Question Paper - Mathematics and Statistics 2014 - 2015-H.S.C-12th Board Exam Maharashtra State Board (MSBSHSE)

Account
Register

Share

Books Shortlist
Your shortlist is empty
SubjectMathematics and Statistics
Year2014 - 2015 (March)

Topics
Marks
Topics
Marks

Marks: 80
Q: 1[12]
Q: 1.1 | Select and write the most appropriate answer from the given alternatives in each of the following sub-questions :[6]
Q: 1.1.1[2]

if  A=[[2,0,0],[0,2,0],[0,0,2]] then A6=  ......................

(a) 6A

(b) 12A

(c) 16A

(d) 32A

view question and solution
Q: 1.1.2[2]

The principal solution of cos-1(1/2) is :

(a) π/3

(b) π/6

(c) 2π/3

(d) 3π/2

view question and solution
Q: 1.1.3[2]

If an equation hxy + gx + fy + c = 0 represents a pair of lines, then.........................

(a) fg = ch                       (b) gh = cf

(c) Jh = cg                     (d) hf= - eg

view question and solution
Q: 1.2 | Attempt any THREE of the following [6]
Q: 1.2.1[2]

Write the converse and contrapositive of the statement — “If two triangles are congruent, then their areas are equal.”

view question and solution
Q: 1.2.2[2]
Q: 1.2.3[2]

Find the angle between the planes bar r.(2bar i+barj-bark)=3

view question and solution
Q: 1.2.4[2]

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

view question and solution
Q: 1.2.5[2]
Q: 2[14]
Q: 2.1 | Attempt any TWO of the following [6]
Q: 2.1.1[3]

If A, B, C, D are (1, 1, 1), (2, I, 3), (3, 2, 2), (3, 3, 4) respectively, then find the volume of parallelopiped with AB, AC and AD as the concurrent edges.

view question and solution
Q: 2.1.2[3]

Discuss the statement pattern, using truth table : ~(~p ∧ ~q) v q

view question and solution
Q: 2.1.3[3]
Q: 2.2 |  Attempt any TWO of the following[8]
Q: 2.2.1[4]

Find the direction cosines of the line perpendicular to the lines whose direction ratios are -2, 1,-1 and -3, - 4, 1

view question and solution
Q: 2.2.2[4]
Q: 2.2.3[4]

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.

view question and solution
Q: 3[14]
Q: 3.1 | Attempt any TWO of the following[6]
Q: 3.1.1[3]

If θ is the acute angle between the lines represented by equation ax2 + 2hxy + by2 = 0  then prove that tantheta=|(2sqrt(h^2-ab))/(a+b)|, a+b!=0

view question and solution
Q: 3.1.2[3]

If the lines (x-1)/2=(y+1)/3=(z-1)/4  and (x-3)/1=(y-k)/2=z/1 intersect each other then find value of k

view question and solution
Q: 3.1.3[3]

Construct the switching circuit for the following statement : [p v (~ p ∧ q)] v [(- q ∧ r) v ~ p]

view question and solution
Q: 3.2 | Attempt any TWO of the following[8]
Q: 3.2.1[4]

Find the general solution of : cos x - sin x = 1.

view question and solution
Q: 3.2.2[4]
Q: 3.2.3[4]
Q: 4[12]
Q: 4.1 | Select and write the most appropriate answer from the given alternatives in each of the following sub-questions[6]
Q: 4.1.1[2]

A random variable X has the following probability distribution:

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

(a) 0.8

(b) 0.9

(c) 0.7

(d) 1.1

view question and solution
Q: 4.1.2[2]

If int_0^alpha3x2dx=8 then the value of α is :

(a) 0

(b) -2

(c) 2

(d) ±2

view question and solution
Q: 4.1.3[2]

The differential equation of y=c/x+c2 is :

(a)x^4(dy/dx)^2-xdy/dx=y

(b)(d^2y)/dx^2+xdy/dx+y=0

(c)x^3(dy/dx)^2+xdy/dx=y

(d)(d^2y)/dx^2+dy/dx-y=0

view question and solution
Q: 4.2 | Attempt any THREE of the following[6]
Q: 4.2.1[2]

Evaluate : int e^x[(sqrt(1-x^2)sin^-1x+1)/(sqrt(1-x^2))]dx

view question and solution
Q: 4.2.2[2]

If   y=sqrt(sinx+sqrt(sinx+sqrt(sinx+..... oo))), then show that dy/dx=cosx/(2y-1)

view question and solution
Q: 4.2.3[2]

Evaluate :int_0^(pi/2)1/(1+cosx)dx

view question and solution
Q: 4.2.4[2]
Q: 4.2.5[2]

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

view question and solution
Q: 5[14]
Q: 5.1 | Attempt any TWO of the following[6]
Q: 5.1.1[3]
Q: 5.1.2[3]
Q: 5.1.3[3]

If f(x)=[tan(pi/4+x)]^(1/x),

= k                        ,for x=0

is continuous at x=0 , find k.

view question and solution
Q: 5.2 | Attempt any TWO of the following :[8]
Q: 5.2.1[4]
Q: 5.2.2[4]
Q: 5.2.3[4]

Evaluate :int_0^pi(xsinx)/(1+sinx)dx

view question and solution
Q: 6[14]
Q: 6.1 | Attempt any two of the following [6]
Q: 6.1.1[3]
Q: 6.1.2[3]
Q: 6.1.3[3]

Let the p. m. f. (probability mass function) of random variable x be

p(x)=(4/x)(5/9)^x(4/9)^(4-x), x=0, 1, 2, 3, 4

=0 otherwise

find E(x) and var (x)

view question and solution
Q: 6.2 | Attempt any two of the following [8]
Q: 6.2.1[4]

Examine the maxima and minima of the function f(x) = 2x3 - 21x2 + 36x - 20 . Also, find the maximum and minimum values of f(x).

view question and solution
Q: 6.2.2[4]

Solve the differential equation (x2 + y2)dx- 2xydy = 0

view question and solution
Q: 6.2.3[4]

Given the p. d. f. (probability density function) of a continuous random variable x as :

f(x)=x^2/3, -1

= 0 , otherwise

Determine the c. d. f. (cumulative distribution function) of x and hence find P(x < 1), P(x ≤ -2), P(x > 0), P(1 < x < 2)

view question and solution
S