Science All General Science Aptitude

The law associated with the heating effect of electric current is A. Joule's law. Joule's law describes the relationship between the heat generated by a current passing through a conductor and the resistance of that conductor. It states that the heat produced (in joules) is directly proportional to the resistance of the conductor, the square of the current passing through it, and the time for which the current flows.

According to formula the acceleration due to gravity (g) is given by = GM/r²

The value of acceleration due to gravity ‘g’ depends on:
a. Constant of Gravitation ‘G’
b. Mass of the earth ‘M’
d. Radius of the earth ‘R’ ?'

D. a, b, d is the correct option

Among the options provided, the element that forms the maximum number of compounds is D. Carbon (C). Carbon is known for its ability to form a vast number of compounds due to its unique bonding properties, allowing it to form stable molecules with a wide variety of elements, including itself, hydrogen, oxygen, nitrogen, and many others.

A body at rest can have energy. Rest does not imply the absence of energy; it means the absence of motion. Objects at rest still possess potential energy due to their position or state, such as gravitational potential energy or stored energy in a compressed spring. Therefore, the correct answer is D. Energy.

The curved surface area of a hemisphere with radius \(r\) is \(2\pi r^2\) and the curved surface area of a cone with radius \(r\) and slant height \(l\) is \(\pi rl\).

For the cone, the slant height (\(l\)) can be found using the Pythagorean theorem as \(l = \sqrt{r^2 + h^2}\), where \(h\) is the height of the cone.

The volume of the hemisphere (\(V_{\text{hemisphere}}\)) equals the volume of the cone (\(V_{\text{cone}}}\)) since the material is conserved.

The volume of the hemisphere is \(\dfrac{2}{3}\pi r^3\) and the volume of the cone is \(\dfrac{1}{3}\pi r^2h\).

Equating the volumes:

\(\dfrac{2}{3}\pi r^3 = \dfrac{1}{3}\pi r^2h\)

This gives \(h = 2r\), as the \(r^2\) terms cancel out.

The slant height (\(l\)) of the cone becomes:

\(l = \sqrt{r^2 + (2r)^2} = \sqrt{5r^2} = r\sqrt{5}\)

The curved surface area of the cone is:

\(\text{Curved surface area of cone} = \pi rl = \pi r(r\sqrt{5}) = \pi r^2\sqrt{5}\)

The ratio of curved surface areas (hemisphere to cone) is:

\(\dfrac{\text{Curved surface area of hemisphere}}{\text{Curved surface area of cone}} = \dfrac{2\pi r^2}{\pi r^2\sqrt{5}} = \dfrac{2}{\sqrt{5}} = \dfrac{2\sqrt{5}}{5}\)

Thus, the correct answer is B. \(2/\sqrt{5}\).

The work done (\(W\)) in moving a charge (\(q\)) across a potential difference (\(V\)) is given by the formula:

\[W = q \times V\]

Where:
\(W\) = Work done
\(q\) = Charge
\(V\) = Potential difference

Given:
\(q = 5\) C (charge)
\(V = 16\) V (potential difference)

Plugging the values into the formula:

\[W = 5 \, \text{C} \times 16 \, \text{V} = 80 \, \text{J}\]

Therefore, the work done in moving a charge of 5 C across two points having a potential difference of 16 V is \(80 \, \text{J}\), which corresponds to option D.

The correct statement regarding gas exchange in the lungs is:

C. Oxygen diffuses from lungs into blood and carbon dioxide diffuses from blood into lungs.

During the process of respiration in the lungs, oxygen from the inhaled air diffuses across the alveolar membranes into the bloodstream (from lungs into blood), while carbon dioxide, produced as a waste product in the body's cells, diffuses from the bloodstream into the alveoli to be exhaled out of the body (from blood into lungs).

Mendeleev's periodic table, while a groundbreaking achievement in organizing the elements, had some challenges. The element that Mendeleev initially struggled to assign a correct position to in his table was C. Hydrogen.

Hydrogen's placement in the periodic table was debated due to its unique properties. Its behavior somewhat resembled that of alkali metals like lithium and sodium, but it also exhibited characteristics similar to halogens. Mendeleev placed hydrogen separately from the main group elements, in a position above lithium, but its exact placement and relationship within the table were not as definitive as the placements of other elements at that time.

The atmospheric pressure at sea level is approximately 1 atmosphere (atm).
Therefore, the correct answer is B. 1 atm. This pressure is commonly used as a reference point for atmospheric pressure at sea level under standard conditions.

The person who demonstrated that objects of different masses would reach the ground together when dropped from the same height was D. Galileo Galilei.