AIEEE Questions

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i. The 'Swachh Survekshan 2017' survey results were recently announced by Urban Development Minister M Venkaiah Naidu. The total 434 cities of India were surveyed. Indore in Madhya Pradesh is India’s cleanest city while Gonda in Uttar Pradesh is the dirtiest.

ii. Gujarat has the maximum of 12 cities among the top 50 clean cities, closely followed by Madhya Pradesh with 11 and Andhra Pradesh with eight. Uttar Pradesh accounted for half of the bottom 50 cities in the cleanliness ranking.

Top 10 clean cities of India in 2017 are:

Indore (MP)
Bhopal (MP)
Visakhapatnam (Andhra Pradesh)
Surat (Gujarat)
Mysuru (Karnataka)
Tiruchirapally (Tamil Nadu)
New Delhi Municipal Council (New Delhi)
Navi Mumbai (Mumbai)
Tirupati (Andhra Pradesh)
Vadodara (Gujarat).

Top 5 Dirtiest cities of India (with Rank) in 2017 are:

Gonda (UP)- 434,
Bhusawal (Maharashtra)- 433,
Bagaha (Bihar)- 432,
Hardoi (Uttarakhand)- 431,
Katihar (Bihar)- 430.

We know that I = PTR/100

11 = (2x30xR)/100

R = 18.333 %

The number of exhaustive events = 100 C₁ = 100.

We have 25 primes from 1 to 100.

Number of favourable cases are 75.

Required probability = 75/50 = 3/2.

I = (600x11x5)/100 = 330 Paise = Rs. 3.30

Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ x ⁶C₁)

As remaining person can be any one among three couples left.

Required probability = (⁵C₂ x ⁶C₁)/¹⁰C₅
= (10 x 6)/252 = 5/21

My fahter's mother's only daughter-in-law is my father's wife i.e. my mother. My mother's daughter is my sister. My sister's father is my father.