MAT 2002 Question Paper

Let CP of 1 m of cloth = Rs. $$x$$ and SP = Rs. $$y$$

=> Profit on selling 1 m cloth = Rs. $$(y-x)$$

According to ques,

=> $$33(y-x)=11y$$

=> $$3y-3x=y$$

=> $$2y=3x$$

=> $$\frac{x}{y}=\frac{2}{3}$$

Let $$x=2$$ and $$y=3$$

$$\therefore$$ Profit % = $$\frac{(y-x)}{x}\times100$$

= $$\frac{(3-2)}{2}\times100=50\%$$

=> Ans - (B)

There are 6 bowlers, 3 wicket keepers and 11 batsman in all. The number of ways in which a team of 4 bowlers, 2 wicket keepers and 5 batsman can be chosen

= $$C^6_4\times C^3_2\times C^{11}_5$$

= $$(\frac{6\times5}{1\times2})\times(\frac{3\times2}{1\times2})\times(\frac{11\times10\times9\times8\times7}{1\times2\times3\times4\times5})$$

= $$15\times3\times462=20790$$

=> Ans - (A)

Let rate of interest be $$r\%$$. Let the amount that Sanjay borrowed be Rs. $$100x$$ and time period = 2 years

Simple Interest = $$\frac{P\times r\times t}{100}$$

=> $$\frac{100x\times r\times2}{100}=4000$$

=> $$rx=2,000$$ ------------(i)

Also, difference between S.I. and C.I. for 2 years = $$\frac{Pr^2}{100^2}$$

=> $$\frac{100x\times r^2}{100^2}=200$$

=> $$r^2x=20,000$$ ------------(ii)

Dividing equation (ii) by (i), => $$r=10$$

$$\therefore$$ Rate of interest = 10%

=> Ans - (D)

Distance between 1st and 21st post = $$(21-1)\times50=1000$$ m = $$1$$ km

Thus, the train travels 1 km in 1 minute.

=> Speed of train, i.e. distance travelled in 60 minutes = $$1\times60=60$$ km/hr

=> Ans - (B)

Width of the track is the difference between the radius of outer circle and inner circle = $$R-r$$

Inner circumference = $$2\pi r=352$$

=> $$2\times\frac{22}{7}\times r=352$$

=> $$r=56$$ m

Similarly, $$2\pi R=396$$

=> $$R=63$$ m

$$\therefore$$ Width of the track = $$63-56=7$$ m

=> Ans - (D)

Let the total number of guests be $$x$$

Number of rice bowls = $$\frac{x}{2}$$

Number of bowls of daal = $$\frac{x}{3}$$

Number of bowls of meat = $$\frac{x}{4}$$

=> $$\frac{x}{2}+\frac{x}{3}+\frac{x}{4}=65$$

=> $$\frac{6x+4x+3x}{12}=65$$

=> $$\frac{13x}{12}=65$$

=> $$x=5\times12=60$$

$$\therefore$$ 60 guests were present.

=> Ans - (C)

5 questions can be selected in the following ways : (2 question from first group and 3 question from second group) or (3 question from first group and 2 question from second group)

=> Number of ways = $$(C_2^4\times C_3^4)$$ $$+(C_3^4\times C_2^4)$$

= $$24+24=48$$

=> Ans - (B)

Runs scored in first 10 overs = $$3.2\times10=32$$

Runs required = $$282-32=250$$

> Run rate required to score 250 runs in 40 overs = $$\frac{250}{40}=6.25$$

=> Ans - (A)