CMAT 2021 Slot 2 Question Paper

Number of electronics engineers initially = $$\frac{2}{3}\times\ 252\ =\ 168$$
So number of computer engineers initially = 252-168 =84
Now number of computer engineers recruited to make ratio 1:1 = 168-84 =84
Let average age of computer engineers be x
so total age  will be 168x
Now average age of electronics engineers will be : x+2
So total age will be : (x+2) 168
Now as per given
Total age = 336(22)
Equating we get :
336(22) = 336(x+1)
we get x=21
so B and C are correct

we have :

Triangles PSR and PSQ are right triangles 
so using pythaghoras theorem
we get
441 = $$PS^2+9x^2$$
81 =$$PS^2+x^2$$
subtracting we get
360=$$8x^2$$
$$x^2\ =45$$
x=$$3\sqrt{\ 5}$$
QR = 4x = $$12\sqrt{\ 5}$$

Let speed of Raj be v1 and speed of Rahul be v2 
Now Rahul reaches 5 seconds before Raj and beats him by 50m
so Raj covers 50m in 5 seconds
so v1 = 10m/s
Now When Raj covers 950m Rahul covers 1000m (in the same time )
so we get $$\frac{v1}{v2}=\frac{1000}{950}$$
v1 =$$\frac{200}{19}\ =10\ \frac{10}{19}\ $$ m/sec

Let cost price be 1000 per Kg of rice 
Now to make 25% profit at 1000
He will sell 800 gm of rice
Now C.P of 800 gm of rice = 800
Now he sold at 10% less than 1000 so S.P = 900
Now therefore profit = $$\frac{900-800}{800}\times\ 100\ =\ \frac{100}{8}=12.5\ \%$$

Let quadratic equation be $$x^2+bx+c\ =0$$
Now Sarika made a mistake in reading b , so she would have read c correctly 
so c/1 = product of roots =192   (1)
Meera made a mistake in reading the constant term of the equation so she would have read b correctly
now sum of roots = -b/1 =-28  (2)
we get b =28 , c =192
so quadratic becomes
$$x^2+28x+192$$
we get (x+16)(x+12) =0
roots are -16 , -12

In these type of questions
we go through the options :
Now when x=6 or -6 the value of y is 0
so let us put value of y=0 in all options and check which option satisfies x=6 and -6
Putting x=6 and y=0 in option A
we get |6+0|-|6-0| = 0
But RHS =6 so this option is discarded
Now putting in option B
|6-0|+|6+0| =12
But RHS is 10
so this option is also discarded .
Now option C we get
|6|-0 =6
so we can say graph can be of |x|-|y|=6
Now satisfying option D
we get |6+0|-|6-0|=0
So we can say 6,0 and -6,0 satisfies option D as well
Now you have to eliminate between C and D
If you observe |x+y|-|x-y|=0 will pass through origin
and the graph here is not passing through origin so you can eliminate option D
Therefore the graph will be |x|-|y|=6

Let girls be x 
Total employees will be 80+x
now total value of money will be same :
i.e Average of 1employee (Number of employees ) will be equal to (Average of boys)* Number of boys +(Average of girls)*Number of girls
we get 48000(80+x) = 50,000(80)+40,000(x)
48(80+x) = 50(80) +40x
we get 8x =160
x=20

Curved Surface area of roller = $$2\pi\ rh$$ 
Cost = Area covered* cost per meter square 
so we get total cost = $$2\times\ \frac{22}{7}\times\ \frac{7}{20}\times\ 4\times\ 4\times\ 2000$$
=Rs 70,400

Total value for USA and Japan = 54+45 = 99 
Total value for Australia and Japan = 18+27 = 45
The ratio of the total exports of the USA and Japan to the total exports of Australia and France = 99:45 = 11:5

Total countries = 10 
So average angle will be 360/10 = 36
Now therefore countries subtending angle>35 are 5 .