100 results found for "dependent-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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समीकरणों (9x+16y=77) और (27x+48y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (9x+16y=77) and (27x+48y=s) to be consistent and dependent?
#linear equations
#expert
#consistent dependent
#parameter
A (229)
B (230)
C (231)
D (232)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 2
Why this answer is correct
The correct answer is C. (231). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=231).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=231)।
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समीकरणों (7x+13y=67) और (21x+39y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (7x+13y=67) and (21x+39y=s) to be consistent and dependent?
#linear equations
#hard
#consistent dependent
#parameter
A (199)
B (200)
C (201)
D (202)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=201).
Step 2
Why this answer is correct
The correct answer is C. (201). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=201).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=201)।
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समीकरणों (6x+11y=53) और (18x+33y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (6x+11y=53) and (18x+33y=s) to be consistent and dependent?
#linear equations
#hard
#consistent dependent
#parameter
A (157)
B (158)
C (159)
D (160)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=159).
Step 2
Why this answer is correct
The correct answer is C. (159). To be consistent and dependent, the second equation must be (3) times the first. Hence, (s=159).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (s=159)।
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समीकरणों (5x+6y=31) और (15x+18y=r) के संगत और आश्रित होने के लिए (r) क्या होगा?
What should (r) be for the equations (5x+6y=31) and (15x+18y=r) to be consistent and dependent?
#linear equations
#hard
#consistent dependent
#parameter
A (90)
B (91)
C (92)
D (93)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (3) times the first. Hence, (r=93).
Step 2
Why this answer is correct
The correct answer is D. (93). To be consistent and dependent, the second equation must be (3) times the first. Hence, (r=93).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (3) गुना होना चाहिए। अतः (r=93)।
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समीकरणों (4x+5y=29) और (8x+10y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for the equations (4x+5y=29) and (8x+10y=s) to be consistent and dependent?
#linear equations
#hard
#consistent dependent
#parameter
A (56)
B (57)
C (58)
D (59)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=58).
Step 2
Why this answer is correct
The correct answer is C. (58). To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=58).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (2) गुना होना चाहिए। अतः (s=58)।
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समीकरण (4x+5y=29) और (8x+10y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for (4x+5y=29) and (8x+10y=s) to be consistent and dependent?
#linear equations
#consistent dependent
#parameter
A (56)
B (57)
C (58)
D (59)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent the second equation must be (2) times the first. Hence (s=58).
Step 2
Why this answer is correct
The correct answer is C. (58). To be consistent and dependent the second equation must be (2) times the first. Hence (s=58).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (2) गुना होना चाहिए। अतः (s=58)।
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समीकरण (2x+5y=17) और (4x+10y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for (2x+5y=17) and (4x+10y=s) to be consistent and dependent?
#linear equations
#consistent dependent
#parameter
A (32)
B (33)
C (34)
D (35)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=34).
Step 2
Why this answer is correct
The correct answer is C. (34). To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=34).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (2) गुना होना चाहिए। अतः (s=34)।
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समीकरण (x+4y=9) और (2x+8y=s) के संगत और आश्रित होने के लिए (s) क्या होगा?
What should (s) be for (x+4y=9) and (2x+8y=s) to be consistent and dependent?
#linear equations
#consistent dependent
#parameter
A (16)
B (17)
C (18)
D (19)
Explanation opens after your attempt
Step 1
Concept
To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=18).
Step 2
Why this answer is correct
The correct answer is C. (18). To be consistent and dependent, the second equation must be (2) times the first. Hence, (s=18).
Step 3
Exam Tip
संगत और आश्रित होने के लिए दूसरा समीकरण पहले का (2) गुना होना चाहिए। अतः (s=18)।
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नीचे में से कौन-सा युग्म संगत और आश्रित है?
Which of the following pairs is consistent and dependent?
#linear equations
#mcq
#consistent dependent
A (2x+y=7) और (4x+3y=14) / (2x+y=7) and (4x+3y=14)
B (x-2y=5) और (3x-6y=15) / (x-2y=5) and (3x-6y=15)
C (x+y=3) और (2x+2y=7) / (x+y=3) and (2x+2y=7)
D (3x+5y=8) और (x+2y=6) / (3x+5y=8) and (x+2y=6)
Explanation opens after your attempt
Correct Answer
B. (x-2y=5) और (3x-6y=15) / (x-2y=5) and (3x-6y=15)
Step 1
Concept
In the second option the second equation is (3) times the first. Therefore both are the same line and the pair is dependent.
Step 2
Why this answer is correct
The correct answer is B. (x-2y=5) और (3x-6y=15) / (x-2y=5) and (3x-6y=15). In the second option the second equation is (3) times the first. Therefore both are the same line and the pair is dependent.
Step 3
Exam Tip
दूसरे विकल्प में दूसरा समीकरण पहले का (3) गुना है। इसलिए दोनों एक ही रेखा हैं और युग्म आश्रित है।
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किस स्थिति में दो रैखिक समीकरणों का युग्म संगत और आश्रित कहलाता है?
In which condition is a pair of two linear equations called consistent and dependent?
#linear equations
#consistent dependent
#condition
A जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
B जब (a_1 / a_2 \ne b_1 / b_2) हो / When \(a_1 / b_2\)
C जब (a_1 / a_2=b_1 / b_2 \ne c_1 / c_2) हो / When \(a_1 / c_2\)
D जब रेखाएं कटती हों / When lines intersect
Explanation opens after your attempt
Correct Answer
A. जब (a_1 / a_2=b_1 / b_2=c_1 / c_2) हो / When \(a_1 / c_2\)
Step 1
Concept
If all three ratios are equal both equations represent the same line. This is a consistent and dependent pair.
Step 2
Why this answer is correct
The correct answer is A. जब \(a_1 / a_2=b_1 / b_2=c_1 / c_2\) हो / When \(a_1 / c_2\). If all three ratios are equal both equations represent the same line. This is a consistent and dependent pair.
Step 3
Exam Tip
तीनों अनुपात बराबर हों तो दोनों समीकरण समान रेखा दर्शाते हैं। यही संगत और आश्रित युग्म है।
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संगत और आश्रित युग्म में हलों की संख्या क्या होती है?
How many solutions are there in a consistent and dependent pair?
#linear equations
#consistent dependent
#infinite solutions
A एक हल / One solution
B कोई हल नहीं / No solution
C ठीक दो हल / Exactly two solutions
D अनंत हल / Infinitely many solutions
Explanation opens after your attempt
Correct Answer
D. अनंत हल / Infinitely many solutions
Step 1
Concept
In a consistent and dependent pair both equations represent the same line. Therefore every common point is a solution.
Step 2
Why this answer is correct
The correct answer is D. अनंत हल / Infinitely many solutions. In a consistent and dependent pair both equations represent the same line. Therefore every common point is a solution.
Step 3
Exam Tip
संगत और आश्रित युग्म में दोनों समीकरण एक ही रेखा दर्शाते हैं। इसलिए हर सामान्य बिंदु हल होता है।
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किस युग्म का ग्राफ संगत और आश्रित युग्म दिखाता है?
Which pair shows a consistent and dependent pair on the graph?
#graphical method
#dependent pair
#coincident lines
#infinite solutions
A (2x-y=7), (4x-2y=14)
B (2x-y=7), (4x-2y=15)
C (2x-y=7), (x+y=1)
D (x-y=7), (2x+y=14)
Explanation opens after your attempt
Correct Answer
A. (2x-y=7), (4x-2y=14)
Step 1
Concept
The second equation is (2) times the first, so the lines are coincident. Coincident lines give a consistent and dependent pair.
Step 2
Why this answer is correct
The correct answer is A. (2x-y=7), (4x-2y=14). The second equation is (2) times the first, so the lines are coincident. Coincident lines give a consistent and dependent pair.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है, इसलिए रेखाएं संपाती हैं। संपाती रेखाएं संगत और आश्रित युग्म देती हैं।
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कौन-सा समीकरण युग्म संगत और आश्रित है?
Which pair of equations is consistent and dependent?
#consistent dependent
#coincident lines
#infinite solutions
A (2x+y=6) और (4x+2y=12) / (2x+y=6) and (4x+2y=12)
B (x+y=5) और (x+y=7) / (x+y=5) and (x+y=7)
C (x-y=2) और (x+y=4) / (x-y=2) and (x+y=4)
D (x=1) और (y=2) / (x=1) and (y=2)
Explanation opens after your attempt
Correct Answer
A. (2x+y=6) और (4x+2y=12) / (2x+y=6) and (4x+2y=12)
Step 1
Concept
The second equation is (2) times the first. Hence the lines are coincident and the pair is consistent dependent.
Step 2
Why this answer is correct
The correct answer is A. (2x+y=6) और (4x+2y=12) / (2x+y=6) and (4x+2y=12). The second equation is (2) times the first. Hence the lines are coincident and the pair is consistent dependent.
Step 3
Exam Tip
दूसरा समीकरण पहले का (2) गुना है। इसलिए दोनों रेखाएँ संपाती हैं और युग्म संगत आश्रित 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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हिमनदों से पोषित हिमालयी नदियों की तुलना वर्षा पर निर्भर प्रायद्वीपीय नदियों से कैसे की जाती है?
How are glacier fed Himalayan rivers compared with rain dependent Peninsular rivers?
#himalayan-rivers
#peninsular-rivers
#perennial
A हिमालयी नदियां सामान्यतः अधिक बारहमासी होती हैं / Himalayan rivers are generally more perennial
B प्रायद्वीपीय नदियां हमेशा हिमनदी होती हैं / Peninsular rivers are always glacial
C दोनों केवल ज्वार से चलती हैं / Both flow only by tides
D दोनों समुद्र तक कभी नहीं पहुंचतीं / Both never reach the sea
Explanation opens after your attempt
Correct Answer
A. हिमालयी नदियां सामान्यतः अधिक बारहमासी होती हैं / Himalayan rivers are generally more perennial
Step 1
Concept
Himalayan rivers get water from both glaciers and rainfall. For exams remember the link between source and flow.
Step 2
Why this answer is correct
The correct answer is A. हिमालयी नदियां सामान्यतः अधिक बारहमासी होती हैं / Himalayan rivers are generally more perennial. Himalayan rivers get water from both glaciers and rainfall. For exams remember the link between source and flow.
Step 3
Exam Tip
हिमालयी नदियों को हिमनद और वर्षा दोनों से जल मिलता है। परीक्षा में स्रोत और प्रवाह का संबंध याद रखें।
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औपनिवेशिक नकदी फसल नीति किसानों को बाजार पर निर्भर कैसे बना सकती थी?
How could colonial cash crop policy make peasants dependent on markets?
#cash-crops
#peasants
#colonial-economy
A खाद्य फसलों की जगह बिकाऊ फसलों पर दबाव डालकर / By pressuring them toward saleable crops instead of food crops
B किसानों को सभी करों से मुक्त करके / By exempting peasants from all taxes
C खेती को पूरी तरह समाप्त करके / By ending farming completely
D स्थानीय बाजार बंद करके / By closing local markets
Explanation opens after your attempt
Correct Answer
A. खाद्य फसलों की जगह बिकाऊ फसलों पर दबाव डालकर / By pressuring them toward saleable crops instead of food crops
Step 1
Concept
Cash crop and tax policy affected peasant livelihoods. For exams remember rural crisis.
Step 2
Why this answer is correct
The correct answer is A. खाद्य फसलों की जगह बिकाऊ फसलों पर दबाव डालकर / By pressuring them toward saleable crops instead of food crops. Cash crop and tax policy affected peasant livelihoods. For exams remember rural crisis.
Step 3
Exam Tip
नकदी फसल और कर नीति ने किसानों की आजीविका को प्रभावित किया। परीक्षा में ग्रामीण संकट याद रखें।
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बैटल ऑफ द बुल्ज में जर्मन योजना मौसम और ईंधन पर क्यों निर्भर थी?
Why was the German plan in the Battle of the Bulge dependent on weather and fuel?
#world history
#world wars
#battle of bulge
#fuel
A खराब मौसम मित्र वायु शक्ति घटाता था और ईंधन तेज बख्तरबंद बढ़त के लिए जरूरी था / Bad weather reduced Allied air power and fuel was needed for fast armored advance
B जर्मनी के पास असीमित ईंधन था / Germany had unlimited fuel
C वह युद्ध समुद्र में था / The battle was at sea
D जापान ने ईंधन भेजा / Japan sent fuel
Explanation opens after your attempt
Correct Answer
A. खराब मौसम मित्र वायु शक्ति घटाता था और ईंधन तेज बख्तरबंद बढ़त के लिए जरूरी था / Bad weather reduced Allied air power and fuel was needed for fast armored advance
Step 1
Concept
The German offensive depended on limited resources and weather. For exams understand weakness of the final offensive.
Step 2
Why this answer is correct
The correct answer is A. खराब मौसम मित्र वायु शक्ति घटाता था और ईंधन तेज बख्तरबंद बढ़त के लिए जरूरी था / Bad weather reduced Allied air power and fuel was needed for fast armored advance. The German offensive depended on limited resources and weather. For exams understand weakness of the final offensive.
Step 3
Exam Tip
जर्मन आक्रमण की सफलता सीमित संसाधनों और मौसम पर निर्भर थी। परीक्षा में अंतिम आक्रमण की कमजोरी समझें।
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गुडेम पहाड़ियों में आंदोलन करने वाले आदिवासी किस चीज पर अधिक निर्भर थे?
What were the tribals protesting in the Gudem Hills mostly dependent on?
#tribals
#gudem-hills
#forest-livelihood
A जंगलों और वन उपज पर / Forests and forest produce
B समुद्री जहाजों पर / Sea ships
C बड़े कारखानों पर / Large factories
D विदेशी बैंकों पर / Foreign banks
Explanation opens after your attempt
Correct Answer
A. जंगलों और वन उपज पर / Forests and forest produce
Step 1
Concept
The life of hill tribals was closely linked with forests.
Step 2
Why this answer is correct
Forest produce grazing and cultivation supported their livelihood.
Step 3
Exam Tip
In tribal questions treat forests as the main context. चरण 1: पहाड़ी आदिवासियों का जीवन जंगलों से जुड़ा था। चरण 2: वन उपज चराई और खेती से उनकी रोजी चलती थी। चरण 3: आदिवासी प्रश्नों में जंगल को मुख्य संदर्भ मानें।
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फ्लोएम में भोजन का स्थानांतरण ऊर्जा पर निर्भर क्यों है?
Why is translocation of food in phloem energy dependent?
#phloem
#translocation
#energy
#sieve-tubes
A क्योंकि शर्करा को चलनी नलिकाओं में सक्रिय रूप से लादा जाता है / Because sugar is actively loaded into sieve tubes
B क्योंकि भोजन को फेफड़ों में भेजा जाता है / Because food is sent to lungs
C क्योंकि पत्तियाँ रक्त छानती हैं / Because leaves filter blood
D क्योंकि जाइलम स्टार्च बनाता है / Because xylem makes starch
Explanation opens after your attempt
Correct Answer
A. क्योंकि शर्करा को चलनी नलिकाओं में सक्रिय रूप से लादा जाता है / Because sugar is actively loaded into sieve tubes
Step 1
Concept
Sugar made in leaves is loaded into phloem.
Step 2
Why this answer is correct
This loading uses energy.
Step 3
Exam Tip
A pressure difference then moves food to parts that need it. चरण 1: पत्तियों में बनी शर्करा को फ्लोएम में लादा जाता है। चरण 2: यह लादना ऊर्जा की सहायता से होता है। चरण 3: दाब अंतर बनने पर भोजन जरूरत वाले भागों तक चलता है।
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जाइलम में जल का ऊपर जाना केवल जड़ से धक्का लगने पर निर्भर नहीं माना जाता। पत्तियां इसमें कैसे मदद करती हैं?
Upward movement of water in xylem is not considered dependent only on push from roots. How do leaves help in it?
#xylem
#transpiration-pull
#water-transport
A वाष्पोत्सर्जन से ऊपर की ओर खिंचाव बनाकर / By creating upward pull through transpiration
B भोजन को अम्ल में बदलकर / By changing food into acid
C रक्त में हीमोग्लोबिन बनाकर / By making haemoglobin in blood
D मूत्राशय में जल जमा करके / By storing water in urinary bladder
Explanation opens after your attempt
Correct Answer
A. वाष्पोत्सर्जन से ऊपर की ओर खिंचाव बनाकर / By creating upward pull through transpiration
Step 1
Concept
Water vapour leaves from leaves.
Step 2
Why this answer is correct
This creates an upward pull in xylem.
Step 3
Exam Tip
This pull helps move water from roots to leaves. चरण 1: पत्तियों से जल वाष्प बाहर निकलती है। चरण 2: इससे जाइलम में ऊपर की ओर खिंचाव पैदा होता है। चरण 3: यह खिंचाव जड़ों से पत्तियों तक जल पहुंचाने में मदद करता है।
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शरीर में जीवन प्रक्रियाएं अलग अलग होते हुए भी एक दूसरे पर निर्भर क्यों हैं?
Why are life processes dependent on each other though they are different?
#life processes
#integration
#nutrition respiration transport excretion
A क्योंकि पोषण पदार्थ देता है श्वसन ऊर्जा देता है परिवहन पहुंचाता है और उत्सर्जन अपशिष्ट हटाता है / Because nutrition gives materials respiration gives energy transport delivers and excretion removes wastes
B क्योंकि सभी केवल नाम हैं / Because all are only names
C क्योंकि केवल पाचन जीव को जीवित रखता है / Because only digestion keeps an organism alive
D क्योंकि उत्सर्जन भोजन बनाता है / Because excretion makes food
Explanation opens after your attempt
Correct Answer
A. क्योंकि पोषण पदार्थ देता है श्वसन ऊर्जा देता है परिवहन पहुंचाता है और उत्सर्जन अपशिष्ट हटाता है / Because nutrition gives materials respiration gives energy transport delivers and excretion removes wastes
Step 1
Concept
Each life process performs a different function.
Step 2
Why this answer is correct
Cells need nutrients oxygen energy and waste removal together.
Step 3
Exam Tip
Therefore life processes work together to maintain life. चरण 1: प्रत्येक जीवन प्रक्रिया अलग काम करती है। चरण 2: फिर भी कोशिकाओं को पोषण ऑक्सीजन ऊर्जा और अपशिष्ट निष्कासन साथ साथ चाहिए। चरण 3: इसलिए जीवन प्रक्रियाएं मिलकर जीवन बनाए रखती हैं।
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फ्लोएम में भोजन का परिवहन ऊर्जा पर निर्भर क्यों माना जाता है?
Why is food transport in phloem considered energy dependent?
#phloem
#translocation
#energy
A क्योंकि भोजन को स्रोत से आवश्यकता वाले भागों तक सक्रिय रूप से भेजना पड़ता है / Because food must be actively moved from source to parts that need it
B क्योंकि फ्लोएम केवल मृत कोशिकाओं से बना होता है / Because phloem is made only of dead cells
C क्योंकि भोजन अपने आप वायु में उड़ता है / Because food flies in air by itself
D क्योंकि फ्लोएम केवल जल को नीचे गिराता है / Because phloem only drops water downward
Explanation opens after your attempt
Correct Answer
A. क्योंकि भोजन को स्रोत से आवश्यकता वाले भागों तक सक्रिय रूप से भेजना पड़ता है / Because food must be actively moved from source to parts that need it
Step 1
Concept
Food is made in leaves.
Step 2
Why this answer is correct
It must reach storage and growing parts.
Step 3
Exam Tip
This translocation may need energy. चरण 1: भोजन पत्तियों में बनता है। चरण 2: उसे भंडारण और वृद्धि वाले भागों तक पहुंचाना होता है। चरण 3: इस स्थानांतरण में ऊर्जा की जरूरत पड़ सकती 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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