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

The rate of growth of bacteria is proportional to the number present. If initially, there were 1000 bacteria and the number doubles in 1 hour, find the number of bacteria after `5/2` hours  `("Given"  sqrt(2) = 1.414)`

Bernoulli distribution is a particular case of binomial distribution if n = ______

For Bernoulli Distribution, state formula for E(X) and V(X).

For X ~ B(n, p) and P(X = x) = `""^8"C"_x(1/2)^x (1/2)^(8 - x)`, then state value of n and p

If a fair coin is tossed 10 times. Find the probability of getting at most six heads.

Find the vector equation of the lines passing through the point having position vector `(-hati - hatj + 2hatk)` and parallel to the line `vecr = (hati + 2hatj + 3hatk) + λ(3hati + 2hatj + hatk)`.

Verify Lagrange’s mean value theorem for the function f(x) = `sqrt(x + 4)` on the interval [0, 5].

The dual of statement p ∧ [∼ q ∨ (p ∧ q) ∨∼ r] is ______.

Find `dy/dx`, if y = (sin x)^{tan x} – x^{log x}.

Bacteria increase at the rate proportional to the number of bacteria present. If the original number N doubles in 3 hours, find in how many hours the number of bacteria will be 4N?

Write the dual of `(p → q) ∨ (q → p)`. 

If y = `log(x + sqrt(x^2 + 4))`, show that `dy/dx = 1/sqrt(x^2 + 4)`

In a single throw of a die, a random variable X is defined as the prime number on its upper face. Find the variance of X.

Find the acute angle between the lines `(x - 1)/1 = (y - 2)/-1 = (z - 3)/2` and `barr = (hati + 2hatj + 3hatk) + λ(2hati + hatj + hatk)`.

Two number are selected at random (without replacement but with different arrangement) from the first four positive integers. Let X denote the larger of the two numbers obtained. Find expectation of X.

The probability of hitting a target in any shot is 0.2. If 5 shots are fired, find the probability that the target will be hit at least twice.

If y = `9^(log_3x)`, find `dy/dx`.

In three throws with a pair of dice find the chance of throwing doublets at least twice.

A fair coin is tossed 8 times. Find the probability that it shows heads at most once.

The probability distribution of a r.v. X is given below:

Find the standard deviation of X.