SNAP 2015 Question Paper

Average speed = Total distance/total time

Let us consider total distance =180km

Case 1 :  man covers half of his journey by train at 90 km/hr

               Distance= 90km => time t1=$$\frac{90}{90}$$=1hr

Remaining distance = 90km

Case 2 :  man covers one-third of the remainder by bus at 30 km/hr

                Distance = 30km => time t2=$$\frac{30}{30}$$=1hr

Case 3 : man covers rest by cycle at 10 km/hr

             Distance = 60km => time t3=$$\frac{60}{10}$$=6hr

Therefore Average speed = $$\frac{180}{1+1+6}$$= 22.5km/hr

Let age of john 5 years ago be x years

age of his grandfather 5 years ago will be 5x

25 years from now there ages will be x+30 and 5x+30 respectively

Given 5x+30 =2(x+30) => x=10

So there present ages would be x+5=15 and 5x+5=55

Ratio = 3:11

Going in the reverse order 

When a number is divided by 6, the remainder is 2 => the number is of the form 6k+2

When 6k+2 is divided by 5,the remainder is 3 => the number is of the form 5(6k+2)+3 = 30k+13

When 30k+13 is divided by 3, the remainder is 1.

The remaining is 30k + 12, so when 30k+12 is divided by 4, the remainder is 2

This can also have another possibility of 1, 0 to be the remainders when successively divided by 3 and 4.

Among the given options 1, 2 satisfies this condition.

The number of zeros in n! = highest power of 5 in n! 

Highest power of 5 in 1024! = [$$\frac{1024}{5}$$] + [$$\frac{1024}{25}$$] +[$$\frac{1024}{125}$$] + [$$\frac{1024}{625}$$] where [ ]is the greatest integer function.

Highest power of 5 in 1024! = 204+ 40+ 8+ 1 = 253

X=3+2$$\sqrt{\ 2}$$

$$\frac{1}{x}=3-2\sqrt{\ 2}$$

$$x^2+\frac{1}{x^2}=\left(x\ +\frac{1}{x}\right)^2-2$$ = $$6^2-2=34$$

For calculating the units digit ,you only take last digit in each number and start multiplying them and when ever a 2 digit number is generated,you take only the units digit of that as well and go on.

Therefore 13*27*63*51*98*46 = 3*7*3*1*8*6 = 21*3*1*8*6 = 1*3*1*8*6 = 24*6 = 4*6 = 24 = 4

Let us assume that he uses x grams of weight instead of 1000gm.

Now, SP=CP*$$\frac{1000}{x}$$

$$\frac{SP}{CP}=\frac{1000}{X}$$

$$\frac{SP}{CP}-1=\frac{1000}{X}-1$$

$$\frac{5}{100}=\frac{1000}{X}-1$$

$$\frac{5}{100}+1=\frac{1000}{X}$$

$$\frac{105}{100}=\frac{1000}{X}$$

X=952.381

shares are divided in the ratio of their efficiency.

Let us assume that a work of 24units is to be done

A does 4 units of work every day

B does 3 units of work everyday

C does 2 units of work everyday.

So shares will be divided in the ratio 4:3:2

So C's share will be $$\frac{2}{9}\cdot2700$$ = 600 Rs

The number of ways of selecting 2 vowels from U,I,A,E = $$4_{c_2}$$ = 6

The number of ways of selecting 3 consonants from N,V,R,S,L = $$5_{c_3}$$ = 10

After selecting you can arrange them is 5! ways.

Total number of words = 6*10*120 = 7200

Let efficiencies of A,B,C be a,b,c respectively.

Given a+b+c = $$\frac{W}{12}$$ => Total work = 12(a+b+c)

They worked together for 3 hours. So work done in 3 hours = 3(a+b+c)

Remaining= 9(a+b+c) which is filled by a and b only in 10 hours

So $$a+b\ =\frac{\left(9\left(a+b+c\right)\right)}{10}$$

On solving a+b=9c 

So W= 12(9c+c)=120c

Time taken by C alone = $$\frac{120c}{c}$$=120 hours