3. A no. of cats got together and decided to kill between them 99919 mice. every cat kills equal no. of mice. write a program to find no. of cats?

No. of Cats: 163, 613, or 99919

declare
-- Local variables here
i integer;
begin
-- Test statements here
for i in 1..99919 loop
if mod(99919,i) = 0 then
dbms_output.put_line (i);
end if;
end loop;
end;

4. Cube has colors blue, red ,yellow each on two opposite sides. cube is divided into "32 small cubes and 4 large cubes". question: how many cubes (on 36 cubes) have blue at least one side. how many cubes have colors on two sides?

If you paint the cube such that:

Blue and Blue are on opposite sides
Red and Red are on opposite side
Yellow and Yellow are on opposite side

And, since the question didnt state where the 32 smaller could be, Im placing the 32 smaller cubes on the sides with Blue paint. Thus:

32 cubes have Blue on at least one side.
20 cubes have have colors on two sides.

8. A, B and C starts from a point on a circle. A and B goes clockwise and C anticlockwise. A meets C after 88s B meets C after 110s. After how many seconds A meets B?

Ans: 440s

Let velocity of A,B and C be a,b,c resp.
2(pi)r/88 = a+c
2(pi)r/110 = b+c
we have to find 2(pi)r/a-b
Ans: 440

9. What is the probability of getting 2 prime nos. from 1 to 20?

Given that there are 8 Prime Numbers under 20, and if the limit is only random numbers under 20 then there is a 40% chance of getting a prime number.

14. If there are 2 wheelers and 4 wheelers parked in a school located at the heart of the city, find the number of 4 wheelers parked there if there were 58 wheels are parked there?

we check according to the answers for eg. 14x4=56 and 1x2=2 then also total 58 wheel
thus 14 is the max no of 4 wheelers.
But less than 14 also possible so goes through the option.

15. 10 Men Can Complete A Piece Of Work In 15 Days And 15 Women Can Complete The Same Work In 12 Days. If All The 10 Men And 15 Women Work Together , In How Many Days Will The Work Get Completed?

1 women=1/15
1 men = 110
if both men and women works together they will complete the work by 6 days
=(1/10)+(1/15)
=(15+10)/150
=25/150
=1/6 (i.e)
6 days

18. In a right-angled triangle, the square of the hypotenuse is twice the product of the other two sides. Then one of the acute angles of the triangle is…
A. 450
B. 300
C. 600
D. 150

3 sides are p,q, sqrt(2pq).
now if it is sright-angle then 2pq=p^2+q^2;
cos(angle)=sqrt(p/2q);
sin(angle)=sqrt(q/2p);
So sin(2*angle)=2*sin(angle)*cos(angle);
sin(2*angle)=1;

So angle=45;

22. Find a number that divide 37,67,97 reminders will be 1,2,3 respectively?

we can transform this ques into:>
find a number which devides 36 ,65,94?

now will be able to find the ans..

23. One man or two women or three boys can do a work in 44 days then one man, one women and one boy together can finish the same work in ---- days?

Exactly 24 days...

1 man do 1/44 job per day
2 woman do 1/44 job per day
3 children do 1/44 job per day

so
1man , 1 woman , 1 child..
1/44+1/88+1/132 job per day

so 11/264 = 1/t where t is the time taken..

now 264/11 = 24 = t

24. In how many ways can a lock be opened if that lock has three digit number lock if
i) the last digit is 9
ii) and sum of the first two digits is less than or equal to the last digit

our number is xy9
now if x is 0 then y has 10 options
now if x is 1 then y has 9 options (except 9)
now if x is 2 then y has 8 options (except 9 and 8)
.
.
.
now if x is 9 then y has 1 option (that is 0)

25. A cube has a side of 4cm.b The cube is painted red on all six side. This cube is then cut into 125 smaller cubes. How many of these smaller cubes will have only one side of their sides painted?

The 4cm cube is divide into 125 smaller cubes:
that means that the 4cm cube = 5 smaller cubes in height, width, and depth

Also, given that the 4cm is painted red on all six side:
- only those smaller cubes that touch no outer surface will be free of red paint, thus:
- 27 smaller cubes have no red paint on them
- 98 smaller cubes have some red paint on them

How many of these smaller cubes will have only one side of their sides painted?
- only those smaller cubes that do not touch the edges of the 4cm cube will have only one side painted, thus:
- 54 smaller cubes have only one side painted
- 36 smaller cubes have two sides painted
- 8 smaller cubes have three sides painted

29. (1- 1/6) (1-1/7).... (1- (1/ (n+4))) (1-(1/ (n+5))) = ?

=(5/6)*(6/7)*(7/8)*...((n+3)/(n+4))*((n+4)/(n+5))

=5/n+5

30. A motor cycle stunts man belonging to a fair, rides over the with vertical walls of a circular well at an average speed of 54 kph for 5 minutes. If the radius of the well is 5 meters then the distance travelled is :
a) 2.5 kms
b) 3.5 kms
c) 4.5 kms
d) 5.5 kms
e) None of the above

c) 4.5 kms

54 kilometers per hours = 54000 meters per hour
54000 meters / 60 minutes = 900 meters per minute
900 meters * 5 minutes of traveling time = 4500 meters travel
4500 meters = 4.5 kilometers traveled in 5 minutes

32. Form 8 digit numbers by using 1,2,3,4,5 with repetition allowed and must be divisible by 4?

There are 78125 8 digit numbers form from the numbers 1, 2, 3, 4, and 5 that are evenly divisionable by 4. I think thats just a few too many than could be listed here.

34. (loga)^2-(logb)^2 =?

(log a + log b)(log a- log b)
=log ab . log a/b

35. With just six weights and a balance scale, you can weigh any unit number of kgs from 1 to 364. What could be the six weights?

The six weights will be 1 kg, 3kg,9kg, 27kg, 81 kg, and 243kg.
for instance to weigh 2kg= 3kg-1kg...and so on for all the weights