[Download PDF] AP ICET 16th May 2016 Paper with Solutions

Instructions

For the following questions answer them individually

Question 141

The mode of the frequency distribution given below is

Video Solution

Question 142

The arithmetic mean of the observations 29, 30, 31, ...., 289 is

Video Solution

Solution

No of terms here is 289-29+1 = 261

$$\therefore\ $$The arithmetic mean of the observations = $$\frac{\frac{261}{2}\left(289+29\right)}{261}$$

= $$\frac{318}{2}$$

= 159

Hence, the correct answer is Option B

Question 143

The median of the following data is

Video Solution

Question 144

The geometric mean of the observations 1, 4, 9, 27, 256 is

Video Solution

Solution

G.M. of the given observations = $$\sqrt[\ 5]{\left(1\right)\left(4\right)\left(9\right)\left(27\right)\left(256\right)}$$

$$=\sqrt[\ 5]{1\times2^2\times3^2\times3^3\times2^8}$$

$$=\sqrt[\ 5]{2^{10}\times3^5}$$

$$=2^2\times3$$

$$=12$$

Question 145

If the standard deviation of 7, 10, 13, 16, ...., 121 is $$\sigma$$, then the standard deviation of 50, 71, 92, 113, ...., 848 is

Video Solution

Question 146

If 7 coins are tossed at random, then the probability that even number of heads appear is

Video Solution

Question 147

If two fair dice are thrown at random, then the probability that the sum of the digits on their faces is a prime number is

Video Solution

Solution

Cases when the sum of the numbers on the dice is a prime number (1,1),(2,1),(1,2),(3,2),(2,3),(6,1),(1,6),(6,5),(5,6),(4,3),(3,4),(2,5),(5,2),(1,4),(4,1)

Hence total of 15 cases out of a possible 36. Probability is 15/36 or 5/12

Question 148

The probability that A can solve a problem is $$\frac{7}{12}$$ and for B it is $$\frac{9}{17}$$. If both If both of them try independently, then the probability that the problem is solved is

Video Solution

Solution

Probability that the problem is solved = 1- (Probability that the problem is not solved)=1-($$\frac{5}{12}\times\ \frac{8}{17}$$= 1-(40/204)=164/204=41/51

Question 149

If the letters of the word WISDOM are permuted at random, then the probability that the vowels do not cometogether is

Video Solution

Solution

Total permutation possible = 6!=720

Number of combination in which vowels (O,I) are together= 5!(2!)=240

Hence the number of permutation in which vowels are not together =720-240=480

Probability= 480/720=2/3

Question 150

If a number is chosen at random from the first 58 natural numbers, then the probability that the number chosen is a prime number is

Video Solution

Solution

The prime numbers in the first 58 natural numbers = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53

Number of prime numbers in the first 58 natural numbers = 16

Hence probability = $$\frac{16}{58}$$ = $$\frac{8}{29}$$

CAT Content

AP ICET 16th May 2016

The mode of the frequency distribution given below is

The arithmetic mean of the observations 29, 30, 31, ...., 289 is

The median of the following data is

The geometric mean of the observations 1, 4, 9, 27, 256 is

If the standard deviation of 7, 10, 13, 16, ...., 121 is $$\sigma$$, then the standard deviation of 50, 71, 92, 113, ...., 848 is

If 7 coins are tossed at random, then the probability that even number of heads appear is

If two fair dice are thrown at random, then the probability that the sum of the digits on their faces is a prime number is

The probability that A can solve a problem is $$\frac{7}{12}$$ and for B it is $$\frac{9}{17}$$. If both If both of them try independently, then the probability that the problem is solved is

If the letters of the word WISDOM are permuted at random, then the probability that the vowels do not cometogether is

If a number is chosen at random from the first 58 natural numbers, then the probability that the number chosen is a prime number is

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