This problem involves the properties of triangles, specifically the Midpoint Theorem. When the midpoints of the sides of a triangle are joined, they form a smaller triangle. The Midpoint Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side. We will use this theorem to find the side lengths of triangle XYZ and then calculate its perimeter.
\[ \text{Perimeter of PQR} = 3 \times s \]
Given perimeter is 24 cm, so
\[ 24 \text{ cm} = 3 \times s \]
\[ s = \frac{24}{3} \text{ cm} \]
\[ s = 8 \text{ cm} \]
Thus, \(PQ = QR = RP = 8 \text{ cm}\).
\[ XY = \frac{1}{2} PR \]
\[ XY = \frac{1}{2} \times 8 \text{ cm} \]
\[ XY = 4 \text{ cm} \]
\[ YZ = \frac{1}{2} PQ \]
\[ YZ = \frac{1}{2} \times 8 \text{ cm} \]
\[ YZ = 4 \text{ cm} \]
\[ ZX = \frac{1}{2} QR \]
\[ ZX = \frac{1}{2} \times 8 \text{ cm} \]
\[ ZX = 4 \text{ cm} \]
\[ \text{Perimeter of XYZ} = XY + YZ + ZX \]
\[ \text{Perimeter of XYZ} = 4 \text{ cm} + 4 \text{ cm} + 4 \text{ cm} \]
\[ \text{Perimeter of XYZ} = 12 \text{ cm} \]
C) 12 cm — As calculated, the perimeter of triangle XYZ is 12 cm.
There is a 40% increase in an amount in 4 years at simple interest. What will be the compound interest on Rs. 6,000 after 3 years at the same rate?
First, we need to determine the annual simple interest rate using the given information about the 40% increase in 4 years. Once the rate is found, we will use it to calculate the compound interest on Rs. 6,000 for 3 years.
Let the principal amount be \(P\). The increase in amount is 40% of \(P\), which means the simple interest (SI) earned is \(0.40P\).
Given:
The formula for simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]Substitute the known values:
\[ 0.40P = \frac{P \times R \times 4}{100} \]To find the rate (\(R\)), we can cancel \(P\) from both sides (assuming \(P \neq 0\)):
\[ 0.40 = \frac{R \times 4}{100} \]Multiply both sides by 100:
\[ 40 = 4R \]Divide by 4:
\[ R = \frac{40}{4} = 10\% \]So, the annual interest rate is 10%.
Now, we need to find the compound interest (CI) on Rs. 6,000 for 3 years at a 10% annual rate.
Given:
The formula for the amount (\(A\)) in compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]Substitute the values:
\[ A = 6000 \left(1 + \frac{10}{100}\right)^3 \]Simplify the term inside the parenthesis:
\[ A = 6000 \left(1 + 0.1\right)^3 \]\[ A = 6000 \left(1.1\right)^3 \]
Calculate \((1.1)^3\):
\[ (1.1)^3 = 1.1 \times 1.1 \times 1.1 = 1.21 \times 1.1 = 1.331 \]Now, calculate the amount:
\[ A = 6000 \times 1.331 \]\[ A = 7986 \]
The compound interest (CI) is the amount minus the principal:
\[ \text{CI} = A - P \]\[ \text{CI} = 7986 - 6000 \]
\[ \text{CI} = 1986 \]
The compound interest is Rs. 1,986.
B) Rs. 1,986 — This is the correct compound interest calculated using the derived rate of 10%.
As on June 2015, (in absolute terms) what is India's rank globally in terms of contribution to greenhouse gas emissions?
The question asks for India's global rank in greenhouse gas (GHG) emissions in absolute terms as of June 2015. This requires knowledge of global GHG emission statistics around that period.
Correct Option: C) 4 th
This is a blood relation problem. We need to trace the relationship backward from the end of the statement to the beginning to determine how Chitra is related to Divya.
C) Daughter-in-law — As derived from the step-by-step analysis, Divya is Chitra's mother-in-law, which means Chitra is Divya's daughter-in-law.
The question asks to identify the first Indian company to join the EP100 campaign, which is an initiative led by 'The Climate Group'. This requires knowledge of specific corporate sustainability commitments and campaigns.
D) Mahindra & Mahindra became the first Indian company to join 'The Climate Group's' EP100 campaign in 2016. They pledged to double their energy productivity by 2030, setting a significant benchmark for corporate sustainability in India.
The problem presents a number series with a missing term. To find the missing number, we need to identify the pattern or rule governing the series. We will examine the relationship between consecutive terms.
Correct Option: C) 39
The question asks to identify a large and versatile space telescope launched in 1990 into low Earth orbit. This requires knowledge of major space telescopes and their launch dates and characteristics.
B) Hubble — The Hubble Space Telescope (HST) was launched by NASA and ESA in April 1990. It is indeed one of the largest and most versatile space telescopes, primarily observing in the visible and ultraviolet spectra, and it operates in a low Earth orbit. It has provided groundbreaking images and data that have revolutionized astronomy.
The question asks to identify which of the given countries does NOT share a land boundary with India. This requires knowledge of India's geographical borders with its neighboring countries.
C) Tajikistan is a Central Asian country and does not share a direct land boundary with India. Afghanistan lies between India and Tajikistan, preventing a direct border.
The question asks to identify the profession of Sadhana Shivdasani, who passed away in December 2015. This is a general knowledge question related to prominent personalities.
Correct Option: D) Actress
The problem asks us to identify the word that is different from the rest, meaning three words share a common characteristic while one does not. We need to analyze the relationship between the given words.
Blackboard, Paper, and Slate are all surfaces or materials upon which one can write or draw. They serve as a medium for inscription.
Chalk, on the other hand, is an instrument or a medium used for writing on surfaces like a blackboard or slate. It is not a surface itself.
Blackboard, Paper, and Slate are all writing surfaces/materials, while Chalk is a writing tool.
D) Chalk — Chalk is a writing tool, whereas Blackboard, Paper, and Slate are all surfaces or materials used for writing.