Given, box contains 2 washers, 3 nuts and 4 bolts

Now,

P(drawing 2 washers followed by 3 nuts followed by 4 bolts)

Hence, the required probability will be .

Given equation is =

Since above relation is true for all real values of x.

Substituting x=0

We get

Applying

e=0

Given determinant

Applying

Applying

Given,

P(A) = probability of selection of A = 0.3

P(B) = probability of selection of B = 0.4

P(A∩B) = probability of selection of both A and B = 0.5

So,

probability of selection of either A or B will be

Let, S be the total sample space

If, n(S) = 100, then

n(E₁) = students fail in chemistry = 30

n(E₂) = students fail in maths = 20

and, n(E₁∩E₂) = students fail in both chemistry and maths = 10

Now,

And,

Therefore,

The required probability that he will fail in chemistry if he has failed in maths will be,

.

Given: -

Initially let the work can be completed in n days when 150 workers work on every day.

However every day 4 workers are being dropped from the work so that work took 8 more days to be finisheD.

Finally, it takes (n + 8) days to finish the works.

Work equivalent when 150 workers work without being dropped = 150 × n

Work equivalent when workers are dropped day by day = 150 + (150 - 4) + (150 - 8) +...... + (150 - 4(n + 8)).

So,

150×n = 150 + (150 - 4) + ........ + (150 - 4×(n + 8))

150×n = 150×n + 150×8 - 4×(1 + 2 + 3 + ...... + (n + 8))

(n + 8)(n + 9) = 600

+ 17n - 528 = 0

n = - 33 or n = 16

Since the number of days cannot be negative, n = 16.

∴ In 24 days the work is completeD.

We know that given series in GP where a = I, r = I and n = 400

Thus, s =

=

=

=  [ i⁴ = 1]

=  = 0

Given,

So the binary number is 11111

To calculate Standard deviation, we fist calculate Variance
SD=

Variance=
here x is a mean.
so =14
For variance, calculate ,for each value of xi

8-14=-6

12-14=-2

13-14=-1

15-14=1

22-14=8

Variance==106/5=21.2

Standard deviation=