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

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

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"

Concept: Statement Patterns and Logical Equivalence

For manufacturing x units, labour cost is 150 – 54x and processing cost is x^{2}. Price of each unit is p = 10800 – 4x^{2}. Find the value of x for which Total cost is decreasing.

Concept: Increasing and Decreasing Functions

For manufacturing x units, labour cost is 150 – 54x and processing cost is x^{2}. Price of each unit is p = 10800 – 4x^{2}. Find the values of x for which Revenue is increasing.

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 = ?

Concept: Methods of Integration: Integration Using Partial Fractions

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)`

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`

Concept: Derivatives of Functions in Parametric Forms

For manufacturing x units, labour cost is 150 – 54x and processing cost is x^{2}. Price of each unit is p = 10800 – 4x^{2}. Find the value of x for which Total cost is decreasing.

Concept: Increasing and Decreasing Functions

For manufacturing x units, labour cost is 150 – 54x and processing cost is x^{2}. Price of each unit is p = 10800 – 4x^{2}. Find the values of x for which Revenue is increasing.

Concept: Increasing and Decreasing Functions

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

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 |

l_{x} |
1000 | 850 | 760 | 360 | 25 | 0 |

Concept: Life Tables

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

(p ∧ ~ q) → (~ p ∧ ~ q)

Concept: Statement Patterns and Logical Equivalence

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

n^{2} ≥ 1

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)

Concept: Statement Patterns and Logical Equivalence

**Choose the correct alternative:**

The false statement in the following is ______.

Concept: Truth Value of Statement

The price P for demand D is given as P = 183 + 120 D – 3D^{2}.

Find D for which the price is increasing.

Concept: Increasing and Decreasing Functions

Find the area of the region bounded by the parabola y^{2} = 4x and the line x = 3.

Concept: Area Under Simple Curves

For the differential equation, find the particular solution (x – y^{2}x) dx – (y + x^{2}y) dy = 0 when x = 2, y = 0

Concept: Differential Equations

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

y = Ae^{3x} + Be^{–3x}

Concept: Formation of Differential Equation by Eliminating Arbitary Constant

**Choose the correct alternative.**

The difference between face value and present worth is called ______.

Concept: Discount