**A basket contains 3 blue, 5 black and 3 red balls. If two balls are drawn at random, what is the probability that none of them is blue?**- 22/55
- 3/55
- 28/55
- 9/11
- None of these

Answer : Option C.

Here n(S) =^{11}C_{2}

Now two balls can be drawn from 5(black)+3(red) balls = 8 balls in^{8}C_{2}ways.

Therefore n(E) =^{8}C_{2}

Now, P(E) = (^{8}C_{2}/^{11}C_{2}) = (28/55)

Other method:

Required probability

= 1-(27/55) = (28/55)

**A basket contains 3 blue, 5 black and 3 red balls. If 2 balls are drawn at random, what is the probability that one is black and one is red?**- 2/11
- 8/11
- 9/11
- 3/11
- None of these

Answer : Option B.

Selecting 1 black ball out of 5 -^{5}C_{1}ways Selecting on red ball out of 3 -^{3}C_{1 }ways

he required probability = (^{5}C_{1}*^{3}C_{1}) / (^{11}C_{2}) = (5*3) / 55 = 3/11**Ramesh takes twice as much time as Mahesh and thrice as much time as Suresh to complete a job. If working together, they can complete the job in 4 days, then the time taken by each of them separately to complete the work is**- 36, 24 and 16 days
- 20, 16 and 12 days
- 24, 12 and 8 days
- 20, 18 and 15 days
- None of these

Answer : Option C.

We are given that R = 2M = 3S. This means that Suresh is thrice efficient than Ramesh and Mahesh is twice efficient than Ramesh. So let us assume that Ramesh can do 1 unit work per day. so Mahesh will do 2 units per day and Suresh will do 3 units of the work per day. So the total work done by all three in one day is 6 units. Now they together take 4 days to complete the work. So the total work is 6 x 4 = 24 units and individually Ramesh, Mahesh and Suresh will take 24 days, 12 days and 8 days respectively.**A man buys a land and gives for it 20 times the annual rent Find the rate of interest he gets for his money**- 10%
- 24%
- 45%
- 18%
- 5%

Answer : Option E.

let annual rent is 1 Rs. so buys the land at 20 Rs. So by investing Rs.20 he is getting Rs.1 as interest. so on Rs.100 he gets Rs.5 . so rate%=5%.Hence option E is the answer.**What will be the compound interest on a sum of Rs. 7200/- at 5 p.c.p.a. in 2 years?**- Rs. 841/-
- Rs. 738/-
- Rs. 793/-
- Rs. 812/-
- Rs.694/-

Answer : Option B.

Compound interest = P[(1+(R/100))^{2}-1]

So CI = 7200 [(1+(5/100))^{2}-1] = 738iNautix Preparation Links- Sample Aptitude Questions of iNautix
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**In a rhombus ABCD the diagonals AC and BD intersect at the point (3, 4). If the point 'A' is (1, 2), the diagonal BD has the equation**- x – y – 1 = 0
- x – y + 1 = 0
- x + y – 1 = 0
- x + y – 7 = 0
- x + y – 2 = 0

Answer : Option D.

Slope of AC = (2-4)/(1-3) = 1. As diagonals in a rhombus bisect each other at 90°, so slope of BD = -1. Also diagonal BD has to lie on the point (3, 4), so equation of the line is y - 4 = - 1(x - 3) => x + y – 7 = 0.**A circle has two parallel chords of lengths 6 cm and 8 cm. If the chords are 1 cm apart and the centre is on the same side of the chords, then the diameter of the circle is of length:**- 5cm
- 6cm
- 10cm
- 12cm
- None of these

Answer : Option C.

In the given figure, EB = 3 cm, FD = 4 cm, EF = 1 cm

Let OF = a cm

In triangle OFD, r^{2}= a^{2}+ 4^{2}& in triangle OEB, r^{2}= (a+1)^{2}+ 3^{2}

Solving the above two equations, we get a = 3cm

Putting the value of a in any of the above equation, we get r = 5 cm

Therefore, diameter = 10 cm**An express train travelled at an average speed of 100 kmph, stopping for 3 minutes after every 75 km. A local train travelled at a speed of 50 kmph, stopping for 1 minute after every 25 km. If the trains began travelling at the same time, how many kilometres did the local train travel in the time it took the express train to travel 600 km?**- 900km
- 307.5km
- 1200km
- 100km
- 300km

Answer : Option B.

For 600 kms. The Express train needs 6 hrs. for the distance travelled @ 100 kmph. and it will stop for ( 600/75 )= 8. So there must be 7 stoppages in between where it stops for 3 min. each totalling upto 21 min. So total time will be 6 hrs.21 min.

Now the Local train travelling @ 50 kmph. will cover 300 kms. in 6 hrs. and in rest 9 min. it will travel 7.5 kms.( 300/25=12 stoppages where it will stop for 12 min. So, 21- 12 = 9 ). The total distance becomes 300 + 7.5 = 307.5 km.

ALTERNATE SOLUTION

We can also think that since speed of express train is double the local speed, so local train will tavel less than 600 km, Only option b has such option and hence is the required answer.**In how many different ways can the letters of the word 'PARTY' be arranged?**- 120
- 2005
- 2400
- 720
- None of these

Answer : Option A.

Total no. of ways =5 x 4 x3 x 2 x 1 = 120**A & B together can complete a piece of work in 16 days, B alone can complete the same work in 24 days. In how many days can A alone complete the same work ?**- 34 days
- 50 days
- 48 days
- 42 days
- None of these

Answer : Option C.

Let A alone can complete the work in x days and B alone can complete the work in 24days.

Therefore, according to the given conditions,

1/x + 1/24 = 1/16,

1/x = 1/48

So, A's one day work is 1/48 which means that A will complete the entire work in 48days.

Therefore, the answer is option C.