###### Advertisements

###### Advertisements

**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

**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

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

Concept: Discount

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

(p ∧ ~ q) → (~ p ∧ ~ q)

Concept: Statement Patterns and Logical Equivalence

The false statement in the following is ______.

Concept: Statement Patterns and Logical Equivalence

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

(p ∧ ~ q) → (~ p ∧ ~ q)

Concept: Statement Patterns and Logical Equivalence

The false statement in the following is ______.

Concept: Statement Patterns and Logical Equivalence

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

For 50 students of a class, the regression equation of marks in statistics (X) on the marks in accountancy (Y) is 3y − 5x + 180 = 0. The variance of marks in statistics is `(9/16)^"th"` of the variance of marks in accountancy. Find the correlation coefficient between marks in two subjects.

Concept: Properties of Regression Coefficients

The following table shows the production of gasoline in U.S.A. for the years 1962 to 1976.

Year |
1962 | 1963 | 1964 | 1965 | 1966 | 1967 | 1968 | 1969 |

Production (million barrels) |
0 | 0 | 1 | 1 | 2 | 3 | 4 | 5 |

Year |
1970 | 1971 | 1972 | 1973 | 1974 | 1975 | 1976 | |

Production (million barrels) |
6 | 7 | 8 | 9 | 8 | 9 | 10 |

- Obtain trend values for the above data using 5-yearly moving averages.
- Plot the original time series and trend values obtained above on the same graph.

Concept: Measurement of Secular Trend

In a cattle breeding firm, it is prescribed that the food ration for one animal must contain 14, 22, and 1 unit of nutrients A, B, and C respectively. Two different kinds of fodder are available. Each unit weight of these two contains the following amounts of these three nutrients:

Nutrient\Fodder |
Fodder 1 |
Fodder2 |

Nutrient A | 2 | 1 |

Nutrient B | 2 | 3 |

Nutrient C | 1 | 1 |

The cost of fodder 1 is ₹ 3 per unit and that of fodder ₹ 2 per unit. Formulate the L.P.P. to minimize the cost.

Concept: Linear Programming Problem (L.P.P.)

A toy manufacturing company produces five types of toys. Each toy has to go through three machines A, B, C in the order ABC. The time required in hours for each process is given in the following table.

Type |
1 |
2 |
3 |
4 |
5 |

Machine A |
16 | 20 | 12 | 14 | 22 |

Machine B |
10 | 12 | 4 | 6 | 8 |

Machine C |
8 | 18 | 16 | 12 | 10 |

Solve the problem for minimizing the total elapsed time.

Concept: Types of Sequencing Problem

**Choose the correct alternative:**

Negation of p → (p ˅ ~q) is

Concept: Logical Connective, Simple and Compound Statements

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

Concept: Logical Connective, Simple and Compound Statements

**Examine whether the statement pattern**

[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.

Concept: Statement Patterns and Logical Equivalence

**Complete the truth table.**

p |
q |
r |
q → r |
r → p |
(q → r) ˅ (r → p) |

T | T | T | T | `square` | T |

T | T | F | F | `square` | `square` |

T | F | T | T | `square` | T |

T | F | F | T | `square` | `square` |

F | T | T | `square` | F | T |

F | T | F | `square` | T | `square` |

F | F | T | `square` | F | T |

F | F | F | `square` | T | `square` |

The given statement pattern is a `square`

Concept: Statement Patterns and Logical Equivalence

If p ∨ q is true, then the truth value of ∼ p ∧ ∼ q is ______.

Concept: Algebra of Statements

Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."

Concept: Logical Connective, Simple and Compound Statements