HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find feasible solution for the following system of linear inequation graphically.

3x + 4y ≥ 12, 4x + 7y ≤ 28, x ≥ 0, y ≥ 0

The slope of the tangent to the curve x = sin θ and y = cos 2θ at θ = `π/6` is ______.

The perpendicular distance of the plane `bar r. (3 hat i + 4 hat j + 12 hat k) = 78` from the origin is ______.

If a line drawn from the point A( 1, 2, 1) is perpendicular to the line joining P(1, 4, 6) and Q(5, 4, 4) then find the co-ordinates of the foot of the perpendicular.

Given that X ~ B(n= 10, p). If E(X) = 8 then the value of

p is ...........

(a) 0.6

(b) 0.7

(c) 0.8

(d) 0.4

The Cartesian equations of line are 3x -1 = 6y + 2 = 1 - z. Find the vector equation of line.

The Cartesian equations of line are 3x+1=6y-2=1-z find its equation in vector form.

Find the separate equations of the lines represented by the equation 3x² – 10xy – 8y² = 0.

The Cartestation equation of  line is `(x-6)/2=(y+4)/7=(z-5)/3` find its vector equation.

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

Find the coordinates of the point where the line through the points A(3, 4, 1) and B(5, 1, 6) crosses the XZ plane. Also find the angle which this line makes with the XZ plane.

Find the value of p, so that the lines `l_1:(1-x)/3=(7y-14)/p=(z-3)/2 and l_2=(7-7x)/3p=(y-5)/1=(6-z)/5 ` are perpendicular to each other. Also find the equations of a line passing through a point (3, 2, – 4) and parallel to line l₁.

The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 4 will hit the target.

Let `A(bara)` and `B(barb)` be any two points in the space and `R(barr)` be a point on the line segment AB dividing it internally in the ratio m : n, then prove that `bar r=(mbarb+nbara)/(m+n)`. Hence find the position vector of R which divides the line segment joining the points A(1, –2, 1) and B(1, 4, –2) internally in the ratio 2 : 1.

Given X ~ B (n, p)
If n = 10 and p = 0.4, find E(X) and var (X).

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs
(i) none
(ii) not more than one
(iii) more than one
(iv) at least one, will fuse after 150 days of use.

A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?

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.