The question asks to identify the system formed by the brain and spinal cord in the human body. This requires knowledge of the basic divisions of the nervous system.
Correct Option: B) central nervous system — The central nervous system (CNS) is composed of the brain and the spinal cord. It is the primary control center of the body, responsible for processing information and coordinating actions.
To find the average of the first 'n' natural numbers, we can use the formula for the sum of the first 'n' natural numbers and then divide by 'n'. Alternatively, for a sequence of numbers in arithmetic progression, the average is simply the average of the first and last terms.
The sum of the first \(n\) natural numbers is given by the formula:
\[ S_n = \frac{n(n+1)}{2} \]For \(n = 30\), the sum \(S_{30}\) is:
\[ S_{30} = \frac{30(30+1)}{2} = \frac{30 \times 31}{2} = 15 \times 31 = 465 \]The average is the sum divided by the number of terms:
\[ \text{Average} = \frac{S_n}{n} = \frac{465}{30} = 15.5 \]For an arithmetic progression, the average is given by:
\[ \text{Average} = \frac{\text{First term} + \text{Last term}}{2} \]In this case, the first term is 1 and the last term is 30.
\[ \text{Average} = \frac{1 + 30}{2} = \frac{31}{2} = 15.5 \]C) 15.5 is the correct average of the first 30 natural numbers.
The question asks to identify the organization responsible for developing the Long-Range Glide Bomb (LRGB) GAURAV. This requires knowledge of India's defence research and development institutions and their specific roles.
Correct Option: C) Defence Research and Development Organisation (DRDO) is the correct answer. DRDO is the primary government agency in India responsible for the research, development, and testing of military technology, including advanced weapon systems like the Long-Range Glide Bomb (LRGB) GAURAV.
To solve this problem, we first need to determine the cost price (CP) of the watch. We are given the selling price (SP) and the loss percentage. Once the CP is known, we can calculate the new profit percentage when the watch is sold at a different selling price.
A) 15% is the correct answer. The cost price of the watch is ₹1,280. When sold for ₹1,472, the profit is ₹192, which translates to a 15% profit on the cost price.
The question asks to identify the correct title of the book authored by Vijay Lokapally on Virat Kohli, specifically the 2023 revised and updated World Cup Edition. This requires knowledge of popular sports biographies and their authors.
Correct Option: C) Driven: The Virat Kohli Story (Revised and Updated World Cup Edition)
This is the correct title of the book by Vijay Lokapally about Virat Kohli, with the specified edition.
The angle of elevation of the top of a small tree from a point on the ground 300 m away from the foot of the tree was 30°. When the tree grew taller, its angle of elevation became 60° from the same point. By how much did the tree grow?
\(\frac{100}{\sqrt{3}}\) m
200\(\sqrt{3}\) m
\(\frac{200}{\sqrt{3}}\) m
100\(\sqrt{3}\) m
This problem involves trigonometry, specifically the tangent function, to calculate heights based on angles of elevation and distance from the base. We will set up two right-angled triangles, one for the initial height of the tree and another for its final height, and then find the difference to determine how much the tree grew.
Define variables:
Calculate initial height (\(h_1\)):
In the first right-angled triangle, we have:
We know that \(\tan(30^\circ) = \frac{1}{\sqrt{3}}\). So,
\[ \frac{1}{\sqrt{3}} = \frac{h_1}{300} \]\[ h_1 = \frac{300}{\sqrt{3}} \text{ m} \]Calculate final height (\(h_2\)):
In the second right-angled triangle, we have:
We know that \(\tan(60^\circ) = \sqrt{3}\). So,
\[ \sqrt{3} = \frac{h_2}{300} \]\[ h_2 = 300\sqrt{3} \text{ m} \]Calculate the growth of the tree:
The amount by which the tree grew is the difference between its final and initial heights:
Simplify the expression:
To subtract, find a common denominator:
Correct Option: B) \(200\sqrt{3}\) m
The sum of the interior angles of any quadrilateral is 360°. Given the ratio of the angles, we can represent each angle as a multiple of a common factor. Then, we sum these angles and equate them to 360° to find the common factor. Once the common factor is known, we can calculate the value of each angle and find the difference between the greatest and the smallest angles.
Let the angles of the quadrilateral be \(2x\), \(5x\), \(7x\), and \(10x\), where \(x\) is the common ratio factor.
The sum of the interior angles of a quadrilateral is 360°.
Set up the equation by summing the angles and equating it to 360°:
\[ 2x + 5x + 7x + 10x = 360^\circ \]Combine the terms on the left side:
\[ (2 + 5 + 7 + 10)x = 360^\circ \]\[ 24x = 360^\circ \]Solve for \(x\):
\[ x = \frac{360^\circ}{24} \]\[ x = 15^\circ \]Now, calculate each angle:
Find the difference between the greatest and the smallest angles:
\[ \text{Difference} = \text{Greatest angle} - \text{Smallest angle} \]\[ \text{Difference} = 150^\circ - 30^\circ \]\[ \text{Difference} = 120^\circ \]B) 120° is the difference between the greatest and the smallest angles, as calculated.
The question asks to identify the scheme under which the Department of Posts launched the 2024 philately scholarship scheme. This requires knowledge of various government schemes and their objectives.
Correct Option: C) The 2024 philately scholarship scheme was launched by the Department of Posts under the Deen Dayal SPARSH Yojana. SPARSH stands for "Scholarship for Promotion of Aptitude & Research in Stamps as a Hobby". This scheme was launched by the Department of Posts to promote philately among school children. It provides annual scholarships to students of Standard VI to IX who have a good academic record and also pursue philately as a hobby.
The question asks to identify the scientist who coined the term 'protoplasm' for the fluid substance within a cell. This is a direct factual recall question from the history of cell biology.
Correct Option: C) Purkinje