HSC Science (Computer Science) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

Find the probability of throwing at most 2 sixes in 6 throws of a single die.

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?

A fair coin is tossed 8 times. Find the probability that it shows heads exactly 5 times.

Find the vector equation of the lines which passes through the point with position vector `4hati - hatj +2hatk` and is in the direction of `-2hati + hatj + hatk`

A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.

By computing the shortest distance determine whether the following pairs of lines intersect or not: \[\frac{x - 1}{2} = \frac{y + 1}{3} = z \text{ and } \frac{x + 1}{5} = \frac{y - 2}{1}; z = 2\]

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is `1/100`. What is the probability that he will win a prize at least once. 

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is \[\frac{1}{100} .\]  What is the probability that he will win a prize exactly once.

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is `1/100`  What is the probability that he will win a prize at least twice.

 The equation of a line is 2x -2 = 3y +1 = 6z -2 find the direction ratios and also find the vector equation of the line. 

A person makes two types of gift items A and B requiring the services of a cutter and a finisher.  Gift item A requires 4 hours of the cutter's time and 2 hours of finisher's time. Fifth item B requires 2 hours of the cutter's time and 4 hours of finisher's time. The cutter and finisher have 208 hours and 152 hours available time respectively every month. The profit on one gift item of type A is ₹ 75 and on one gift item of type, B is ₹ 125. Assuming that the person can sell all the gift items produced, determine how many gift items of each type should he make every month to obtain the best returns?

Write the dual of the following.

p ∨ (q ∧ r)

Write the dual of the following.

p ∧ (q ∧ r)

Write the dual of the following.

(p ∨ q) ∧ (r ∨ s)

Write the dual of the following.

p ∧ ∼ q

Write the dual of the following.

(∼ p ∨ q) ∧ (∼ r ∧ s)

Write the dual of the following.

∼ p ∧ (∼ q ∧ (p ∨ q) ∧ ∼ r)

Write the dual of the following.

[∼ (p ∨ q)] ∧ [p ∨ ∼ (q ∧ ∼ s)]

Write the dual of the following.

c ∨ {p ∧ (q ∨ r)}