MAT 2013 Question Paper

Given radius of the cylinder, r = 12 cm

It is also given that a spherical iron ball is dropped into the cylinder and the water level raised by 6.75 cm

Hence volume of water displaced = volume of the iron ball

Height of the raised water level, h = 6.75 m

Volume of water displaced = πr^2h

= π × 12 × 12 × 6.75 cm^3

So, Volume of iron ball = π × 12 × 12 × 6.75 cm^3 ... (1)

But, volume of iron ball =4/3πr^3  ...(2)

From (1) and (2) we get

4/3πr^3 = π × 12 × 12 × 6.75

On solving, we get

r^3 = 729

r^3 = 3^6

Therefore, r' = 9 

Radius of the iron ball is 9 cm

Let the selling price of the article = Rs. 100

Therefore, 

Profit = Rs. 26

So, Cost price of the article = S.P. - Profit

= 100 - 26 = Rs. 74

So,

Required % = (34 x 74)/100

= 25.16%

Since, 

S.I. = Principal∗Rate∗Time/100

Therefore, 1200 + 1200∗7∗r/12∗100 = Amount (A) 

1200 + 7r = A .........(i)

and 1016 + 1016∗5∗r/2∗100 = A

Therefore, 1016 + 25.4r = A ...(ii)

1016 + 25.4r = 1200 + 7r

So,

25.4r - 7r = 1200 - 1016

18.4r = 184 

r = 184/18.4 

= 10% per annum

According to question

P+R+2Q=59...........1

Q+R+3P=68 .........2

P+3Q+3R=108 .................3

Multiply equation (2) by 3

And subtract equation (iii) from it,

Then P=12 years

Present age of Mahesh years

Present age of Anup 

Let present age of Shyam 

Then, present age of Anup $=\frac{x-\mathrm{6/}}{18}$

$\frac{x-\mathrm{6/}}{18}=3$

$\mathrm{So,\; x}-6=3\times 18=54$

$Therefore,\; x=54+6$

$=60$

First let us take out the circumferences of both circles.

Radius of inner circle = 100 m

∴Circumference of the inner track= 2πr

                                                    = 2×3.14×100

                                                    = 628 m 

Radius of outer track= 102 m

So, Circumference of outer track=2πr = 2×3.14×102 = 753.6 m

Time taken by A = 1 min 30 sec = 90 sec

Time taken by B = 1 min 32 sec = 92 sec

Speed of A = Distance covered by A/ Time taken 

                    = 628/90

                    = 6.98 m/s

Speed of B = Distance covered by B /time taken 

                   =753.6/92

                   =8.19 m/s

  Speed of A is smaller than the speed of B.

  So, B runs faster.

Speed = distance  / time

40 = distance / (t + 10)

50 = distance / (t - 5)

4/5 = (t-5)/(t+10)

4t + 40 = 5t - 25

t = 65 min

distance = speed * time

= 40 * (75/60)  --- in hours

= 50 km

You have to choose Odd-Even or Even-Odd. 

The probabilities of both events are the same: at the start there’s the same amount of odds and evens. 

So  calculate for one of them and multiply by 22.

First number being odd: 10/20 = 1/2

Second number being even: 10/19

Overall = 10/19*2 *2 = 10/19

According to the question,

time 1/amount of work done 1 = time 2/amount of work done 2

(12*8*.9):(9000/2)::(6*x*.8):(12000/3)

So,on solving , we get

x=16 h/day

Let there are x inlet pipes.

work done by inlet =1/9

work done by outlet=1/6

Here 6-x is the outlets

x/9-(6-x)/6=1/9

5x=20

x=4

Then there will be 4 inlet pipes the will to fill the tank