How many triangles are there in the given figure?
To determine the number of triangles in the given figure, we need to systematically count all the triangles formed by the intersecting lines and shapes.
Adding all these, we have:
Total = 4 + 4 + 12 + 4 = 24 triangles.
Correct Option: D) 20
This is a logical reasoning question where we need to evaluate the given conclusions based solely on the information provided in the statement. We must not assume any external information or general knowledge. The statement defines a specific age group (27 to 32 years) for candidates who should be young, energetic, and dynamic. We need to check if the conclusions logically follow from this definition.
B) Neither conclusion I nor II follows
Both conclusions make assumptions about individuals outside the specified age range (27-32 years) which are not supported by the statement. The statement only defines characteristics for a specific group, not for those outside it.
This is a coding-decoding problem where each letter is assigned a specific digit. We need to identify the code for each letter from the given coded words and then apply that mapping to find the code for 'CRAPE'.
Correct Option: B) 76421
The problem asks us to evaluate two conclusions based on a given statement. We need to determine which conclusions logically follow from the statement. The statement emphasizes that the world's nature (good or evil) is subjective, created by each individual's perception.
Correct Option: A) Both conclusions I and II follow
To simplify the multiplication of decimals, we can convert them into fractions or multiply them as whole numbers and then place the decimal point correctly. The key is to count the total number of decimal places in the numbers being multiplied.
D) 0.002 — As calculated by both methods, the product of \(0.004\) and \(0.5\) is \(0.002\).
The question asks for the term describing the repetition of sound due to the reflection of sound waves. We need to identify the correct scientific term from the given options.
D) Echo is the correct term. An echo occurs when sound waves reflect off a distant surface (like a wall, cliff, or mountain) and return to the listener, creating a distinct repetition of the original sound. For a distinct echo to be heard, the reflecting surface must be at a sufficient distance from the sound source so that the reflected sound arrives at least 0.1 seconds after the original sound (due to the persistence of hearing).
To find the vertical height of the right pyramid, we need to use the Pythagorean theorem. First, we'll determine the side length of the square base using its diagonal. Then, we'll find the distance from the center of the base to a vertex. Finally, we'll use the slant edge and this distance to calculate the vertical height.
Find the side length of the square base:
Let the side length of the square base be \(a\). The diagonal of a square is given by the formula \(d = a\sqrt{2}\).
Given diagonal \(d = 16\) units.
\[ 16 = a\sqrt{2} \]\[ a = \frac{16}{\sqrt{2}} = \frac{16\sqrt{2}}{2} = 8\sqrt{2} \text{ units} \]Find the distance from the center of the base to a vertex:
The center of the square base is the intersection of its diagonals. The distance from the center to any vertex is half the length of the diagonal.
Distance from center to vertex \[= \frac{1}{2} \times \text{diagonal} = \frac{1}{2} \times 16 = 8 \text{ units}\]
Calculate the vertical height:
Consider a right-angled triangle formed by the vertical height (\(h\)), the slant edge (\(l\)), and the distance from the center of the base to a vertex (\(r\)). Here, \(r\) is the base of this right triangle, \(h\) is the perpendicular, and \(l\) is the hypotenuse.
We have \(l = 17\) units (slant edge) and \(r = 8\) units (distance from center to vertex).
According to the Pythagorean theorem:
\[ h^2 + r^2 = l^2 \]\[ h^2 + 8^2 = 17^2 \]\[ h^2 + 64 = 289 \]\[ h^2 = 289 - 64 \]\[ h^2 = 225 \]\[ h = \sqrt{225} \]\[ h = 15 \text{ units} \]Correct Option: B) 15
The question asks for the scientific field that studies the relationship between animals and their environment. We need to identify the correct biological term from the given options.
Correct Option: A) Ecology — This is the branch of biology that studies the interactions among organisms and their biophysical environment, including both biotic and abiotic components. This directly addresses the relationship of animals with their environment.
The question describes a chemical reaction where copper sulphate solution reacts with iron metal to form copper metal. We need to identify the type of reaction based on the changes in the reactants.
Correct Option: C) Single displacement reaction. In this reaction, a more reactive metal (iron) displaces a less reactive metal (copper) from its salt solution (copper sulphate).
The question asks to identify the type of system Rustom-2 is, developed by DRDO. This requires knowledge of current Indian defence projects and their classifications.
C) Unmanned Combat Aerial Vehicle — Rustom-2, developed by DRDO, is a Medium Altitude Long Endurance (MALE) Unmanned Aerial Vehicle (UAV). It is designed for surveillance and reconnaissance missions and has the capability to be armed, thus falling under the category of an Unmanned Combat Aerial Vehicle (UCAV).