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In ΔABC, if AD ⊥ BC, then which of these is always true?
When AD is the altitude from vertex A to side BC, it divides ΔABC into two right triangles, ΔABD and ΔACD. Using the property of the area of a triangle, we know that the area can be expressed in two ways: 1. Area = (1/2) × base × height = (1/2) × BC × AD. 2. Area = (1/2) × AB × AC × sin(∠BAC). EquatRead more
When AD is the altitude from vertex A to side BC, it divides ΔABC into two right triangles, ΔABD and ΔACD. Using the property of the area of a triangle, we know that the area can be expressed in two ways:
1. Area = (1/2) × base × height = (1/2) × BC × AD.
2. Area = (1/2) × AB × AC × sin(∠BAC).
Equating the two expressions for the area:
(1/2) × BC × AD = (1/2) × AB × AC × sin(∠BAC).
Since sin(∠BAC) = AD / AB (from the definition of sine in ΔABD), substituting this value simplifies the equation to:
BC × AD = AB × AC.
Thus, the correct answer is AB × AC = BC × AD.
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The total number of factors of a prime number is
A prime number is defined as a number greater than 1 that has exactly two distinct positive divisors: 1 and the number itself. For example, if we consider the prime number 7, its only factors are 1 and 7. Thus, by definition, any prime number will always have exactly two factors: 1 and the number itRead more
A prime number is defined as a number greater than 1 that has exactly two distinct positive divisors: 1 and the number itself. For example, if we consider the prime number 7, its only factors are 1 and 7.
Thus, by definition, any prime number will always have exactly two factors: 1 and the number itself. This makes the total number of factors of a prime number equal to 2.
The other options are incorrect because:
– “1” is incorrect since a prime number has two factors, not one.
– “Zero” is incorrect since every number has at least one factor (itself).
– “3” is incorrect since a prime number cannot have more than two factors.
Thus, the correct answer is 2.
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The HCF of two numbers is 18 and their product is 12960. Their LCM will be
The HCF of two numbers is 18, and their product is 12960. To find their LCM, we use the relationship between HCF and LCM: HCF × LCM = Product of the two numbers. Substituting the given values: 18 × LCM = 12960. Solving for LCM: LCM = 12960 / 18 LCM = 720. Thus, the LCM of the two numbers is 720. ExpRead more
The HCF of two numbers is 18, and their product is 12960. To find their LCM, we use the relationship between HCF and LCM:
HCF × LCM = Product of the two numbers.
Substituting the given values:
18 × LCM = 12960.
Solving for LCM:
LCM = 12960 / 18
LCM = 720.
Thus, the LCM of the two numbers is 720.
Explanation:
The formula HCF × LCM = Product of the numbers is a fundamental property of HCF and LCM. Since the HCF and the product are given, we can directly calculate the LCM using this formula. The other options (420, 600, and 800) do not satisfy this relationship and are therefore incorrect.
Thus, the correct answer is 720.
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Class 10 Maths Chapter 10 MCQ?
Chapter 10 Circles in Class 10 Maths explores tangents, chords, and their properties. MCQs assess understanding of concepts like tangent-radius perpendicularity and related theorems. These questions enhance geometric reasoning and visualization skills while reinforcing practical applications in engiRead more
Chapter 10 Circles in Class 10 Maths explores tangents, chords, and their properties. MCQs assess understanding of concepts like tangent-radius perpendicularity and related theorems. These questions enhance geometric reasoning and visualization skills while reinforcing practical applications in engineering and design. Mastery of this chapter ensures a strong foundation in geometry for future studies.
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Charge on conductiong sphere resides
In a conducting sphere, excess charge distributes itself on the outer surface due to mutual repulsion among like charges. This occurs because charges in a conductor move freely and arrange themselves to minimize repulsive forces, ensuring zero electric field inside the conductor. Answer: (d) On theRead more
In a conducting sphere, excess charge distributes itself on the outer surface due to mutual repulsion among like charges. This occurs because charges in a conductor move freely and arrange themselves to minimize repulsive forces, ensuring zero electric field inside the conductor. Answer: (d) On the outer surface of the sphere.
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