# HSC Commerce 12th Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

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Write the converse, inverse, and contrapositive of the following statement.

"If it snows, then they do not drive the car"

Appears in 3 question papers
Chapter: [0.01] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

Write the converse, inverse, and contrapositive of the following statement.

"If it snows, then they do not drive the car"

Appears in 3 question papers
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

If the population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 60 thousand in 40 years, what will be the population in another 20 years? ("Given" sqrt(3/2) = 1.2247)

Appears in 3 question papers
Chapter: [0.018000000000000002] Differential Equation and Applications
Concept: Application of Differential Equations

If x = a sin 2t (1 + cos2t) and y = b cos 2t (1 – cos 2t), find the values of  dy/dx at t = pi/4

Appears in 3 question papers
Chapter: [0.04] Differentiation
Concept: Derivatives of Functions in Parametric Forms

A bill of Rs.7,500 was discounted for Rs. 7,290 at a bank on 28th October 2006. If the rate of interest was 14% p.a., what is the legal due date ?

Appears in 3 question papers
Chapter: [0.09] Commission, Brokerage and Discount
Concept: Commission, Brokerage and Discount

From the following table which relates to the number of animals of a certain
species at age x. complete the life table :

 x 0 1 2 3 4 5 lx 1000 850 760 360 25 0
Appears in 3 question papers
Chapter: [0.11] Demography
Concept: Life Tables

Examine whether the following statement pattern is a tautology, a contradiction or a contingency.

(p ∧ ~ q) → (~ p ∧ ~ q)

Appears in 2 question papers
Chapter: [0.01] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

Use quantifiers to convert the following open sentences defined on N, into a true statement.

n2 ≥ 1

Appears in 2 question papers
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Quantifier and Quantified Statements in Logic

Examine whether the following statement pattern is a tautology, a contradiction or a contingency.

(p ∧ ~ q) → (~ p ∧ ~ q)

Appears in 2 question papers
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Statement Patterns and Logical Equivalence

The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.

Appears in 2 question papers
Chapter: [0.013999999999999999] Applications of Derivatives
Concept: Increasing and Decreasing Functions

Choose the correct alternative:

int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x, then p = ?

Appears in 2 question papers
Chapter: [0.015] Integration
Concept: Methods of Integration: Integration Using Partial Fractions

The equations given of the two regression lines are 2x + 3y - 6 = 0 and 5x + 7y - 12 = 0.

Find:

(a) Correlation coefficient

(b) sigma_x/sigma_y

Appears in 2 question papers
Chapter: [0.023] Linear Regression
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression

Find k, if the function f is continuous at x = 0, where

f(x)=[(e^x - 1)(sinx)]/x^2,      for x ≠ 0

= k                             ,        for x = 0

Appears in 2 question papers
Chapter: [0.03] Continuity
Concept: Continuous Function of Point

If x=a sin 2t(1+cos 2t) and y=b cos 2t(1cos 2t), find dy/dx

Appears in 2 question papers
Chapter: [0.04] Differentiation
Concept: Derivatives of Functions in Parametric Forms

The cost C of producing x articles is given as C = x3-16x2 + 47x.  For what values of x, with the average cost is decreasing'?

Appears in 2 question papers
Chapter: [0.04] Differentiation
Concept: Derivatives of Functions in Parametric Forms

The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.

Appears in 2 question papers
Chapter: [0.05] Applications of Derivative
Concept: Increasing and Decreasing Functions

Cost of assembling x wallclocks is ( x^3/3 - 40x^2) and labour charges are 500x. Find the number of wall clocks to be manufactured for which average cost and marginal cost attain their respective minimum.

Appears in 2 question papers
Chapter: [0.05] Applications of Derivative
Concept: Maxima and Minima

Evaluate : int_3^9 [root(3)(12-x)]/[ root(3)(x) + root(3)(12 - x)]

Appears in 2 question papers
Chapter: [0.07] Definite Integrals
Concept: Applications of Definite Integrals

If f(x) = ("e"^(2"x") - 1)/"ax"   , for x < 0 , a ≠ 0

= 1                                    for x = 0

= ("log" (1 + 7"x"))/"bx" , for x > 0 , b ≠ 0

is continuous at x = 0, then find a and b.

Appears in 2 question papers
Chapter: [0.07] Definite Integrals
Concept: Applications of Definite Integrals

Find the volume of a solid obtained by the complete revolution of the ellipse x^2/36 + y^2/25 = 1 about X-axis.

Appears in 2 question papers
Chapter: [0.07] Definite Integrals
Concept: Applications of Definite Integrals
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