CUET PG 2022 Question Paper Economics Shift-1

Let's number the balls as 1, 2, 3, 4, 5, 6, 7.

We have a condition on ball 3; it can be placed in either box 3 or 4. So, ball 3 has two chances.

All the remaining balls can be placed in any of the five boxes. This can be done in 5*5*5*5*5*5=$$5^6$$

The total number of ways is $$2*5^6$$.

Given, $$10^{0.48} = x, 10^{0.70} = y$$ and $$x^{z} = y^{2}$$

$$(10^{0.48})^z = 10^{0.70}^2$$

$$10^{0.48*z} = 10^{0.70*2} = 10^{1.4}$$

0.48*z=1.4

$$\Rightarrow z = \frac{1.4}{0.48} = 2.91$$

Let's find out the number of ways of arranging 9 different balls in a row.

That can be done in 9! = 3,62,880

Now, let's find out the number of ways to arrange nine different balls in a row so that black, white, red, and green balls come together.

Let's make them a group. And arrange all the balls in a row.

This can be done in 6!*4! = 720*24 = 17,280.

The number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are never together is 

 3,62,880 - 17,280 = 345600

Let's assume the capacity of the tank is 60 units.

A tap can fill the tank in 6 hours. The rate at which this tap fills is $$\frac{60}{6}$$ = 10 units/ hr.

The time this tap takes to fill half the tank is $$\frac{6}{2}=3 hrs$$

Now, 3 more similar taps are opened, so there are 4 taps running at a rate of 10 units/hr.

The rate of all four taps combined is 40 units/hr.

The time taken by these four taps to fill 30 units is $$\frac{30}{40}$$ = $$\frac{3}{4}$$hr  =45 mins.

The total time taken is 3 hrs 45 mins.

Let the distance and original speed be 'd' km and 'k' kmph, respectively.

d/0.8k - d/k = 20/60 => 5d/4k - d/k = 1/3

=> (5d - 4d)/4k = 1/3 => d = 4/3 k

Time taken to cover the distance at the original speed

= d/k = 4/3 hours = 1 hour 20 minutes.

Option B is correct answer.