The question asks about the field in which Raja Ravi Varma was famous. This requires knowledge of prominent Indian historical figures and their contributions to art and culture.
Correct Option: D) Raja Ravi Varma was an iconic figure in the field of painting. His contributions to Indian art are immense, particularly his ability to blend traditional Indian themes with European academic painting techniques.
The question asks for the specific medico-legal term used to describe the dissection and study of a dead human body. This is a direct recall question related to medical terminology, particularly in forensic science.
Correct Option: D) Autopsy
An autopsy, also known as a post-mortem examination, is a surgical procedure performed by a specialist medical doctor called a pathologist on a corpse to determine the cause and manner of death, or to evaluate any disease or injury that may be present. It is a crucial tool in forensic medicine and medical research.
To complete the series, we need to identify the pattern or relationship between consecutive terms. We will calculate the difference between adjacent numbers to see if there's a consistent arithmetic progression or a pattern in the differences.
Therefore, the next term in the series is \(1.2\).
A) 1.2 is the correct answer, as it follows the established pattern of increasing differences.
To determine the lightest metal, we need to compare their densities or atomic masses. Generally, lighter elements tend to have lower atomic masses and often lower densities. We will compare the atomic numbers and approximate atomic masses of the given options.
B) Lithium is the lightest metal among the given options, both in terms of atomic mass and density. It is the least dense solid element at room temperature.
If x - \( \frac{1}{x} \) = 3, then find the value of x⁴ + \( \frac{1}{x^4} \).
The problem asks us to find the value of \(x^4 + \frac{1}{x^4}\) given the equation \(x - \frac{1}{x} = 3\). We can solve this by repeatedly squaring the given equation. First, we square the given equation to find \(x^2 + \frac{1}{x^2}\), and then we square that result to find \(x^4 + \frac{1}{x^4}\).
C) 119 is the correct value for \(x^4 + \frac{1}{x^4}\).
Choose the correct order of signs from the options so as to make the equation correct.
18 - 5 x 50 = 40
The problem requires us to find the correct sequence of mathematical signs (operators and equality) that, when inserted into the given expression, makes the equation true. We will test each option by substituting the signs into the expression and evaluating the result.
Option D provides the signs 'x', '-', '='.
Substitute these signs into the expression:
\[ 18 \times 5 - 50 = 40 \]First, perform the multiplication:
\[ 18 \times 5 = 90 \]Then, substitute this back into the equation:
\[ 90 - 50 = 40 \]Perform the subtraction:
\[ 40 = 40 \]Since both sides of the equation are equal, this option makes the equation correct.
A) -, x, =
Substitute the signs: \(18 - 5 \times 50 = 40\)
Perform multiplication first (BODMAS/PEMDAS): \(5 \times 50 = 250\)
Then, \(18 - 250 = -232\)
So, \(-232 = 40\), which is incorrect.
B) x, =, -
Substitute the signs: \(18 \times 5 = 50 - 40\)
Left side: \(18 \times 5 = 90\)
Right side: \(50 - 40 = 10\)
So, \(90 = 10\), which is incorrect.
C) =, -, x
Substitute the signs: \(18 = 5 - 50 \times 40\)
Perform multiplication first: \(50 \times 40 = 2000\)
Then, \(5 - 2000 = -1995\)
So, \(18 = -1995\), which is incorrect.
The question asks to identify the Chief Minister who introduced the Fiber Grid internet system in India. This requires knowledge of specific government initiatives and the political leaders associated with them.
C) Chandrababu Naidu — N. Chandrababu Naidu, as the Chief Minister of Andhra Pradesh, launched the ambitious AP Fiber Grid project. This initiative aimed to provide high-speed internet connectivity to every household and government office in the state, making it a pioneering effort in digital infrastructure development at the state level in India.
The question asks to identify India's first National Park. This requires knowledge of the history of national parks in India.
A) Jim Corbett National Park
Jim Corbett National Park, located in Uttarakhand, was established in 1936 as Hailey National Park. It was later renamed Ramganga National Park in the mid-1950s before finally being named Jim Corbett National Park in 1957 in honor of the famous hunter and naturalist Jim Corbett. This makes it India's first national park.
The question asks about the location of the pituitary gland in the human body. This requires knowledge of basic human anatomy and the endocrine system.
Correct Option: D) At the base of the brain
The problem asks for the sum of the internal and external radii of a hollow cylinder given its height, thickness, and the volume of material used. We will use the formula for the volume of a hollow cylinder, which is the difference between the volume of the external cylinder and the internal cylinder. We will then solve for the radii using the given information.
Let \(R\) be the external radius and \(r\) be the internal radius of the hollow cylinder.
The height of the cylinder is given as \(h = 24 \text{ cm}\).
The thickness of the cylinder is given as \(1 \text{ cm}\). The thickness is the difference between the external and internal radii:
\[ R - r = 1 \text{ cm} \quad \text{(Equation 1)} \]The volume of material used in constructing the hollow cylinder is given by the formula:
\[ V = \pi (R^2 - r^2) h \]We are given that the volume of material \(V = 96\pi \text{ cm}^3\). Substitute the given values into the volume formula:
\[ 96\pi = \pi (R^2 - r^2) (24) \]Divide both sides by \(\pi\):
\[ 96 = (R^2 - r^2) (24) \]Divide both sides by 24:
\[ \frac{96}{24} = R^2 - r^2 \]\[ 4 = R^2 - r^2 \]Recall the algebraic identity \(a^2 - b^2 = (a - b)(a + b)\). Apply this to the equation:
\[ 4 = (R - r)(R + r) \]From Equation 1, we know that \(R - r = 1\). Substitute this value into the equation:
\[ 4 = (1)(R + r) \]\[ R + r = 4 \]The sum of the internal and external radii is \(R + r\), which we found to be \(4 \text{ cm}\).
C) 4 cm — The sum of the internal and external radii is \(R + r = 4 \text{ cm}\).