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

Choose the correct options from the given alternatives :

`int f x^x (1 + log x)*dx`

Choose the correct options from the given alternatives :

`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =

Choose the correct options from the given alternatives : 

`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =

`int logx/(log ex)^2*dx` = ______.

Choose the correct options from the given alternatives :

`int (cos2x - 1)/(cos2x + 1)*dx` =

Choose the correct options from the given alternatives :

`int (e^(2x) + e^-2x)/e^x*dx` =

Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`

Integrate the following with respect to the respective variable:

`x^7/(x + 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 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.

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

x³ + y³ = 4ax

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

Ax² + By² = 1

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y = A cos (log x) + B sin (log x)

Obtain the differential equation by eliminating the arbitrary constants from the following equation:

y² = (x + c)³

Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`