The question asks to identify the historical figure who famously uttered the slogan, "Give me blood and I will give you Freedom." This is a direct recall question about a well-known quote from India's freedom struggle.
Correct Option: D) Subhash Chandra Bose
The question asks for the capital of Dadra and Nagar Haveli. This is a factual question related to Indian geography and administrative divisions. To answer this, one needs to recall the capitals of the Union Territories of India.
Correct Option: D) Silvassa is the capital of Dadra and Nagar Haveli. Even after the merger with Daman and Diu, Silvassa remains the administrative headquarters for the Dadra and Nagar Haveli district.
The question asks for the geographical location of Kaziranga National Park. This is a factual question requiring knowledge of India's national parks and their respective states.
Correct Option: C) Kaziranga National Park is located in the state of Assam. It is one of India's most renowned wildlife sanctuaries, famous for its great Indian one-horned rhinoceroses.
The question asks for the pH of pure water. To answer this, we need to recall the definition of pH and the properties of pure water, specifically its autoionization and the resulting concentrations of hydrogen and hydroxide ions.
C) 7 is the correct pH for pure water at \(25^\circ\text{C}\), as it is a neutral substance with equal concentrations of hydrogen and hydroxide ions.
The question asks about the number of members the President can nominate to the Rajya Sabha. This is a direct factual question related to the composition of the Indian Parliament as defined in the Constitution of India.
Correct Option: C) 12 — The President of India has the power to nominate 12 members to the Rajya Sabha from persons having special knowledge or practical experience in respect of such matters as literature, science, art, and social service, as per Article 80(3) of the Indian Constitution.
The question asks to identify the author of the famous collection of fables, 'Panchatantra'. This requires knowledge of ancient Indian literature and their respective authors.
D) Vishnu Sharma is widely credited as the author of the 'Panchatantra'. The 'Panchatantra' is an ancient Indian collection of interconnected animal fables in Sanskrit verse and prose, arranged within a frame story. Its purpose was to impart practical wisdom and ethical conduct to young princes.
The question asks about the field in which the 'Dada Saheb Phalke' award is given. This requires knowledge of prominent Indian awards and their respective categories.
Correct Option: B) Film
Which fraction comes next in the sequence:
\( \frac{1}{2} \), \( \frac{3}{4} \), \( \frac{5}{8} \) , \( \frac{7}{16} \),?
\( \frac{9}{32} \)
\( \frac{10}{17} \)
24
\( \frac{11}{32} \)
To find the next fraction in the sequence, we need to identify the pattern in the numerators and the denominators separately.
Analyze the Numerators:
The numerators are \(1, 3, 5, 7, \dots\). This is a sequence of odd numbers. Each subsequent numerator is obtained by adding 2 to the previous one.
Following this pattern, the next numerator will be \(7 + 2 = 9\).
Analyze the Denominators:
The denominators are \(2, 4, 8, 16, \dots\). This is a sequence where each subsequent denominator is obtained by multiplying the previous one by 2 (powers of 2).
Following this pattern, the next denominator will be \(16 \times 2 = 32\).
Form the Next Fraction:
Combining the next numerator (9) and the next denominator (32), the next fraction in the sequence is \( \frac{9}{32} \).
Correct Option: A) \( \frac{9}{32} \)
Choose the correct alternative that will replace the question mark in the given series
11, 13, 17, 19, 23, 25,?
The given series is a sequence of numbers. We need to identify the pattern or rule governing this sequence to find the next number. By analyzing the differences between consecutive terms, or by looking for specific properties of the numbers, we can deduce the pattern.
C) 29 — The pattern of differences between consecutive terms is an alternating sequence of \(+2\) and \(+4\). Following this pattern, the next number after 25 should be \(25 + 4 = 29\).
The problem asks us to calculate the sum of two squares: \(106 \times 106\) and \(94 \times 94\). We can solve this by direct multiplication and addition, or by using algebraic identities to simplify the calculation.
Calculate each square separately and then add them.
We can express \(106\) as \((100 + 6)\) and \(94\) as \((100 - 6)\). This allows us to use the identities \((a+b)^2 = a^2 + 2ab + b^2\) and \((a-b)^2 = a^2 - 2ab + b^2\).
C) 20072 — As calculated by both direct multiplication and algebraic identity methods, the sum is 20072.