CMAT 2019 Question Paper

Volume left out in the rectangular box = Total volume of the rectangular box - Volume of the cylinder placed within it.

Total volume of the rectangular box of width(a), length(b), and height(c) is given as (V) = $$a\times b\times c$$ cubic units.

= $$6\times 8\times 10$$

= 480 cubic units.

Volume of the solid cylinder of height 'c' and of diameter 'a' is given by (V') = $$\frac{\pi}{4}*a^2*c$$ cubic units.

= $$\frac{\pi}{4} * 6^2 * 10$$

= 90$$\pi$$ cubic units.

Therefore left out volume = 480 - 90$$\pi$$ cubic units.

Given f(x) = $$x^3 - 4x + p$$ and  f(0) and f(1) are of opposite signs.

$$\Rightarrow f(0)\times f(1) < 0$$

$$f(0) = 0^3 - 4*0 + p = p$$

$$f(1) = 1^3 - 4*1 + p = p-3$$

$$\Rightarrow (p)(p-3) < 0$$

$$\Rightarrow 0 < p < 3$$.

Given, speed of a boat in still water (V) =  5 km/hr

Let speed of the stream be V' km/hr.

time taken to go 20km downstream (t) = distance travelled$$\div$$relative speed of the boat 

= $$\frac{20}{V + V'}$$

=$$\frac{20}{5 + V'}$$ hours

time taken to go 20 km upstream (t') =  distance travelled$$\div$$relative speed of the boat 

= $$\frac{20}{V - V'}$$

= $$\frac{20}{5 - V'}$$ hours

Given that t' = 3*t

$$\Rightarrow \frac{20}{5 - V'} = 3\times \frac{20}{5 + V'}$$

$$\Rightarrow 4V' = 10$$

$$\Rightarrow V' = 2.5$$ km/hr.

So the speed of the stream is 2.5 km/hr.

Whenever some cubes are melted to form a single larger cube, the total volume always remains constant.

So, Sum of the volumes of three small cubes = Volume of the larger cube.

Let the side of the lager cube so formed be 'a' cm.

Then $$1^3 + 6^3 + 8^3 = a^3$$

$$\Rightarrow a^3 = 729$$

$$\Rightarrow a = 9$$ cm.

Surface area of cube so formed = 6*$$a^2$$ = $$6\times 9^2 = 6\times 81 = 486  cm^2$$

Speed = Distance travelled$$\div$$time taken

So, for the same distance travelled, Speed is inversely proportional to time taken.

$$Speed\propto \frac{1}{time taken}$$

Given ratio of speeds of three cars  is 5 : 4 : 6.

So, ratio of the time taken to travel same distance is $$\frac{1}{5} : \frac{1}{4} : \frac{1}{6}$$

= 12 : 15 : 10

The given statement indicates a question about the ban of political parties, the first argument is weak as there is no context about teaching the lesson to the political parties.

But the second argument is strong, because if the parties are banned, it will definitely lead to an end of democracy.

Hence, only II is strong.

=> Ans - (B)

Small squares = 6 (ABKD, BCEK, DKLF, KEGL, FLIH, LGJI)

Big squares = 2 (ACGF, DEJH)

Total squares = 8

=> Ans - (C)

Cup is used to drink something with the help of lips. Similarly birds collects grass with the help of beak to make her nest.

=> Ans - (C)

The given statement indicates that if any student is found to use unfair or unethical means in an exam will be disqualified, hence the first conclusion follows since it also debars the student from using unfair means in the exam. But second conclusion does not follow since there is no context about the examination system.

Thus, only conclusion I follows.

=> Ans - (A)

A well is located at one corner and a cabin at another corner opposite to the gate.

Lemon and Coconut trees are on either side of the gate

The mango tree is not at the corner where the cabin is located, => Mango Tree and Well are at the same corners, also Neem Tree and Cabin are at same corners

Thus, only possible combination at diagonally opposite ends is Neem Tree and Lemon Tree.

=> Ans - (D)