State whether the following sentences are right or wrong
The proportion of youth in India’s population is high.
The proportion of youth in India’s population is high.
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Solution and Explanation
The proportion of youth in India’s population is high.
Step 1: Demographics of India
India has a very young population compared to many other nations. According to recent data, a significant proportion of Indians are below the age of 35, and the median age is around 28 years. This makes India one of the youngest countries in the world.
\[ \text{India's demographic pyramid is broad at the base, showing a large young population.} \]
Step 2: Youth Proportion in India
This youthful population contributes greatly to India’s economic potential and workforce dynamism. To realize the demographic dividend, focus must be placed on education, skill development, and job creation.
\[ \textbf{India has a high youth proportion, making it a young and dynamic nation.} \]
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Questions Asked in Maharashtra Class X Board exam
Complete the following activity to prove that the sum of squares of diagonals of a rhombus is equal to the sum of the squares of the sides.
Given: PQRS is a rhombus. Diagonals PR and SQ intersect each other at point T.
To prove: PS\(^2\) + SR\(^2\) + QR\(^2\) + PQ\(^2\) = PR\(^2\) + QS\(^2\)
Activity: Diagonals of a rhombus bisect each other.
In \(\triangle\)PQS, PT is the median and in \(\triangle\)QRS, RT is the median.
\(\therefore\) by Apollonius theorem,
\[\begin{aligned} PQ^2 + PS^2 &= \boxed{\phantom{X}} + 2QT^2 \quad \dots \text{(I)} \\ QR^2 + SR^2 &= \boxed{\phantom{X}} + 2QT^2 \quad \dots \text{(II)} \\ \text{Adding (I) and (II),} \quad PQ^2 + PS^2 + QR^2 + SR^2 &= 2(PT^2 + \boxed{\phantom{X}}) + 4QT^2 \\ &= 2(PT^2 + \boxed{\phantom{X}}) + 4QT^2 \quad (\text{RT = PT}) \\ &= 4PT^2 + 4QT^2 \\ &= (\boxed{\phantom{X}})^2 + (2QT)^2 \\ \therefore \quad PQ^2 + PS^2 + QR^2 + SR^2 &= PR^2 + \boxed{\phantom{X}} \\ \end{aligned}\]
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- Constructions
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- Maharashtra Class X Board - 2025
- Constructions
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