Question 1/10
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 27
यदि किसी द्विघात बहुपद के शून्यक \(3+\sqrt{5}\) और \(3-\sqrt{5}\) हैं, तो उनके योग का प्रकार क्या है?
If the zeroes of a quadratic polynomial are \(3+\sqrt{5}\) and \(3-\sqrt{5}\), what is the type of their sum?
#conjugate-irrationals
#zeroes
#sum
A अपरिमेय संख्या / Irrational number
B परिमेय संख्या / Rational number
C अवास्तविक संख्या / Non-real number
D ऋणात्मक अपरिमेय संख्या / Negative irrational number
Explanation opens after your attempt
Correct Answer
B. परिमेय संख्या / Rational number
Step 1
Concept
The sum is \(3+\sqrt{5}+3-\sqrt{5}=6\), which is rational. Conjugate irrational numbers often have a rational sum.
Step 2
Why this answer is correct
The correct answer is B. परिमेय संख्या / Rational number. The sum is \(3+\sqrt{5}+3-\sqrt{5}=6\), which is rational. Conjugate irrational numbers often have a rational sum.
Step 3
Exam Tip
योग \(3+\sqrt{5}+3-\sqrt{5}=6\) है, जो परिमेय है। संयुग्मी अपरिमेय संख्याओं का योग अक्सर परिमेय होता है।
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Question 2/10
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26
यदि \(\alpha=\sqrt{12}\) और \(\beta=-\sqrt{3}\), तो \(\alpha+\beta\) क्या है?
If \(\alpha=\sqrt{12}\) and \(\beta=-\sqrt{3}\), what is \(\alpha+\beta\)?
#radicals
#real-numbers
#sum
A \(\sqrt{3}\)
B \(3\sqrt{3}\)
C \(-\sqrt{3}\)
D (0)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{3}\)
Step 1
Concept
\(\sqrt{12}=2\sqrt{3}\), so \(\alpha+\beta=2\sqrt{3}-\sqrt{3}=\sqrt{3}\). Simplifying radicals is important.
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{3}\). \(\sqrt{12}=2\sqrt{3}\), so \(\alpha+\beta=2\sqrt{3}-\sqrt{3}=\sqrt{3}\). Simplifying radicals is important.
Step 3
Exam Tip
\(\sqrt{12}=2\sqrt{3}\), इसलिए \(\alpha+\beta=2\sqrt{3}-\sqrt{3}=\sqrt{3}\)। करणी सरल करना जरूरी है।
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Question 3/10
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि (p(x)=x-2 -mx+9) के शून्यक \(3\sqrt{2}\) और \(\frac{3}{\sqrt{2}}\) हैं, तो (m) क्या होगा?
If zeroes of (p(x)=x-2 -mx+9) are \(3\sqrt{2}\) and \(\frac{3}{\sqrt{2}}\), what is (m)?
#sum
#radical-simplification
#parameter
A \(\frac{9\sqrt{2}}{2}\)
B (9)
C \(3\sqrt{2}\)
D \(\frac{3\sqrt{2}}{2}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{9\sqrt{2}}{2}\)
Step 1
Concept
The sum is \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\). Hence \(m=\frac{9\sqrt{2}}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{9\sqrt{2}}{2}\). The sum is \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\). Hence \(m=\frac{9\sqrt{2}}{2}\).
Step 3
Exam Tip
योग \(3\sqrt{2}+\frac{3}{\sqrt{2}}=\frac{9\sqrt{2}}{2}\) है। इसलिए \(m=\frac{9\sqrt{2}}{2}\) होगा।
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Question 4/10
Hard Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 28
यदि किसी द्विघात बहुपद के परिमेय गुणांक हैं और शून्यक \(4+\sqrt{11}\) है, तो शून्यकों का योग क्या होगा?
If a quadratic polynomial has rational coefficients and one zero is \(4+\sqrt{11}\), what will be the sum of its zeroes?
#rational-coefficients
#conjugate-zeroes
#sum
A (8)
B (4)
C \(2\sqrt{11}\)
D (16-11)
Explanation opens after your attempt
Step 1
Concept
The other zero will be \(4-\sqrt{11}\). The sum is (\(4+\sqrt{11}\)+\(4-\sqrt{11}\)=8).
Step 2
Why this answer is correct
The correct answer is A. (8). The other zero will be \(4-\sqrt{11}\). The sum is (\(4+\sqrt{11}\)+\(4-\sqrt{11}\)=8).
Step 3
Exam Tip
दूसरा शून्यक \(4-\sqrt{11}\) होगा। योग (\(4+\sqrt{11}\)+\(4-\sqrt{11}\)=8) है।
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Question 5/10
Easy Mathematics
Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 25
कौन सा विकल्प परिमेय और अपरिमेय संख्या का योग दिखाता है?
Which option shows the sum of a rational and an irrational number?
#sum
#rational-irrational
#classification
A \(4+\sqrt{7}\)
B \(\sqrt{2}+\sqrt{3}\)
C \(\frac{1}{2}+\frac{3}{4}\)
D (5+9)
Explanation opens after your attempt
Correct Answer
A. \(4+\sqrt{7}\)
Step 1
Concept
(4) is rational and \(\sqrt{7}\) is irrational. Their sum will be irrational.
Step 2
Why this answer is correct
The correct answer is A. \(4+\sqrt{7}\). (4) is rational and \(\sqrt{7}\) is irrational. Their sum will be irrational.
Step 3
Exam Tip
(4) परिमेय है और \(\sqrt{7}\) अपरिमेय है। उनका योग अपरिमेय होगा।
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Question 6/10
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x=-12) और (x=12) पर (x)-अक्ष को काटता है, तो शून्यकों का गुणनफल और योग क्या है?
If a graph cuts the (x)-axis at (x=-12) and (x=12), what are the product and sum of the zeroes?
#opposite zeroes
#product
#sum
A गुणनफल (-144), योग (0) / Product (-144), sum (0)
B गुणनफल (144), योग (0) / Product (144), sum (0)
C गुणनफल (0), योग (24) / Product (0), sum (24)
D गुणनफल (-24), योग (144) / Product (-24), sum (144)
Explanation opens after your attempt
Correct Answer
A. गुणनफल (-144), योग (0) / Product (-144), sum (0)
Step 1
Concept
The zeroes are (-12) and (12), so the product is (-144) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 2
Why this answer is correct
The correct answer is A. गुणनफल (-144), योग (0) / Product (-144), sum (0). The zeroes are (-12) and (12), so the product is (-144) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 3
Exam Tip
शून्यक (-12) और (12) हैं, इसलिए गुणनफल (-144) और योग (0) है। टिप: विपरीत शून्यकों का योग (0) होता है।
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Question 7/10
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x=-10) और (x=10) पर (x)-अक्ष को काटता है, तो शून्यकों का गुणनफल और योग क्या है?
If a graph cuts the (x)-axis at (x=-10) and (x=10), what are the product and sum of the zeroes?
#opposite zeroes
#product
#sum
A गुणनफल (-100), योग (0) / Product (-100), sum (0)
B गुणनफल (100), योग (0) / Product (100), sum (0)
C गुणनफल (0), योग (20) / Product (0), sum (20)
D गुणनफल (-20), योग (100) / Product (-20), sum (100)
Explanation opens after your attempt
Correct Answer
A. गुणनफल (-100), योग (0) / Product (-100), sum (0)
Step 1
Concept
The zeroes are (-10) and (10), so the product is (-100) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 2
Why this answer is correct
The correct answer is A. गुणनफल (-100), योग (0) / Product (-100), sum (0). The zeroes are (-10) and (10), so the product is (-100) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 3
Exam Tip
शून्यक (-10) और (10) हैं, इसलिए गुणनफल (-100) और योग (0) है। टिप: विपरीत शून्यकों का योग (0) होता है।
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Question 8/10
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद के ग्राफ के (x)-अक्ष कटान ((r,0)), ((s,0)), ((t,0)) हैं, तो शून्यकों का योग क्या होगा?
If the (x)-axis intersections of a polynomial graph are ((r,0)), ((s,0)), ((t,0)), what will be the sum of the zeroes?
#symbolic zeroes
#sum
#coordinates
A (r+s+t)
B (rst)
C (0)
D (r-s+t)
Explanation opens after your attempt
Correct Answer
A. (r+s+t)
Step 1
Concept
The zeroes are the first coordinates (r), (s), (t). Tip: read the first coordinate even in symbolic points.
Step 2
Why this answer is correct
The correct answer is A. (r+s+t). The zeroes are the first coordinates (r), (s), (t). Tip: read the first coordinate even in symbolic points.
Step 3
Exam Tip
शून्यक पहले निर्देशांक (r), (s), (t) हैं। टिप: प्रतीकात्मक बिंदुओं में भी पहला निर्देशांक पढ़ें।
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Question 9/10
Hard Mathematics
Chapter 1: Real Numbers 4: HCF and LCM using prime factorisation Class 10 Level 13
यदि \(176=2^4\times11\) और \(264=2^3\times3\times11\), तो इनके महत्तम समापवर्तक और लघुत्तम समापवर्त्य का योग क्या होगा?
If \(176=2^4\times11\) and \(264=2^3\times3\times11\), what is the sum of their HCF and LCM?
#real-numbers
#hcf
#lcm
#sum
A (704)
B (616)
C (792)
D (880)
Explanation opens after your attempt
Step 1
Concept
HCF \(=2^3\times11=88\).
Step 2
Why this answer is correct
LCM \(=2^4\times3\times11=528\), so the sum is (88+528=616).
Step 3
Exam Tip
When sum is asked, find both values separately. चरण 1: महत्तम समापवर्तक \(2^3\times11=88\) है। चरण 2: लघुत्तम समापवर्त्य \(2^4\times3\times11=528\) है, इसलिए योग (88+528=616) है। चरण 3: योग पूछे जाने पर दोनों मान अलग-अलग निकालें।
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Question 10/10
Hard Mathematics
Chapter 1: Real Numbers 4: HCF and LCM using prime factorisation Class 10 Level 12
यदि \(165=3\times5\times11\) और \(231=3\times7\times11\), तो इनके महत्तम समापवर्तक और लघुत्तम समापवर्त्य का योग क्या होगा?
If \(165=3\times5\times11\) and \(231=3\times7\times11\), what is the sum of their HCF and LCM?
#real-numbers
#hcf
#lcm
#sum
A (1199)
B (1155)
C (1188)
D (1232)
Explanation opens after your attempt
Step 1
Concept
The common prime factors are (3) and (11), so HCF (=33).
Step 2
Why this answer is correct
LCM \(=3\times5\times7\times11=1155\), so the sum is (33+1155=1188).
Step 3
Exam Tip
When sum is asked, find both values separately. चरण 1: समान अभाज्य गुणनखंड (3) और (11) हैं, इसलिए महत्तम समापवर्तक (33) है। चरण 2: लघुत्तम समापवर्त्य \(3\times5\times7\times11=1155\) है, इसलिए योग (33+1155=1188) है। चरण 3: योग पूछे जाने पर दोनों मान अलग-अलग निकालें।
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