AIEEE Questions

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The surface area of a cube = 6a2 =  6 side2

New  Surface area = 6 x 1.44a2

Therefore, 0.44a2a2x100 = 44%

As given
200 cats kill 200 mice in 200 days
1 cats kill 1 mouse in 200 days
Then
8 cats kill 8 mice in 200 days.

50.0 mL 0.0500 M calcium hydroxide, Ca(OH)2 (aq) has the highest pH value.

Sodium hydroxide and Calcium hydroxide are strong bases so they completely ionize in solution. Because they ionize at the same rate, and Calcium hydroxide has the higher pH calculated, then Calcium hydroxide, in fact, has the highest pH.

Nitric acid is a strong acid, so it completely ionizes in water. Whilst nitrous acid is a weak acid. Therefore, the nitric acid solution has the LOWEST ph.

It is explicitly given that all the 4 black balls are different, all the 3 red balls are different and all the 5 blue balls are different. Hence this is a case where all are distinct objects.

Initially let's find out the number of ways in which we can select the black balls. Note that at least 1 black ball must be included in each selection.

Hence, we can select 1 black ball from 4 black balls
or 2 black balls from 4 black balls.
or 3 black balls from 4 black balls.
or 4 black balls from 4 black balls.

Hence, number of ways in which we can select the black balls

= 4C1 + 4C2 + 4C3 + 4C4
= 24-1 ........(A)

Now let's find out the number of ways in which we can select the red balls. Note that at least 1 red ball must be included in each selection.

Hence, we can select 1 red ball from 3 red balls
or 2 red balls from 3 red balls
or 3 red balls from 3 red balls

Hence, number of ways in which we can select the red balls
= 3C1 + 3C2 + 3C3
=23-1........(B)

Hence, we can select 0 blue ball from 5 blue balls (i.e, do not select any blue ball. In this case, only black and red balls will be there)
or 1 blue ball from 5 blue balls
or 2 blue balls from 5 blue balls
or 3 blue balls from 5 blue balls
or 4 blue balls from 5 blue balls
or 5 blue balls from 5 blue balls.

Hence, number of ways in which we can select the blue balls
= 5C0 + 5C1 + 5C2 + … + 5C5
= 25..............(C)

From (A), (B) and (C), required number of ways
=  2524-123-1

The given words are related in a way that, an optimist is a person whose outlook is cheerful. Similarly, a pessimist is a person whose outlook is gloomy.

The answer is not (b) because a pessimist does not have to be mean. Options (c) and (a) are incorrect because neither words describe the outlook of a pessimist.

Hence, Optimist is to cheerful as Pessimist is to Gloomy.

The amount of petrol left after 4 operations  

= 200 × 1-402004  

= 200 × 454  

= 200 × 256625  

= 81.92 litres

Hence the amount of kerosene = 200 - 81.92 = 118. 08 litres

A spreadsheet contains both rows and columns.

We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)
(60 x 30 x 8)/ 150 = (35 x D2 x 6) / 200
D2 = (60 x 30 x 8 x 200) / (150 x 35 x 6) => D2 = 91.42 days =~ 91.5 days.