MAT 2002 Question Paper

Let B's age = $$6x$$ years and A's age = $$x$$ years and C' present age = 10 years

According to ques,

=> $$6x+10=2\times(10+10)$$

=> $$6x=30$$

=> $$x=5$$

$$\therefore$$ A's present age = 5 years

=> Ans - (A)

Effective discount = $$20+30-(\frac{20\times30}{100})$$

= $$50-6=44\%$$

=> Ans - (B)

Rate of leak = $$2.25\times\frac{60}{5.5}=\frac{270}{11}$$ tonnes/hr and rate of pump = $$12$$ tonnes/hr

To suffice 92 tonnes, time taken by ship = $$92\div(\frac{270}{11}-12)$$

= $$92\times\frac{11}{138}=\frac{22}{3}$$ hr

=> Average rate of sailing = distance/time

= $$77\div\frac{22}{3}$$

= $$77\times\frac{3}{22}=10.5$$ km/hr

=> Ans - (D)

Total number of events that would occur by flipping six coins = $$2^6=64$$

Probability that no tail occurs = $$\frac{1}{64}$$

=> Probability of occurring at least one tail = $$1-\frac{1}{64}=\frac{63}{64}$$

=> Ans - (C)

Side of square = Radius of arc = 10 cm

Now, area of shaded region = $$2\times[$$ area (sector ABD) $$-$$ area ($$\triangle$$ ABD) $$]$$

= $$2\times[(\frac{\theta}{360^\circ}\times\pi r^2)-(\frac{1}{2})\times b\times h]$$

= $$2\times[(\frac{90^\circ}{360^\circ}\times\pi \times100)-(\frac{1}{2}\times 10\times 10)]$$

= $$2\times(25\pi-50)$$

= $$(50\pi-100)$$ $$cm^2$$

=> Ans - (C)

Position of X and Y is fixed, as all three boys are together with X in center and three girls together with Y in center.

Number of arrangement for boys = $$(3-1)!=2!=2$$

and similarly for girls = $$2!=2$$

$$\therefore$$ Total number of ways = $$2\times2=4$$

=> Ans - (C)

The degree will not change even when it is look through a magnifying glass, it will remain same = $$2\left(\frac{1^\circ}{2}\right)$$

=> Ans - (D)

Relative speed = $$3.75+4.5=8.25$$ km/hr = $$8.25\times\frac{5}{18}=\frac{13.75}{6}$$ m/s

Time taken for them to meet first time = distance/speed

= $$726\div\frac{13.75}{6}$$

= $$726\times\frac{6}{13.75}=316.8$$ sec

= $$\frac{316.8}{60}=5.28$$ minutes

=> Ans - (C)

To make a 25% solution, containing 48 ml alcohol, water added

= $$48\times\frac{100}{25}=144$$ ml

=> Ans - (C)

When the bus started, let total male passengers be $$3x$$ and female passengers be $$x$$

=> Total number of passengers = $$4x$$

At first stop, number of male passengers = $$(4x-16)\times\frac{3}{4}=3x-12$$

and female passengers = $$(4x-16)\times\frac{1}{4}+6=x+2$$

According to ques,

=> $$\frac{3x-12}{x+2}=\frac{2}{1}$$

=> $$3x-12=2x+4$$

=> $$x=16$$

$$\therefore$$ Total passengers initially = $$4\times16=64$$

=> Ans - (A)