100 results found for "continuous 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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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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पश्चिमी घाट को पूर्वी घाट की तुलना में अधिक निरंतर पर्वत श्रृंखला मानने का सही कारण क्या है?
What is the correct reason for considering the Western Ghats more continuous than the Eastern Ghats?
#indian geography
#western ghats
#eastern ghats
#sahyadri
#continuous range
A पश्चिमी घाट पश्चिमी तट के साथ लंबी और कम कटी हुई श्रृंखला बनाते हैं / Western Ghats form a long and less broken range along the western coast
B पश्चिमी घाट पूरी तरह गंगा मैदान में स्थित हैं / Western Ghats are completely located in the Ganga Plain
C पश्चिमी घाट हिमालय की सबसे बाहरी श्रेणी हैं / Western Ghats are the outermost range of the Himalayas
D पश्चिमी घाट केवल रेतीले टीले हैं / Western Ghats are only sandy dunes
Explanation opens after your attempt
Correct Answer
A. पश्चिमी घाट पश्चिमी तट के साथ लंबी और कम कटी हुई श्रृंखला बनाते हैं / Western Ghats form a long and less broken range along the western coast
Step 1
Concept
The Western Ghats form a relatively continuous mountain wall along the western coast while the Eastern Ghats are cut by many rivers. For exams, link the Western Ghats with Sahyadri and rainfall barrier.
Step 2
Why this answer is correct
The correct answer is A. पश्चिमी घाट पश्चिमी तट के साथ लंबी और कम कटी हुई श्रृंखला बनाते हैं / Western Ghats form a long and less broken range along the western coast. The Western Ghats form a relatively continuous mountain wall along the western coast while the Eastern Ghats are cut by many rivers. For exams, link the Western Ghats with Sahyadri and rainfall barrier.
Step 3
Exam Tip
पश्चिमी घाट पश्चिमी तट के साथ अपेक्षाकृत निरंतर पर्वत दीवार बनाते हैं जबकि पूर्वी घाट कई नदियों से कटे हैं। परीक्षा में पश्चिमी घाट को सह्याद्रि और वर्षा अवरोधक से जोड़ें।
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लगातार रेखा की पहचान क्या है?
What is the identity of a continuous line?
#continuous line
#unbroken
#line
A बीच में बहुत अंतराल / Many gaps in between
B बिना टूटे आगे बढ़ना / Moving without break
C केवल बिंदु होना / Being only dots
D रंगहीन होना / Being colourless
Explanation opens after your attempt
Correct Answer
B. बिना टूटे आगे बढ़ना / Moving without break
Step 1
Concept
A continuous line moves without stopping. Exam tip: understand continuous line as unbroken mark.
Step 2
Why this answer is correct
The correct answer is B. बिना टूटे आगे बढ़ना / Moving without break. A continuous line moves without stopping. Exam tip: understand continuous line as unbroken mark.
Step 3
Exam Tip
लगातार रेखा बिना रुके चलती है। परीक्षा में continuous line को unbroken mark समझें।
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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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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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पूर्वी घाट के असतत स्वरूप और पश्चिमी घाट के निरंतर स्वरूप को किससे समझा जा सकता है?
How can the discontinuous nature of Eastern Ghats and continuous nature of Western Ghats be understood?
#indian geography
#eastern ghats
#western ghats
#river cutting
A नदी कटाव और तटीय समानांतरता से / By river cutting and coastal parallelism
B समुद्री प्रवाल निर्माण से / By marine coral formation
C हिमनदी जमाव से / By glacial deposition
D रेगिस्तानी बालू से / By desert sand
Explanation opens after your attempt
Correct Answer
A. नदी कटाव और तटीय समानांतरता से / By river cutting and coastal parallelism
Step 1
Concept
The Eastern Ghats are cut by many rivers while the Western Ghats are more continuous parallel to the coast. For exams, remember their comparison separately.
Step 2
Why this answer is correct
The correct answer is A. नदी कटाव और तटीय समानांतरता से / By river cutting and coastal parallelism. The Eastern Ghats are cut by many rivers while the Western Ghats are more continuous parallel to the coast. For exams, remember their comparison separately.
Step 3
Exam Tip
पूर्वी घाट कई नदियों से कटे हैं जबकि पश्चिमी घाट तट के समानांतर अधिक निरंतर हैं। परीक्षा में दोनों की तुलना अलग-अलग याद रखें।
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पश्चिमी घाट की ऊंचाई सामान्यतः किस घाट की तुलना में अधिक निरंतर है?
The height of the Western Ghats is generally more continuous compared to which Ghats?
#indian geography
#western ghats
#eastern ghats
#rainfall barrier
A हिमालय / Himalayas
B पूर्वी घाट / Eastern Ghats
C अरावली / Aravalli
D शिवालिक / Shiwalik
Explanation opens after your attempt
Correct Answer
B. पूर्वी घाट / Eastern Ghats
Step 1
Concept
The Western Ghats are more continuous and wall-like than the Eastern Ghats. For exams, remember them as a rainfall barrier.
Step 2
Why this answer is correct
The correct answer is B. पूर्वी घाट / Eastern Ghats. The Western Ghats are more continuous and wall-like than the Eastern Ghats. For exams, remember them as a rainfall barrier.
Step 3
Exam Tip
पश्चिमी घाट पूर्वी घाट की तुलना में अधिक निरंतर और स्पष्ट पर्वतीय दीवार जैसे हैं। परीक्षा में पश्चिमी घाट को वर्षा अवरोधक के रूप में याद रखें।
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हिमाद्रि को हिमालय की सबसे ऊंची और सतत श्रेणी कहने का मुख्य कारण क्या है?
What is the main reason for calling Himadri the highest and most continuous Himalayan range?
#himadri
#greater-himalaya
#glaciers
A इसमें उच्च शिखर और व्यापक हिमनद मिलते हैं / It has high peaks and extensive glaciers
B यह समुद्री प्रवालों से बनी है / It is made of marine corals
C यह केवल नई जलोढ़ मिट्टी है / It is only new alluvial soil
D यह थार की पवनों से बनी है / It is formed by winds of Thar
Explanation opens after your attempt
Correct Answer
A. इसमें उच्च शिखर और व्यापक हिमनद मिलते हैं / It has high peaks and extensive glaciers
Step 1
Concept
Himadri is an inner Himalayan range with high peaks and glaciers. For exams remember the Himadri and perennial river source link.
Step 2
Why this answer is correct
The correct answer is A. इसमें उच्च शिखर और व्यापक हिमनद मिलते हैं / It has high peaks and extensive glaciers. Himadri is an inner Himalayan range with high peaks and glaciers. For exams remember the Himadri and perennial river source link.
Step 3
Exam Tip
हिमाद्रि ऊंचे शिखरों और हिमनदों वाली आंतरिक हिमालयी श्रेणी है। परीक्षा में हिमाद्रि और बारहमासी नदी स्रोत संबंध याद रखें।
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पश्चिमी घाट की निरंतर ऊंची दीवार जैसा स्वरूप मानसून को किस प्रकार प्रभावित करता है?
How does the continuous high wall like form of Western Ghats affect the monsoon?
#western-ghats
#monsoon
#rain-shadow
A नम पवनों को ऊपर उठाकर पवनाभिमुख वर्षा और पवनविमुख वर्षाछाया बनाता है / It lifts moist winds causing windward rain and leeward rain shadow
B सभी पवनों को हिमालय की ओर लौटा देता है / It sends all winds back to Himalaya
C पूर्वी तट पर प्रवाल बनाता है / It forms corals on eastern coast
D थार में बर्फ गिराता है / It causes snow in Thar
Explanation opens after your attempt
Correct Answer
A. नम पवनों को ऊपर उठाकर पवनाभिमुख वर्षा और पवनविमुख वर्षाछाया बनाता है / It lifts moist winds causing windward rain and leeward rain shadow
Step 1
Concept
Western Ghats influence both orographic rainfall and rain shadow. For exams remember windward and leeward slopes.
Step 2
Why this answer is correct
The correct answer is A. नम पवनों को ऊपर उठाकर पवनाभिमुख वर्षा और पवनविमुख वर्षाछाया बनाता है / It lifts moist winds causing windward rain and leeward rain shadow. Western Ghats influence both orographic rainfall and rain shadow. For exams remember windward and leeward slopes.
Step 3
Exam Tip
पश्चिमी घाट ओरोग्राफिक वर्षा और वर्षाछाया दोनों को प्रभावित करते हैं। परीक्षा में पवनाभिमुख और पवनविमुख ढाल याद रखें।
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पश्चिमी घाटों की निरंतर और ऊंची स्थिति किस जलवायु प्रक्रिया को अधिक प्रभावी बनाती है?
The continuous and high position of the Western Ghats makes which climatic process more effective?
#western-ghats
#orographic-rainfall
#monsoon
A ओरोग्राफिक वर्षा / Orographic rainfall
B लवणीय दलदल निर्माण / Saline marsh formation
C प्रवाल विरंजन / Coral bleaching
D हिमनदी संचयन / Glacial accumulation
Explanation opens after your attempt
Correct Answer
A. ओरोग्राफिक वर्षा / Orographic rainfall
Step 1
Concept
Western Ghats force moist monsoon winds upward and cause rainfall. For exams remember windward and leeward slopes.
Step 2
Why this answer is correct
The correct answer is A. ओरोग्राफिक वर्षा / Orographic rainfall. Western Ghats force moist monsoon winds upward and cause rainfall. For exams remember windward and leeward slopes.
Step 3
Exam Tip
पश्चिमी घाट नम मानसूनी पवनों को ऊपर उठाकर वर्षा कराते हैं। परीक्षा में पवनाभिमुख और पवनविमुख ढाल याद रखें।
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पश्चिमी घाट और पूर्वी घाट में से कौन अधिक सतत माना जाता है?
Which is considered more continuous Western Ghats or Eastern Ghats?
#western-ghats
#eastern-ghats
#comparison
A पश्चिमी घाट / Western Ghats
B पूर्वी घाट / Eastern Ghats
C दोनों समान रूप से टूटे हुए / Both equally broken
D दोनों समुद्र में हैं / Both are in the sea
Explanation opens after your attempt
Correct Answer
A. पश्चिमी घाट / Western Ghats
Step 1
Concept
Western Ghats are more continuous than Eastern Ghats. For exams remember Eastern Ghats are cut by rivers.
Step 2
Why this answer is correct
The correct answer is A. पश्चिमी घाट / Western Ghats. Western Ghats are more continuous than Eastern Ghats. For exams remember Eastern Ghats are cut by rivers.
Step 3
Exam Tip
पश्चिमी घाट पूर्वी घाट की तुलना में अधिक सतत हैं। परीक्षा में पूर्वी घाट को नदियों से कटा हुआ याद रखें।
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यदि (p(-1)>0) और (p(4)<0), तो निरंतर बहुपद आलेख के लिए कौन सा कथन उचित है?
If (p(-1)>0) and (p(4)<0), which statement is suitable for a continuous polynomial graph?
#sign change zero graph
A (-1) और (4) दोनों शून्यक हैं / Both (-1) and (4) are zeroes
B बीच में कम से कम एक (x)-अक्ष कटान हो सकता है / There may be at least one (x)-axis intersection between them
C कोई कटान संभव नहीं है / No intersection is possible
D आलेख केवल (y)-अक्ष को काटेगा / The graph will cut only the (y)-axis
Explanation opens after your attempt
Correct Answer
B. बीच में कम से कम एक (x)-अक्ष कटान हो सकता है / There may be at least one (x)-axis intersection between them
Step 1
Concept
A sign change suggests (p(x)=0) in between. Tip: a polynomial graph does not break.
Step 2
Why this answer is correct
The correct answer is B. बीच में कम से कम एक (x)-अक्ष कटान हो सकता है / There may be at least one (x)-axis intersection between them. A sign change suggests (p(x)=0) in between. Tip: a polynomial graph does not break.
Step 3
Exam Tip
चिह्न बदलने से बीच में (p(x)=0) होने का संकेत मिलता है। टिप: बहुपद आलेख टूटता नहीं है।
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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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यदि (p(x)=x-2 +kx+25) पूर्ण वर्ग बहुपद है और (k<0), तो (k) क्या है?
If (p(x)=x-2 +kx+25) is a perfect square polynomial and (k<0), what is (k)?
#perfect square
#parameter
#quadratic
A (-10)
B (-5)
C (5)
D (10)
Explanation opens after your attempt
Step 1
Concept
For (x-2 +kx+25=(x-5)2 ), (k=-10). In a perfect square, the middle term is (2ab).
Step 2
Why this answer is correct
The correct answer is A. (-10). For (x-2 +kx+25=(x-5)2 ), (k=-10). In a perfect square, the middle term is (2ab).
Step 3
Exam Tip
(x-2 +kx+25=(x-5)2 ) होने पर (k=-10)। पूर्ण वर्ग में मध्य पद (2ab) होता है।
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(p(x)=x-2 +14x+53) का न्यूनतम मान क्या है?
What is the minimum value of (p(x)=x-2 +14x+53)?
#quadratic
#minimum
#value
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(x-2 +14x+53=(x+7)2 +4), so the minimum value is (4). A square term is never negative.
Step 2
Why this answer is correct
The correct answer is B. (4). (x-2 +14x+53=(x+7)2 +4), so the minimum value is (4). A square term is never negative.
Step 3
Exam Tip
(x-2 +14x+53=(x+7)2 +4), इसलिए न्यूनतम मान (4) है। वर्ग पद कभी ऋणात्मक नहीं होता।
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(p(x)=x-2 -12x+40) का न्यूनतम मान किस (x) पर आता है?
At which (x) does (p(x)=x-2 -12x+40) attain its minimum value?
#quadratic
#minimum
#completing square
A (x=4)
B (x=5)
C (x=6)
D (x=12)
Explanation opens after your attempt
Step 1
Concept
(x-2 -12x+40=(x-6)2 +4), so the minimum occurs at (x=6). Completing the square is useful.
Step 2
Why this answer is correct
The correct answer is C. (x=6). (x-2 -12x+40=(x-6)2 +4), so the minimum occurs at (x=6). Completing the square is useful.
Step 3
Exam Tip
(x-2 -12x+40=(x-6)2 +4), इसलिए न्यूनतम (x=6) पर आता है। वर्ग पूर्ण करना उपयोगी तरीका है।
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यदि (p(x)=3x-3 -12x), तो (p(-2)+p(2)) का मान क्या है?
If (p(x)=3x-3 -12x), what is the value of (p(-2)+p(2))?
#evaluation
#opposite inputs
#cubic
A (-24)
B (0)
C (24)
D (48)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=0) and (p(2)=0), so the sum is (0). Handle signs carefully for opposite inputs.
Step 2
Why this answer is correct
The correct answer is B. (0). (p(-2)=0) and (p(2)=0), so the sum is (0). Handle signs carefully for opposite inputs.
Step 3
Exam Tip
(p(-2)=0) और (p(2)=0), इसलिए योग (0) है। विपरीत मानों पर संकेतों को सावधानी से रखें।
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यदि (p(x)=5x-2 -4x+3), तो (p(x)+p(-x)) क्या होगा?
If (p(x)=5x-2 -4x+3), what is (p(x)+p(-x))?
#polynomial transformation
#even odd terms
#evaluation
A \(10x^2+6\)
B \(10x^2-8x+6\)
C \(5x^2+6\)
D (8x+6)
Explanation opens after your attempt
Correct Answer
A. \(10x^2+6\)
Step 1
Concept
(p(-x)=5x-2 +4x+3), so the sum is \(10x^2+6\). Odd-power terms change signs when (-x) is substituted.
Step 2
Why this answer is correct
The correct answer is A. \(10x^2+6\). (p(-x)=5x-2 +4x+3), so the sum is \(10x^2+6\). Odd-power terms change signs when (-x) is substituted.
Step 3
Exam Tip
(p(-x)=5x-2 +4x+3), इसलिए योग \(10x^2+6\) है। (-x) रखने पर विषम घात वाले पद का संकेत बदलता है।
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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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(p(x)=4x-6 -5x-4 +2x-2 -11) में \(x^5\) का गुणांक क्या है?
What is the coefficient of \(x^5\) in (p(x)=4x-6 -5x-4 +2x-2 -11)?
#missing term
#coefficient
#polynomial
A (0)
B (2)
C (4)
D (-5)
Explanation opens after your attempt
Step 1
Concept
The \(x^5\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^5\).
Step 2
Why this answer is correct
The correct answer is A. (0). The \(x^5\)-term is missing, so its coefficient is (0). Treat the missing term as \(0x^5\).
Step 3
Exam Tip
\(x^5\) का पद अनुपस्थित है, इसलिए उसका गुणांक (0) है। अनुपस्थित पद को \(0x^5\) मानें।
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