद्धि में बदलाव से होती हैं। चरण 2: वृद्धि में समय लगता है। चरण 3: इसलिए प्रकाशानुवर्तन जैसी प्रतिक्रियाएं धीमी दिखती हैं।
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कुछ शहरी क्षेत्रों में असहयोग आंदोलन धीमा क्यों पड़ा?
Why did the Non-Cooperation Movement slow down in some urban areas?
#urban areas
#khadi
#limitations
A खादी कई लोगों के लिए महंगी थी / Khadi was costly for many people
B विदेशी कपड़ा बिल्कुल उपलब्ध नहीं था / Foreign cloth was not available at all
C सरकार ने स्वराज दे दिया था / The government had granted swaraj
D सभी वकील तुरंत जेल चले गए थे / All lawyers had immediately gone to jail
Explanation opens after your attempt
Correct Answer
A. खादी कई लोगों के लिए महंगी थी / Khadi was costly for many people
Step 1
Concept
Boycotting foreign cloth was not easy for everyone.
Step 2
Why this answer is correct
Khadi could be costly for poor people.
Step 3
Exam Tip
Therefore the movement slowed in some towns. चरण 1: विदेशी कपड़ों का बहिष्कार आसान नहीं था। चरण 2: खादी गरीब लोगों के लिए महंगी पड़ सकती थी। चरण 3: इसलिए कुछ शहरों में आंदोलन की गति घट गई।
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अम्ल को पानी में धीरे धीरे मिलाने की प्रक्रिया किस ऊर्जा परिवर्तन से जुड़ी है?
The slow addition of acid to water is related to which energy change?
#science
#class10
#medium
#acid-dilution
#exothermic
A ऊष्मा निकलती है / Heat is released
B ऊष्मा हमेशा शून्य रहती है / Heat always remains zero
C प्रकाश अवशोषित होता है / Light is absorbed
D ध्वनि बनती है / Sound is formed
Explanation opens after your attempt
Correct Answer
A. ऊष्मा निकलती है / Heat is released
Step 1
Concept
Heat is released when acid is added to water.
Step 2
Why this answer is correct
Release of heat makes it an exothermic process.
Step 3
Exam Tip
Therefore slow addition is safer. चरण 1: अम्ल को पानी में मिलाने पर ऊष्मा निकलती है। चरण 2: ऊष्मा निकलना ऊष्माक्षेपी प्रक्रिया है। चरण 3: इसलिए धीरे धीरे मिलाना सुरक्षित होता है।
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प्रतिऑक्सीकारक भोजन में किस प्रक्रिया की गति घटाते हैं?
Which process do antioxidants slow down in food?
#science
#class10
#expert
#antioxidants
#oxidation
A ऑक्सीकरण / Oxidation
B विस्थापन / Displacement
C वैद्युत वियोजन / Electrolytic decomposition
D जस्तीकरण / Galvanisation
Explanation opens after your attempt
Correct Answer
A. ऑक्सीकरण / Oxidation
Step 1
Concept
Oils and fats spoil by oxidation.
Step 2
Why this answer is correct
Antioxidants slow oxidation.
Step 3
Exam Tip
This reduces rancidity. चरण 1: तेल और वसा ऑक्सीकरण से खराब होते हैं। चरण 2: प्रतिऑक्सीकारक ऑक्सीकरण को धीमा करते हैं। चरण 3: इससे विकृतगंधिता कम होती है।
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प्रतिऑक्सीकारक खाद्य पदार्थों में किस प्रक्रिया को धीमा करते हैं?
Which process do antioxidants slow down in food?
#science
#class10
#expert
#antioxidants
#oxidation
A ऑक्सीकरण / Oxidation
B विस्थापन / Displacement
C वैद्युत वियोजन / Electrolytic decomposition
D जस्तीकरण / Galvanisation
Explanation opens after your attempt
Correct Answer
A. ऑक्सीकरण / Oxidation
Step 1
Concept
Oils and fats spoil by oxidation.
Step 2
Why this answer is correct
Antioxidants reduce the rate of this process.
Step 3
Exam Tip
This decreases rancidity. चरण 1: तेल और वसा ऑक्सीकरण से खराब होते हैं। चरण 2: प्रतिऑक्सीकारक इस प्रक्रिया की गति घटाते हैं। चरण 3: इससे विकृतगंधिता कम होती है।
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प्रतिऑक्सीकारक खाद्य पदार्थों में किस रासायनिक प्रक्रिया को धीमा करते हैं?
Which chemical process do antioxidants slow down in food?
#science
#class10
#expert
#antioxidants
#oxidation
A ऑक्सीकरण / Oxidation
B विस्थापन / Displacement
C वैद्युत वियोजन / Electrolytic decomposition
D जस्तीकरण / Galvanisation
Explanation opens after your attempt
Correct Answer
A. ऑक्सीकरण / Oxidation
Step 1
Concept
Oils and fats spoil by oxidation.
Step 2
Why this answer is correct
Antioxidants reduce the rate of this process.
Step 3
Exam Tip
This decreases rancidity. चरण 1: तेल और वसा ऑक्सीकरण से खराब होते हैं। चरण 2: प्रतिऑक्सीकारक इस प्रक्रिया की गति घटाते हैं। चरण 3: इससे विकृतगंधिता कम होती है।
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श्वसन को दहन से धीमी और नियंत्रित ऊर्जा मुक्त करने वाली प्रक्रिया क्यों समझा जा सकता है?
Why can respiration be understood as a slow and controlled energy releasing process compared with combustion?
#science
#class10
#expert
#respiration
#combustion
A क्योंकि ग्लूकोज का ऑक्सीकरण नियंत्रित ढंग से ऊर्जा देता है / Because oxidation of glucose releases energy in a controlled way
B क्योंकि इसमें कोई ऊर्जा नहीं निकलती / Because no energy is released
C क्योंकि इसमें अवक्षेप बनता है / Because precipitate forms
D क्योंकि यह केवल भौतिक परिवर्तन है / Because it is only a physical change
Explanation opens after your attempt
Correct Answer
A. क्योंकि ग्लूकोज का ऑक्सीकरण नियंत्रित ढंग से ऊर्जा देता है / Because oxidation of glucose releases energy in a controlled way
Step 1
Concept
Glucose is oxidised in respiration.
Step 2
Why this answer is correct
Energy is obtained in a controlled way not suddenly.
Step 3
Exam Tip
Therefore respiration is an energy releasing chemical process. चरण 1: श्वसन में ग्लूकोज का ऑक्सीकरण होता है। चरण 2: ऊर्जा अचानक नहीं बल्कि नियंत्रित रूप से मिलती है। चरण 3: इसलिए श्वसन ऊर्जा मुक्त करने वाली रासायनिक प्रक्रिया है।
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प्रतिऑक्सीकारक खाद्य पदार्थों में किस प्रक्रिया को धीमा करते हैं?
Which process do antioxidants slow down in food materials?
#science
#class10
#medium
#antioxidants
#oxidation
A गलन / Melting
B ऑक्सीकरण / Oxidation
C छानना / Filtration
D अवक्षेपण / Precipitation
Explanation opens after your attempt
Correct Answer
B. ऑक्सीकरण / Oxidation
Step 1
Concept
Oils and fats in food can spoil by oxidation.
Step 2
Why this answer is correct
Antioxidants slow the rate of oxidation.
Step 3
Exam Tip
Therefore they help prevent rancidity. चरण 1: खाद्य पदार्थों में तेल और वसा ऑक्सीकरण से खराब हो सकते हैं। चरण 2: प्रतिऑक्सीकारक ऑक्सीकरण की गति कम करते हैं। चरण 3: इसलिए वे विकृतगंधिता रोकने में सहायक होते हैं।
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प्रतिऑक्सीकारक किस प्रक्रिया को धीमा करते हैं?
Which process do antioxidants slow down?
#science
#class10
#antioxidants
#oxidation
A ऑक्सीकरण / Oxidation
B जमना / Freezing
C गलन / Melting
D छानना / Filtration
Explanation opens after your attempt
Correct Answer
A. ऑक्सीकरण / Oxidation
Step 1
Concept
Antioxidants help protect food from spoilage.
Step 2
Why this answer is correct
They slow down oxidation.
Step 3
Exam Tip
They are important in preventing rancidity. चरण 1: प्रतिऑक्सीकारक भोजन को खराब होने से बचाने में मदद करते हैं। चरण 2: ये ऑक्सीकरण की प्रक्रिया को धीमा करते हैं। चरण 3: विकृतगंधिता रोकने में इनका उपयोग महत्वपूर्ण 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)=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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निम्न में से (y) में बहुपद कौन सा है?
Which of the following is a polynomial in (y)?
#polynomial-in-y
#one-variable
A \(y^2-3y+2\)
B \(\frac{1}{y}+4\)
C \(\sqrt{y}+5\)
D \(y^{-2}+1\)
Explanation opens after your attempt
Correct Answer
A. \(y^2-3y+2\)
Step 1
Concept
In \(y^2-3y+2\), the powers of (y) are whole numbers. A polynomial can be in one variable such as (y).
Step 2
Why this answer is correct
The correct answer is A. \(y^2-3y+2\). In \(y^2-3y+2\), the powers of (y) are whole numbers. A polynomial can be in one variable such as (y).
Step 3
Exam Tip
\(y^2-3y+2\) में (y) की घातें पूर्ण संख्याएँ हैं। बहुपद किसी एक चर जैसे (y) में भी हो सकता है।
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क्या \(4x^2-3\sqrt{x}+1\) (x) में बहुपद है?
Is \(4x^2-3\sqrt{x}+1\) a polynomial in (x)?
#not-polynomial
#root-variable
A हाँ / Yes
B नहीं / No
C केवल जब (x) धनात्मक हो / Only when (x) is positive
D केवल जब (x=1) हो / Only when (x=1)
Explanation opens after your attempt
Correct Answer
B. नहीं / No
Step 1
Concept
\(\sqrt{x}=x^{\frac{1}{2}}\), and \(\frac{1}{2}\) is not a whole number. So it is not a polynomial in (x).
Step 2
Why this answer is correct
The correct answer is B. नहीं / No. \(\sqrt{x}=x^{\frac{1}{2}}\), and \(\frac{1}{2}\) is not a whole number. So it is not a polynomial in (x).
Step 3
Exam Tip
\(\sqrt{x}=x^{\frac{1}{2}}\) है और \(\frac{1}{2}\) पूर्ण संख्या नहीं है। इसलिए यह (x) में बहुपद नहीं है।
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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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निम्न में से कौन सा (x) में बहुपद है?
Which of the following is a polynomial in (x)?
#polynomials
#one-variable
#easy
#definition
A \(x^2+3x+5\)
B \(\frac{1}{x}+2\)
C \(\sqrt{x}+1\)
D \(x^{-2}+4\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+3x+5\)
Step 1
Concept
A polynomial has only non-negative integer powers of (x). In exams check the power of every term.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+3x+5\). A polynomial has only non-negative integer powers of (x). In exams check the power of every term.
Step 3
Exam Tip
बहुपद में (x) की घात केवल पूर्णांक और अशून्य नहीं बल्कि ऋणात्मक नहीं होनी चाहिए। परीक्षा में हर पद की घात जांचें।
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यदि (p(x)=x-2 -4x+6), तो (p(x+1)-p(x)) का मान क्या है?
If (p(x)=x-2 -4x+6), what is the value of (p(x+1)-p(x))?
#polynomial-substitution
#difference
#expert
A (2x-3)
B (2x+3)
C (x-3)
D \(x^2-3\)
Explanation opens after your attempt
Step 1
Concept
(p(x+1)=x-2 -2x+3) and (p(x+1)-p(x)=2x-3). In such questions, substitute (x+1) carefully first.
Step 2
Why this answer is correct
The correct answer is A. (2x-3). (p(x+1)=x-2 -2x+3) and (p(x+1)-p(x)=2x-3). In such questions, substitute (x+1) carefully first.
Step 3
Exam Tip
(p(x+1)=x-2 -2x+3) और (p(x+1)-p(x)=2x-3) है। ऐसे प्रश्नों में पहले (x+1) को सावधानी से प्रतिस्थापित करें।
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यदि (p(x)=x-2 -8x+16) है, तो (p(4+t)) का मान क्या है?
If (p(x)=x-2 -8x+16), what is the value of (p(4+t))?
#substitution
#perfect-square
#polynomial
A \(t^2\)
B \(t^2+4\)
C (4t)
D \(t^2-16\)
Explanation opens after your attempt
Correct Answer
A. \(t^2\)
Step 1
Concept
(p(x)=(x-4)2 ), so (p(4+t)=t-2 ). In such questions, first form a perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(t^2\). (p(x)=(x-4)2 ), so (p(4+t)=t-2 ). In such questions, first form a perfect square.
Step 3
Exam Tip
(p(x)=(x-4)2 ), इसलिए (p(4+t)=t-2 )। ऐसे प्रश्नों में पहले पूर्ण वर्ग बनाना आसान होता है।
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यदि (p(x)=x-3 -1), तो निम्न में से कौन-सा रैखिक गुणनखंड है?
If (p(x)=x-3 -1), which of the following is a linear factor?
#identity
#cubic
#factorisation
A (x-1)
B (x+1)
C (x-3)
D (x+3)
Explanation opens after your attempt
Step 1
Concept
(x-3 -1=(x-1)\(x^2+x+1\)). Therefore (x-1) is a linear factor.
Step 2
Why this answer is correct
The correct answer is A. (x-1). (x-3 -1=(x-1)\(x^2+x+1\)). Therefore (x-1) is a linear factor.
Step 3
Exam Tip
(x-3 -1=(x-1)\(x^2+x+1\)) है। इसलिए (x-1) रैखिक गुणनखंड है।
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यदि (p(x)=x-2 -ax+b) के शून्यक (a) और (b) हैं, तो कौन-सा संबंध सही है?
If the zeroes of (p(x)=x-2 -ax+b) are (a) and (b), which relation is correct?
#symbolic-zeroes
#relations
#concept
A (a+b=a) और (ab=b) / (a+b=a) and (ab=b)
B (a-b=a) और (a+b=b) / (a-b=a) and (a+b=b)
C \(a^2+b^2=a\) और (ab=1) / \(a^2+b^2=a\) and (ab=1)
D (a+b=b) और (ab=a) / (a+b=b) and (ab=a)
Explanation opens after your attempt
Correct Answer
A. (a+b=a) और (ab=b) / (a+b=a) and (ab=b)
Step 1
Concept
The sum of zeroes from the polynomial is (a) and the product is (b). Hence if the zeroes are (a,b), then (a+b=a) and (ab=b).
Step 2
Why this answer is correct
The correct answer is A. (a+b=a) और (ab=b) / (a+b=a) and (ab=b). The sum of zeroes from the polynomial is (a) and the product is (b). Hence if the zeroes are (a,b), then (a+b=a) and (ab=b).
Step 3
Exam Tip
शून्यकों का योग बहुपद से (a) और गुणनफल (b) है। इसलिए यदि शून्यक (a,b) हैं, तो (a+b=a) और (ab=b) होना चाहिए।
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यदि (p(x)=x-2 +px+q) और (p(1)=0,\ p(2)=0), तो (p+q) क्या है?
If (p(x)=x-2 +px+q) and (p(1)=0,\ p(2)=0), what is (p+q)?
#coefficient-finding
#zeroes
#quadratic
A -(1)
B (1)
C -(2)
D (2)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (1) and (2), so the polynomial is \(x^2-3x+2\). Thus (p=-3,\ q=2), and (p+q=-1).
Step 2
Why this answer is correct
The correct answer is A. -(1). The zeroes are (1) and (2), so the polynomial is \(x^2-3x+2\). Thus (p=-3,\ q=2), and (p+q=-1).
Step 3
Exam Tip
शून्यक (1) और (2) हैं, इसलिए बहुपद \(x^2-3x+2\) है। अतः (p=-3,\ q=2) और (p+q=-1)।
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यदि (p(x)=2x-2 +x-6), तो (2p(1)-p(-2)) का मान क्या है?
If (p(x)=2x-2 +x-6), what is the value of (2p(1)-p(-2))?
#evaluation
#polynomial
#expression
A -(6)
B (0)
C (6)
D -(12)
Explanation opens after your attempt
Step 1
Concept
(p(1)=2+1-6=-3) and (p(-2)=8-2-6=0). Therefore (2p(1)-p(-2)=-6).
Step 2
Why this answer is correct
The correct answer is A. -(6). (p(1)=2+1-6=-3) and (p(-2)=8-2-6=0). Therefore (2p(1)-p(-2)=-6).
Step 3
Exam Tip
(p(1)=2+1-6=-3) और (p(-2)=8-2-6=0)। इसलिए (2p(1)-p(-2)=-6)।
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यदि (p(x)=x-2 -6x+8), तो शून्यकों के वर्गों से बना मोनिक बहुपद कौन-सा है?
If (p(x)=x-2 -6x+8), which monic polynomial has the squares of its zeroes as zeroes?
#transformed-zeroes
#squares
#quadratic
A \(x^2-20x+64\)
B \(x^2-6x+8\)
C \(x^2-12x+16\)
D \(x^2-16x+64\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-20x+64\)
Step 1
Concept
The original zeroes are (2) and (4), so the new zeroes are (4) and (16). The new polynomial is \(x^2-20x+64\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-20x+64\). The original zeroes are (2) and (4), so the new zeroes are (4) and (16). The new polynomial is \(x^2-20x+64\).
Step 3
Exam Tip
मूल शून्यक (2) और (4) हैं, इसलिए नए शून्यक (4) और (16) हैं। नया बहुपद \(x^2-20x+64\) है।
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यदि (p(x)=x-2 +2x+c) का कोई वास्तविक शून्यक नहीं है, तो (c) के लिए कौन-सी शर्त सही है?
If (p(x)=x-2 +2x+c) has no real zero, which condition on (c) is correct?
#discriminant
#real-zeroes
#parameter
A (c>1)
B (c=1)
C (c<1)
D (c=0)
Explanation opens after your attempt
Step 1
Concept
For no real zero, the discriminant must satisfy (4-4c<0). This gives (c>1).
Step 2
Why this answer is correct
The correct answer is A. (c>1). For no real zero, the discriminant must satisfy (4-4c<0). This gives (c>1).
Step 3
Exam Tip
कोई वास्तविक शून्यक नहीं होने के लिए विविक्तकर (4-4c<0) चाहिए। इससे (c>1) मिलता है।
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यदि (p(x)=x-2 -7x+12) है, तो (p(x)) का ग्राफ (x)-अक्ष को किन बिंदुओं पर काटेगा?
If (p(x)=x-2 -7x+12), at which points will the graph of (p(x)) cut the (x)-axis?
#graph-zeroes
#quadratic
#intercepts
A ((3,0),(4,0))
B ((0,3),(0,4))
C ((2,0),(6,0))
D ((0,0),(7,0))
Explanation opens after your attempt
Correct Answer
A. ((3,0),(4,0))
Step 1
Concept
(x-2 -7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). The (x)-axis points are ((3,0)) and ((4,0)).
Step 2
Why this answer is correct
The correct answer is A. ((3,0),(4,0)). (x-2 -7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). The (x)-axis points are ((3,0)) and ((4,0)).
Step 3
Exam Tip
(x-2 -7x+12=(x-3)(x-4)), इसलिए शून्यक (3) और (4) हैं। (x)-अक्ष पर बिंदु ((3,0)) और ((4,0)) होंगे।
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यदि (p(x)=x-2 +5x+6) और (r(x)=p(-x)), तो (r(x)) के शून्यक कौन-से हैं?
If (p(x)=x-2 +5x+6) and (r(x)=p(-x)), what are the zeroes of (r(x))?
#transformed-zeroes
#reflection
#quadratic
A (2,3)
B -(2,-3)
C (1,6)
D -(1,-6)
Explanation opens after your attempt
Step 1
Concept
The zeroes of (p(x)) are (-2) and (-3). For (p(-x)=0), (-x=-2) or (-x=-3), so (x=2,3).
Step 2
Why this answer is correct
The correct answer is A. (2,3). The zeroes of (p(x)) are (-2) and (-3). For (p(-x)=0), (-x=-2) or (-x=-3), so (x=2,3).
Step 3
Exam Tip
(p(x)) के शून्यक (-2) और (-3) हैं। (p(-x)=0) के लिए (-x=-2) या (-x=-3), इसलिए (x=2,3)।
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यदि (p(x)=x-3 -3x-2 -4x+12), तो पूर्ण गुणनखंड रूप क्या है?
If (p(x)=x-3 -3x-2 -4x+12), what is the complete factor form?
#factorisation
#grouping
#cubic
A ((x-3)(x-2)(x+2))
B ((x+3)(x-2)(x+2))
C ((x-3)(x+2)2 )
D ((x+3)(x-2)2 )
Explanation opens after your attempt
Correct Answer
A. ((x-3)(x-2)(x+2))
Step 1
Concept
By grouping, (x-2 (x-3)-4(x-3)=(x-3)\(x^2-4\)). Thus the factors are ((x-3)(x-2)(x+2)).
Step 2
Why this answer is correct
The correct answer is A. ((x-3)(x-2)(x+2)). By grouping, (x-2 (x-3)-4(x-3)=(x-3)\(x^2-4\)). Thus the factors are ((x-3)(x-2)(x+2)).
Step 3
Exam Tip
समूहीकरण से (x-2 (x-3)-4(x-3)=(x-3)\(x^2-4\)) मिलता है। इसलिए गुणनखंड ((x-3)(x-2)(x+2)) हैं।
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यदि (p(x)=x-2 -4x+3) है, तो कौन-सा मान (p(x)<0) बनाता है?
If (p(x)=x-2 -4x+3), which value makes (p(x)<0)?
#sign-of-polynomial
#quadratic
#zeroes
A (2)
B (0)
C (4)
D -(1)
Explanation opens after your attempt
Step 1
Concept
(p(x)=(x-1)(x-3)), and it is negative for (1<x<3). Therefore (x=2) is correct.
Step 2
Why this answer is correct
The correct answer is A. (2). (p(x)=(x-1)(x-3)), and it is negative for (1<x<3). Therefore (x=2) is correct.
Step 3
Exam Tip
(p(x)=(x-1)(x-3)) है और (1<x<3) में मान ऋणात्मक होता है। इसलिए (x=2) सही है।
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यदि (p(x)=x-2 -2x+k) का न्यूनतम मान (3) है, तो (k) क्या है?
If the minimum value of (p(x)=x-2 -2x+k) is (3), what is (k)?
#complete-square
#minimum-value
#quadratic
A (4)
B (3)
C (2)
D (1)
Explanation opens after your attempt
Step 1
Concept
(x-2 -2x+k=(x-1)2 +k-1), so the minimum value is (k-1). From (k-1=3), (k=4).
Step 2
Why this answer is correct
The correct answer is A. (4). (x-2 -2x+k=(x-1)2 +k-1), so the minimum value is (k-1). From (k-1=3), (k=4).
Step 3
Exam Tip
(x-2 -2x+k=(x-1)2 +k-1), इसलिए न्यूनतम मान (k-1) है। (k-1=3) से (k=4)।
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यदि (p(x)=x-2 +ax+a) में (p(1)=0), तो (a) क्या है?
If (p(x)=x-2 +ax+a) and (p(1)=0), what is (a)?
#evaluation
#parameter
#polynomial
A -\(\frac{1}{2}\)
B -(1)
C \(\frac{1}{2}\)
D (1)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{1}{2}\)
Step 1
Concept
(p(1)=1+a+a=0), so (2a=-1). Therefore \(a=-\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{1}{2}\). (p(1)=1+a+a=0), so (2a=-1). Therefore \(a=-\frac{1}{2}\).
Step 3
Exam Tip
(p(1)=1+a+a=0), इसलिए (2a=-1)। अतः \(a=-\frac{1}{2}\) है।
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यदि (p(x)=x-4 -16), तो \(x^2+4\) के कारण वास्तविक शून्यकों पर क्या प्रभाव पड़ता है?
For (p(x)=x-4 -16), what effect does \(x^2+4\) have on real zeroes?
#quartic
#real-zeroes
#factor
A यह कोई वास्तविक शून्यक नहीं देता / It gives no real zero
B यह शून्यक (2) देता है / It gives zero (2)
C यह शून्यक (-2) देता है / It gives zero (-2)
D यह दो वास्तविक शून्यक देता है / It gives two real zeroes
Explanation opens after your attempt
Correct Answer
A. यह कोई वास्तविक शून्यक नहीं देता / It gives no real zero
Step 1
Concept
(x-4 -16=\(x^2-4\)\(x^2+4\)). The factor \(x^2+4\) is never (0) for real (x).
Step 2
Why this answer is correct
The correct answer is A. यह कोई वास्तविक शून्यक नहीं देता / It gives no real zero. (x-4 -16=\(x^2-4\)\(x^2+4\)). The factor \(x^2+4\) is never (0) for real (x).
Step 3
Exam Tip
(x-4 -16=\(x^2-4\)\(x^2+4\)) है। \(x^2+4\) वास्तविक (x) के लिए कभी (0) नहीं होता।
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यदि (p(x)=5x-2 -20x+20), तो इसके शून्यकों का योग क्या है?
If (p(x)=5x-2 -20x+20), what is the sum of its zeroes?
#sum-zeroes
#quadratic
#formula
A (4)
B (5)
C -(4)
D (2)
Explanation opens after your attempt
Step 1
Concept
The sum is \(-\frac{b}{a}=-\frac{-20}{5}=4\). Even if a common factor is removed first, the sum remains the same.
Step 2
Why this answer is correct
The correct answer is A. (4). The sum is \(-\frac{b}{a}=-\frac{-20}{5}=4\). Even if a common factor is removed first, the sum remains the same.
Step 3
Exam Tip
योग \(-\frac{b}{a}=-\frac{-20}{5}=4\) है। पहले सामान्य गुणनखंड निकालना चाहें तो भी योग वही रहेगा।
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यदि (p(x)=x-2 +2x-24), तो (p(x)) का कौन-सा गुणनखंड है?
If (p(x)=x-2 +2x-24), which is a factor of (p(x))?
#factorisation
#quadratic
#polynomial
A (x-4)
B (x+4)
C (x-6)
D (x+2)
Explanation opens after your attempt
Step 1
Concept
(x-2 +2x-24=(x-4)(x+6)). Therefore (x-4) is a factor.
Step 2
Why this answer is correct
The correct answer is A. (x-4). (x-2 +2x-24=(x-4)(x+6)). Therefore (x-4) is a factor.
Step 3
Exam Tip
(x-2 +2x-24=(x-4)(x+6)) है। इसलिए (x-4) एक गुणनखंड है।
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यदि (p(x)=x-2 -12x+35), तो \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}\) क्या है, जहाँ \(\alpha,\beta\) शून्यक हैं?
If (p(x)=x-2 -12x+35), what is \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}\), where \(\alpha,\beta\) are zeroes?
#zeroes
#reciprocal-expression
#expert
A \(\frac{5}{12}\)
B \(\frac{6}{11}\)
C \(\frac{12}{5}\)
D \(\frac{11}{24}\)
Explanation opens after your attempt
Correct Answer
D. \(\frac{11}{24}\)
Step 1
Concept
\(\alpha+\beta=12\) and \(\alpha\beta=35\). \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}=\frac{\alpha+\beta-2}{\alpha\beta-\alpha-\beta+1}=\frac{10}{24}=\frac{5}{12}\).
Step 2
Why this answer is correct
The correct answer is D. \(\frac{11}{24}\). \(\alpha+\beta=12\) and \(\alpha\beta=35\). \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}=\frac{\alpha+\beta-2}{\alpha\beta-\alpha-\beta+1}=\frac{10}{24}=\frac{5}{12}\).
Step 3
Exam Tip
\(\alpha+\beta=12\) और \(\alpha\beta=35\) हैं। \(\frac{1}{\alpha-1}+\frac{1}{\beta-1}=\frac{\alpha+\beta-2}{\alpha\beta-\alpha-\beta+1}=\frac{10}{24}=\frac{5}{12}\)।
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यदि (p(x)=x-3 +px-2 +qx+15) के शून्यक (-1,3,-5) हैं, तो (p+q) क्या है?
If the zeroes of (p(x)=x-3 +px-2 +qx+15) are (-1,3,-5), what is (p+q)?
#cubic-zeroes
#coefficients
#trap
A (0)
B (2)
C -(2)
D (4)
Explanation opens after your attempt
Step 1
Concept
The sum of zeroes is (-3), so (p=3). The pairwise product sum is (-3+5-15=-13), so (q=-13) and (p+q=-10).
Step 2
Why this answer is correct
The correct answer is B. (2). The sum of zeroes is (-3), so (p=3). The pairwise product sum is (-3+5-15=-13), so (q=-13) and (p+q=-10).
Step 3
Exam Tip
शून्यकों का योग (-3) है, इसलिए (p=3)। युग्म गुणनफलों का योग (-3+5-15=-13), इसलिए (q=-13) और (p+q=-10)।
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यदि (p(x)=x-2 +4x+4), तो (p(-2+h)) का मान क्या है?
If (p(x)=x-2 +4x+4), what is the value of (p(-2+h))?
#substitution
#identity
#polynomial
A \(h^2\)
B (h)
C \(h^2+4\)
D (2h)
Explanation opens after your attempt
Correct Answer
A. \(h^2\)
Step 1
Concept
(p(x)=(x+2)2 ), so (p(-2+h)=h-2 ). Perfect square form makes substitution easier.
Step 2
Why this answer is correct
The correct answer is A. \(h^2\). (p(x)=(x+2)2 ), so (p(-2+h)=h-2 ). Perfect square form makes substitution easier.
Step 3
Exam Tip
(p(x)=(x+2)2 ), इसलिए (p(-2+h)=h-2 )। पूर्ण वर्ग रूप से प्रतिस्थापन आसान हो जाता है।
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यदि (x=2) पर (p(x)=x-3 +mx-10) का मान (0) है, तो (m) क्या है?
If the value of (p(x)=x-3 +mx-10) at (x=2) is (0), what is (m)?
#evaluation
#parameter
#cubic
A (1)
B -(1)
C (2)
D -(2)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8+2m-10=0). This gives (2m=2) and (m=1).
Step 2
Why this answer is correct
The correct answer is A. (1). (p(2)=8+2m-10=0). This gives (2m=2) and (m=1).
Step 3
Exam Tip
(p(2)=8+2m-10=0) है। इससे (2m=2) और (m=1) मिलता है।
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यदि (p(x)=2x-2 -7x+5), तो शून्यकों के योग और गुणनफल का अंतर क्या है?
If (p(x)=2x-2 -7x+5), what is the difference between the sum and product of its zeroes?
#sum-product
#quadratic
#zeroes
A (1)
B (2)
C \(\frac{1}{2}\)
D (3)
Explanation opens after your attempt
Step 1
Concept
The sum is \(\frac{7}{2}\) and the product is \(\frac{5}{2}\). Their difference is \(\frac{7}{2}-\frac{5}{2}=1\).
Step 2
Why this answer is correct
The correct answer is A. (1). The sum is \(\frac{7}{2}\) and the product is \(\frac{5}{2}\). Their difference is \(\frac{7}{2}-\frac{5}{2}=1\).
Step 3
Exam Tip
योग \(\frac{7}{2}\) और गुणनफल \(\frac{5}{2}\) है। उनका अंतर \(\frac{7}{2}-\frac{5}{2}=1\) है।
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यदि (p(x)=x-2 -kx+36) के शून्यक धनात्मक और अनुपात (1:4) में हैं, तो (k) क्या है?
If the zeroes of (p(x)=x-2 -kx+36) are positive and in the ratio (1:4), what is (k)?
#ratio-zeroes
#parameter
#quadratic
A (15)
B (12)
C (9)
D (18)
Explanation opens after your attempt
Step 1
Concept
Let the zeroes be (t) and (4t), then \(4t^2=36\) gives (t=3). The sum is (15), so (k=15).
Step 2
Why this answer is correct
The correct answer is A. (15). Let the zeroes be (t) and (4t), then \(4t^2=36\) gives (t=3). The sum is (15), so (k=15).
Step 3
Exam Tip
शून्यक (t) और (4t) मानें, तो \(4t^2=36\) से (t=3) है। योग (15) है, इसलिए (k=15)।
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यदि (p(x)=ax-2 +bx+c) और (p(1)=p(2)=p(3)=0), तो कौन-सा निष्कर्ष सही है?
If (p(x)=ax-2 +bx+c) and (p(1)=p(2)=p(3)=0), which conclusion is correct?
#degree
#number-of-zeroes
#concept
A (p(x)) शून्य बहुपद है / (p(x)) is the zero polynomial
B (p(x)) रेखीय बहुपद है / (p(x)) is a linear polynomial
C (a=1) है / (a=1)
D (c=3) है / (c=3)
Explanation opens after your attempt
Correct Answer
A. (p(x)) शून्य बहुपद है / (p(x)) is the zero polynomial
Step 1
Concept
A polynomial of degree at most (2) can have three distinct zeroes only if it is the zero polynomial. A non-zero polynomial cannot have more distinct zeroes than its degree.
Step 2
Why this answer is correct
The correct answer is A. (p(x)) शून्य बहुपद है / (p(x)) is the zero polynomial. A polynomial of degree at most (2) can have three distinct zeroes only if it is the zero polynomial. A non-zero polynomial cannot have more distinct zeroes than its degree.
Step 3
Exam Tip
अधिकतम द्विघात बहुपद के तीन अलग-अलग शून्यक तभी हो सकते हैं जब वह शून्य बहुपद हो। घात से अधिक अलग शून्यक असंभव होते हैं।
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यदि (p(x)=x-2 -5x+6), तो (p(2)+p(3)) का मान क्या है?
If (p(x)=x-2 -5x+6), what is the value of (p(2)+p(3))?
#evaluation
#zeroes
#quadratic
A (0)
B (1)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(2) and (3) are zeroes of (p(x)), so (p(2)=0) and (p(3)=0). Hence the sum is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). (2) and (3) are zeroes of (p(x)), so (p(2)=0) and (p(3)=0). Hence the sum is (0).
Step 3
Exam Tip
(2) और (3), (p(x)) के शून्यक हैं, इसलिए (p(2)=0) और (p(3)=0)। इसलिए योग (0) है।
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यदि (p(x)=x-2 -2x-8), तो (p(x+3)) के शून्यक कौन-से हैं?
If (p(x)=x-2 -2x-8), what are the zeroes of (p(x+3))?
#transformed-zeroes
#quadratic
#expert
A -(5,1)
B -(1,5)
C (2,-4)
D -(3,3)
Explanation opens after your attempt
Step 1
Concept
The zeroes of (p(x)) are (4) and (-2). From (x+3=4) or (x+3=-2), the zeroes are (1) and (-5).
Step 2
Why this answer is correct
The correct answer is A. -(5,1). The zeroes of (p(x)) are (4) and (-2). From (x+3=4) or (x+3=-2), the zeroes are (1) and (-5).
Step 3
Exam Tip
(p(x)) के शून्यक (4) और (-2) हैं। (x+3=4) या (x+3=-2) से शून्यक (1) और (-5) मिलते हैं।
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यदि (p(x)=x-3 -9x), तो इसके कितने भिन्न वास्तविक शून्यक हैं?
If (p(x)=x-3 -9x), how many distinct real zeroes does it have?
#distinct-zeroes
#cubic
#factorisation
A (3)
B (2)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
(x-3 -9x=x(x-3)(x+3)), so the zeroes are (-3,0,3). Hence there are (3) distinct real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (3). (x-3 -9x=x(x-3)(x+3)), so the zeroes are (-3,0,3). Hence there are (3) distinct real zeroes.
Step 3
Exam Tip
(x-3 -9x=x(x-3)(x+3)), इसलिए शून्यक (-3,0,3) हैं। अतः भिन्न वास्तविक शून्यक (3) हैं।
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यदि (p(x)=x-3 +ax-2 +bx-12) के शून्यक (1,3,-4) हैं, तो (a+b) क्या है?
If the zeroes of (p(x)=x-3 +ax-2 +bx-12) are (1,3,-4), what is (a+b)?
#cubic-zeroes
#coefficients
#expert
A -(9)
B (9)
C -(7)
D (7)
Explanation opens after your attempt
Step 1
Concept
The sum (1+3-4=0), so (a=0). The sum of pairwise products is (3-4-12=-13), so (b=-13) and (a+b=-13).
Step 2
Why this answer is correct
The correct answer is A. -(9). The sum (1+3-4=0), so (a=0). The sum of pairwise products is (3-4-12=-13), so (b=-13) and (a+b=-13).
Step 3
Exam Tip
योग (1+3-4=0) है, इसलिए (a=0)। युग्म गुणनफलों का योग (3-4-12=-13), इसलिए (b=-13) और (a+b=-13)।
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यदि (p(x)=x-4 -5x-2 +4), तो इसके वास्तविक शून्यक कौन-से हैं?
If (p(x)=x-4 -5x-2 +4), what are its real zeroes?
#quartic
#biquadratic
#zeroes
A -(2,-1,1,2)
B -(4,-1,1,4)
C -(2,0,1,2)
D -(1,1)
Explanation opens after your attempt
Correct Answer
A. -(2,-1,1,2)
Step 1
Concept
(x-4 -5x-2 +4=\(x^2-1\)\(x^2-4\)). Therefore the real zeroes are (-2,-1,1,2).
Step 2
Why this answer is correct
The correct answer is A. -(2,-1,1,2). (x-4 -5x-2 +4=\(x^2-1\)\(x^2-4\)). Therefore the real zeroes are (-2,-1,1,2).
Step 3
Exam Tip
(x-4 -5x-2 +4=\(x^2-1\)\(x^2-4\)) है। इसलिए वास्तविक शून्यक (-2,-1,1,2) हैं।
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यदि (p(x)=4x-2 -4x+1), तो इसके शून्यक क्या हैं?
If (p(x)=4x-2 -4x+1), what are its zeroes?
#equal-zeroes
#perfect-square
#quadratic
A \(\frac{1}{2},\frac{1}{2}\)
B (1,1)
C -\(\frac{1}{2},-\frac{1}{2}\)
D (2,2)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2},\frac{1}{2}\)
Step 1
Concept
(4x-2 -4x+1=(2x-1)2 ), so the zero \(\frac{1}{2}\) occurs twice. Perfect square form gives equal zeroes directly.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2},\frac{1}{2}\). (4x-2 -4x+1=(2x-1)2 ), so the zero \(\frac{1}{2}\) occurs twice. Perfect square form gives equal zeroes directly.
Step 3
Exam Tip
(4x-2 -4x+1=(2x-1)2 ), इसलिए शून्यक \(\frac{1}{2}\) दो बार है। पूर्ण वर्ग रूप तुरंत समान शून्यक देता है।
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यदि (p(x)=2x-2 +mx+18) का एक शून्यक (3) है, तो दूसरा शून्यक क्या है?
If one zero of (p(x)=2x-2 +mx+18) is (3), what is the other zero?
#one-zero-given
#product-zeroes
#quadratic
A (3)
B -(3)
C (6)
D -(6)
Explanation opens after your attempt
Step 1
Concept
The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The product is \(\frac{18}{2}=9\). Since one zero is (3), the other is (3).
Step 3
Exam Tip
गुणनफल \(\frac{18}{2}=9\) है। एक शून्यक (3) है, इसलिए दूसरा (3) होगा।
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यदि (p(x)=x-2 -3x-28), तो (p(x)) के शून्यकों के मध्य दूरी क्या है?
If (p(x)=x-2 -3x-28), what is the distance between its zeroes?
#zeroes
#distance
#factorisation
A (11)
B (7)
C (4)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(x)=(x-7)(x+4)), so the zeroes are (7) and (-4). The distance is (|7-(-4)|=11).
Step 2
Why this answer is correct
The correct answer is A. (11). (p(x)=(x-7)(x+4)), so the zeroes are (7) and (-4). The distance is (|7-(-4)|=11).
Step 3
Exam Tip
(p(x)=(x-7)(x+4)), इसलिए शून्यक (7) और (-4) हैं। दूरी (|7-(-4)|=11) है।
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यदि (p(x)=x-2 -11x+30) और (q(x)=p(x-2)), तो (q(x)) के शून्यक कौन-से हैं?
If (p(x)=x-2 -11x+30) and (q(x)=p(x-2)), what are the zeroes of (q(x))?
#transformed-zeroes
#polynomial
#expert
A (7,8)
B (3,4)
C (5,6)
D (2,11)
Explanation opens after your attempt
Step 1
Concept
The zeroes of (p(x)) are (5) and (6). For (p(x-2)=0), (x-2=5) or (x-2=6), so the zeroes are (7,8).
Step 2
Why this answer is correct
The correct answer is A. (7,8). The zeroes of (p(x)) are (5) and (6). For (p(x-2)=0), (x-2=5) or (x-2=6), so the zeroes are (7,8).
Step 3
Exam Tip
(p(x)) के शून्यक (5) और (6) हैं। (p(x-2)=0) के लिए (x-2=5) या (x-2=6), इसलिए शून्यक (7,8) हैं।
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यदि (p(x)=x-2 +bx+16) के शून्यक परस्पर व्युत्क्रम हैं, तो (b) के बारे में क्या कहा जा सकता है?
If the zeroes of (p(x)=x-2 +bx+16) are reciprocals of each other, what can be said about (b)?
#reciprocal-zeroes
#product
#concept
A ऐसा संभव नहीं है / It is not possible
B (b=0)
C (b=16)
D (b=-16)
Explanation opens after your attempt
Correct Answer
A. ऐसा संभव नहीं है / It is not possible
Step 1
Concept
Reciprocal zeroes must have product (1). Here the product is (16), so it is not possible.
Step 2
Why this answer is correct
The correct answer is A. ऐसा संभव नहीं है / It is not possible. Reciprocal zeroes must have product (1). Here the product is (16), so it is not possible.
Step 3
Exam Tip
परस्पर व्युत्क्रम शून्यकों का गुणनफल (1) होना चाहिए। यहाँ गुणनफल (16) है, इसलिए यह संभव नहीं है।
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यदि (p(x)=3x-2 -12x+15), तो वास्तविक शून्यकों के बारे में सही निष्कर्ष क्या है?
For (p(x)=3x-2 -12x+15), what is the correct conclusion about real zeroes?
#real-zeroes
#complete-square
#quadratic
A कोई वास्तविक शून्यक नहीं / No real zeroes
B दो समान वास्तविक शून्यक / Two equal real zeroes
C दो भिन्न वास्तविक शून्यक / Two distinct real zeroes
D एक शून्यक (5) / One zero (5)
Explanation opens after your attempt
Correct Answer
A. कोई वास्तविक शून्यक नहीं / No real zeroes
Step 1
Concept
(p(x)=3\(x^2-4x+5\)=3((x-2)2 +1)), which is always positive. Hence there are no real zeroes.
Step 2
Why this answer is correct
The correct answer is A. कोई वास्तविक शून्यक नहीं / No real zeroes. (p(x)=3\(x^2-4x+5\)=3((x-2)2 +1)), which is always positive. Hence there are no real zeroes.
Step 3
Exam Tip
(p(x)=3\(x^2-4x+5\)=3((x-2)2 +1)), जो सदा धनात्मक है। इसलिए कोई वास्तविक शून्यक नहीं है।
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यदि (p(x)=x-3 -6x-2 +12x-8), तो (p(x)) का शून्यक किस गुणनता के साथ है?
If (p(x)=x-3 -6x-2 +12x-8), what is the zero of (p(x)) with its multiplicity?
#multiplicity
#cubic
#identity
A (2) गुणनता (3) / (2) with multiplicity (3)
B (3) गुणनता (2) / (3) with multiplicity (2)
C -(2) गुणनता (3) / (-2) with multiplicity (3)
D (1) गुणनता (3) / (1) with multiplicity (3)
Explanation opens after your attempt
Correct Answer
A. (2) गुणनता (3) / (2) with multiplicity (3)
Step 1
Concept
This is (p(x)=(x-2)3 ), so (2) is a zero three times. Recognizing cube identities is useful.
Step 2
Why this answer is correct
The correct answer is A. (2) गुणनता (3) / (2) with multiplicity (3). This is (p(x)=(x-2)3 ), so (2) is a zero three times. Recognizing cube identities is useful.
Step 3
Exam Tip
यह (p(x)=(x-2)3 ) है, इसलिए (2) तीन बार शून्यक है। घन पूर्ण पहचान को पहचानना उपयोगी है।
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यदि किसी द्विघात बहुपद के शून्यक \(2+\sqrt{3}\) और \(2-\sqrt{3}\) हैं, तो मोनिक बहुपद कौन-सा है?
If the zeroes of a quadratic polynomial are \(2+\sqrt{3}\) and \(2-\sqrt{3}\), which is the monic polynomial?
#construct-polynomial
#surd-zeroes
#quadratic
A \(x^2-4x+1\)
B \(x^2+4x+1\)
C \(x^2-2x+3\)
D \(x^2-4x+7\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x+1\)
Step 1
Concept
The sum is (4) and the product is (1). Therefore the monic polynomial is \(x^2-4x+1\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x+1\). The sum is (4) and the product is (1). Therefore the monic polynomial is \(x^2-4x+1\).
Step 3
Exam Tip
योग (4) और गुणनफल (1) है। अतः मोनिक बहुपद \(x^2-4x+1\) होगा।
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यदि (p(x)=x-2 -4x+1), तो शून्यकों के व्युत्क्रमों का योग क्या है?
If (p(x)=x-2 -4x+1), what is the sum of reciprocals of its zeroes?
#reciprocal-zeroes
#quadratic
#formula
A (4)
B (1)
C (-4)
D \(\frac{1}{4}\)
Explanation opens after your attempt
Step 1
Concept
The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here \(\alpha+\beta=4\) and \(\alpha\beta=1\), so the answer is (4).
Step 2
Why this answer is correct
The correct answer is A. (4). The sum of reciprocals is \(\frac{\alpha+\beta}{\alpha\beta}\). Here \(\alpha+\beta=4\) and \(\alpha\beta=1\), so the answer is (4).
Step 3
Exam Tip
शून्यकों के व्युत्क्रमों का योग \(\frac{\alpha+\beta}{\alpha\beta}\) होता है। यहाँ \(\alpha+\beta=4\) और \(\alpha\beta=1\), इसलिए उत्तर (4) है।
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यदि \(\alpha,\beta\), \(x^2-9x+20\) के शून्यक हैं, तो (\(\alpha+2\)\(\beta+2\)) का मान क्या है?
If \(\alpha,\beta\) are zeroes of \(x^2-9x+20\), what is the value of (\(\alpha+2\)\(\beta+2\))?
#zeroes
#algebraic-expression
#quadratic
A (42)
B (38)
C (31)
D (24)
Explanation opens after your attempt
Step 1
Concept
\(\alpha+\beta=9\) and \(\alpha\beta=20\). (\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4=20+18+4=42).
Step 2
Why this answer is correct
The correct answer is A. (42). \(\alpha+\beta=9\) and \(\alpha\beta=20\). (\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4=20+18+4=42).
Step 3
Exam Tip
\(\alpha+\beta=9\) और \(\alpha\beta=20\) हैं। (\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4=20+18+4=42)।
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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)=x-3 -4x-2 -7x+10) और (x-1) इसका गुणनखंड है, तो शेष द्विघात गुणनखंड क्या है?
If (p(x)=x-3 -4x-2 -7x+10) and (x-1) is a factor, what is the remaining quadratic factor?
#division
#factorisation
#cubic
A \(x^2-3x-10\)
B \(x^2+3x-10\)
C \(x^2-5x+10\)
D \(x^2-4x-7\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x-10\)
Step 1
Concept
Dividing (p(x)) by (x-1) gives \(x^2-3x-10\). Verify by multiplying ((x-1)\(x^2-3x-10\)=p(x)).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x-10\). Dividing (p(x)) by (x-1) gives \(x^2-3x-10\). Verify by multiplying ((x-1)\(x^2-3x-10\)=p(x)).
Step 3
Exam Tip
(p(x)) को (x-1) से भाग देने पर \(x^2-3x-10\) मिलता है। गुणा करके जाँचें कि ((x-1)\(x^2-3x-10\)=p(x))।
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यदि (p(x)=2x-2 -5x-3), तो \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\) क्या है, जहाँ \(\alpha,\beta\) शून्यक हैं?
If (p(x)=2x-2 -5x-3), what is \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha}\), where \(\alpha,\beta\) are zeroes?
#zeroes
#ratio-expression
#expert
A -\(\frac{37}{6}\)
B \(\frac{37}{6}\)
C -\(\frac{25}{6}\)
D \(\frac{25}{6}\)
Explanation opens after your attempt
Correct Answer
A. -\(\frac{37}{6}\)
Step 1
Concept
\(\alpha+\beta=\frac{5}{2}\) and \(\alpha\beta=-\frac{3}{2}\). (\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\(\alpha+\beta\)2 -2\alpha\beta}{\alpha\beta}=-\frac{37}{6}).
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{37}{6}\). \(\alpha+\beta=\frac{5}{2}\) and \(\alpha\beta=-\frac{3}{2}\). (\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\(\alpha+\beta\)2 -2\alpha\beta}{\alpha\beta}=-\frac{37}{6}).
Step 3
Exam Tip
\(\alpha+\beta=\frac{5}{2}\) और \(\alpha\beta=-\frac{3}{2}\) हैं। (\frac{\alpha}{\beta}+\frac{\beta}{\alpha}=\frac{\(\alpha+\beta\)2 -2\alpha\beta}{\alpha\beta}=-\frac{37}{6})।
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यदि (p(x)=x-2 -6x+s) का एक शून्यक दूसरे से (2) अधिक है, तो (s) का मान क्या है?
If one zero of (p(x)=x-2 -6x+s) is (2) more than the other, what is (s)?
#zeroes
#difference
#parameter
A (8)
B (9)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
Let the zeroes be (t) and (t+2), then (2t+2=6) gives (t=2). The product is \(2\cdot4=8\), so (s=8).
Step 2
Why this answer is correct
The correct answer is A. (8). Let the zeroes be (t) and (t+2), then (2t+2=6) gives (t=2). The product is \(2\cdot4=8\), so (s=8).
Step 3
Exam Tip
शून्यक (t) और (t+2) मानें, तो (2t+2=6) से (t=2)। गुणनफल \(2\cdot4=8\), इसलिए (s=8)।
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यदि (x=2) और (x=-3), (p(x)=ax-2 +bx+c) के शून्यक हैं, तो \(\frac{c}{a}\) क्या है?
If (x=2) and (x=-3) are zeroes of (p(x)=ax-2 +bx+c), what is \(\frac{c}{a}\)?
#zeroes
#coefficient-relation
#quadratic
A -(6)
B (6)
C -(1)
D (1)
Explanation opens after your attempt
Step 1
Concept
The product of zeroes is (2\cdot(-3)=-6), and it equals \(\frac{c}{a}\). Pay special attention to the sign in products.
Step 2
Why this answer is correct
The correct answer is A. -(6). The product of zeroes is (2\cdot(-3)=-6), and it equals \(\frac{c}{a}\). Pay special attention to the sign in products.
Step 3
Exam Tip
शून्यकों का गुणनफल (2\cdot(-3)=-6) है और यह \(\frac{c}{a}\) के बराबर होता है। गुणनफल में संकेत पर विशेष ध्यान दें।
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यदि (p(x)=x-3 -2x-2 -13x-10) है, तो इनमें से कौन (p(x)) का शून्यक है?
If (p(x)=x-3 -2x-2 -13x-10), which of the following is a zero of (p(x))?
#zero-test
#cubic
#polynomial
A (5)
B (2)
C -(1)
D -(2)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.
Step 2
Why this answer is correct
The correct answer is D. -(2). (p(-2)=-8-8+26-10=0), so (-2) is a zero. Test small option values by direct substitution.
Step 3
Exam Tip
(p(-2)=-8-8+26-10=0), इसलिए (-2) शून्यक है। विकल्पों में दिए छोटे मानों को सीधे रखकर जाँचें।
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यदि \(\alpha\) और \(\beta\), \(3x^2-10x+7\) के शून्यक हैं, तो \(\alpha^2+\beta^2\) का मान क्या है?
If \(\alpha\) and \(\beta\) are zeroes of \(3x^2-10x+7\), what is the value of \(\alpha^2+\beta^2\)?
#zeroes
#identity
#quadratic
A \(\frac{58}{9}\)
B \(\frac{100}{9}\)
C \(\frac{14}{3}\)
D \(\frac{49}{9}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{58}{9}\)
Step 1
Concept
Here \(\alpha+\beta=\frac{10}{3}\) and \(\alpha\beta=\frac{7}{3}\). Hence (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=\frac{100}{9}-\frac{14}{3}=\frac{58}{9}).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{58}{9}\). Here \(\alpha+\beta=\frac{10}{3}\) and \(\alpha\beta=\frac{7}{3}\). Hence (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=\frac{100}{9}-\frac{14}{3}=\frac{58}{9}).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=\frac{10}{3}\) और \(\alpha\beta=\frac{7}{3}\) हैं। इसलिए (\alpha-2 +\beta-2 =\(\alpha+\beta\)2 -2\alpha\beta=\frac{100}{9}-\frac{14}{3}=\frac{58}{9})।
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यदि (p(x)=x-2 +rx+9) के दोनों शून्यक समान और ऋणात्मक हैं, तो (r) का मान क्या होगा?
If both zeroes of (p(x)=x-2 +rx+9) are equal and negative, what is the value of (r)?
#equal-zeroes
#discriminant
#sign
A (6)
B (-6)
C (3)
D (-3)
Explanation opens after your attempt
Step 1
Concept
For equal zeroes, \(r^2-36=0\), so \(r=\pm6\). For negative zeroes the sum must be positive (6), hence (r=6).
Step 2
Why this answer is correct
The correct answer is A. (6). For equal zeroes, \(r^2-36=0\), so \(r=\pm6\). For negative zeroes the sum must be positive (6), hence (r=6).
Step 3
Exam Tip
समान शून्यकों के लिए \(r^2-36=0\), अतः \(r=\pm6\)। ऋणात्मक शून्यक के लिए योग धनात्मक (6) होना चाहिए, इसलिए (r=6)।
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यदि (p(x)=x-2 -(m+4)x+4m) के शून्यक (4) और (m) हैं, तो कौन-सा कथन सही है?
If the zeroes of (p(x)=x-2 -(m+4)x+4m) are (4) and (m), which statement is correct?
#zeroes
#coefficients
#concept
A यह हर वास्तविक (m) के लिए सही है / It is true for every real (m)
B यह केवल (m=4) के लिए सही है / It is true only for (m=4)
C यह केवल (m=0) के लिए सही है / It is true only for (m=0)
D यह कभी सही नहीं है / It is never true
Explanation opens after your attempt
Correct Answer
A. यह हर वास्तविक (m) के लिए सही है / It is true for every real (m)
Step 1
Concept
The sum (4+m) and product (4m) match the given polynomial. Therefore the statement is true for every real (m).
Step 2
Why this answer is correct
The correct answer is A. यह हर वास्तविक (m) के लिए सही है / It is true for every real (m). The sum (4+m) and product (4m) match the given polynomial. Therefore the statement is true for every real (m).
Step 3
Exam Tip
योग (4+m) और गुणनफल (4m) हैं, जो दिए बहुपद से मिलते हैं। इसलिए कथन हर वास्तविक (m) के लिए सही है।
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यदि (p(x)=2x-3 +kx-2 -11x+5) को (x+1) से भाग देने पर शेष (7) है, तो (k) क्या है?
If (p(x)=2x-3 +kx-2 -11x+5) leaves remainder (7) when divided by (x+1), what is (k)?
#remainder-theorem
#parameter
#trap
A (5)
B (-9)
C (-11)
D (3)
Explanation opens after your attempt
Step 1
Concept
By the remainder theorem (p(-1)=7), so (-2+k+11+5=7). This gives (k=-7), so none of the listed options is correct.
Step 2
Why this answer is correct
The correct answer is B. (-9). By the remainder theorem (p(-1)=7), so (-2+k+11+5=7). This gives (k=-7), so none of the listed options is correct.
Step 3
Exam Tip
शेष प्रमेय से (p(-1)=7), इसलिए (-2+k+11+5=7)। इससे (k=-7) नहीं बल्कि (k=-7) आता है, इसलिए विकल्पों में सही मान नहीं 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)=2x-2 -7x+3), तो (p(x+1)-p(x-1)) क्या होगा?
If (p(x)=2x-2 -7x+3), what will (p(x+1)-p(x-1)) be?
#composition
#substitution
#polynomial
A (8x-14)
B (8x+14)
C (4x-14)
D (4x+14)
Explanation opens after your attempt
Correct Answer
A. (8x-14)
Step 1
Concept
(p(x+1)=2x-2 -3x-2) and (p(x-1)=2x-2 -11x+12), so the difference is (8x-14). Substitute the whole expression in place of (x).
Step 2
Why this answer is correct
The correct answer is A. (8x-14). (p(x+1)=2x-2 -3x-2) and (p(x-1)=2x-2 -11x+12), so the difference is (8x-14). Substitute the whole expression in place of (x).
Step 3
Exam Tip
(p(x+1)=2x-2 -3x-2) और (p(x-1)=2x-2 -11x+12), इसलिए अंतर (8x-14) है। पूरे व्यंजक को (x) की जगह रखें।
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यदि (p(x)=x-3 +ax-2 +bx+20), (p(1)=0) और (p(-4)=0), तो (a-b) का मान क्या है?
If (p(x)=x-3 +ax-2 +bx+20), (p(1)=0), and (p(-4)=0), what is the value of (a-b)?
#parameter
#zeros
#cubic polynomial
A (13)
B (15)
C (17)
D (19)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a+b=-21) and (4a-b=11), so (a=-2), (b=-19), and (a-b=17). When two zeros are given, form two equations.
Step 2
Why this answer is correct
The correct answer is C. (17). The conditions give (a+b=-21) and (4a-b=11), so (a=-2), (b=-19), and (a-b=17). When two zeros are given, form two equations.
Step 3
Exam Tip
शर्तों से (a+b=-21) और (4a-b=11) मिलते हैं, इसलिए (a=-2), (b=-19) और (a-b=17)। दो शून्य दिए हों तो दो समीकरण बनाएं।
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यदि (p(x)=x-2 -8x+15), तो (p(x)-p(3)) क्या है?
If (p(x)=x-2 -8x+15), what is (p(x)-p(3))?
#evaluation
#subtraction
#polynomial
A \(x^2-8x+15\)
B \(x^2-8x+12\)
C \(x^2-8x+9\)
D \(x^2-8x\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-8x+15\)
Step 1
Concept
(p(3)=9-24+15=0), so (p(x)-p(3)=x-2 -8x+15). Find (p(3)) first.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-8x+15\). (p(3)=9-24+15=0), so (p(x)-p(3)=x-2 -8x+15). Find (p(3)) first.
Step 3
Exam Tip
(p(3)=9-24+15=0), इसलिए (p(x)-p(3)=x-2 -8x+15)। पहले (p(3)) निकालें।
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यदि (p(x)=4x-2 -3x+2), तो (p(3x)) क्या है?
If (p(x)=4x-2 -3x+2), what is (p(3x))?
#substitution
#composition
#polynomial
A \(36x^2-9x+2\)
B \(12x^2-9x+2\)
C \(36x^2-3x+2\)
D \(4x^2-9x+2\)
Explanation opens after your attempt
Correct Answer
A. \(36x^2-9x+2\)
Step 1
Concept
(p(3x)=4(3x)2 -3(3x)+2=36x-2 -9x+2). Square the whole (3x).
Step 2
Why this answer is correct
The correct answer is A. \(36x^2-9x+2\). (p(3x)=4(3x)2 -3(3x)+2=36x-2 -9x+2). Square the whole (3x).
Step 3
Exam Tip
(p(3x)=4(3x)2 -3(3x)+2=36x-2 -9x+2)। पूरे (3x) का वर्ग करें।
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यदि (p(x)=x-2 -2x+4), तो (p(x+3)) क्या होगा?
If (p(x)=x-2 -2x+4), what is (p(x+3))?
#composition
#substitution
#polynomial
A \(x^2+4x+7\)
B \(x^2+4x+9\)
C \(x^2+6x+7\)
D \(x^2+6x+9\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+4x+7\)
Step 1
Concept
(p(x+3)=(x+3)2 -2(x+3)+4=x-2 +4x+7). Substitute the whole (x+3) in place of (x).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+4x+7\). (p(x+3)=(x+3)2 -2(x+3)+4=x-2 +4x+7). Substitute the whole (x+3) in place of (x).
Step 3
Exam Tip
(p(x+3)=(x+3)2 -2(x+3)+4=x-2 +4x+7)। (x) की जगह पूरा (x+3) रखें।
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कौन सा बहुपद (x=0) को शून्य बनाता है लेकिन शून्य बहुपद नहीं है?
Which polynomial makes (x=0) a zero but is not the zero polynomial?
#zero at zero
#constant term
#polynomial
A \(x^2+9\)
B \(4x^3-7x\)
C (5)
D \(x^4+1\)
Explanation opens after your attempt
Correct Answer
B. \(4x^3-7x\)
Step 1
Concept
Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 2
Why this answer is correct
The correct answer is B. \(4x^3-7x\). Substituting (x=0) in \(4x^3-7x\) gives (0), and it is not the zero polynomial. For (x=0), the constant term must be (0).
Step 3
Exam Tip
\(4x^3-7x\) में (x=0) रखने पर (0) मिलता है और यह शून्य बहुपद नहीं है। (x=0) के लिए अचर पद (0) होना चाहिए।
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यदि (p(x)=x-5 +ax-3 +b) में (p(0)=0), तो कौन सा निष्कर्ष निश्चित है?
If (p(x)=x-5 +ax-3 +b) has (p(0)=0), which conclusion is certain?
#constant term
#zero
#evaluation
A (b=0)
B (a=0)
C (1) शून्य है / (1) is a zero
D घात (3) है / Degree is (3)
Explanation opens after your attempt
Step 1
Concept
(p(0)=b), so (p(0)=0) certainly gives (b=0). The other conclusions are not necessary.
Step 2
Why this answer is correct
The correct answer is A. (b=0). (p(0)=b), so (p(0)=0) certainly gives (b=0). The other conclusions are not necessary.
Step 3
Exam Tip
(p(0)=b) होता है, इसलिए (p(0)=0) से (b=0) निश्चित है। बाकी निष्कर्ष जरूरी नहीं हैं।
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यदि (p(x)=x-2 +px+q), (p(0)=12) और (p(3)=0), तो (p) का मान क्या है?
If (p(x)=x-2 +px+q), (p(0)=12), and (p(3)=0), what is the value of (p)?
#parameter
#quadratic
#evaluation
A (-7)
B (-6)
C (-5)
D (-4)
Explanation opens after your attempt
Step 1
Concept
(p(0)=q=12) and (p(3)=9+3p+12=0), so (3p=-21) and (p=-7). Find the constant term first.
Step 2
Why this answer is correct
The correct answer is A. (-7). (p(0)=q=12) and (p(3)=9+3p+12=0), so (3p=-21) and (p=-7). Find the constant term first.
Step 3
Exam Tip
(p(0)=q=12) और (p(3)=9+3p+12=0), इसलिए (3p=-21) और (p=-7)। पहले अचर पद निकालें।
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(p(x)=x-3 -x-2 -4x+4) में (p(2)-p(-2)) क्या है?
For (p(x)=x-3 -x-2 -4x+4), what is (p(2)-p(-2))?
#evaluation
#difference
#cubic
A (0)
B (8)
C (16)
D (24)
Explanation opens after your attempt
Step 1
Concept
(p(2)=0) and (p(-2)=-16), so (p(2)-p(-2)=16). While subtracting, the sign of the second value changes.
Step 2
Why this answer is correct
The correct answer is C. (16). (p(2)=0) and (p(-2)=-16), so (p(2)-p(-2)=16). While subtracting, the sign of the second value changes.
Step 3
Exam Tip
(p(2)=0) और (p(-2)=-16), इसलिए (p(2)-p(-2)=16)। घटाते समय दूसरे मान का संकेत बदलता है।
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(p(x)=x-3 -3x-2 -4x+12) में (p(2)) और (p(-2)) का गुणनफल क्या है?
What is the product of (p(2)) and (p(-2)) for (p(x)=x-3 -3x-2 -4x+12)?
#evaluation
#product
#cubic
A (-32)
B (0)
C (32)
D (64)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8-12-8+12=0), so the product is (0). If one value is (0), the whole product is (0).
Step 2
Why this answer is correct
The correct answer is B. (0). (p(2)=8-12-8+12=0), so the product is (0). If one value is (0), the whole product is (0).
Step 3
Exam Tip
(p(2)=8-12-8+12=0), इसलिए गुणनफल (0) होगा। एक मान (0) हो तो पूरा गुणनफल (0) होता है।
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यदि (p(x)=x-3 -6x-2 +12x-8), तो (p(5)) क्या है?
If (p(x)=x-3 -6x-2 +12x-8), what is (p(5))?
#identity
#cubic
#evaluation
A (8)
B (18)
C (27)
D (32)
Explanation opens after your attempt
Step 1
Concept
It is ((x-2)3 ), so (p(5)=(5-2)3 =27). Recognizing identities reduces calculation.
Step 2
Why this answer is correct
The correct answer is C. (27). It is ((x-2)3 ), so (p(5)=(5-2)3 =27). Recognizing identities reduces calculation.
Step 3
Exam Tip
यह ((x-2)3 ) है, इसलिए (p(5)=(5-2)3 =27)। पहचान पहचानने से गणना कम होती है।
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