Hi Nisha, the results and solutions for all Dashcats are up. Please let us know if there is still a problem.

The number of 7s that 42! has is [$$\frac{42}{7}$$] = 6
The number of 7s that 56! has is [$$\frac{56}{7}$$] + [$$\frac{56}{7^2}$$] = 9
So, all the values from 42! to 55! are multiples of $$7^6$$

Hi Himanshu, a good way to prepare for Vocab is to try to find out the meanings of new words as you come across them during your preparation and to use those words in your day-to-day life. This will help you assimilate those words. It's a bad idea to try to learn words from Vocab lists by rote. Having said that, the concentration on Vocab in CAT has been decreasing in the last few years. There was no Vocab question in CAT 2015.

Hi Prerana, problems on Indices and Surds are mostly on rationalizing the denominator. So, the first step in most problems would be to rationalize the denominator. Even if it is a series question involving a series of finite or infinite surds, try to see if there is a common pattern using which the denominators of each surd can be rationalized. Generally in such questions, the successive terms get cancelled till the last term, which can then be calculated easily.

Check out our concepts on Surds and Indices here:

https://cracku.in/cat/quant-and-di/logarithms-surds-indices

x+y+z=30

total ordered solutions=32c2

here we want different number of balls means unordered cases

case when two are equal

so 2x+y=30
so y=30-2x

so x will vary from 0 to 15 so 16 values but this will also contain case when all are equal so remove that case so 15 value and ways to arrange them 3!/2!=3

and when all r equal=1 case

(ordered-3*when two are same-all same)
=((32c2-3*15-1)=450

The best way to solve Syllogism questions is to draw Venn Diagrams based on the given relations. This will give you a fool-proof answer.

As 528^1567 is a multiple of 528, u can get remainder by dividing 528 with 13 & 54 as 8 & 42 respectively.

my answer is just a guess
relative speed between both trains = 30km/hr =(25/3)m/s
assume both trains r of equal length, so d+d=2d
t=27s
sub these values in d= s*t
2d= (25/3)*27 = 225 from which we get d=112.5m

prob of winning =1/6

prob of losing =5/6

now let A win in 1st go then prob=1/6

if A lose in 1st go then A will win in 3rd go so B has to lose in his 1st go so

(5/6)*(5/6)*(1/6)

when A win in 3rd go then

(5/6)^4*1/6

this will go tiill infinity

1/6+(5/6)^2*1/6+(5/6)^4*1/6..............

sum of infinite terms of GP

a/1-r

1/6*(1/(1-25/36)

6/9=2/3

Bhai, not very sure:
medians divide each other in the ratio 2:1. and every median divides the triangle in 2 parts of equal area.
so when u draw the fig, u get the sides of triangle BQR n BRC. calculate area of these 2 triangles and same is area of CQA. solving, ans comes as 64. plz correct me if I m wrong

Medain and Mean formulas are included in this Geometry formulas sheet, Download it now.