HSC Science (Electronics) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

An examination consists of 10 multiple choice questions, in each of which a candidate has to deduce which one of five suggested answers is correct. A completely unprepared student guesses each answer completely randomly. What is the probability that this student gets 8 or more questions correct? Draw the appropriate morals.

The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that all 8 machines.

The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that 7 or 8 machines.

The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that at most 6 machines will produce all bolts within specification. 

The probability that a machine develops a fault within the first 3 years of use is 0.003. If 40 machines are selected at random, calculate the probability that 38 or more will not develop any faults within the first 3 years of use.

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 0.

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 1.

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 2.

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 3 or more, terminals will require attention during the next week.

In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.
Calculate the probabilities of obtaining an answer yes from 0, 1, 2, 3, 4 of the pupils.

In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.

Find the probability that the visitor obtains answer yes from at least 2 pupils:

1. when the number of pupils questioned remains at 4.
2. when the number of pupils questioned is increased to 8.

It is observed that it rains on 12 days out of 30 days. Find the probability that it rains exactly 3 days of week.

It is observed that it rains on 12 days out of 30 days. Find the probability that it it will rain at least 2 days of a given week.

If the probability of success in a single trial is 0.01. How many trials are required in order to have a probability greater than 0.5 of getting at least one success?

In binomial distribution with five Bernoulli’s trials, the probability of one and two success are 0.4096 and 0.2048 respectively. Find the probability of success.

Use quantifiers to convert the following open sentences defined on N, into a true statement.

n² ≥ 1

The separate equations of the lines represented by `3x^2 - 2sqrt(3)xy - 3y^2` = 0 are ______ 

The equation 4x² + 4xy + y² = 0 represents two ______ 

Auxillary equation of 2x² + 3xy − 9y² = 0 is ______ 

If 2x + y = 0 is one of the line represented by 3x² + kxy + 2y² = 0 then k = ______