The question asks for the year in which the Battle of Haldighati was fought. This is a direct factual question from Indian history, specifically related to the Mughal period and Rajput resistance.
Correct Option: B) 1576
The Battle of Haldighati was fought on June 18, 1576, between the forces of Maharana Pratap, the Rajput ruler of Mewar, and the Mughal army of Emperor Akbar, led by Man Singh I of Amber. Although the battle was inconclusive in terms of a decisive victory for either side immediately, it is a significant event in Indian history symbolizing Rajput valor and resistance against the Mughals.
The problem provides a ratio between two variables, \(p\) and \(q\), and asks for the ratio of an expression involving \(p\) and \(q\). We can express one variable in terms of the other using the given ratio, or more efficiently, divide the entire expression by \(q\) (or \(p\)) to work with the ratio \(\frac{p}{q}\).
Given the ratio \(p : q = 9 : 2\), we can write this as a fraction:
\[ \frac{p}{q} = \frac{9}{2} \]We need to find the ratio \((4p + 7q) : (4p - 7q)\). This can be written as a fraction:
\[ \frac{4p + 7q}{4p - 7q} \]To use the given ratio \(\frac{p}{q}\), we can divide both the numerator and the denominator of the expression by \(q\). This is a valid operation as long as \(q \neq 0\).
\[ \frac{\frac{4p + 7q}{q}}{\frac{4p - 7q}{q}} = \frac{\frac{4p}{q} + \frac{7q}{q}}{\frac{4p}{q} - \frac{7q}{q}} \]Simplify the terms:
\[ \frac{4\left(\frac{p}{q}\right) + 7}{4\left(\frac{p}{q}\right) - 7} \]Now, substitute the value of \[\frac{p}{q} = \frac{9}{2}\] into the expression:
\[ \frac{4\left(\frac{9}{2}\right) + 7}{4\left(\frac{9}{2}\right) - 7} \]Perform the multiplication in the numerator and denominator:
\[ \frac{2 \times 9 + 7}{2 \times 9 - 7} = \frac{18 + 7}{18 - 7} \]Calculate the final values:
\[ \frac{25}{11} \]Express the result as a ratio:
\[ 25 : 11 \]C) 25 : 11 is the correct ratio obtained after substituting the given ratio and simplifying the expression.
The question asks to identify the odd one out from a given list of animals: Cow, Goat, Rabbit, Cat. This is a classification-based question where we need to find a common characteristic among three of the animals and identify the one that does not share that characteristic.
C) Cat — Cow, Goat, and Rabbit are all herbivores, meaning they primarily eat plants. A Cat, on the other hand, is a carnivore, meaning its diet consists mainly of meat. This fundamental difference in diet makes the Cat the odd one out.
The question asks for the unit used to measure the thickness of the ozone layer. We need to identify the standard unit specifically designated for this purpose.
Correct Option: B) The Dobson unit (DU) is the standard unit for measuring the total amount of ozone in a column overhead. One Dobson Unit corresponds to a layer of ozone that would be \(0.01 \text{ mm}\) thick at standard temperature and pressure (\(0^\circ \text{C}\) and \(1 \text{ atm}\)). A typical ozone layer thickness is around \(300 \text{ DU}\).
The question asks to identify the calligrapher from Akbar's court who was given the title 'Zarrin Qalam' (golden pen). This requires knowledge of prominent artists and scholars associated with the Mughal Emperor Akbar.
Correct Option: C) Muhammad Husayn was one of the most celebrated calligraphers during Akbar's reign. His mastery of the Nastaliq style earned him the prestigious title of 'Zarrin Qalam' (Golden Pen) from Emperor Akbar himself.
The problem involves decoding a word based on a given numerical code for another word. We need to identify the pattern or rule used to convert the letters of "SCHOOL" into the number 72. Once the rule is established, we will apply the same rule to the word "FLOWER" to find its corresponding code.
C) 79 is the correct answer. The coding rule is to sum the alphabetical positions of the letters in the word.
A circle of radius 8 cm circumscribes a square. The length of the side of the square is:
2\(\sqrt{2}\) cm
6\(\sqrt{2}\) cm
8\(\sqrt{2}\) cm
4\(\sqrt{2}\) cm
When a circle circumscribes a square, the diameter of the circle is equal to the diagonal of the square. We can use the Pythagorean theorem to relate the side of the square to its diagonal.
C) The length of the side of the square is \(8\sqrt{2}\) cm.
The question asks to identify the membrane-bound sac filled with digestive enzymes. This points directly to a specific organelle known for its role in cellular digestion and waste breakdown.
Correct Option: C) Lysosomes are membrane-bound organelles found in eukaryotic cells. They are often referred to as the "recycling centers" or "waste disposal units" of the cell because they contain a variety of hydrolytic enzymes (digestive enzymes) that can break down waste materials, cellular debris, foreign invaders like bacteria and viruses, and worn-out organelles. These enzymes function optimally in an acidic environment, which is maintained within the lysosome.
This problem involves work and time. We need to calculate the individual work rates of A and B, determine the total work, and then use the information about B finishing the remaining work to find out how many days A and B worked together.
A can complete the work in 56 days. So, A's one day's work is:
\[ \text{A's 1 day work} = \frac{1}{56} \]B can complete the work in 70 days. So, B's one day's work is:
\[ \text{B's 1 day work} = \frac{1}{70} \]B finished the remaining work in 34 days. The amount of work B did alone is:
\[ \text{Work done by B alone} = \text{B's 1 day work} \times 34 = \frac{1}{70} \times 34 = \frac{34}{70} = \frac{17}{35} \]The total work is 1. The work done by A and B together is:
\[ \text{Work done by A and B together} = 1 - \text{Work done by B alone} = 1 - \frac{17}{35} = \frac{35 - 17}{35} = \frac{18}{35} \]A and B's combined one day's work is:
\[ \text{A and B's 1 day work} = \frac{1}{56} + \frac{1}{70} \]To add these fractions, find the Least Common Multiple (LCM) of 56 and 70.
Prime factorization of 56: \(2^3 \times 7\)
Prime factorization of 70: \(2 \times 5 \times 7\)
LCM(56, 70) = \(2^3 \times 5 \times 7 = 8 \times 5 \times 7 = 280\)
Now, add the fractions:
\[ \text{A and B's 1 day work} = \frac{5}{280} + \frac{4}{280} = \frac{5 + 4}{280} = \frac{9}{280} \]Let \(D\) be the number of days A and B worked together. The work done by them together is \(\frac{18}{35}\).
\[ D \times \left(\text{A and B's 1 day work}\right) = \frac{18}{35} \]\[ D \times \frac{9}{280} = \frac{18}{35} \]\[ D = \frac{18}{35} \times \frac{280}{9} \]\[ D = \frac{18}{9} \times \frac{280}{35} \]\[ D = 2 \times 8 \]\[ D = 16 \]So, A and B worked together for 16 days. This means A left after 16 days.
A) 16
This question tests knowledge of the fundamental rights enshrined in the Indian Constitution, specifically focusing on Article 17. The approach is to recall the specific provisions of Article 17 and then identify which option accurately reflects it.
Correct Option: B) abolition of the practice of untouchability