100 results found for "cubic plus sine" in Class 10.
यदि (x-a), (x-b) और (x-c) किसी घन बहुपद के गुणनखंड हैं, तो उसका एक संभावित बहुपद कौन सा है?
If (x-a), (x-b), and (x-c) are factors of a cubic polynomial, which is a possible polynomial?
#polynomials
#cubic
#factors
#hard
A (x-3 -(a+b+c)x-2 +(ab+bc+ca)x-abc)
B (x-3 +(a+b+c)x-2 +(ab+bc+ca)x+abc)
C (x-3 -(ab+bc+ca)x-2 +(a+b+c)x-abc)
D (x-3 +abcx-2 -(a+b+c)x+ab+bc+ca)
Explanation opens after your attempt
Correct Answer
A. (x-3 -(a+b+c)x-2 +(ab+bc+ca)x-abc)
Step 1
Concept
Expanding ((x-a)(x-b)(x-c)) gives the first form. Remember the link between zeroes and factors.
Step 2
Why this answer is correct
The correct answer is A. (x-3 -(a+b+c)x-2 +(ab+bc+ca)x-abc). Expanding ((x-a)(x-b)(x-c)) gives the first form. Remember the link between zeroes and factors.
Step 3
Exam Tip
((x-a)(x-b)(x-c)) फैलाने पर पहला रूप मिलता है। शून्यकों और गुणनखंडों का संबंध याद रखें।
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निम्न में से त्रिघात बहुपद कौन सा है?
Which of the following is a cubic polynomial?
#cubic-polynomial
#degree
A \(x^3-4x+2\)
B \(x^2+9\)
C (6x-1)
D (12)
Explanation opens after your attempt
Correct Answer
A. \(x^3-4x+2\)
Step 1
Concept
A cubic polynomial has degree (3). In \(x^3-4x+2\), the highest power is (3).
Step 2
Why this answer is correct
The correct answer is A. \(x^3-4x+2\). A cubic polynomial has degree (3). In \(x^3-4x+2\), the highest power is (3).
Step 3
Exam Tip
त्रिघात बहुपद की घात (3) होती है। \(x^3-4x+2\) में सबसे बड़ी घात (3) है।
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यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को (-1) पर काटता है और (2) पर छूता है तो अलग-अलग वास्तविक शून्यक कितने हैं?
If the graph of a cubic polynomial crosses the (x)-axis at (-1) and touches it at (2), how many distinct real zeroes are there?
#cubic
#distinct-zeroes
#graph
A दो / Two
B तीन / Three
C एक / One
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
The distinct zeroes are only (-1) and (2). A touching zero may be repeated but its distinct value is counted once.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. The distinct zeroes are only (-1) and (2). A touching zero may be repeated but its distinct value is counted once.
Step 3
Exam Tip
अलग-अलग शून्यक केवल (-1) और (2) हैं। छूने वाला शून्यक दोहराया हो सकता है पर अलग मान एक ही गिना जाता है।
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यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर छूता और काटता है, तो अलग वास्तविक शून्यक कितने होंगे?
If the graph of a cubic polynomial touches or crosses the (x)-axis at two distinct points, how many distinct real zeroes will it have?
#cubic
#distinct zeroes
#graph reading
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
Distinct zeroes are counted from distinct meeting points with the (x)-axis. Tip: degree gives the maximum, but the actual count is read from the graph.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Distinct zeroes are counted from distinct meeting points with the (x)-axis. Tip: degree gives the maximum, but the actual count is read from the graph.
Step 3
Exam Tip
अलग शून्यक अलग (x)-अक्ष मिलने वाले बिंदुओं की संख्या से मिलते हैं। टिप: घात से अधिकतम संख्या मिलती है, वास्तविक गिनती ग्राफ से पढ़ें।
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यदि किसी घन बहुपद का ग्राफ (x)-अक्ष को केवल एक बार काटता है, तो वास्तविक शून्यकों की संख्या क्या मानी जाएगी?
If the graph of a cubic polynomial cuts the (x)-axis only once, what is the number of real zeroes?
#cubic graph
#real zero
#count
A एक / One
B दो / Two
C तीन / Three
D शून्य / Zero
Explanation opens after your attempt
Step 1
Concept
There is only one intersection, so there is one real zero. Tip: a cubic can have at most three real zeroes, not necessarily three.
Step 2
Why this answer is correct
The correct answer is A. एक / One. There is only one intersection, so there is one real zero. Tip: a cubic can have at most three real zeroes, not necessarily three.
Step 3
Exam Tip
कटान केवल एक है इसलिए एक वास्तविक शून्यक है। टिप: घन बहुपद में अधिकतम तीन वास्तविक शून्यक हो सकते हैं, जरूरी नहीं कि तीन हों।
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किसी घन बहुपद का आलेख (x)-अक्ष को तीन अलग-अलग बिंदुओं पर काटता है। वास्तविक शून्यकों की संख्या क्या है?
The graph of a cubic polynomial cuts the (x)-axis at three distinct points. What is the number of real zeroes?
#cubic graph zeroes
A तीन / Three
B दो / Two
C एक / One
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
Three intersection points show three real zeroes. Tip: count each distinct (x)-axis intersection.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Three intersection points show three real zeroes. Tip: count each distinct (x)-axis intersection.
Step 3
Exam Tip
तीन कटान बिंदु तीन वास्तविक शून्यक बताते हैं। टिप: प्रत्येक अलग (x)-अक्ष कटान को गिनें।
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एक कक्षा में कुल (74) विद्यार्थी हैं। लड़कों की संख्या का (3) गुना और लड़कियों की संख्या का (2) गुना मिलाकर (186) है। लड़कियों की संख्या क्या है?
In a class, there are (74) students. Three times the number of boys plus twice the number of girls is (186). What is the number of girls?
#linear equations
#word problem
#class strength
#hard
#class 10
A (36)
B (38)
C (40)
D (42)
Explanation opens after your attempt
Step 1
Concept
Let boys be (x) and girls be (y). From (x+y=74) and (3x+2y=186), (x=38), so (y=36).
Step 2
Why this answer is correct
The correct answer is A. (36). Let boys be (x) and girls be (y). From (x+y=74) and (3x+2y=186), (x=38), so (y=36).
Step 3
Exam Tip
लड़के (x) और लड़कियां (y) मानें। (x+y=74) और (3x+2y=186) से (x=38), इसलिए (y=36)।
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दो संख्याओं का योग (52) है। बड़ी संख्या का (3) गुना और छोटी संख्या का (2) गुना मिलाकर (136) है। बड़ी संख्या क्या है?
The sum of two numbers is (52). Three times the larger number plus twice the smaller number is (136). What is the larger number?
#linear equations
#word problem
#numbers
#hard
#class 10
A (28)
B (30)
C (32)
D (34)
Explanation opens after your attempt
Step 1
Concept
Let the larger number be (x) and the smaller be (y). From (x+y=52) and (3x+2y=136), (x=32).
Step 2
Why this answer is correct
The correct answer is C. (32). Let the larger number be (x) and the smaller be (y). From (x+y=52) and (3x+2y=136), (x=32).
Step 3
Exam Tip
मान लें बड़ी संख्या (x) और छोटी (y) है। (x+y=52) और (3x+2y=136) से (x=32)।
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एक कक्षा में लड़कों और लड़कियों की कुल संख्या (68) है। लड़कों की संख्या का (2) गुना और लड़कियों की संख्या मिलाकर (112) है। लड़कियों की संख्या क्या है?
In a class, the total number of boys and girls is (68). Twice the number of boys plus the number of girls is (112). What is the number of girls?
#linear equations
#word problem
#class strength
#hard
#class 10
A (20)
B (22)
C (26)
D (24)
Explanation opens after your attempt
Step 1
Concept
Let boys be (x) and girls be (y). From (x+y=68) and (2x+y=112), (x=44), so (y=24).
Step 2
Why this answer is correct
The correct answer is D. (24). Let boys be (x) and girls be (y). From (x+y=68) and (2x+y=112), (x=44), so (y=24).
Step 3
Exam Tip
लड़के (x) और लड़कियां (y) मानें। (x+y=68) और (2x+y=112) से (x=44), इसलिए (y=24)।
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किसी संख्या (x) के वर्ग में उसके (3) गुने को जोड़ने पर (10) मिलता है। सही समीकरण कौन-सा है?
The square of a number (x) plus (3) times the number is (10). Which equation is correct?
#quadratic-equations
#word-problem
#formation
A \(x+3x^2=10\)
B \(x^2+3x=10\)
C (2x+3=10)
D \(x^2-3x=10\)
Explanation opens after your attempt
Correct Answer
B. \(x^2+3x=10\)
Step 1
Concept
Square means \(x^2\) and (3) times means (3x). In word problems, convert the sentence slowly into an equation.
Step 2
Why this answer is correct
The correct answer is B. \(x^2+3x=10\). Square means \(x^2\) and (3) times means (3x). In word problems, convert the sentence slowly into an equation.
Step 3
Exam Tip
वर्ग का अर्थ \(x^2\) और (3) गुना का अर्थ (3x) है। शब्द प्रश्न में वाक्य को धीरे-धीरे समीकरण में बदलें।
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कौन-सा बहुपद घन बहुपद है?
Which polynomial is a cubic polynomial?
#cubic_polynomial
#degree
#classification
A \(x^3-2x+1\)
B \(x^2+4\)
C (7x-9)
D (5)
Explanation opens after your attempt
Correct Answer
A. \(x^3-2x+1\)
Step 1
Concept
A cubic polynomial has degree (3). The highest power in \(x^3-2x+1\) is (3).
Step 2
Why this answer is correct
The correct answer is A. \(x^3-2x+1\). A cubic polynomial has degree (3). The highest power in \(x^3-2x+1\) is (3).
Step 3
Exam Tip
घन बहुपद की घात (3) होती है। \(x^3-2x+1\) की सबसे बड़ी घात (3) है।
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अनुक्रम \(9,16,23,30,\ldots\) में (a+2d) का मान क्या है?
In the sequence \(9,16,23,30,\ldots\), what is the value of (a+2d)?
#ap
#a plus 2d
#third term
#medium
A (16)
B (30)
C (23)
D (7)
Explanation opens after your attempt
Step 1
Concept
Here (a=9) and (d=7), so (a+2d=9+14=23). (a+2d) equals the third term.
Step 2
Why this answer is correct
The correct answer is C. (23). Here (a=9) and (d=7), so (a+2d=9+14=23). (a+2d) equals the third term.
Step 3
Exam Tip
यहां (a=9) और (d=7), इसलिए (a+2d=9+14=23)। (a+2d) तीसरे पद के बराबर होता है।
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अनुक्रम \(21,26,31,36,\ldots\) में (a+d) का मान क्या है?
In the sequence \(21,26,31,36,\ldots\), what is the value of (a+d)?
#ap
#a plus d
#second term
#medium
A (21)
B (26)
C (31)
D (36)
Explanation opens after your attempt
Step 1
Concept
Here (a=21) and (d=5), so (a+d=26). (a+d) is the second term.
Step 2
Why this answer is correct
The correct answer is B. (26). Here (a=21) and (d=5), so (a+d=26). (a+d) is the second term.
Step 3
Exam Tip
यहां (a=21) और (d=5), इसलिए (a+d=26) है। (a+d) दूसरा पद होता है।
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अनुक्रम \(3,8,13,18,\ldots\) में (a+2d) का मान क्या है?
In the sequence \(3,8,13,18,\ldots\), what is the value of (a+2d)?
#ap
#a plus 2d
#third term
#medium
A (8)
B (18)
C (13)
D (5)
Explanation opens after your attempt
Step 1
Concept
Here (a=3) and (d=5), so (a+2d=3+10=13). (a+2d) equals the third term.
Step 2
Why this answer is correct
The correct answer is C. (13). Here (a=3) and (d=5), so (a+2d=3+10=13). (a+2d) equals the third term.
Step 3
Exam Tip
यहां (a=3) और (d=5), इसलिए (a+2d=3+10=13)। (a+2d) तीसरे पद के बराबर होता है।
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अनुक्रम \(16,20,24,28,\ldots\) में (a+d) का मान क्या है?
In the sequence \(16,20,24,28,\ldots\), what is the value of (a+d)?
#ap
#a plus d
#second term
#medium
A (16)
B (18)
C (20)
D (24)
Explanation opens after your attempt
Step 1
Concept
Here (a=16) and (d=4), so (a+d=20). (a+d) is actually the second term.
Step 2
Why this answer is correct
The correct answer is C. (20). Here (a=16) and (d=4), so (a+d=20). (a+d) is actually the second term.
Step 3
Exam Tip
यहां (a=16) और (d=4), इसलिए (a+d=20)। (a+d) वास्तव में दूसरा पद होता है।
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किस विकल्प में परिमेय और अपरिमेय संख्या का योग अपरिमेय है?
In which option is the sum of a rational and an irrational number irrational?
#rational-plus-irrational
#classification
#real-numbers
A \(4+\sqrt{13}\)
B \(\sqrt{9}+7\)
C \(\sqrt{16}-3\)
D \(\frac{5}{2}+1\)
Explanation opens after your attempt
Correct Answer
A. \(4+\sqrt{13}\)
Step 1
Concept
(4) is rational and \(\sqrt{13}\) is irrational, so the sum is irrational. In exams identify square roots of perfect squares first.
Step 2
Why this answer is correct
The correct answer is A. \(4+\sqrt{13}\). (4) is rational and \(\sqrt{13}\) is irrational, so the sum is irrational. In exams identify square roots of perfect squares first.
Step 3
Exam Tip
(4) परिमेय है और \(\sqrt{13}\) अपरिमेय है, इसलिए योग अपरिमेय है। परीक्षा में पूर्ण वर्ग के वर्गमूल को पहले पहचानें।
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कौन सा विकल्प सिद्ध करता है कि \(\frac{3}{2}+\sqrt{5}\) अपरिमेय है?
Which option proves that \(\frac{3}{2}+\sqrt{5}\) is irrational?
#rational plus irrational
#proof
#class 10
#real numbers
A क्योंकि \(\frac{3}{2}\) अपरिमेय है / Because \(\frac{3}{2}\) is irrational
B क्योंकि परिमेय संख्या में अपरिमेय संख्या जोड़ने पर परिणाम अपरिमेय होता है / Because adding an irrational number to a rational number gives an irrational result
C क्योंकि \(\sqrt{5}\) पूर्णांक है / Because \(\sqrt{5}\) is an integer
D क्योंकि हर भिन्न अपरिमेय होती है / Because every fraction is irrational
Explanation opens after your attempt
Correct Answer
B. क्योंकि परिमेय संख्या में अपरिमेय संख्या जोड़ने पर परिणाम अपरिमेय होता है / Because adding an irrational number to a rational number gives an irrational result
Step 1
Concept
\(\frac{3}{2}\) is rational and \(\sqrt{5}\) is irrational.
Step 2
Why this answer is correct
If their sum were rational, then \(\sqrt{5}\) would become the difference of two rational numbers, which is impossible.
Step 3
Exam Tip
For rational-plus-irrational questions, contradiction is a very useful method. चरण 1: \(\frac{3}{2}\) परिमेय संख्या है और \(\sqrt{5}\) अपरिमेय संख्या है। चरण 2: यदि उनका योग परिमेय मानें तो \(\sqrt{5}\) को दो परिमेय संख्याओं के अंतर के रूप में लिखना पड़ेगा जो असंभव है। चरण 3: परिमेय और अपरिमेय के योग वाले प्रश्नों में विरोधाभास विधि बहुत उपयोगी है।
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यदि \(x=3+\sqrt{2}\) है तो (x) के बारे में क्या सही है?
If \(x=3+\sqrt{2}\) then what is true about (x)?
#rational plus irrational
#class 10
#real numbers
A (x) परिमेय है / (x) is rational
B (x) अपरिमेय है / (x) is irrational
C (x=5) है / (x=5)
D (x) प्राकृतिक संख्या है / (x) is a natural number
Explanation opens after your attempt
Correct Answer
B. (x) अपरिमेय है / (x) is irrational
Step 1
Concept
(3) is rational and \(\sqrt{2}\) is irrational.
Step 2
Why this answer is correct
The sum of a rational and an irrational number is irrational.
Step 3
Exam Tip
Adding an irrational number to an integer does not give an integer. चरण 1: (3) परिमेय है और \(\sqrt{2}\) अपरिमेय है। चरण 2: परिमेय और अपरिमेय का योग अपरिमेय होता है। चरण 3: किसी पूर्णांक में अपरिमेय संख्या जोड़ने से वह पूर्णांक नहीं रहता।
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यदि \(a=3+\sqrt{2}\), तो (a) की प्रकृति क्या है?
If \(a=3+\sqrt{2}\), what is the nature of (a)?
#rational plus irrational
#real numbers
#class 10
A परिमेय / Rational
B अपरिमेय / Irrational
C पूर्ण वर्ग / Perfect square
D ऋणात्मक पूर्णांक / Negative integer
Explanation opens after your attempt
Correct Answer
B. अपरिमेय / Irrational
Step 1
Concept
(3) is rational and \(\sqrt{2}\) is irrational.
Step 2
Why this answer is correct
The sum of a rational and an irrational number is irrational.
Step 3
Exam Tip
Adding an integer does not remove the irrational nature of the surd. चरण 1: (3) परिमेय है और \(\sqrt{2}\) अपरिमेय है। चरण 2: परिमेय और अपरिमेय का योग अपरिमेय होता है। चरण 3: पूर्णांक जोड़ने से मूल की अपरिमेयता समाप्त नहीं होती।
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यदि (x) अपरिमेय है, तो (x+3) के परिमेय होने की संभावना के बारे में सही कथन क्या है?
If (x) is irrational, what is correct about the possibility of (x+3) being rational?
#proof idea
#irrational plus rational
#class 10
A यह हमेशा परिमेय होगा / It will always be rational
B यह कभी परिमेय नहीं हो सकता / It can never be rational
C यह तभी परिमेय होगा जब (x=3) हो / It will be rational only when (x=3)
D यह तभी परिमेय होगा जब (x) ऋणात्मक हो / It will be rational only when (x) is negative
Explanation opens after your attempt
Correct Answer
B. यह कभी परिमेय नहीं हो सकता / It can never be rational
Step 1
Concept
(3) is rational.
Step 2
Why this answer is correct
If (x+3) were rational, then (x=(x+3)-3) would also be rational, contradicting the given fact.
Step 3
Exam Tip
The contradiction method is useful in such questions. चरण 1: (3) एक परिमेय संख्या है। चरण 2: यदि (x+3) परिमेय हो, तो (x=(x+3)-3) भी परिमेय होगा, जो दी गई बात के विरुद्ध है। चरण 3: ऐसे प्रश्नों में विरोध विधि तेज काम करती है।
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यदि \(x=\sqrt{5}-2\), तो (x) के बारे में सही कथन कौन-सा है?
If \(x=\sqrt{5}-2\), which statement about (x) is correct?
#rational plus irrational
#surd
#class 10
#hard
A (x) परिमेय है / (x) is rational
B (x) अपरिमेय है / (x) is irrational
C (x) पूर्णांक है / (x) is an integer
D (x=0) है / (x=0)
Explanation opens after your attempt
Correct Answer
B. (x) अपरिमेय है / (x) is irrational
Step 1
Concept
\(\sqrt{5}\) is irrational and (2) is rational.
Step 2
Why this answer is correct
Subtracting a rational number from an irrational number gives an irrational number.
Step 3
Exam Tip
When an integer is subtracted from a surd, focus on the nature of the surd. चरण 1: \(\sqrt{5}\) अपरिमेय है और (2) परिमेय है। चरण 2: अपरिमेय संख्या में से परिमेय संख्या घटाने पर परिणाम अपरिमेय रहता है। चरण 3: किसी मूल से पूर्णांक घटाने पर भी मूल की प्रकृति पर ध्यान दें।
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यदि कोई संख्या (12q+5) के रूप में है, तो उसे (12) से भाग देने पर शेषफल क्यों (5) होगा?
If a number is of the form (12q+5), why will its remainder be (5) when divided by (12)?
#real-numbers
#bq-plus-r
#conceptual
A क्योंकि (12q), (12) का गुणज है और (5<12) / Because (12q) is a multiple of (12) and (5<12)
B क्योंकि (q) हमेशा (5) होता है / Because (q) is always (5)
C क्योंकि (12) शेषफल है / Because (12) is the remainder
D क्योंकि (5) भाजक से बड़ा है / Because (5) is greater than the divisor
Explanation opens after your attempt
Correct Answer
A. क्योंकि (12q), (12) का गुणज है और (5<12) / Because (12q) is a multiple of (12) and (5<12)
Step 1
Concept
(12q) is exactly divisible by (12).
Step 2
Why this answer is correct
The leftover part is (5), and it is less than (12), so it is the remainder.
Step 3
Exam Tip
In (bq+r), (bq) is the multiple and (r) is the remainder. चरण 1: (12q), (12) से पूर्णतः विभाजित होता है। चरण 2: बचा हुआ (5) है और यह (12) से छोटा है, इसलिए वही शेषफल है। चरण 3: (bq+r) में (bq) गुणज और (r) शेषफल 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-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-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 (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)=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-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 (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)=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 (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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(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)=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)=x-3 +ax-2 +bx-10) में (x=1) और (x=5) दोनों शून्य हैं, तो (a) क्या है?
If (x=1) and (x=5) are both zeros of (p(x)=x-3 +ax-2 +bx-10), what is (a)?
#zeros
#cubic
#parameter
A (-7)
B (-6)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
(p(1)=0) gives (a+b=9) and (p(5)=0) gives (5a+b=-23), so (a=-8). None of the listed choices is correct.
Step 2
Why this answer is correct
The correct answer is B. (-6). (p(1)=0) gives (a+b=9) and (p(5)=0) gives (5a+b=-23), so (a=-8). None of the listed choices is correct.
Step 3
Exam Tip
(p(1)=0) से (a+b=9) और (p(5)=0) से (5a+b=-23), इसलिए (a=-8) नहीं बल्कि (a=-8) आता है। विकल्पों में कोई सही नहीं है।
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यदि (p(x)=x-3 +ax-2 +bx+18) में (x=1) और (x=-2) दोनों शून्य हैं, तो (a+b) क्या है?
If (x=1) and (x=-2) are both zeros of (p(x)=x-3 +ax-2 +bx+18), what is (a+b)?
#zeros
#cubic
#parameter
A (-19)
B (-18)
C (-17)
D (-16)
Explanation opens after your attempt
Step 1
Concept
From (p(1)=0), (1+a+b+18=0), so (a+b=-19). This condition is directly enough for the asked sum.
Step 2
Why this answer is correct
The correct answer is A. (-19). From (p(1)=0), (1+a+b+18=0), so (a+b=-19). This condition is directly enough for the asked sum.
Step 3
Exam Tip
(p(1)=0) से (1+a+b+18=0), इसलिए (a+b=-19)। पूछे गए योग के लिए यह शर्त सीधे पर्याप्त है।
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यदि (p(x)=x-3 +ax+b), (p(1)=6) और (p(-2)=-9), तो (a) का मान क्या है?
If (p(x)=x-3 +ax+b), (p(1)=6), and (p(-2)=-9), what is the value of (a)?
#parameter
#cubic
#evaluation
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a+b=5) and (-2a+b=-1). Subtracting gives (3a=6), so (a=2).
Step 2
Why this answer is correct
The correct answer is C. (3). The conditions give (a+b=5) and (-2a+b=-1). Subtracting gives (3a=6), so (a=2).
Step 3
Exam Tip
शर्तों से (a+b=5) और (-2a+b=-1) मिलते हैं। घटाने पर (3a=6) नहीं बल्कि (3a=6), इसलिए (a=2)।
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यदि (p(x)=x-3 +ax+b), (p(2)=13) और (p(-1)=-7), तो (a+b) का मान क्या है?
If (p(x)=x-3 +ax+b), (p(2)=13), and (p(-1)=-7), what is the value of (a+b)?
#parameter
#cubic
#evaluation
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The conditions give (2a+b=5) and (-a+b=-6), so \(a=\frac{11}{3}\) and \(b=-\frac{7}{3}\). Hence \(a+b=\frac{4}{3}\), so none of the listed choices is correct.
Step 2
Why this answer is correct
The correct answer is B. (2). The conditions give (2a+b=5) and (-a+b=-6), so \(a=\frac{11}{3}\) and \(b=-\frac{7}{3}\). Hence \(a+b=\frac{4}{3}\), so none of the listed choices is correct.
Step 3
Exam Tip
शर्तों से (2a+b=5) और (-a+b=-6) मिलते हैं, इसलिए \(a=\frac{11}{3}\) और \(b=-\frac{7}{3}\)। अतः \(a+b=\frac{4}{3}\) नहीं बल्कि विकल्पों में कोई सही नहीं होता।
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(p(x)=4x-3 -11x-2 +6x+2) के लिए (p(2)) का मान क्या है?
What is the value of (p(2)) for (p(x)=4x-3 -11x-2 +6x+2)?
#evaluation
#cubic
#substitution
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(2)=32-44+12+2=2). Evaluate each term separately and then add.
Step 2
Why this answer is correct
The correct answer is B. (2). (p(2)=32-44+12+2=2). Evaluate each term separately and then add.
Step 3
Exam Tip
(p(2)=32-44+12+2=2)। हर पद का मान अलग निकालकर जोड़ें।
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यदि (p(x)=kx-3 +2x-2 -7x+5) और (p(-1)=16), तो (k) का मान क्या है?
If (p(x)=kx-3 +2x-2 -7x+5) and (p(-1)=16), what is the value of (k)?
#evaluation
#parameter
#cubic polynomial
A (-2)
B (-1)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=-k+2+7+5=14-k), so (14-k=16) and (k=-2). Watch signs carefully when substituting a negative value.
Step 2
Why this answer is correct
The correct answer is A. (-2). (p(-1)=-k+2+7+5=14-k), so (14-k=16) and (k=-2). Watch signs carefully when substituting a negative value.
Step 3
Exam Tip
(p(-1)=-k+2+7+5=14-k), इसलिए (14-k=16) और (k=-2)। ऋणात्मक मान रखने पर संकेतों को ध्यान से देखें।
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यदि (p(x)=x-3 +ax-2 +bx-12), (p(2)=0) और (p(3)=0), तो (a+b) का मान क्या है?
If (p(x)=x-3 +ax-2 +bx-12), (p(2)=0), and (p(3)=0), what is the value of (a+b)?
#parameter
#zeros
#cubic polynomial
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
The conditions give (2a+b=2) and (3a+b=-5), so (a=-7), (b=16), and (a+b=9). When two values are given, form two equations.
Step 2
Why this answer is correct
The correct answer is C. (9). The conditions give (2a+b=2) and (3a+b=-5), so (a=-7), (b=16), and (a+b=9). When two values are given, form two equations.
Step 3
Exam Tip
शर्तों से (2a+b=2) और (3a+b=-5) मिलते हैं, इसलिए (a=-7), (b=16) और (a+b=9)। दो मान दिए हों तो दो समीकरण बनाएं।
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यदि (p(x)=x-3 -7x+6), तो इनमें से कौन-सा (p(x)) का गुणनखंड नहीं है?
If (p(x)=x-3 -7x+6), which of the following is not a factor of (p(x))?
#factor-check
#cubic
#trap
A (x+3)
B (x-1)
C (x-2)
D (x+3)
Explanation opens after your attempt
Step 1
Concept
(p(-3)=-27+21+6=0), so (x+3) is actually a factor. This reveals an option error, so check each option using (p(a)).
Step 2
Why this answer is correct
The correct answer is A. (x+3). (p(-3)=-27+21+6=0), so (x+3) is actually a factor. This reveals an option error, so check each option using (p(a)).
Step 3
Exam Tip
(p(-3)=-27+21+6=0), इसलिए (x+3) वास्तव में गुणनखंड है। सही जाँच में यह प्रश्न विकल्प-त्रुटि दिखाता है, इसलिए हर विकल्प को (p(a)) से जाँचें।
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यदि (p(x)=\sqrt{5}x-3 -\frac{2}{3}x+1), तो यह किस प्रकार का बहुपद है?
If (p(x)=\sqrt{5}x-3 -\frac{2}{3}x+1), what type of polynomial is it?
#classification
#cubic
#real-coefficients
A घन बहुपद / Cubic polynomial
B द्विघात बहुपद / Quadratic polynomial
C रेखीय बहुपद / Linear polynomial
D बहुपद नहीं / Not a polynomial
Explanation opens after your attempt
Correct Answer
A. घन बहुपद / Cubic polynomial
Step 1
Concept
The coefficients \(\sqrt{5}\) and \(-\frac{2}{3}\) are real numbers and the highest power is (3). Hence it is a cubic polynomial.
Step 2
Why this answer is correct
The correct answer is A. घन बहुपद / Cubic polynomial. The coefficients \(\sqrt{5}\) and \(-\frac{2}{3}\) are real numbers and the highest power is (3). Hence it is a cubic polynomial.
Step 3
Exam Tip
गुणांक \(\sqrt{5}\) और \(-\frac{2}{3}\) वास्तविक संख्याएँ हैं और सबसे बड़ी घात (3) है। इसलिए यह घन बहुपद है।
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यदि (p(x)=x-3 +x-2 -10x+8) और (x=1) शून्यक है, तो शेष द्विघात गुणनखंड क्या है?
If (p(x)=x-3 +x-2 -10x+8) and (x=1) is a zero, what is the remaining quadratic factor?
#division
#factorisation
#cubic
A \(x^2+2x-8\)
B \(x^2-x+8\)
C \(x^2+8x-2\)
D \(x^2-2x-8\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+2x-8\)
Step 1
Concept
Since (x=1) is a zero, (x-1) is a factor. Division gives \(x^2+2x-8\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+2x-8\). Since (x=1) is a zero, (x-1) is a factor. Division gives \(x^2+2x-8\).
Step 3
Exam Tip
(x=1) शून्यक होने से (x-1) गुणनखंड है। भाग देने पर \(x^2+2x-8\) मिलता है।
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यदि (p(x)=x-3 +3x-2 -4x-12), तो निम्न में से कौन-सा गुणनखंड है?
If (p(x)=x-3 +3x-2 -4x-12), which of the following is a factor?
#factor-theorem
#cubic
#polynomial
A (x+3)
B (x-3)
C (x+2)
D (x-4)
Explanation opens after your attempt
Step 1
Concept
(p(-3)=-27+27+12-12=0), so (x+3) is a factor. For (x+a), test (x=-a).
Step 2
Why this answer is correct
The correct answer is A. (x+3). (p(-3)=-27+27+12-12=0), so (x+3) is a factor. For (x+a), test (x=-a).
Step 3
Exam Tip
(p(-3)=-27+27+12-12=0), इसलिए (x+3) गुणनखंड है। (x+a) के लिए (x=-a) रखकर जाँचें।
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यदि (p(x)=x-3 -6x-2 +11x-6), तो (p(x)) के शून्यक कौन-से हैं?
If (p(x)=x-3 -6x-2 +11x-6), what are the zeroes of (p(x))?
#cubic
#zeroes
#factorisation
A (1,2,3)
B (-1,-2,-3)
C (1,-2,3)
D (2,3,6)
Explanation opens after your attempt
Correct Answer
A. (1,2,3)
Step 1
Concept
(x-3 -6x-2 +11x-6=(x-1)(x-2)(x-3)). Zeroes are read directly from the factors.
Step 2
Why this answer is correct
The correct answer is A. (1,2,3). (x-3 -6x-2 +11x-6=(x-1)(x-2)(x-3)). Zeroes are read directly from the factors.
Step 3
Exam Tip
(x-3 -6x-2 +11x-6=(x-1)(x-2)(x-3)) है। गुणनखंडों से शून्यक सीधे मिलते हैं।
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यदि (p(x)=x-3 -4x-2 +x+6), तो इनमें से कौन (p(x)) का शून्यक है?
If (p(x)=x-3 -4x-2 +x+6), which of these is a zero of (p(x))?
#zero-test
#cubic
#polynomial
A (2)
B (1)
C (-1)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(2)=8-16+2+6=0), so (2) is a zero. Test small integer options first.
Step 2
Why this answer is correct
The correct answer is A. (2). (p(2)=8-16+2+6=0), so (2) is a zero. Test small integer options first.
Step 3
Exam Tip
(p(2)=8-16+2+6=0), इसलिए (2) शून्यक है। विकल्पों में छोटे पूर्णांकों को पहले जाँचें।
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(p(x)=x-3 +2x-2 -4x-8) में (p(2)-p(-2)) क्या है?
For (p(x)=x-3 +2x-2 -4x-8), 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 -2x-2 -3x+4) में (p(1)) और (p(-1)) का गुणनफल क्या है?
What is the product of (p(1)) and (p(-1)) for (p(x)=x-3 -2x-2 -3x+4)?
#evaluation
#product
#cubic
A (-4)
B (0)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-2-3+4=0) and (p(-1)=-1-2+3+4=4), so the product is (0). Find both values first.
Step 2
Why this answer is correct
The correct answer is B. (0). (p(1)=1-2-3+4=0) and (p(-1)=-1-2+3+4=4), so the product is (0). Find both values first.
Step 3
Exam Tip
(p(1)=1-2-3+4=0) और (p(-1)=-1-2+3+4=4), इसलिए गुणनफल (0) है। पहले दोनों मान निकालें।
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यदि (p(x)=x-3 +3x-2 +3x+1), तो (p(-2)) क्या है?
If (p(x)=x-3 +3x-2 +3x+1), what is (p(-2))?
#identity
#cubic
#evaluation
A (-1)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
It is ((x+1)3 ), so (p(-2)=(-1)3 =-1). Recognizing identities reduces calculation.
Step 2
Why this answer is correct
The correct answer is A. (-1). It is ((x+1)3 ), so (p(-2)=(-1)3 =-1). Recognizing identities reduces calculation.
Step 3
Exam Tip
यह ((x+1)3 ) है, इसलिए (p(-2)=(-1)3 =-1)। पहचान पहचानने से गणना कम होती है।
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यदि (p(x)=2x-3 -8x), तो (p(-2)+p(2)) का मान क्या है?
If (p(x)=2x-3 -8x), what is the value of (p(-2)+p(2))?
#evaluation
#opposite inputs
#cubic
A (-16)
B (0)
C (16)
D (32)
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)=x-3 +ax-2 +bx-6) में (x=1) और (x=2) दोनों शून्य हैं, तो (a) क्या है?
If (x=1) and (x=2) are both zeros of (p(x)=x-3 +ax-2 +bx-6), what is (a)?
#zeros
#cubic
#parameter
A (-4)
B (-3)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=0) gives (a+b=5) and (p(2)=0) gives (2a+b=-1), so (a=-6). None of the listed choices is correct.
Step 2
Why this answer is correct
The correct answer is A. (-4). (p(1)=0) gives (a+b=5) and (p(2)=0) gives (2a+b=-1), so (a=-6). None of the listed choices is correct.
Step 3
Exam Tip
(p(1)=0) से (a+b=5) और (p(2)=0) से (2a+b=-1), इसलिए (a=-6) नहीं बल्कि (a=-6) आता है। विकल्पों में कोई सही नहीं है।
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यदि (p(x)=x-3 +ax-2 +bx+12) में (x=1) और (x=-3) दोनों शून्य हैं, तो (a+b) क्या है?
If (x=1) and (x=-3) are both zeros of (p(x)=x-3 +ax-2 +bx+12), what is (a+b)?
#zeros
#cubic
#parameter
A (-13)
B (-12)
C (-11)
D (-10)
Explanation opens after your attempt
Step 1
Concept
From (p(1)=0), we directly get (a+b=-13). The second condition checks consistency, but the first is enough for the asked sum.
Step 2
Why this answer is correct
The correct answer is A. (-13). From (p(1)=0), we directly get (a+b=-13). The second condition checks consistency, but the first is enough for the asked sum.
Step 3
Exam Tip
(p(1)=0) से (a+b=-13) सीधे मिलता है। दूसरी शर्त संगति जांचती है लेकिन पूछे गए योग के लिए पहली शर्त पर्याप्त है।
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(p(x)=x-3 -x-2 +x-1) के लिए (p(1)) क्या है?
What is (p(1)) for (p(x)=x-3 -x-2 +x-1)?
#evaluation
#cubic
#zero
A (-1)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-1+1-1=0). Add alternating signs in order.
Step 2
Why this answer is correct
The correct answer is B. (0). (p(1)=1-1+1-1=0). Add alternating signs in order.
Step 3
Exam Tip
(p(1)=1-1+1-1=0)। वैकल्पिक संकेतों को क्रम से जोड़ें।
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यदि (p(x)=2x-3 +rx-2 +s), (p(0)=-3) और (p(1)=4), तो (r) क्या है?
If (p(x)=2x-3 +rx-2 +s), (p(0)=-3), and (p(1)=4), what is (r)?
#parameter
#evaluation
#cubic
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(0)=s=-3) and (p(1)=2+r-3=4), so (r=5). First use (x=0) to find the constant term.
Step 2
Why this answer is correct
The correct answer is C. (5). (p(0)=s=-3) and (p(1)=2+r-3=4), so (r=5). First use (x=0) to find the constant term.
Step 3
Exam Tip
(p(0)=s=-3) और (p(1)=2+r-3=4), इसलिए (r=5)। पहले (x=0) से अचर पद निकालें।
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यदि (p(x)=x-3 +ax+b), (p(1)=6) और (p(-1)=-4), तो (a) का मान क्या है?
If (p(x)=x-3 +ax+b), (p(1)=6), and (p(-1)=-4), what is the value of (a)?
#parameter
#cubic
#evaluation
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The conditions give (1+a+b=6) and (-1-a+b=-4). Solving them gives (a=4).
Step 2
Why this answer is correct
The correct answer is C. (4). The conditions give (1+a+b=6) and (-1-a+b=-4). Solving them gives (a=4).
Step 3
Exam Tip
शर्तों से (1+a+b=6) और (-1-a+b=-4) मिलते हैं। इन्हें हल करने पर (a=4) मिलता है।
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किस मान के लिए (p(x)=x-3 -5x-2 +mx+8) में (p(1)=0) होगा?
For what value of (m) will (p(1)=0) in (p(x)=x-3 -5x-2 +mx+8)?
#parameter
#evaluation
#cubic
A (-4)
B (-3)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-5+m+8=m+4), so (m=-4). Substitute the given value and solve the equation.
Step 2
Why this answer is correct
The correct answer is A. (-4). (p(1)=1-5+m+8=m+4), so (m=-4). Substitute the given value and solve the equation.
Step 3
Exam Tip
(p(1)=1-5+m+8=m+4), इसलिए (m=-4)। दिए गए मान को रखकर समीकरण हल करें।
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(p(x)=3x-3 -8x-2 +7x-2) के लिए (p(2)) का मान क्या है?
What is the value of (p(2)) for (p(x)=3x-3 -8x-2 +7x-2)?
#evaluation
#cubic
#substitution
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
(p(2)=24-32+14-2=4). Evaluate each term separately and then add.
Step 2
Why this answer is correct
The correct answer is B. (4). (p(2)=24-32+14-2=4). Evaluate each term separately and then add.
Step 3
Exam Tip
(p(2)=24-32+14-2=4)। हर पद का मान अलग निकालकर जोड़ें।
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यदि (p(x)=kx-3 -2x-2 +5x-4) और (p(1)=7), तो (k) का मान क्या है?
If (p(x)=kx-3 -2x-2 +5x-4) and (p(1)=7), what is the value of (k)?
#evaluation
#parameter
#cubic polynomial
A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
(p(1)=k-2+5-4=k-1), so (k-1=7) and (k=8). Substitute first and then form a simple equation.
Step 2
Why this answer is correct
The correct answer is C. (8). (p(1)=k-2+5-4=k-1), so (k-1=7) and (k=8). Substitute first and then form a simple equation.
Step 3
Exam Tip
(p(1)=k-2+5-4=k-1), इसलिए (k-1=7) और (k=8)। मान रखने के बाद सरल समीकरण बनाएं।
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किस बहुपद के शून्यक (0), (2) और (-3) हैं?
Which polynomial has zeroes (0), (2), and (-3)?
#polynomials
#formation
#cubic
#hard
A \(x^3+x^2-6x\)
B \(x^3-x^2-6x\)
C \(x^3+x^2+6x\)
D \(x^3-5x^2+6x\)
Explanation opens after your attempt
Correct Answer
A. \(x^3+x^2-6x\)
Step 1
Concept
From the zeroes, the polynomial is (x(x-2)(x+3)). Expanding gives \(x^3+x^2-6x\).
Step 2
Why this answer is correct
The correct answer is A. \(x^3+x^2-6x\). From the zeroes, the polynomial is (x(x-2)(x+3)). Expanding gives \(x^3+x^2-6x\).
Step 3
Exam Tip
शून्यकों से बहुपद (x(x-2)(x+3)) बनेगा। इसे फैलाने पर \(x^3+x^2-6x\) मिलता है।
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बहुपद \(2x^3-9x^2+13x-6\) का एक गुणनखंड कौन सा है?
Which is a factor of \(2x^3-9x^2+13x-6\)?
#polynomials
#factor_check
#cubic
#hard
A (x-1)
B (x+1)
C (x-4)
D (x+3)
Explanation opens after your attempt
Step 1
Concept
(p(1)=2-9+13-6=0), so (x-1) is a factor. In option checking, try small values first.
Step 2
Why this answer is correct
The correct answer is A. (x-1). (p(1)=2-9+13-6=0), so (x-1) is a factor. In option checking, try small values first.
Step 3
Exam Tip
(p(1)=2-9+13-6=0) है इसलिए (x-1) गुणनखंड है। विकल्प जांच में छोटे मान पहले लगाएं।
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यदि (p(x)=x-3 +px-2 +qx-6) के शून्यक (1), (2) और (3) हैं, तो (p+q) का सही मान क्या है?
If the zeroes of (p(x)=x-3 +px-2 +qx-6) are (1), (2), and (3), what is the correct value of (p+q)?
#polynomials
#cubic
#coefficient_matching
#hard
A (5)
B (-5)
C (17)
D (-17)
Explanation opens after your attempt
Step 1
Concept
From ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6), (p=-6) and (q=11). Hence (p+q=5).
Step 2
Why this answer is correct
The correct answer is A. (5). From ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6), (p=-6) and (q=11). Hence (p+q=5).
Step 3
Exam Tip
((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6) से (p=-6) और (q=11)। अतः (p+q=5) है।
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यदि (p(x)=x-3 +px-2 +qx-6) के शून्यक (1), (2) और (3) हैं, तो (p+q) का मान क्या है?
If the zeroes of (p(x)=x-3 +px-2 +qx-6) are (1), (2), and (3), what is (p+q)?
#polynomials
#cubic
#coefficients
#hard
A (-5)
B (5)
C (11)
D (0)
Explanation opens after your attempt
Step 1
Concept
The polynomial is ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6). Hence (p=-6), (q=11), so (p+q=5).
Step 2
Why this answer is correct
The correct answer is A. (-5). The polynomial is ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6). Hence (p=-6), (q=11), so (p+q=5).
Step 3
Exam Tip
बहुपद ((x-1)(x-2)(x-3)=x-3 -6x-2 +11x-6) है। इसलिए (p=-6), (q=11) और (p+q=5) नहीं बल्कि (5) है।
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बहुपद (p(x)=ax-3 +bx-2 +cx+d) में \(a\ne0\) है। यदि (p(x)) को रैखिक बहुपद कहा जाए, तो यह कथन क्यों गलत है?
In the polynomial (p(x)=ax-3 +bx-2 +cx+d), \(a\ne0\). Why is it wrong to call (p(x)) a linear polynomial?
#polynomials
#degree
#cubic
#hard
A क्योंकि घात (1) है / Because degree is (1)
B क्योंकि घात (2) है / Because degree is (2)
C क्योंकि घात (3) है / Because degree is (3)
D क्योंकि स्थिर पद (d) है / Because constant term is (d)
Explanation opens after your attempt
Correct Answer
C. क्योंकि घात (3) है / Because degree is (3)
Step 1
Concept
The highest power is (3), so the polynomial is cubic. In exams, always check the highest non-zero exponent.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि घात (3) है / Because degree is (3). The highest power is (3), so the polynomial is cubic. In exams, always check the highest non-zero exponent.
Step 3
Exam Tip
सबसे बड़ी घात (3) है इसलिए बहुपद घन है। परीक्षा में हमेशा सबसे बड़े शून्येतर घातांक को देखें।
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(p(x)=2x-3 +x-2 -5x+2) में (p(2)) और (p(-1)) का अंतर (p(2)-p(-1)) क्या है?
For (p(x)=2x-3 +x-2 -5x+2), what is the difference (p(2)-p(-1))?
#evaluation
#difference
#cubic
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(2)=16+4-10+2=12) and (p(-1)=-2+1+5+2=6), so the difference is (6). Find both values separately.
Step 2
Why this answer is correct
The correct answer is D. (6). (p(2)=16+4-10+2=12) and (p(-1)=-2+1+5+2=6), so the difference is (6). Find both values separately.
Step 3
Exam Tip
(p(2)=16+4-10+2=12) और (p(-1)=-2+1+5+2=6), इसलिए अंतर (6) है। दोनों मान अलग निकालें।
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(p(x)=2x-3 +x-2 -5x+2) में (p(1)) और (p(-1)) का गुणनफल क्या है?
What is the product of (p(1)) and (p(-1)) for (p(x)=2x-3 +x-2 -5x+2)?
#evaluation
#product
#cubic
A (-12)
B (-8)
C (0)
D (12)
Explanation opens after your attempt
Step 1
Concept
(p(1)=2+1-5+2=0), and (p(-1)=-2+1+5+2=6), so the product is (0). The correct option is (0).
Step 2
Why this answer is correct
The correct answer is A. (-12). (p(1)=2+1-5+2=0), and (p(-1)=-2+1+5+2=6), so the product is (0). The correct option is (0).
Step 3
Exam Tip
(p(1)=0) नहीं बल्कि (2+1-5+2=0), और (p(-1)=-2+1+5+2=6), इसलिए गुणनफल (0) है। सही विकल्प (0) है।
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यदि (p(x)=x-3 -3x-2 +3x-1), तो (p(2)) क्या है?
If (p(x)=x-3 -3x-2 +3x-1), what is (p(2))?
#identity
#cubic
#evaluation
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
It is ((x-1)3 ), so (p(2)=(2-1)3 =1). Recognizing identities reduces calculation.
Step 2
Why this answer is correct
The correct answer is B. (1). It is ((x-1)3 ), so (p(2)=(2-1)3 =1). Recognizing identities reduces calculation.
Step 3
Exam Tip
यह ((x-1)3 ) है, इसलिए (p(2)=(2-1)3 =1)। पहचान पहचानने से गणना कम होती है।
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यदि (p(x)=x-3 -4x), तो (p(-2)+p(2)) का मान क्या है?
If (p(x)=x-3 -4x), what is the value of (p(-2)+p(2))?
#evaluation
#opposite inputs
#cubic
A (-8)
B (0)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(p(-2)=0) and (p(2)=0), so the sum is (0). It behaves like an odd polynomial.
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). It behaves like an odd polynomial.
Step 3
Exam Tip
(p(-2)=0) और (p(2)=0), इसलिए योग (0) है। यह विषम बहुपद जैसा व्यवहार करता है।
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यदि (p(x)=x-3 +ax-2 +bx+4) में (x=1) और (x=-1) दोनों शून्य हैं, तो (a) क्या है?
If (x=1) and (x=-1) are both zeros of (p(x)=x-3 +ax-2 +bx+4), what is (a)?
#zeros
#cubic
#parameter
A (-4)
B (-2)
C (2)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1+a+b+4=0) and (p(-1)=-1+a-b+4=0); adding gives (2a+8=0), so (a=-4). Add signs carefully.
Step 2
Why this answer is correct
The correct answer is A. (-4). (p(1)=1+a+b+4=0) and (p(-1)=-1+a-b+4=0); adding gives (2a+8=0), so (a=-4). Add signs carefully.
Step 3
Exam Tip
(p(1)=1+a+b+4=0) और (p(-1)=-1+a-b+4=0), इसलिए (2a+4=0) नहीं बल्कि जोड़ने पर (2a+8=0), अतः (a=-4)। संकेतों को सावधानी से जोड़ें।
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यदि (p(x)=x-3 +ax-2 +bx+6) में (x=1) और (x=-2) दोनों शून्य हैं, तो (a-b) क्या है?
If (x=1) and (x=-2) are both zeros of (p(x)=x-3 +ax-2 +bx+6), what is (a-b)?
#zeros
#cubic
#simultaneous equations
A (-2)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
The conditions give (a+b=-7) and (4a-2b=2), so (a=-2), (b=-5), and (a-b=3). The correct value is (3).
Step 2
Why this answer is correct
The correct answer is C. (4). The conditions give (a+b=-7) and (4a-2b=2), so (a=-2), (b=-5), and (a-b=3). The correct value is (3).
Step 3
Exam Tip
शर्तों से (a+b=-7) और (4a-2b=2), इसलिए (a=-2), (b=-5) और (a-b=3)। सही गणना से (a-b=3) मिलता है।
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(p(x)=x-3 +x-2 +x+1) के लिए (p(-1)) क्या है?
What is (p(-1)) for (p(x)=x-3 +x-2 +x+1)?
#evaluation
#cubic
#zero
A (-2)
B (0)
C (1)
D (2)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=-1+1-1+1=0). Add alternating signs in order.
Step 2
Why this answer is correct
The correct answer is B. (0). (p(-1)=-1+1-1+1=0). Add alternating signs in order.
Step 3
Exam Tip
(p(-1)=-1+1-1+1=0)। वैकल्पिक संकेतों को क्रम से जोड़ें।
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यदि (p(x)=x-3 +rx-2 +s), (p(0)=5) और (p(1)=9), तो (r) क्या है?
If (p(x)=x-3 +rx-2 +s), (p(0)=5), and (p(1)=9), what is (r)?
#parameter
#evaluation
#cubic
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(0)=s=5) and (p(1)=1+r+5=9), so (r=3). First use (x=0) to find the constant term.
Step 2
Why this answer is correct
The correct answer is C. (3). (p(0)=s=5) and (p(1)=1+r+5=9), so (r=3). First use (x=0) to find the constant term.
Step 3
Exam Tip
(p(0)=s=5) और (p(1)=1+r+5=9), इसलिए (r=3)। पहले (x=0) से अचर पद निकालें।
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यदि (p(x)=x-3 +px+q), (p(1)=4) और (p(-1)=-2), तो (p) का मान क्या है?
If (p(x)=x-3 +px+q), (p(1)=4), and (p(-1)=-2), what is the value of (p)?
#parameter
#cubic
#evaluation
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The conditions give (1+p+q=4) and (-1-p+q=-2), so (p=2). Subtracting the two equations is quick.
Step 2
Why this answer is correct
The correct answer is B. (2). The conditions give (1+p+q=4) and (-1-p+q=-2), so (p=2). Subtracting the two equations is quick.
Step 3
Exam Tip
शर्तों से (1+p+q=4) और (-1-p+q=-2), इसलिए (p=2)। दो समीकरणों को घटाना तेज तरीका है।
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किस मान के लिए (p(x)=x-3 -4x-2 +mx+6) में (p(1)=0) होगा?
For what value of (m) will (p(1)=0) in (p(x)=x-3 -4x-2 +mx+6)?
#parameter
#evaluation
#cubic
A (-3)
B (-2)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-4+m+6=m+3), so (m=-3). Substitute the given value and form a simple equation.
Step 2
Why this answer is correct
The correct answer is A. (-3). (p(1)=1-4+m+6=m+3), so (m=-3). Substitute the given value and form a simple equation.
Step 3
Exam Tip
(p(1)=1-4+m+6=m+3), इसलिए (m=-3)। दिए गए मान को रखकर सरल समीकरण बनाएं।
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(p(x)=2x-3 -9x-2 +12x-5) के लिए (p(2)) का मान क्या है?
What is the value of (p(2)) for (p(x)=2x-3 -9x-2 +12x-5)?
#evaluation
#cubic
#substitution
A (-1)
B (0)
C (1)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(2)=16-36+24-5=-1). Evaluate each term separately and then add.
Step 2
Why this answer is correct
The correct answer is A. (-1). (p(2)=16-36+24-5=-1). Evaluate each term separately and then add.
Step 3
Exam Tip
(p(2)=16-36+24-5=-1)। प्रत्येक पद का मान अलग निकालकर जोड़ें।
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(p(x)=x-3 -2x-2 -5x+6) के लिए कौन सा मान (p(x)=0) बनाता है?
For (p(x)=x-3 -2x-2 -5x+6), which value makes (p(x)=0)?
#zero
#cubic polynomial
#evaluation
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-2-5+6=0), so (1) is a zero of this polynomial. Substituting options is a quick method.
Step 2
Why this answer is correct
The correct answer is A. (1). (p(1)=1-2-5+6=0), so (1) is a zero of this polynomial. Substituting options is a quick method.
Step 3
Exam Tip
(p(1)=1-2-5+6=0), इसलिए (1) इस बहुपद का शून्य है। विकल्पों को रखकर जांचना तेज तरीका है।
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कौन सा व्यंजक (x) में बहुपद है लेकिन (x) में द्विघात नहीं है?
Which expression is a polynomial in (x) but not quadratic in (x)?
#classification
#cubic
#not quadratic
A \(4x^2-3x+1\)
B \(6x^3-2x+9\)
C \(x^2+\frac{5}{x}\)
D \(7\sqrt{x}+2\)
Explanation opens after your attempt
Correct Answer
B. \(6x^3-2x+9\)
Step 1
Concept
\(6x^3-2x+9\) is a polynomial and its degree is (3), so it is not quadratic. Classify by degree.
Step 2
Why this answer is correct
The correct answer is B. \(6x^3-2x+9\). \(6x^3-2x+9\) is a polynomial and its degree is (3), so it is not quadratic. Classify by degree.
Step 3
Exam Tip
\(6x^3-2x+9\) बहुपद है और इसकी घात (3) है, इसलिए यह द्विघात नहीं है। घात से वर्गीकरण करें।
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कौन सा कथन (p(x)=x-3 +1) के बारे में सही है?
Which statement about (p(x)=x-3 +1) is correct?
#cubic
#degree
#classification
A यह रैखिक बहुपद है / It is a linear polynomial
B यह द्विघात बहुपद है / It is a quadratic polynomial
C यह घन बहुपद है / It is a cubic polynomial
D यह बहुपद नहीं है / It is not a polynomial
Explanation opens after your attempt
Correct Answer
C. यह घन बहुपद है / It is a cubic polynomial
Step 1
Concept
In (p(x)=x-3 +1), the highest power is (3), so it is a cubic polynomial. Decide the type of a polynomial by its degree.
Step 2
Why this answer is correct
The correct answer is C. यह घन बहुपद है / It is a cubic polynomial. In (p(x)=x-3 +1), the highest power is (3), so it is a cubic polynomial. Decide the type of a polynomial by its degree.
Step 3
Exam Tip
(p(x)=x-3 +1) में सबसे बड़ी घात (3) है इसलिए यह घन बहुपद है। बहुपद का प्रकार उसकी घात से तय करें।
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(p(x)=x-3 -4x-2 +x+6) में (p(-1)) का मान क्या है?
What is the value of (p(-1)) in (p(x)=x-3 -4x-2 +x+6)?
#cubic polynomial
#evaluation
#zero
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(p(-1)=-1-4-1+6=0). Therefore (-1) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(-1)=-1-4-1+6=0). Therefore (-1) is a zero of this polynomial.
Step 3
Exam Tip
(p(-1)=-1-4-1+6=0)। इसलिए (-1) इस बहुपद का शून्य है।
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(q(x)=x-3 +2x-2 -5x-6) के लिए (q(-2)) क्या होगा?
For (q(x)=x-3 +2x-2 -5x-6), what is (q(-2))?
#evaluation
#negative input
#cubic
A (0)
B (2)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(q(-2)=-8+8+10-6=4). Check the sign of every term separately when substituting a negative value.
Step 2
Why this answer is correct
The correct answer is C. (4). (q(-2)=-8+8+10-6=4). Check the sign of every term separately when substituting a negative value.
Step 3
Exam Tip
(q(-2)=-8+8+10-6=4)। ऋणात्मक मान रखते समय प्रत्येक पद का संकेत अलग जांचें।
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कौन सा विकल्प \(2x^3-5x^2+x-4\) की घात और नियत पद को सही बताता है?
Which option correctly gives the degree and constant term of \(2x^3-5x^2+x-4\)?
#degree
#constant-term
#cubic-polynomial
A घात (3), नियत पद (-4) / Degree (3), constant term (-4)
B घात (2), नियत पद (1) / Degree (2), constant term (1)
C घात (1), नियत पद (-5) / Degree (1), constant term (-5)
D घात (4), नियत पद (2) / Degree (4), constant term (2)
Explanation opens after your attempt
Correct Answer
A. घात (3), नियत पद (-4) / Degree (3), constant term (-4)
Step 1
Concept
The highest power is (3) and the term without (x) is (-4). So the correct pair is degree (3), constant term (-4).
Step 2
Why this answer is correct
The correct answer is A. घात (3), नियत पद (-4) / Degree (3), constant term (-4). The highest power is (3) and the term without (x) is (-4). So the correct pair is degree (3), constant term (-4).
Step 3
Exam Tip
सबसे बड़ी घात (3) है और बिना (x) वाला पद (-4) है। इसलिए सही जोड़ी घात (3), नियत पद (-4) है।
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यदि (p(x)=x-3 -2x-2 +x), तो (p(1)) का मान क्या है?
If (p(x)=x-3 -2x-2 +x), what is the value of (p(1))?
#cubic-polynomial
#zero
#substitution
A (0)
B (1)
C (2)
D (-1)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-2+1=0). Therefore (1) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(1)=1-2+1=0). Therefore (1) is a zero of this polynomial.
Step 3
Exam Tip
(p(1)=1-2+1=0) है। इसलिए (1) इस बहुपद का शून्य है।
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कौन सा विकल्प \(x^3-1\) के प्रकार को सही बताता है?
Which option correctly describes the type of \(x^3-1\)?
#cubic-binomial
#classification
#terms
A रैखिक द्विपदी / Linear binomial
B द्विघात त्रिपदी / Quadratic trinomial
C त्रिघात द्विपदी / Cubic binomial
D नियत एकपदी / Constant monomial
Explanation opens after your attempt
Correct Answer
C. त्रिघात द्विपदी / Cubic binomial
Step 1
Concept
\(x^3-1\) has degree (3) and (2) terms. So it is a cubic binomial.
Step 2
Why this answer is correct
The correct answer is C. त्रिघात द्विपदी / Cubic binomial. \(x^3-1\) has degree (3) and (2) terms. So it is a cubic binomial.
Step 3
Exam Tip
\(x^3-1\) की घात (3) है और इसमें (2) पद हैं। इसलिए यह त्रिघात द्विपदी है।
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यदि (r(x)=x-3 -4x), तो (r(-2)) का मान क्या है?
If (r(x)=x-3 -4x), what is the value of (r(-2))?
#substitution
#cubic-polynomial
#zero
A (0)
B (2)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
(r(-2)=(-2)3 -4(-2)=-8+8=0). Brackets are important for negative values.
Step 2
Why this answer is correct
The correct answer is A. (0). (r(-2)=(-2)3 -4(-2)=-8+8=0). Brackets are important for negative values.
Step 3
Exam Tip
(r(-2)=(-2)3 -4(-2)=-8+8=0) है। ऋणात्मक मानों में कोष्ठक लगाना जरूरी है।
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बहुपद (p(x)=x-3 -3x-2 +3x-1) का कौन सा मान (0) देता है?
Which value gives (0) for the polynomial (p(x)=x-3 -3x-2 +3x-1)?
#zero
#cubic polynomial
#evaluation
A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-3+3-1=0), so (1) is a zero of this polynomial. Substituting options can quickly identify the zero.
Step 2
Why this answer is correct
The correct answer is B. (1). (p(1)=1-3+3-1=0), so (1) is a zero of this polynomial. Substituting options can quickly identify the zero.
Step 3
Exam Tip
(p(1)=1-3+3-1=0), इसलिए (1) इस बहुपद का शून्य है। विकल्पों को रखने से शून्य जल्दी मिल सकता है।
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निम्न में से किस बहुपद का प्रमुख गुणांक (-2) है?
Which polynomial has leading coefficient (-2)?
#leading-coefficient
#cubic-polynomial
#easy
A \(5x^2-2x+1\)
B \(-2x^3+4x+7\)
C \(x^2-2\)
D (3x-2)
Explanation opens after your attempt
Correct Answer
B. \(-2x^3+4x+7\)
Step 1
Concept
The leading term of \(-2x^3+4x+7\) is \(-2x^3\). So the leading coefficient is (-2).
Step 2
Why this answer is correct
The correct answer is B. \(-2x^3+4x+7\). The leading term of \(-2x^3+4x+7\) is \(-2x^3\). So the leading coefficient is (-2).
Step 3
Exam Tip
\(-2x^3+4x+7\) का प्रमुख पद \(-2x^3\) है। इसलिए प्रमुख गुणांक (-2) है।
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\(5x^3+2x^2-x+8\) में \(x^3\) का गुणांक क्या है?
What is the coefficient of \(x^3\) in \(5x^3+2x^2-x+8\)?
#coefficient
#cubic-term
#polynomial
A (5)
B (2)
C (-1)
D (8)
Explanation opens after your attempt
Step 1
Concept
The multiplier of \(x^3\) is (5). A coefficient is identified from its related term.
Step 2
Why this answer is correct
The correct answer is A. (5). The multiplier of \(x^3\) is (5). A coefficient is identified from its related term.
Step 3
Exam Tip
\(x^3\) के साथ लगा गुणक (5) है। गुणांक हमेशा संबंधित पद से पहचाना जाता है।
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(p(x)=2x-3 +3x-2 -5) में (x) का गुणांक क्या है?
What is the coefficient of (x) in (p(x)=2x-3 +3x-2 -5)?
#coefficient
#missing term
#cubic
A (2)
B (3)
C (0)
D (-5)
Explanation opens after your attempt
Step 1
Concept
There is no (x)-term, so its coefficient is (0). Treat the missing term as (0x).
Step 2
Why this answer is correct
The correct answer is C. (0). There is no (x)-term, so its coefficient is (0). Treat the missing term as (0x).
Step 3
Exam Tip
इसमें (x) का पद उपस्थित नहीं है इसलिए उसका गुणांक (0) है। अनुपस्थित पद को (0x) समझें।
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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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(p(x)=x-3 -6x-2 +11x-6) में (p(1)) का मान क्या है?
What is the value of (p(1)) in (p(x)=x-3 -6x-2 +11x-6)?
#evaluation
#cubic polynomial
#zero
A (0)
B (1)
C (6)
D (11)
Explanation opens after your attempt
Step 1
Concept
(p(1)=1-6+11-6=0). Therefore (1) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). (p(1)=1-6+11-6=0). Therefore (1) is a zero of this polynomial.
Step 3
Exam Tip
(p(1)=1-6+11-6=0)। इसलिए (1) इस बहुपद का शून्य है।
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(p(x)=4x-3 -2x-2 +7x-1) में \(x^3\) के पद का गुणांक क्या है?
What is the coefficient of the \(x^3\) term in (p(x)=4x-3 -2x-2 +7x-1)?
#coefficient
#cubic term
#polynomial
A (4)
B (-2)
C (7)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The coefficient attached to \(x^3\) is (4). Identify the exponent and coefficient separately.
Step 2
Why this answer is correct
The correct answer is A. (4). The coefficient attached to \(x^3\) is (4). Identify the exponent and coefficient separately.
Step 3
Exam Tip
\(x^3\) के साथ गुणांक (4) जुड़ा है। घात और गुणांक को अलग अलग पहचानें।
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यदि किसी बहुपद की घात (3) है, तो उसे क्या कहते हैं?
If a polynomial has degree (3), what is it called?
#polynomials
#cubic
#easy
#degree
A घन बहुपद / Cubic polynomial
B द्विघात बहुपद / Quadratic polynomial
C रैखिक बहुपद / Linear polynomial
D नियत बहुपद / Constant polynomial
Explanation opens after your attempt
Correct Answer
A. घन बहुपद / Cubic polynomial
Step 1
Concept
A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.
Step 2
Why this answer is correct
The correct answer is A. घन बहुपद / Cubic polynomial. A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.
Step 3
Exam Tip
घात (3) वाला बहुपद घन बहुपद कहलाता है। सबसे बड़ी घात ही नाम तय करती है।
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\(2x^3+x^2+x+8\) किस प्रकार का बहुपद है?
What type of polynomial is \(2x^3+x^2+x+8\)?
#polynomials
#cubic
#easy
#type
A रैखिक / Linear
B द्विघात / Quadratic
C घन / Cubic
D नियत / Constant
Explanation opens after your attempt
Correct Answer
C. घन / Cubic
Step 1
Concept
The highest power is (3), so it is a cubic polynomial. Classify a polynomial by its degree.
Step 2
Why this answer is correct
The correct answer is C. घन / Cubic. The highest power is (3), so it is a cubic polynomial. Classify a polynomial by its degree.
Step 3
Exam Tip
सबसे बड़ी घात (3) है इसलिए यह घन बहुपद है। बहुपद का प्रकार उसकी घात से तय करें।
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यदि (p(x)=x-3 -3x), तो (p\(\sqrt{3}\)) का मान क्या है?
If (p(x)=x-3 -3x), what is (p\(\sqrt{3}\))?
#cubic
#polynomial zero
#irrational
A (0)
B (3)
C \(3\sqrt{3}\)
D \(-3\sqrt{3}\)
Explanation opens after your attempt
Step 1
Concept
(\(\sqrt{3}\)3 =3\sqrt{3}), so \(3\sqrt{3}-3\sqrt{3}=0\). Simplifying powers is the key step in such questions.
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\sqrt{3}\)3 =3\sqrt{3}), so \(3\sqrt{3}-3\sqrt{3}=0\). Simplifying powers is the key step in such questions.
Step 3
Exam Tip
(\(\sqrt{3}\)3 =3\sqrt{3}), इसलिए \(3\sqrt{3}-3\sqrt{3}=0\) है। परीक्षा में ऐसे प्रश्नों में घात को सरल करना मुख्य कदम है।
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यदि (p(x)=x-3 -2x), तो (p\(\sqrt{2}\)) क्या है?
If (p(x)=x-3 -2x), what is (p\(\sqrt{2}\))?
#cubic polynomial
#irrational value
#zero
A (0)
B \(\sqrt{2}\)
C \(2\sqrt{2}\)
D (4)
Explanation opens after your attempt
Step 1
Concept
(\(\sqrt{2}\)3 =2\sqrt{2}), so \(2\sqrt{2}-2\sqrt{2}=0\). Remember (\(\sqrt{a}\)3 =a\sqrt{a}).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\sqrt{2}\)3 =2\sqrt{2}), so \(2\sqrt{2}-2\sqrt{2}=0\). Remember (\(\sqrt{a}\)3 =a\sqrt{a}).
Step 3
Exam Tip
(\(\sqrt{2}\)3 =2\sqrt{2}), इसलिए \(2\sqrt{2}-2\sqrt{2}=0\) है। परीक्षा में (\(\sqrt{a}\)3 =a\sqrt{a}) याद रखें।
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यदि \(\alpha=1+\sqrt{2}\) और \(\beta=1-\sqrt{2}\), तो \(\alpha^3+\beta^3\) क्या है?
If \(\alpha=1+\sqrt{2}\) and \(\beta=1-\sqrt{2}\), what is \(\alpha^3+\beta^3\)?
#cubic-expression
#conjugates
#irrational
A (14)
B (-4)
C (2)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(\alpha+\beta=2\) and \(\alpha\beta=-1\), so (\alpha-3 +\beta-3 =23 -3(-1)(2)=14). Use (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)).
Step 2
Why this answer is correct
The correct answer is A. (14). \(\alpha+\beta=2\) and \(\alpha\beta=-1\), so (\alpha-3 +\beta-3 =23 -3(-1)(2)=14). Use (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)).
Step 3
Exam Tip
\(\alpha+\beta=2\) और \(\alpha\beta=-1\), इसलिए (\alpha-3 +\beta-3 =23 -3(-1)(2)=14)। घन योग में (\alpha-3 +\beta-3 =\(\alpha+\beta\)3 -3\alpha\beta\(\alpha+\beta\)) लगाएँ।
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यदि बहुपद (p(x)=5(x+1)(x-2)(x-4)) है तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?
If (p(x)=5(x+1)(x-2)(x-4)), at how many distinct points will the graph cut the (x)-axis?
#cubic
#factor-form
#distinct-intercepts
A तीन / Three
B दो / Two
C एक / One
D पाँच / Five
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.
Step 3
Exam Tip
गुणनखंडों से शून्यक (-1), (2), और (4) हैं। तीन अलग शून्यक तीन अलग (x)-प्रतिच्छेद देते हैं।
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ग्राफ (x)-अक्ष को ((-2,0)), ((0,0)), और ((5,0)) पर काटता है। कौन सा कथन सही है?
The graph cuts the (x)-axis at ((-2,0)), ((0,0)), and ((5,0)). Which statement is correct?
#multiple-zeroes
#origin
#cubic
A शून्यक (-2,0,5) हैं / The zeroes are (-2,0,5)
B शून्यक केवल (-2) और (5) हैं / The zeroes are only (-2) and (5)
C शून्यक ((0,0)) नहीं हो सकता / ((0,0)) cannot give a zero
D शून्यकों की संख्या दो है / The number of zeroes is two
Explanation opens after your attempt
Correct Answer
A. शून्यक (-2,0,5) हैं / The zeroes are (-2,0,5)
Step 1
Concept
The origin also lies on the (x)-axis so (0) is also a zero. Write the (x)-values of all intercepts.
Step 2
Why this answer is correct
The correct answer is A. शून्यक (-2,0,5) हैं / The zeroes are (-2,0,5). The origin also lies on the (x)-axis so (0) is also a zero. Write the (x)-values of all intercepts.
Step 3
Exam Tip
मूल बिंदु भी (x)-अक्ष पर है इसलिए (0) भी शून्यक है। सभी (x)-प्रतिच्छेदों के (x)-मान लिखें।
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