In an isosceles triangle ABC, given that AB = AC = 25 cm and BC = 14 cm, we need to find the measure of the altitude from A to BC. Let the altitude from A meet BC at point D. Since the triangle is isosceles, the altitude AD also acts as the median, dividing BC into two equal parts: BD = DC = BC / 2Read more
In an isosceles triangle ABC, given that AB = AC = 25 cm and BC = 14 cm, we need to find the measure of the altitude from A to BC.
Let the altitude from A meet BC at point D. Since the triangle is isosceles, the altitude AD also acts as the median, dividing BC into two equal parts:
BD = DC = BC / 2 = 14 / 2 = 7 cm.
Now, consider ΔABD, which is a right triangle because AD is perpendicular to BC. Using the Pythagorean theorem:
AB² = AD² + BD²
25² = AD² + 7²
625 = AD² + 49
AD² = 625 – 49
AD² = 576
AD = √576 = 24 cm.
Thus, the measure of the altitude from A on BC is 24 cm.
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.
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.
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.
In ΔABC, given that ∠B = 90°, AB = 6 cm, and BC = 8 cm, we can determine sin A using the definition of sine in a right triangle. First, calculate the hypotenuse AC using the Pythagorean theorem: AC² = AB² + BC² AC² = 6² + 8² AC² = 36 + 64 AC² = 100 AC = √100 = 10 cm Now, recall that sin A is definedRead more
In ΔABC, given that ∠B = 90°, AB = 6 cm, and BC = 8 cm, we can determine sin A using the definition of sine in a right triangle.
First, calculate the hypotenuse AC using the Pythagorean theorem:
AC² = AB² + BC²
AC² = 6² + 8²
AC² = 36 + 64
AC² = 100
AC = √100 = 10 cm
Now, recall that sin A is defined as the ratio of the length of the side opposite to ∠A (BC) to the hypotenuse (AC):
sin A = (opposite side) / (hypotenuse)
sin A = BC / AC
sin A = 8 / 10
Similarity of triangles is based on the principle that when two triangles have the same shape but not necessarily the same size, they are considered similar. This occurs if and only if their corresponding angles are equal. When the angles are equal, the ratios of the lengths of their corresponding sRead more
Similarity of triangles is based on the principle that when two triangles have the same shape but not necessarily the same size, they are considered similar. This occurs if and only if their corresponding angles are equal. When the angles are equal, the ratios of the lengths of their corresponding sides are also equal (this is known as the Angle-Angle or AA criterion for similarity).
The other options are incorrect because:
– “Their corresponding sides are equal” describes congruence, not similarity.
– “Their perimeters are equal” does not guarantee similarity, as triangles with the same perimeter can have different shapes.
– “Their areas are equal” also does not ensure similarity, as triangles with the same area can have different shapes and dimensions.
Thus, the correct answer is “Their corresponding angles are equal.”
1. Equality and Inclusivity: - Ensures equal voting rights for all adult citizens regardless of background. - Promotes inclusivity by allowing diverse participation in the democratic process. 2. Representation: - Enables fair representation of varied interests within the population. - Elected leaderRead more
1. Equality and Inclusivity:
– Ensures equal voting rights for all adult citizens regardless of background.
– Promotes inclusivity by allowing diverse participation in the democratic process.
2. Representation:
– Enables fair representation of varied interests within the population.
– Elected leaders accountable to the entire citizenry, enhancing democratic values.
3. Political Stability:
– Offers a peaceful means for citizens to express preferences and effect change.
– Reduces potential unrest or dissatisfaction by providing a legitimate outlet for grievances.
4. Enhanced Legitimacy:
– Governments elected through universal franchise gain greater legitimacy.
– Increases trust in governance as leaders are chosen through a fair process.
5. Empowerment and Participation:
– Empowers citizens by granting a voice in decision-making.
– Encourages civic engagement and active involvement in societal affairs.
6. Accountability and Responsiveness:
– Prompts politicians to be responsive to citizen needs to secure votes.
– Holds elected representatives accountable for their actions and decisions.
7. Guard Against Tyranny:
– Acts as a safeguard against authoritarianism and oppression.
– Prevents any group from monopolizing power, ensuring a fair democratic system.
In conclusion, universal adult franchise is pivotal in upholding the principles of democracy, ensuring fair representation, political stability, citizen empowerment, and accountability in governance.
Significance of "All Persons are Equal Before the Law" in Democracy: 1. Fair Treatment: Ensures equal treatment of individuals irrespective of differences like race, religion, or wealth. 2. Rule of Law: Upholds the principle that laws apply uniformly to everyone, including government officials. 3. RRead more
Significance of “All Persons are Equal Before the Law” in Democracy:
1. Fair Treatment: Ensures equal treatment of individuals irrespective of differences like race, religion, or wealth.
2. Rule of Law: Upholds the principle that laws apply uniformly to everyone, including government officials.
3. Rights Protection: Safeguards individual rights and dignity, preventing discrimination and human rights abuses.
4. Social Harmony: Reduces societal divisions by promoting equality and fostering trust and cohesion.
5. Accountability: Holds all individuals accountable for their actions, preventing misuse of power.
6. Citizen Confidence: Encourages citizen participation and trust in legal institutions, fostering civic engagement.
In conclusion, the principle of equality before the law is vital in democracies, ensuring fairness, protecting rights, promoting social unity, and upholding the rule of law.
In the 1930s, Muslim leaders felt separate from Hindus in a united India. The Muslim League, led by Jinnah, argued for a separate Muslim nation - Pakistan. Key steps towards this: 1937 elections: League gained power in Muslim areas, but Congress wouldn't share power, causing mistrust. 1940: League fRead more
In the 1930s, Muslim leaders felt separate from Hindus in a united India. The Muslim League, led by Jinnah, argued for a separate Muslim nation – Pakistan. Key steps towards this:
1937 elections: League gained power in Muslim areas, but Congress wouldn’t share power, causing mistrust.
1940: League formally demanded Pakistan to protect Muslim interests.
1946: Attempts to unite India (Cabinet Mission Plan & Simla Conference) failed.
1946: Violence between Hindus and Muslims showed peaceful coexistence was hard.
1947: Mountbatten Plan divided India. Though both sides were unhappy, Pakistan was born on August 14th.
Problems with James Mill's Periodisation: 1. Eurocentric Bias: Mill's categorization reflects a Eurocentric viewpoint, emphasizing British colonial rule as the starting point of Indian "civilization." 2. Oversimplification: Dividing history into Hindu, Muslim, and British periods oversimplifies IndiRead more
Problems with James Mill’s Periodisation:
1. Eurocentric Bias: Mill’s categorization reflects a Eurocentric viewpoint, emphasizing British colonial rule as the starting point of Indian “civilization.”
2. Oversimplification: Dividing history into Hindu, Muslim, and British periods oversimplifies India’s complex socio-cultural evolution, neglecting diverse indigenous contributions.
3. Neglect of Indigenous History: Marginalizes indigenous Indian history, undermining its richness and depth, presenting it as subordinate to external influences.
4. Imposition of Western Framework: Imposing Western concepts fails to capture indigenous perspectives and continuity, distorting the understanding of India’s historical evolution.
5. Colonial Interpretation: Favors British colonial narratives, justifying British rule as a necessary stage of progress, overlooking the complexities of pre-colonial Indian society.
This framework lacks depth, distorts indigenous history, and reinforces colonial biases, offering a skewed understanding of India’s historical progression.
In an isosceles triangle ABC, if AB = AC = 25 cm and BC = 14 cm, then the measure of altitude from A on BC is
In an isosceles triangle ABC, given that AB = AC = 25 cm and BC = 14 cm, we need to find the measure of the altitude from A to BC. Let the altitude from A meet BC at point D. Since the triangle is isosceles, the altitude AD also acts as the median, dividing BC into two equal parts: BD = DC = BC / 2Read more
In an isosceles triangle ABC, given that AB = AC = 25 cm and BC = 14 cm, we need to find the measure of the altitude from A to BC.
Let the altitude from A meet BC at point D. Since the triangle is isosceles, the altitude AD also acts as the median, dividing BC into two equal parts:
BD = DC = BC / 2 = 14 / 2 = 7 cm.
Now, consider ΔABD, which is a right triangle because AD is perpendicular to BC. Using the Pythagorean theorem:
AB² = AD² + BD²
25² = AD² + 7²
625 = AD² + 49
AD² = 625 – 49
AD² = 576
AD = √576 = 24 cm.
Thus, the measure of the altitude from A on BC is 24 cm.
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See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-6/
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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See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-6/
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.
Click here for more:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-1/
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.
Click here for more:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-1/
In ΔABC, if ∠B = 90°, AB = 6 cm, and BC = 8 cm, then sin A equals:
In ΔABC, given that ∠B = 90°, AB = 6 cm, and BC = 8 cm, we can determine sin A using the definition of sine in a right triangle. First, calculate the hypotenuse AC using the Pythagorean theorem: AC² = AB² + BC² AC² = 6² + 8² AC² = 36 + 64 AC² = 100 AC = √100 = 10 cm Now, recall that sin A is definedRead more
In ΔABC, given that ∠B = 90°, AB = 6 cm, and BC = 8 cm, we can determine sin A using the definition of sine in a right triangle.
First, calculate the hypotenuse AC using the Pythagorean theorem:
AC² = AB² + BC²
AC² = 6² + 8²
AC² = 36 + 64
AC² = 100
AC = √100 = 10 cm
Now, recall that sin A is defined as the ratio of the length of the side opposite to ∠A (BC) to the hypotenuse (AC):
sin A = (opposite side) / (hypotenuse)
sin A = BC / AC
sin A = 8 / 10
Thus, the correct answer is 8/10.
Click here for more:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-6/
Two triangles are similar if:
Similarity of triangles is based on the principle that when two triangles have the same shape but not necessarily the same size, they are considered similar. This occurs if and only if their corresponding angles are equal. When the angles are equal, the ratios of the lengths of their corresponding sRead more
Similarity of triangles is based on the principle that when two triangles have the same shape but not necessarily the same size, they are considered similar. This occurs if and only if their corresponding angles are equal. When the angles are equal, the ratios of the lengths of their corresponding sides are also equal (this is known as the Angle-Angle or AA criterion for similarity).
The other options are incorrect because:
– “Their corresponding sides are equal” describes congruence, not similarity.
– “Their perimeters are equal” does not guarantee similarity, as triangles with the same perimeter can have different shapes.
– “Their areas are equal” also does not ensure similarity, as triangles with the same area can have different shapes and dimensions.
Thus, the correct answer is “Their corresponding angles are equal.”
Click here for more:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-6/
In a democracy why is universal adult franchise important?
1. Equality and Inclusivity: - Ensures equal voting rights for all adult citizens regardless of background. - Promotes inclusivity by allowing diverse participation in the democratic process. 2. Representation: - Enables fair representation of varied interests within the population. - Elected leaderRead more
1. Equality and Inclusivity:
– Ensures equal voting rights for all adult citizens regardless of background.
– Promotes inclusivity by allowing diverse participation in the democratic process.
2. Representation:
– Enables fair representation of varied interests within the population.
– Elected leaders accountable to the entire citizenry, enhancing democratic values.
3. Political Stability:
– Offers a peaceful means for citizens to express preferences and effect change.
– Reduces potential unrest or dissatisfaction by providing a legitimate outlet for grievances.
4. Enhanced Legitimacy:
– Governments elected through universal franchise gain greater legitimacy.
– Increases trust in governance as leaders are chosen through a fair process.
5. Empowerment and Participation:
– Empowers citizens by granting a voice in decision-making.
– Encourages civic engagement and active involvement in societal affairs.
6. Accountability and Responsiveness:
– Prompts politicians to be responsive to citizen needs to secure votes.
– Holds elected representatives accountable for their actions and decisions.
7. Guard Against Tyranny:
– Acts as a safeguard against authoritarianism and oppression.
– Prevents any group from monopolizing power, ensuring a fair democratic system.
In conclusion, universal adult franchise is pivotal in upholding the principles of democracy, ensuring fair representation, political stability, citizen empowerment, and accountability in governance.
See lessWhat do you understand by the term “all persons are equal before the law”? Why do you think it is important in a democracy?
Significance of "All Persons are Equal Before the Law" in Democracy: 1. Fair Treatment: Ensures equal treatment of individuals irrespective of differences like race, religion, or wealth. 2. Rule of Law: Upholds the principle that laws apply uniformly to everyone, including government officials. 3. RRead more
Significance of “All Persons are Equal Before the Law” in Democracy:
1. Fair Treatment: Ensures equal treatment of individuals irrespective of differences like race, religion, or wealth.
2. Rule of Law: Upholds the principle that laws apply uniformly to everyone, including government officials.
3. Rights Protection: Safeguards individual rights and dignity, preventing discrimination and human rights abuses.
4. Social Harmony: Reduces societal divisions by promoting equality and fostering trust and cohesion.
5. Accountability: Holds all individuals accountable for their actions, preventing misuse of power.
6. Citizen Confidence: Encourages citizen participation and trust in legal institutions, fostering civic engagement.
In conclusion, the principle of equality before the law is vital in democracies, ensuring fairness, protecting rights, promoting social unity, and upholding the rule of law.
See lessDiscuss those developments of the 1937–47 period that led to the creation of Pakistan.
In the 1930s, Muslim leaders felt separate from Hindus in a united India. The Muslim League, led by Jinnah, argued for a separate Muslim nation - Pakistan. Key steps towards this: 1937 elections: League gained power in Muslim areas, but Congress wouldn't share power, causing mistrust. 1940: League fRead more
In the 1930s, Muslim leaders felt separate from Hindus in a united India. The Muslim League, led by Jinnah, argued for a separate Muslim nation – Pakistan. Key steps towards this:
1937 elections: League gained power in Muslim areas, but Congress wouldn’t share power, causing mistrust.
See less1940: League formally demanded Pakistan to protect Muslim interests.
1946: Attempts to unite India (Cabinet Mission Plan & Simla Conference) failed.
1946: Violence between Hindus and Muslims showed peaceful coexistence was hard.
1947: Mountbatten Plan divided India. Though both sides were unhappy, Pakistan was born on August 14th.
What is the problem with the periodisation of Indian history that James Mill offers?
Problems with James Mill's Periodisation: 1. Eurocentric Bias: Mill's categorization reflects a Eurocentric viewpoint, emphasizing British colonial rule as the starting point of Indian "civilization." 2. Oversimplification: Dividing history into Hindu, Muslim, and British periods oversimplifies IndiRead more
Problems with James Mill’s Periodisation:
1. Eurocentric Bias: Mill’s categorization reflects a Eurocentric viewpoint, emphasizing British colonial rule as the starting point of Indian “civilization.”
2. Oversimplification: Dividing history into Hindu, Muslim, and British periods oversimplifies India’s complex socio-cultural evolution, neglecting diverse indigenous contributions.
3. Neglect of Indigenous History: Marginalizes indigenous Indian history, undermining its richness and depth, presenting it as subordinate to external influences.
4. Imposition of Western Framework: Imposing Western concepts fails to capture indigenous perspectives and continuity, distorting the understanding of India’s historical evolution.
5. Colonial Interpretation: Favors British colonial narratives, justifying British rule as a necessary stage of progress, overlooking the complexities of pre-colonial Indian society.
This framework lacks depth, distorts indigenous history, and reinforces colonial biases, offering a skewed understanding of India’s historical progression.
See less