36. How many numbers are there whose factorial ends with 17 zeros?
a)6
b)5
c)0
d)11

To solve this first we find a number which ends with 17 zeros and further we will find the total numbers with that condition
Let X! be the number which ends with 17 zeros
Now, X!/5 + X!/25 = 17 ----[1]

(For those who don't know how we obtained this,
The number of trailing zeros of a number can be found out using the following method
For instance, consider we have to find the total number of trailing zeros of 70!
We would do that as follows:
5|70
  ----
  |14
  ----
   2
Now, total number of zeros trailing is 14+2=16 )
In equation [1], we find that no number satisfy the given condition i.e. 70!, 70!..74! have 16 zeros and 75! has 18 zeros
Hence the answer is 0

37. Two persons A and B do a work in 30 and 40 days respectively. If both do together, A start the first day and on other day work done by exactly one of them. Finally they divide the earning in ratio 1:1. How many days the work be completed?

Here earning ratio is 1:1 so half(1/2) of work done by both(A and B).
now work done by A in one day = 1/30
work done by B in one day = 1/40
total time taken by A for 1/2 of work = (1/2)/(1/30) = 15 days
total time taken by B for 1/2 of work = (1/2)/(1/40) = 20 days
so total time required to complete the work = 15+20 = 35 days

38. Two circles lying in the first quadrant, touch each other externally. Both the axes makes tangents with both the circles. If the distance between the two centre of the circles is 8 cm, find the difference in their radii?

First draw a rough figure assigning Centers o1 and o2 for smaller and larger circles respectively
Suppose Radius of smaller and larger circle are r1 and r2 respectively
By radius of smaller circle we can find out the length of PQ
PQ=r1/sin 45=root(2)
r2=PQ=root(2) (Since angle of arc is 60)
Now find the Area covered by arcs=pi/4+pi/3
Area which not covered in common region=ar(o1PQ)+ar(o2PQ)=root(3)/2 +1/2
So Area of common region=7pi/12-(1+root(3))/2

39. Two circles intersect each other @ two points P and Q ...smaller circle has radius 1cm...if arc extended by smaller circle is 90 degree and that of the larger circle in 60 degree at their corresponding centres .Find out the common area of the circles?

let the radius of first circle be (R,R)
let the radius of second cirlce br(r,r)
itis because its lies on line y=x int the first quadrant.so we need to find(R-r)
accoding to distance formula;
d=(sqrroot(x2-x1)^2+(y2-y1)^2);x1=r,y1=r,x2=R,y2=R;
replacing values;
d=(sqroot(R-r)^2+(R-r)^2);here dis given as 8 int the ques;
8=(sqrrrot(2(R-r)^2)
8=root2(R-r)
so;R-r=4root(2);

40. The value of 99^n is a number which starts with digit 8. What can be the minimum value of n?

99^n
99^1= 99
99^2= 9801
99^3= 970299
take only starting two digit, other digit will not change the solution..
=99*98*97*96*95....
=99*98*97*.....*89
so 11 will be the answer

## No comments:

## Post a Comment