Prime factors of 45 are 3 x 3 x 5 i.e. 3 and 5.

The smallest number to be multiplied by 45 so that it may have 3 distinct prime factors is 2.

Number become 90 (45x2) and factors are 2x3x3x5.

Probability of at least one attending the class = 1- probability of none attending

Let probability of A, B and C attending the class be a, b, c respectively.

Thus, probability of not attending the class by A, B and C is (1 - a), (1 - b) and (1 – c) respectively.

The probability of exactly one of A or B attending = a(1 - b) + b(1 - a) = 710

= a + b – 2ab = 710 (1)

Similarly, for B or C = b + c – 2bc = 410 (2)

And, for C or A = c + a – 2ca = 710 (3)

Probability of all three attending (i.e. abc) = 99100 (4)

From (1), (2) and (3): 2(a + b + c – ab – bc - ca) = 710 +410 + 710 = 1810 = 95

a + b + c – ab – bc – ca = 910

Probability of none attending = (1 - a)(1 - b)(1 – c) = 1 – a – b – c + ab + bc + ca – abc

Probability of none attending = 1 – (a + b + c – ab – bc – ca + abc)

Probability of none attending = 1 – (910 + 99100) = 1100

Probability of at least one attending = 1 – probability of none attending

Probability of at least one attending = 1 – 1100 = 99100

As any drawn fruit will be a banana so the probability of drawing a banana is 1

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The shopkeeper sold two T-shirts for Rs. 2400

Selling Price of one T-shirt = Rs. 1200

Profit = 33.33%

Cost Price = S.P. * 100100+P% = 1200 * 100100+33.33 = 1200 * 100133.33 = 1200 * 34 ≈ Rs. 900

4₂₃*5₂₀*3₂*11₀6₂*5₅*2₄₆*5₁₀*5₅ = (2₂)₂₃3*5₂₀*3₂*1(3*2)2*5₅+10+5*2₄₆ = 2₄₆*5₂₀*3₂*12₂*3₂*5₂₀*2₄₆ = 12₂ = 14