Advertisement Remove all ads

# Mathematics and Statistics 2017-2018 HSC Arts 12th Board Exam Question Paper Solution

Advertisement Remove all ads
Mathematics and Statistics
Marks: 80 Academic Year: 2017-2018
Date & Time: 3rd March 2018, 11:00 am
Duration: 3h
Advertisement Remove all ads

[12] 1
[6] 1.1 | Select and write the appropriate answer from the given alternative in each of the following sub-question
[2] 1.1.1

If A = [(2,-3),(4,1)], then adjoint of matrix A is

(A) [(1,3),(-4,2)]

(B) [(1,-3),(-4,2)]

(C)  [(1,3),(4,-2)]

(D) [(-1,-3),(-4,2)]

Concept: Determinants - Adjoint Method
Chapter: [0.02] Matrices
[2] 1.1.2

The principal solutions of sec x = 2/sqrt3 are _____

pi/3,(11pi)/6

pi/6, (11pi)/6

pi/4,(11pi)/4

pi/6,(11pi)/4

Concept: Trigonometric Functions - General Solution of Trigonometric Equation of the Type
Chapter: [0.03] Trigonometric Functions
[2] 1.1.3

The measure of the acute angle between the lines whose direction ratios are 3, 2, 6 and –2, 1, 2 is ______.

Concept: Angle Between Two Lines
Chapter: [0.08] Three Dimensional Geometry
[6] 1.2 | Attempt Any Three of the Following
[2] 1.2.1

Write the negations of the following statements :

1) All students of this college live in the hostel

2) 6 is an even number or 36 is a perfect square.

Concept: Mathematical Logic - Sentences and Statement in Logic
Chapter: [0.01] Mathematical Logic
[2] 1.2.2

If a line makes angles α, β, γ with co-ordinate axes, prove that cos 2α + cos2β + cos2γ+ 1 = 0.

Concept: Trigonometric Functions - Trigonometric equations
Chapter: [0.03] Trigonometric Functions
[2] 1.2.3

Find the distance of the point (1, 2, –1) from the plane x - 2y + 4z - 10 = 0 .

Concept: Distance of a Point from a Plane
Chapter: [0.016] Line and Plane [0.1] Plane
[2] 1.2.4

Find the vector equation of the lines which passes through the point with position vector 4hati - hatj +2hatk and is in the direction of -2hati + hatj + hatk

Concept: Equation of a Line in Space
Chapter: [0.013999999999999999] Pair of Straight Lines [0.09] Line
[2] 1.2.5

if bara = 3hati - 2hatj+7hatk, barb  = 5hati + hatj -2hatkand barc = hati + hatj - hatk then find bara.(barbxxbarc)

Concept: Scalar Triple Product of Vectors
Chapter: [0.015] Vectors [0.07] Vectors
[14] 2
[6] 2.1 | Attempt Any Two of the Following
[3] 2.1.1

By vector method prove that the medians of a triangle are concurrent.

Concept: Vector and Cartesian Equations of a Line - Medians of a Triangle Are Concurrent
Chapter: [0.07] Vectors
[3] 2.1.2

Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)

Concept: Logical Connective, Simple and Compound Statements
Chapter: [0.01] Mathematical Logic [0.01] Mathematical Logic [0.011000000000000001] Mathematical Logic
[3] 2.1.3

If the origin is the centroid of the triangle whose vertices are A(2, p, –3), B(q, –2, 5) and C(–5, 1, r), then find the values of p, q, r.

Concept: Section Formula
Chapter: [0.015] Vectors [0.07] Vectors
[8] 2.2 | Attempt Any Two of Following
[4] 2.2.1

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.

Concept: Pair of Straight Lines - Pair of Lines Passing Through Origin - Homogenous Equation
Chapter: [0.04] Pair of Straight Lines
[4] 2.2.2

In triangle ABC prove that tan((C-A)/2) = ((c-a)/(c+a))cot  B/2

Concept: Trigonometric Functions - Trigonometric equations
Chapter: [0.03] Trigonometric Functions
Advertisement Remove all ads
[4] 2.2.3

Find the inverse of the matrix A = [(1,2,-2),(-1,3,0),(0,-2,1)]using elementary row transformations.

Concept: Matrices - Inverse of a Matrix Existance
Chapter: [0.02] Matrices
[14] 3
[6] 3.1 | Attempt Any Two of the Following
[3] 3.1.1

Find the joint equation of the pair of lines passing through the origin which are perpendicular respectively to the lines represented by 5x2 +2xy- 3y2 = 0.

Concept: Pair of Straight Lines - Pair of Lines Passing Through Origin - Homogenous Equation
Chapter: [0.04] Pair of Straight Lines
[3] 3.1.2

Find the angle between the lines (x -1)/4 = (y - 3)/1 = z/8  and (x-2)/2 = (y + 1)/2 = (z-4)/1

Concept: Concept of Line - Equation of Line Passing Through Given Point and Parallel to Given Vector
Chapter: [0.09] Line
[3] 3.1.3

Write converse, inverse and contrapositive of the following conditional statement :

If an angle is a right angle then its measure is 90°.

Concept: Mathematical Logic - Difference Between Converse, Contrapositive, Contradiction
Chapter: [0.01] Mathematical Logic
[8] 3.2 | Attempt Any Two of the Following
[4] 3.2.1

Prove that sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)

Concept: Inverse Trigonometric Functions - Inverse Trigonometric Functions - Principal Value Branch
Chapter: [0.03] Trigonometric Functions
[4] 3.2.2

Find the vector equation of the plane passing through the points A(1, 0, 1), B(1, –1, 1) and C(4, –3, 2).

Concept: Plane - Equation of Plane Passing Through the Given Point and Perpendicular to Given Vector
Chapter: [0.1] Plane
[4] 3.2.3

Solve the following LPP by graphical method:

Minimize Z = 7x + y subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0

Concept: Graphical Method of Solving Linear Programming Problems
Chapter: [0.017] Linear Programming [0.11] Linear Programming Problems
[12] 4
[6] 4.1 | Select and write the appropriate answer from the given alternatives in each of the following sub-questions :
[2] 4.1.1

Let the p. m. f. of a random variable X be __

P(x) = (3-x)/10 for x = -1,0,1,2

= 0                        otherwise

Then E(X ) is ________.

1

2

0

-1

Concept: Probability Distribution - Expected Value, Variance and Standard Deviation of a Discrete Random Variable
Chapter: [0.19] Probability Distribution
[2] 4.1.2

if int_0^k 1/(2+ 8x^2) dx = pi/16 then the value of k is ________.

(A) 1/2

(B) 1/3

(C) 1/4

(D) 1/5

Concept: Definite Integral as the Limit of a Sum
Chapter: [0.15] Integration
[2] 4.1.3

Integrating factor of linear differential equation x (dy)/(dx) + 2y =x^2 log x is ____________

1/x^2

1/x

x

x^2

Concept: Differential Equations - Linear Differential Equation
Chapter: [0.17] Differential Equation
[6] 4.2 | Attempt Any Three of The Following
[2] 4.2.1

Evaluate int e^x [(cosx - sin x)/sin^2 x]dx

Concept: Properties of Definite Integrals
Chapter: [0.15] Integration
[2] 4.2.2

if y = tan^2(log x^3), find (dy)/(dx)

Concept: Derivatives of Composite Functions - Chain Rule
Chapter: [0.021] Differentiation [0.13] Differentiation
[2] 4.2.3

Find the area of ellipse x^2/1 + y^2/4 = 1

Concept: Area of the Region Bounded by a Curve and a Line
Chapter: [0.16] Applications of Definite Integral
Advertisement Remove all ads
[2] 4.2.4

Obtain the differential equation by eliminating the arbitrary constants from the following equation :

y = c_1e^(2x) + c_2e^(-2x)

Concept: Formation of Differential Equation by Eliminating Arbitary Constant
Chapter: [0.17] Differential Equation
[2] 4.2.5

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

Concept: Bernoulli Trials and Binomial Distribution
Chapter: [0.027999999999999997] Binomial Distribution [0.2] Bernoulli Trials and Binomial Distribution
[14] 5
[6] 5.1 | Attempt any TWO of the following
[3] 5.1.1

Evaluate int 1/(3+ 2 sinx + cosx) dx

Concept: Methods of Integration: Integration by Substitution
Chapter: [0.023] Indefinite Integration [0.15] Integration
[3] 5.1.2

If x = acos^3t, y = asin^3 t,

Show that (dy)/(dx) =- (y/x)^(1/3)

Concept: Derivatives of Functions in Parametric Forms
Chapter: [0.13] Differentiation
[3] 5.1.3

Examine the continuity of the function:

f(x) = (log100 + log(0.01+x))/"3x"," for "x != 0 =  100/3 for x = 0; at x = 0.

Concept: Definition of Continuity - Defination of Continuity of a Function at a Point
Chapter: [0.12] Continuity
[8] 5.2 | Attempt any TWO of the following
[4] 5.2.1

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

Concept: Maxima and Minima
Chapter: [0.022000000000000002] Applications of Derivatives [0.14] Applications of Derivative
[4] 5.2.2

Prove that int 1/(a^2 - x^2) dx = 1/"2a" log|(a +x)/(a-x)| + c

Concept: Fundamental Theorem of Calculus
Chapter: [0.15] Integration
[4] 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.

Concept: Methods of Integration: Integration by Parts
Chapter: [0.023] Indefinite Integration [0.15] Integration
[14] 6
[6] 6.1 | Attempt any TWO of the following
[3] 6.1.1

if  f(x) = (x^2-9)/(x-3) + alpha               for x> 3

=5,                                     for x = 3

=2x^2+3x+beta,             for x < 3

is continuous at x  = 3, find α and β.

Concept: Definition of Continuity - Continuity of a Function at a Point
Chapter: [0.12] Continuity
[3] 6.1.2

Find dy/dx if y = tan^(-1) ((5x+ 1)/(3-x-6x^2))

Concept: The Concept of Derivative - Derivative of Inverse Function
Chapter: [0.13] Differentiation
[3] 6.1.3

A fair coin is tossed 9 times. Find the probability that it shows head exactly 5 times.

Concept: Bernoulli Trials and Binomial Distribution
Chapter: [0.027999999999999997] Binomial Distribution [0.2] Bernoulli Trials and Binomial Distribution
[8] 6.2 | Attempt any TWO of the following
[4] 6.2.1

Verify Rolle’s theorem for the following function:

f (x) = x2 - 4x + 10 on [0, 4]

Concept: Mean Value Theorem
Chapter: [0.14] Applications of Derivative
[4] 6.2.2

Find the particular solution of the differential equation:

y(1+logx) dx/dy - xlogx = 0

when y = e2 and x = e

Concept: Methods of Solving First Order, First Degree Differential Equations - Differential Equations with Variables Separable Method
Chapter: [0.17] Differential Equation
[4] 6.2.3

Find the variance and standard deviation of the random variable X whose probability distribution is given below :

 x 0 1 2 3 P(X = x) 1/8 3/8 3/8 1/8
Concept: Probability Distribution - Expected Value, Variance and Standard Deviation of a Discrete Random Variable
Chapter: [0.19] Probability Distribution

#### 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 2017 - 2018

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 2018 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-2018 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.
Advertisement Remove all ads
Share
Notifications

View all notifications

Forgot password?