The question asks to identify the leader who called for Direct Action Day. This is a historical event related to the partition of India and the demand for a separate Muslim state. We need to recall the key figures associated with this event.
Therefore, Muhammad Ali Jinnah was the one who called for Direct Action Day.
Correct Option: C) Muhammad Ali Jinnah
The question asks to identify the scientist who coined the term 'ecology'. This requires knowledge of the history of ecological terminology and key figures in the field.
Correct Option: D) Ernst Haeckel — Ernst Haeckel coined the term "ecology" (Ökologie) in 1866, defining it as the study of the interrelationships between living organisms and their environment.
If x + \( \frac{1}{x} \) = 2, then the value of x² + \( \frac{1}{x^2} \) = ?
The problem provides an equation involving \(x\) and its reciprocal, and asks for the value of an expression involving \(x^2\) and its reciprocal. This can be solved by squaring the given equation and using algebraic identities.
We are given the equation:
\[ x + \frac{1}{x} = 2 \]To find the value of \(x^2 + \frac{1}{x^2}\), we can square both sides of the given equation. Recall the algebraic identity \((a+b)^2 = a^2 + b^2 + 2ab\).
Applying this identity to our equation, where \(a = x\) and \(b = \frac{1}{x}\):
\[ \left(x + \frac{1}{x}\right)^2 = (2)^2 \]\[ x^2 + \left(\frac{1}{x}\right)^2 + 2 \cdot x \cdot \frac{1}{x} = 4 \]Simplify the equation:
\[ x^2 + \frac{1}{x^2} + 2 \cdot 1 = 4 \]\[ x^2 + \frac{1}{x^2} + 2 = 4 \]Subtract 2 from both sides to isolate \(x^2 + \frac{1}{x^2}\):
\[ x^2 + \frac{1}{x^2} = 4 - 2 \]\[ x^2 + \frac{1}{x^2} = 2 \]Correct Option: D) 2
What is the sum of \( \frac{1}{3} \),\( \frac{4}{3} \) and \( \frac{3}{4} \)?
2
\( \frac{29}{12} \)
\( \frac{27}{12} \)
\( \frac{26}{12} \)
To find the sum of fractions, we need to find a common denominator for all fractions. Once a common denominator is found, we convert each fraction to an equivalent fraction with that denominator and then add the numerators.
Correct Option: B) \( \frac{29}{12} \)
The question asks to identify the National Highway that passes through Kaziranga National Park and poses a significant threat to its wildlife. This requires knowledge of the geographical location of Kaziranga National Park and the major National Highways traversing the region.
D) NH-37 — National Highway 37 (now largely renumbered as NH-715 and part of NH-27) runs along the southern boundary of Kaziranga National Park. It is a major transportation artery that unfortunately cuts through critical wildlife corridors, leading to frequent road accidents involving animals, especially during the monsoon season when animals migrate to higher ground. This highway is widely recognized as a significant threat to the park's biodiversity.
The question asks for the annual celebration date of 'World Environment Day'. This is a factual question related to important international days, which are common in competitive exams.
Correct Option: D) 5th June is the correct date for the annual celebration of 'World Environment Day'.
The question asks for the date on which the International Day of Light is observed. This is a factual question related to international observances and general knowledge.
The International Day of Light is celebrated annually on May 16th. This day marks the anniversary of the first successful operation of the laser in 1960 by physicist and engineer Theodore Maiman.
B) 16th May is the correct date for the observance of the International Day of Light.
The question asks to identify the Gupta king who was known for his proficiency in playing the Veena. This requires knowledge of the cultural achievements and personal attributes of prominent Gupta rulers.
Correct Option: D) Samudragupta was a great patron of art and literature. He was also an accomplished musician and poet. His coins depict him playing the Veena, which is a stringed musical instrument. This evidence firmly establishes his proficiency as a Veena player.
To arrange the given words (Family, World, Individual, Community, Country) in a meaningful order, we need to consider a hierarchical or logical progression. A common and meaningful way to arrange these terms is from the smallest unit to the largest, or from the most specific to the most general entity.
Therefore, the logical sequence from smallest to largest is Individual → Family → Community → Country → World.
This translates to the numerical sequence: 3 → 1 → 4 → 5 → 2.
Correct Option: B) 31452
If \(\sqrt{2916}\) = 54 then what is the value of the following?
\(\sqrt{29.16}+\sqrt{0.2916}+\sqrt{0.002916}+
\sqrt{0.00002916}\)
The problem provides the square root of an integer and asks to find the sum of square roots of numbers with the same digits but different decimal point positions. The key is to express each term as a multiple of the given square root and then sum them up.
We are given that \(\sqrt{2916} = 54\).
We need to find the value of \(\sqrt{29.16} + \sqrt{0.2916} + \sqrt{0.002916} + \sqrt{0.00002916}\).
Let's evaluate each term individually:
\[ \sqrt{29.16} = \sqrt{\frac{2916}{100}} = \frac{\sqrt{2916}}{\sqrt{100}} = \frac{54}{10} = 5.4 \]
\[ \sqrt{0.2916} = \sqrt{\frac{2916}{10000}} = \frac{\sqrt{2916}}{\sqrt{10000}} = \frac{54}{100} = 0.54 \]
\[ \sqrt{0.002916} = \sqrt{\frac{2916}{1000000}} = \frac{\sqrt{2916}}{\sqrt{1000000}} = \frac{54}{1000} = 0.054 \]
\[ \sqrt{0.00002916} = \sqrt{\frac{2916}{100000000}} = \frac{\sqrt{2916}}{\sqrt{100000000}} = \frac{54}{10000} = 0.0054 \]
Now, add all the calculated values:
\[ 5.4 + 0.54 + 0.054 + 0.0054 \]
To sum these decimal numbers, align them by their decimal points:
5.4
0.54
0.054
+ 0.0054
---------
5.9994
The sum is \(5.9994\).
B) 5.9994 is the correct sum of the given square root terms.