Date: July 2018
- All questions are compulsory.
- Figures to the right lndicatefull marks.
- Graph paper Is necessary for L.P.P.
- Write answer of every question on separate page.
If p : It is a day time
q : It is warm
Give the verbal statement for the following symbolic statement :
(a) p ^ - q (b) P → q
Chapter: [0.01] Mathematical Logic
Express the truth of each of the following statements using Venn diagrams:
(a) No circles are polygons
(b) Some quadratic equations have equal roots
Chapter: [0.01] Mathematical Logic [0.011000000000000001] Mathematical Logic
Find the values of x and y if
`2 [(x,5),(7,y-3)] [(3,-4),(1,2)] = [(7,6),(15,14)]`
Chapter: [0.012] Matrices [0.02] Matrices
Find `"dy"/"dx"` ; if x = sin^{3}θ , y = cos^{3}θ
Chapter: [0.013000000000000001] Differentiation [0.04] Differentiation
Find `"dy"/"dx"` ; if y = cos^{-1} `("2x" sqrt (1 - "x"^2))`
Chapter: [0.013000000000000001] Differentiation [0.04] Differentiation
Evaluate: ∫ x . log x dx
Chapter: [0.01] Mathematical Logic [0.011000000000000001] Mathematical Logic
The cost C of producing x articles is given as C = x^{3}-16x^{2 }+ 47x. For what values of x, with the average cost is decreasing'?
Chapter: [0.04] Differentiation
Evaluate : `int _0^(pi/4) 1/(1 + "x"^2) "dx"`
Chapter: [0.07] Definite Integrals
Solve the following equations by reduction method:
x+ y+z = 6,
3x-y+3z = 10
5x+ y-4z = 3
Chapter: [0.012] Matrices [0.02] Matrices
Evaluate : `int (2"x" + 1)/(("x" + 1)("x"-2)) "dx"`
Chapter: [0.06] Indefinite Integration
Evaluate `int _0^l "x" (1 - "x")^(3/2) "dx"`
Chapter: [0.07] Definite Integrals
Using the rules of negation, write the negatlon of the following:
(a) p ∧ (q → r)
(b) ~P ∨ ~q
Chapter: [0.01] Mathematical Logic [0.011000000000000001] Mathematical Logic
If the function f is continuous at x = 2 and x = 4 then find the values of a and b.
Where f(x) = x^{2} + ax + b, x < 2
= 3x + 2, 2 ≤ x ≤ 4
= 2ax + 5b, 4 < x
Chapter: [0.06] Indefinite Integration
A manufacturing company produces x items at the total cost of Rs (180+4x). The demand function of this product is P=(240 - x). Find x for which profit is increasing.
Chapter: [0.013999999999999999] Applications of Derivatives
If A = `[(1,2),(3,-1)] , "B" = [(7,1),(2,5)]`
Verify that |AB| = |A|.|B|
Chapter: [0.012] Matrices [0.02] Matrices
Evaluate : `int 1/("x" [("log x")^2 + 4]) "dx"`
Chapter: [0.016] Definite Integration [0.07] Definite Integrals
Find the volume of solid generated by rotating the area bounded by x^{2}+y^{2} =36 and the lines x = 0, x = 3 about X -axis.
Chapter: [0.06] Indefinite Integration
If f is continuous at x = 0, then find f (0).
Where f(x) = `(3^"sin x" - 1)^2/("x" . "log" ("x" + 1)) , "x" ≠ 0`
Chapter: [0.03] Continuity
If x^{7} . y^{9} = (x + y)^{16} then show that `"dy"/"dx" = "y"/"x"`
Chapter: [0.013000000000000001] Differentiation [0.04] Differentiation
In a firm the cost function for output x is given as C = `"x"^3/3 - 20"x"^2 + 70 "x"`. Find the 3 output for which marginal cost (C_{m}) is minimum.
Chapter: [0.05] Applications of Derivative
The price of a T.V. set is Rs 17,000. An agent charges at 3% and earns Rs. 25,500. Find the number of T.V. sets sold by him.
Chapter: [0.09] Commission, Brokerage and Discount
Find the Age-Specific Death Rate (Age SDR) for the following data.
Age groups (In year) |
Population (in '000) |
Number of Dearths |
0 - 10 | 11 | 275 |
10 - 20 | 12 | 180 |
20 - 60 | 9 | 81 |
60 and above | 2 | 32 |
Chapter: [0.11] Demography
The regression equation of y on x is given by 3x + 2y - 26 = O. Find b_{yx}.
Chapter: [0.13] Regression Analysis Introduction
Verify whether the following function can be regarded as p.m.f. of the random variable X:
\[ P(X) = \begin{cases} \frac{x - 1}3 & \quad \text{x } = \text{ 1,2,3}\\ 0 & \quad \text{} , \text{otherwise} \end{cases} \]
Chapter: [0.14] Random Variable and Probability Distribution
If X has a binomial distribution with n = 20 , p = `1/10` , find E (X) and V (X).
Chapter: [0.14] Random Variable and Probability Distribution
Bring out the inconsistency; if any: b_{yx} + b_{xy} = 1.30. and r = 0.75
Chapter: [0.13] Regression Analysis Introduction
A train travelled between two stations. The distance and time were recorded as below:
Distance (Km) | 80 | 120 | 160 | 200 | 240 |
Time (Hr) | 2 | 3 | 4 | 5 | 6 |
Draw scatter diagram and identify the type of correlation.
Chapter: [0.12] Bivariate Data and Correlation
If r = 0.5, σ_{x} = 1 and σ_{y} = 4, then find Cov.(X,Y).
Chapter: [0.12] Bivariate Data and Correlation
Calculate `"e"_0^circ ,"e"_1^circ , "e"_2^circ` from the following:
Age x | 0 | 1 | 2 |
l_{x} | 1000 | 880 | 876 |
T_{x } | - | - | 3323 |
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and Probability Distribution
Calculate the CDR for District A and B and compare them:
Age group (in years) | District A | District B | ||
No.of. persons (in '000) |
No.of. deaths |
No.of. persons (in '000) |
No.of. deaths | |
0 - 15 | 1 | 20 | 2 | 50 |
15 - 60 | 3 | 30 | 7 | 70 |
60 and above | 2 | 40 | 1 | 25 |
Chapter: [0.15] Management Mathematics
The equation of the line of regression of Y on X is 3x + 2y = 26 and X on Y is 6x + y = 31. Find Var. (X) if Var. (Y) = 36.
Chapter: [0.13] Regression Analysis Introduction
Calculate Spearman's Rank Correlation Coefficient between the following marks given by 'two' judges (A) and (B) to •eight' contestants in the elocution competition:
Contestants | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Marks by A | 81 | 72 | 60 | 33 | 29 | 11 | 56 | 42 |
Marks byB | 75 | 56 | 42 | 15 | 30 | 20 | 60 | 80 |
Chapter: [0.12] Bivariate Data and Correlation
Solve the following assignment problem to minimize the cost:
Persons | Jobs | ||
I | II | III | |
A | 7 | 3 | 5 |
B | 2 | 7 | 4 |
C | 6 | 5 | 3 |
D | 3 | 4 | 7 |
Chapter: [0.05] Applications of Derivative
Find the sequence of the following five jobs to be processed on three machines M_{1} M_{2,} , M_{3} that will minimize the total elapsed time to complete the tasks . Each job is to be processed in the order M_{1} - M_{2} - M_{3} :
Jobs | 1 | 2 | 3 | 4 | 5 |
Machine M_{1} | 5 | 11 | 5 | 7 | 6 |
Machine M_{2} | 1 | 4 | 2 | 5 | 3 |
Machine M_{3 } | 1 | 5 | 2 | 3 | 4 |
Chapter: [0.15] Management Mathematics
Minimize: Z = 2x + y
Subject to: x + y ≤ 5
x + 2y ≤ 8
4x + 3y ≥ 12
x ≥ o, y ≥ o
Solve graphically.
Chapter: [0.15] Management Mathematics
Find the graphical solution for the following system of linear equations :
3x + 4y ≥ 12 , 4x + 7y ≤ 28 , y ≥ 1 , x ≥ 0 , y ≥ 0 ,
Hence find the co-ordinates of comer points of the common region.
Chapter: [0.15] Management Mathematics
A wholesaler allows 25% trade discount and 5% cash discount. Find the list price of an article, if it was sold for the net amount of Rs 1,140.
Chapter: [0.09] Commission, Brokerage and Discount
Find the accumulated value after 3 years of an immediate annuity of Rs 2,000 p.a. with interest compounded at 10% p.a. [Given (1.1)^{3} = 1.331]
Chapter: [0.1] Insurance and Annuity
If the difference between true discount and banker's discount on a sum due 4 months hence is Rs 20, find true discount, banker's discount and amount of the bill, the rate of simple interest charged being 5% p.a .
Chapter: [0.09] Commission, Brokerage and Discount
If a random variable X follows Poisson distribution such that P(X = l) =P(X = 2), then find P(X ≥ 1). [Use e^{-2} = 0.1353]
Chapter: [0.027999999999999997] Probability Distributions [0.14] Random Variable and 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 2017 - 2018
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.