HSC Science (Computer Science) 12th Board ExamMaharashtra State Board
Share

Books Shortlist

# Mathematics and Statistics 2014-2015 HSC Science (Computer Science) 12th Board Exam Question Paper Solution

SubjectMathematics and Statistics
Year2014 - 2015 (October)
Mathematics and Statistics
2014-2015 October
Marks: 80

1
1.1 | Select and write the most appropriate answer from the given alternatives in each of the following sub-questions:
1.1.1

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

T, T

T, F

F, T

F, F

Chapter:  Mathematical Logic
Concept: Mathematical Logic - Truth Value of Statement in Logic
1.1.2

If A^-1=1/3[[1,4,-2],[-2,-5,4],[1,-2,1]] and | A | = 3, then (adj. A) = _______

(A)1/9[[1,4,-2],[-2,-5,4],[1,-2,1]]

(B)[[1,-2,1],[4,-5,-2],[-2,4,1]]

(C)[[1,4,-2],[-2,-5,4],[1,-2,1]]

(D)[[-1,-4,2],[2,5,-4],[1,-2,1]]

Chapter:  Matrices
1.1.3

The slopes of the lines given by 12x2 + bxy + y2 = 0 differ by 7. Then the value of b is :

(A) 2

(B) ± 2

(C) ± 1

(D) 1

Chapter:  Pair of Straight Lines
Concept: Acute Angle Between the Lines
1.2 | Attempt any THREE of the following:
1.2.1

In a Δ ABC, with usual notations prove that: (a -bcos C) /(b -a cos C )= cos B/ cos A

Chapter:  Trigonometric Functions
Concept: Trigonometric Functions - Solution of a Triangle
1.2.2

Find ‘k’, if the equation kxy + 10x + 6y + 4 = 0 represents a pair of straight lines.

Chapter:  Pair of Straight Lines
Concept: Acute Angle Between the Lines
1.2.3

If A, B, C, D are four non-collinear points in the plane such that bar(AD)+bar( BD)+bar( CD)=bar O then prove that point D is the centroid of the ΔABC.

Chapter:  Vectors
Concept: Vectors - Centroid Formula for Vector
1.2.4

Find the direction cosines of the line

(x+2)/2=(2y-5)/3; z=-1

Chapter:  Three Dimensional Geometry
Concept: Direction Cosines and Direction Ratios of a Line
1.2.5

Show that the points (1, 1, 1) and (-3, 0, 1) are equidistant from the plane bar r (3bari+4barj-12bark)+13=0

Chapter:  Plane
Concept: Distance of a Point from a Plane
2
2.1 | Attempt any TWO of the following:
2.1.1

Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).

Chapter:  Mathematical Logic
Concept: Mathematical Logic - Truth Tables of Compound Statements
2.1.2

Show that every homogeneous equation of degree two in x and y, i.e., ax2 + 2hxy + by2 = 0 represents a pair of lines passing through origin if h2ab0.

Chapter:  Pair of Straight Lines
Concept: Pair of Straight Lines - Pair of Lines Passing Through Origin - Homogenous Equation
2.1.3

Prove that the volume of a parallelopiped with coterminal edges as   bara ,bar b , barc

Hence find the volume of the parallelopiped with coterminal edges  bar i+barj, barj+bark

Chapter:  Vectors
Concept: Scalar Triple Product of Vectors
2.2 | Attempt any TWO of the following:
2.2.1

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

Chapter:  Matrices
Concept: Elementary Operation (Transformation) of a Matrix
2.2.2

In ΔABC, prove that : tan((a-b)/2)=(a-b)/(a+b)cotC/2

Chapter:  Trigonometric Functions
Concept: Trigonometric Functions - Solution of a Triangle
2.2.3

Show that the lines  (x+1)/-3=(y-3)/2=(z+2)/1;  are coplanar. Find the equation of the plane containing them.

Chapter:  Plane
Concept: Coplanarity of Two Lines
3
3.1 | Attempt any TWO of the following:
3.1.1

Construct the simplified circuit for the following circuit: Chapter:  Mathematical Logic
Concept: Mathematical Logic - Application - Introduction to Switching Circuits
3.1.2

Express -bari-3barj+4bark   as a linear combination of vectors  2bari+barj-4bark,2bari-barj+3bark

Chapter:  Vectors
Concept: Vectors - Linear Combination of Vectors
3.1.3

Find the length of the perpendicular from the point (3, 2, 1) to the line (x-7)/2=(y-7)/2=(z-6)/3=lambda (say)

Chapter:  Three Dimensional Geometry
Concept: Three - Dimensional Geometry - Condition for Perpendicular Lines
3.2 | Attempt any TWO of the following
3.2.1

Show that the angle between any two diagonals of a cube is cos^-1(1/3)

Chapter:  Plane
Concept: Angle Between Line and a Plane
3.2.2

Minimize : Z = 6x + 4y

Subject to the conditions:

3x + 2y ≥ 12,

x + y ≥ 5,

0 ≤ x ≤ 4,

0 ≤ y ≤ 4

Chapter:  Linear Programming Problems
Concept: Graphical Method of Solving Linear Programming Problems
3.2.3

If tan^-1((x-1)/(x-2))+cot^-1((x+2)/(x+1))=pi/4;

Chapter:  Trigonometric Functions
Concept: Basic Concepts of Trigonometric Functions
4
4.1 | Select and write the most appropriate answer from the given alternatives in each of the following sub-questions
4.1.1

If y=sec^-1((sqrtx-1)/(x+sqrtx))+sin_1((x+sqrtx)/(sqrtx-1)),

(A) x

(B) 1/x

(C) 1

(D) 0

Chapter:  Differentiation
Concept: Derivative - Derivative of Inverse Function
4.1.2

If int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx, then the value of I is:

(A) 0

(B) π

(C) π/2

(D) π/4

Chapter:  Integration
Concept: Methods of Integration - Integration by Parts
4.1.3

The solution of the differential equation dy/dx = sec x – y tan x is:

(A) y sec x = tan x + c

(B) y sec x + tan x = c

(C) sec x = y tan x + c

(D) sec x + y tan x = c

Chapter:  Differential Equation
Concept: General and Particular Solutions of a Differential Equation
4.2 | Attempt any THREE of the following:
4.2.1

Evaluate: int1/(xlogxlog(logx))dx

Chapter:  Integration
Concept: Evaluation of Definite Integrals by Substitution
4.2.2

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

Chapter:  Applications of Definite Integral
Concept: Area of the Region Bounded by a Curve and a Line
4.2.3

Find k, such that the function  P(x)=k(4/x) ;x=0,1,2,3,4 k>0

=0 ,otherwise

Chapter:  Bernoulli Trials and Binomial Distribution
Concept: Standard Deviation of Binomial Distribution (P.M.F.)
4.2.4

Given is X ~ B (n, p). If E(X) = 6, and Var(X) = 4.2, find the value of n.

Chapter:  Bernoulli Trials and Binomial Distribution
Concept: Bernoulli Trials and Binomial Distribution - Calculation of Probabilities
4.2.5

Solve the differential equation y-xdy/dx=0

Chapter:  Differential Equation
Concept: Methods of Solving First Order, First Degree Differential Equations - Differential Equations with Variables Separable
5
5.1 | Attempt any TWO of the following:
5.1.1

Discuss the continuity of the function

f(x)=(1-sinx)/(pi/2-x)^2,

= 3,                  for x=π/2

Chapter:  Continuity
Concept: Continuity - Discontinuity of a Function
5.1.2

If f'(x)=k(cosx-sinx), f'(0)=3 " and " f(pi/2)=15, find f'(x).

Chapter:  Applications of Derivative
Concept: Maxima and Minima
5.1.3

Differentiate cos^-1((3cosx-2sinx)/sqrt13) w. r. t. x.

Chapter:  Differentiation
Concept: Derivatives of Inverse Trigonometric Functions
5.2 | Attempt any TWO of the following:
5.2.1

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

Chapter:  Integration
Concept: Methods of Integration - Integration by Substitution
5.2.2

A rectangle has area 50 cm2 . Find its dimensions when its perimeter is the least

Chapter:  Applications of Derivative
Concept: Maxima and Minima - Introduction of Extrema and Extreme Values
5.2.3

Prove that : int_-a^af(x)dx=2int_0^af(x)dx , if f (x) is an even function.

= 0,                   if f (x) is an odd function.

Chapter:  Integration
Concept: Methods of Integration - Integration by Parts
6
6.1 | Attempt any TWO of the following:
6.1.1

If y = f (u) is a differential function of u and u = g(x) is a differential function of x, then prove that y = f [g(x)] is a differential function of x and dy/dx=dy/(du) xx (du)/dx

Chapter:  Applications of Derivative
Concept: Rate of Change of Bodies Or Quantities
6.1.2

Each of the total five questions in a multiple choice examination has four choices, only one of which is correct. A student is attempting to guess the answer. The random variable x is the number of questions answered correctly. What is the probability that the student will give atleast one correct answer?

Chapter:  Probability Distribution
Concept: Probability Distribution of a Discrete Random Variable
6.1.3

If f (x) = x 2 + a, for x ≥ 0  =2sqrt(x^2+1)+b,  is continuous at x = 0, find a and b.

Chapter:  Continuity
Concept: Continuity - Continuity of a Function at a Point
6.2 | Attempt any TWO of the following
6.2.1

Find the approximate value of cos (89°, 30'). [Given is: 1° = 0.0175°C]

Chapter:  Applications of Derivative
Concept: Maxima and Minima
6.2.2

Solve the differential equation:  x+ydy/dx=sec(x^2+y^2) Also find the particular solution if x = y = 0.

Chapter:  Differential Equation
Concept: General and Particular Solutions of a Differential Equation
6.2.3

Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below:

 X=x 1 2 3 P(X=x) 1/5 2/5 2/5
Chapter:  Probability Distribution
Concept: Probability Distribution - Expected Value, Variance and Standard Deviation of a Discrete Random Variable

#### Request Question Paper

If you dont find a question paper, kindly write to us

View All Requests

#### Submit Question Paper

Help us maintain new question papers on shaalaa.com, so we can continue to help students

only jpg, png and pdf files

## Maharashtra State Board previous year question papers 12th Board Exam Mathematics and Statistics with solutions 2014 - 2015

Maharashtra State Board 12th Board Exam Maths question paper solution is key to score more marks in final exams. Students who have used our past year paper solution have significantly improved in speed and boosted their confidence to solve any question in the examination. Our Maharashtra State Board 12th Board Exam Maths question paper 2015 serve as a catalyst to prepare for your Mathematics and Statistics board examination.
Previous year Question paper for Maharashtra State Board 12th Board Exam Maths-2015 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.
By referring the question paper Solutions for Mathematics and Statistics, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of Maharashtra State Board 12th Board Exam.

How Maharashtra State Board 12th Board Exam Question Paper solutions Help Students ?
• Question paper solutions for Mathematics and Statistics will helps students to prepare for exam.
• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.
• For finding solution of question papers no need to refer so multiple sources like textbook or guides.
S