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

The cost of 4 dozen pencils, 3 dozen pens and 2 dozen erasers is Rs. 60. The cost of 2 dozen pencils, 4 dozen pens and 6 dozen erasers is Rs. 90 whereas the cost of 6 dozen pencils, 2 dozen pens and 3 dozen erasers is Rs. 70. Find the cost of each item per dozen by using matrices.

The equation of tangent to the curve y=`y=x^2+4x+1` at

(-1,-2) is...............

(a)  2x -y = 0                        (b)  2x+y-5 = 0

(c)  2x-y-1=0                        (d)  x+y-1=0

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

Find the area bounded by the curve y² = 4ax, x-axis and the lines x = 0 and x = a.

Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`

Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`

The sum of three numbers is 6. When second number is subtracted from thrice the sum of first and third number, we get number 10. Four times the sum of third number is subtracted from five times the sum of first and second number, the result is 3. Using above information, find these three numbers by matrix method.

A random variable X has the following probability distribution:

then E(X)=....................

A fair coin is tossed five times. Find the probability that it shows exactly three times head.

From a lot of 25 bulbs of which 5 are defective a sample of 5 bulbs was drawn at random with replacement. Find the probability that the sample will contain -

(a) exactly 1 defective bulb.

(b) at least 1 defective bulb.

If p ˄ q = F, p → q = F, then the truth value of p and q is :

Find the inverse of the matrix,  `A=[[1,3,3],[1,4,3],[1,3,4]]`by using column transformations.

Find the area of the region bounded by the parabola y² = 4ax and its latus rectum.

Show that:  `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`

Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.

Find the joint equation of the pair of lines through the origin each of which is making an angle of 30° with the line 3x + 2y - 11 = 0

Solve the following equations by the method of reduction :

2x-y + z=1,  x + 2y +3z = 8, 3x + y-4z=1.

Evaluate :`intxlogxdx`

Find the area of the region bounded by the curve y = sinx, the lines x=-π/2 , x=π/2 and X-axis

Show that the function defined by f(x) =|cosx| is continuous function.