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CBSE Class 12 Fashion Studies Question Paper 2026 with Solution PDF
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Let the six numbers \( a_1, a_2, a_3, a_4, a_5, a_6 \) be in A.P., and \( a_1 + a_3 = 10 \). If the mean of these six numbers is \( \frac{19}{2} \) and their variance is \( \sigma^2 \), then \( 8\sigma^2 \) is equal to:
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Let first term \(a\), common difference \(d\).
From \(a_1 + a_3 = a + (a+2d) = 10\)
\[ 2a + 2d = 10 \Rightarrow a + d = 5 \]
Mean of 6 terms = average of first and last term:
\[ \frac{a + (a+5d)}{2} = \frac{19}{2} \Rightarrow 2a + 5d = 19 \]
Using \(a = 5 - d\):
\[ 2(5-d) + 5d = 19 \Rightarrow 10 + 3d = 19 \Rightarrow d = 3 \Rightarrow a = 2 \]
Numbers: \(2,5,8,11,14,17\)
Mean = \(9.5\)
Variance: \[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{6} = 26.25 \]
\[ 8\sigma^2 = 210 \] Quick Tip: For A.P., mean of terms = average of first and last term.
The Battle of Plassey was fought in —
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The Battle of Plassey took place on 23 June 1757 between the British East India Company and Nawab Siraj-ud-Daulah. Quick Tip: Plassey marked the beginning of British political control in India.
Who was the founder of the Maurya Empire?
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Chandragupta Maurya founded the Mauryan Empire around 322 BCE with the help of Chanakya. Quick Tip: He overthrew the Nanda dynasty.
The Revolt of 1857 started from —
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The revolt began on 10 May 1857 at Meerut when Indian soldiers rebelled against British officers. Quick Tip: From Meerut, rebels marched to Delhi.
Who was known as the “Iron Man of India”?
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Patel earned this title for integrating princely states into India after independence. Quick Tip: He was India's first Deputy Prime Minister.
Describe the causes of the Revolt of 1857.
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Causes included political annexations, economic exploitation, military grievances, and use of greased cartridges offensive to soldiers. Quick Tip: It is also called India’s First War of Independence.
Write a short note on the Non-Cooperation Movement.
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Launched by Mahatma Gandhi in 1920, it urged Indians to boycott British institutions, schools, courts, and goods. Quick Tip: It promoted swadeshi and non-violent resistance.
Explain the main features of the Mauryan administration.
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The Mauryan administration was highly centralized with a strong king, council of ministers, provincial governors, and efficient bureaucracy. Quick Tip: Chanakya’s Arthashastra describes this system.
Discuss the impact of British rule on Indian economy.
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British rule led to deindustrialization, drain of wealth, heavy taxation, and decline of traditional industries. Quick Tip: India became a supplier of raw materials for Britain.
Describe the role of Mahatma Gandhi in India’s freedom struggle.
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Gandhi led major movements such as Non-Cooperation, Civil Disobedience, and Quit India using non-violence and satyagraha. Quick Tip: He is known as the Father of the Nation.








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