From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?
Let S be the sample space
Then, n(S) = 52C2= 1326.
Let E = event of getting 2 kings out of 4.
n(E) = 52*512*1= 6.
4C2
=>4*32*1
P(E)=n(E)n(S)=61326=1221
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How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per Kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per Kg ?
By the rule of alligation:
C.P. of 1 kg sugar of 1st kind C.P. of 1 kg sugar of 2nd kind
Therefore, Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st kind be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27 or x = (7 x 27 / 3) = 63 kg.
On what dates of April, 2001 did Wednesday fall?
We shall find the day on 1st April, 2001.
1st April, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001)
Odd days in 1600 years = 0
Odd days in 400 years = 0
Jan. Feb. March April
(31 + 28 + 31 + 1) = 91 days 0 odd days.
Total number of odd days = (0 + 0 + 0) = 0
On 1st April, 2001 it was Sunday.
In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th.
Find the odd one out of the following number series?
9 5 6 14 56 488
The given number series follows a pattern that,
9
9 x 0.5 + 0.5 = 5
5 x 1 + 1 = 6
6 x 2 + 2 = 14
14 x 4 + 4 = 60 (not equals to 56)
60 x 8 + 8 = 488.
Hence, the odd one in the given number series is 56.
A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is
Total time taken = (160/64 + 160/8)hrs = 9/2 hrs.
Average speed = (320 x 2/9) km.hr = 71.11 km/hr.
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed :
Let the no of shots be x. Then,
Shots fired by A =(5/8)x
Shots fired by B = (3/8)x
Killing shots by A = 1/3 of (5/8)x = (5/24)x
Shots missed by B = 1/2 of (3/8)x = (3/16)x
(3/16)x = 27 ⇒ x =144
Birds killed by A = (5/24)x = (5/24)*144 = 30
What will come in place of the question mark (?) in the following number series ?
12, 24, 26.5, 79.5, ?, 330
The given series
12 24 26.5 79.5 ? 330 follows a pattern that,
12 x 2 = 24
24 + 2.5 = 26.5
26.5 x 3 = 79.5
79.5 + 3 = 82.5
82.5 x 4 = 330
Hence, the missing number is 82.5
Find out the wrong number in the following series ?
2880, 480, 92, 24, 8, 4, 4
The given series of numbers follow the rule that,
2880/6 = 480480/5 = 9696/4 = 2424/3 = 88/2 = 44/1 = 4
But 92 is not in the rule. It is the wrong number in the given series.