Date & Time: 8th October 2015, 4:00 pm

Duration: 3h

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: [1] Mathematical Logic

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

`1/9[[1,4,-2],[-2,-5,4],[1,-2,1]]`

`[[1,-2,1],[4,-5,-2],[-2,4,1]]`

`[[1,4,-2],[-2,-5,4],[1,-2,1]]`

`[[-1,-4,2],[2,5,-4],[1,-2,1]]`

Chapter: [2] Matrices

The slopes of the lines given by 12x^{2} + bxy + y^{2} = 0 differ by 7. Then the value of b is :

(A) 2

(B) ± 2

(C) ± 1

(D) 1

Chapter: [4] Pair of Straight Lines

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

Chapter: [3] Trigonometric Functions

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

Chapter: [4] Pair of Straight Lines

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: [7] Vectors

Find the direction cosines of the line

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

Chapter: [8] Three Dimensional Geometry

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

Chapter: [10] Plane

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

Chapter: [1] Mathematical Logic

Show that every homogeneous equation of degree two in x and y, i.e., ax^{2} + 2hxy + by^{2} = 0 represents a pair of lines passing through origin if h^{2}−ab≥0.

Chapter: [4] Pair of Straight Lines

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: [7] Vectors

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

Chapter: [2] Matrices

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

Chapter: [3] Trigonometric Functions

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

Chapter: [10] Plane

Construct the simplified circuit for the following circuit:

Chapter: [1] Mathematical Logic

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

Chapter: [7] Vectors

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

Chapter: [8] Three Dimensional Geometry

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

Chapter: [10] Plane

Minimize : Z = 6x + 4y

Subject to the conditions:

3x + 2y ≥ 12,

x + y ≥ 5,

0 ≤ x ≤ 4,

0 ≤ y ≤ 4

Chapter: [11] Linear Programming Problems

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

Chapter: [3] Trigonometric Functions

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

(A) x

(B) 1/x

(C) 1

(D) 0

Chapter: [13] Differentiation

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: [15] Integration

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: [17] Differential Equation

Evaluate: `int1/(xlogxlog(logx))dx`

Chapter: [15] Integration

Find the area bounded by the curve y^{2} = 4ax, x-axis and the lines x = 0 and x = a.

Chapter: [16] Applications of Definite Integral

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

=0 ,otherwise

Chapter: [20] Bernoulli Trials and Binomial Distribution

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

Chapter: [20] Bernoulli Trials and Binomial Distribution

Solve the differential equation `y-xdy/dx=0`

Chapter: [17] Differential Equation

Discuss the continuity of the function

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

** = 3, for x=π/2**

Chapter: [12] Continuity

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

Chapter: [14] Applications of Derivative

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

Chapter: [13] Differentiation

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

Chapter: [15] Integration

A rectangle has area 50 cm^{2} . Find its dimensions when its perimeter is the least

Chapter: [14] Applications of Derivative

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: [15] Integration

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: [14] Applications of Derivative

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: [19] Probability Distribution

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

Chapter: [12] Continuity

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

Chapter: [14] Applications of Derivative

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

Chapter: [17] Differential Equation

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: [19] Probability Distribution

#### Other Solutions

#### Submit Question Paper

Help us maintain new question papers on Shaalaa.com, so we can continue to help studentsonly jpg, png and pdf files

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

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.