Date: July 2017

(1) All questions are compulsory.

(2) Figure to the right tndtcate full marks.

(3) Answer to every question must be .written on a new page.

(4) Graph paper is necessaryJor L.P.P.

(5) Log table will be provided on demand.

(6) Answer to Section-I and Section-II should be written In two separate answer books.

(7) Question from Section-I attempted in the answer book of Section-II and vice versa wil not be assessed/not given any credit.

vice versa will not be assessed/not given any credit.

Write the negation of the following statements :

(a) Radha likes tea or coffee.

(b) `∃x cc` R such that x + 3 ≥ 10.

Chapter: [0.02] Matrices

If A = `[(1,2), (1,3)]`, find A^{2} - 3A

Chapter: [0.02] Matrices

Discuss the continuity of the function f at x = 0

If f(x) = `(2^(3x) - 1)/tanx`, for x ≠ 0

= 1, for x = 0

Chapter: [0.03] Continuity

Evaluate : `int ("x" + 1)/("x"("x" + log"x")`dx

Chapter: [0.06] Indefinite Integration

Solve the equations x + y = 4 and 2x - y = 5 using the method of reduction.

Chapter: [0.02] Matrices

If the function f is continuous at = 2, then find f(2) where f(x) = `(x^5 - 32)/(x - 2)`, for ≠ 2.

Chapter: [0.03] Continuity

Find the elasticity of demand, if the marginal revenue is 50 and price is Rs 75.

Chapter: [0.013999999999999999] Applications of Derivatives

Differentiate

log (1 + x^{2}) w.r.t. tan^{-1 }(x)

Chapter: [0.04] Differentiation

If p : It is raining

q : It is humid

Write the following statements in symbolic form:

(a) It is raining or humid.

(b) If it is raining then it is humid.

(c) It is raining but not humid.

Chapter: [0.01] Mathematical Logic [0.011000000000000001] Mathematical Logic

Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]

Chapter: [0.01] Mathematical Logic [0.011000000000000001] Mathematical Logic

Evaluate ; `int x^2/(x^6 - 4x^3 + 13)` dx

Chapter: [0.06] Indefinite Integration

If the function f is continuous at x = 0

Where f(x) = 2`sqrt(x^3 + 1)` + a, for x < 0,

= `x^3 + a + b, for x > 0

and f (1) = 2, then find a and b.

Chapter: [0.03] Continuity

For manufacturing x units, labour cost is 150 - 54x, processing cost is x^{2} and revenue R = 10800x - 4x^{3 }. Find the value of x for which Total cost is decreasing.

Chapter: [0.013999999999999999] Applications of Derivatives [0.05] Applications of Derivative

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.

Chapter: [0.013999999999999999] Applications of Derivatives [0.05] Applications of Derivative

The total cost C for producing x units is Rs (x^{2} + 60x + 50) and the price is Rs (180 - x) per unit. For how many units the profit is maximum.

Chapter: [0.03] Continuity

If y = sin ^{-1 }`((8x)/(1 + 16x^2))`, find `(dy)/(dx)`

Chapter: [0.04] Differentiation

If y = 5^{x }+ x^{x, }Find `(dy)/(dx)`.

Chapter: [0.07] Definite Integrals

`int (2x + 1)/((x + 1) ( x - 2))` dx

Chapter: [0.06] Indefinite Integration

Find the inverse of matrix A by using adjoint method; where A = `[(1, 0, 1), (0, 2, 3), (1, 2, 1)]`

Chapter: [0.012] Matrices [0.02] Matrices

Find the area of the region bounded by the curve (parabola) y^{2} = 4x and the line

Chapter: [0.06] Indefinite Integration

Evaluate `int_0^1 (x(sin^-1 x)^2)/sqrt(1 - x^2)` dx

Chapter: [0.07] Definite Integrals

In a class 60% students arc boys and 40% are girls. By admitting 16 boys and 8 girls, the ratio of boys to girls becomes 8 : 5. Find the original number of boys and girls in the class.

Chapter: [0.01] Mathematical Logic

An agent charges 12% commission on the sales. How much does he earn if the total sales amounts to ~ 36,000? How muuch does the seller get from this sale?

Chapter: [0.09] Commission, Brokerage and Discount

Find the Age-Specific Death Rate (SDR) for the following data :

Age groups (in years) |
Population | Number of deaths |

0 - 10 | 11,000 | 220 |

10 - 20 | 12,000 | 240 |

20 - 60 | 9,000 | 180 |

60 and above | 2,000 | 90 |

Chapter: [0.09] Commission, Brokerage and Discount

If the Crude Death Rate (CDR) for the following data is 13.4 per thousand, find x:

Age groups (in years) |
Population | Number of deaths |

0 - 20 | 40,000 | 350 |

20 - 65 | 65,000 | 650 |

65 and above | 15,000 | x |

Chapter: [0.09] Commission, Brokerage and Discount

If a fair die is rolled four times,. what is the probability that two of the rolls will show '1'.

Chapter: [0.14] Random Variable and Probability Distribution

Solve the inequation -8 ≤ 3x - 5 < 7 and represent it on the real number line.

Chapter: [0.14] Random Variable and Probability Distribution

Sketch the graph of | y | ≤ 3 in a coordinate plane.

Chapter: [0.11] Demography

Find the sequence that minimizes the total elapsed time (in hours) required to

complete the following jobs on the machine M_{1} , M_{2} and M_{3} in the order M_{1}M_{2}M_{3} :

Machine Jobs | A | B | C | D |

M_{1} |
5 | 6 | 9 | 5 |

M_{2} |
2 | 4 | 5 | 3 |

M_{3} |
3 | 5 | 6 | 7 |

Chapter: [0.02] Matrices

Find accumulated value after 1 year of annuity immediate in which Rs 20,000 is invested every quarter, at .16% p.a. compounded quarterly.

[Given : (1.04)^{4} = 1.1699]

Chapter: [0.09] Commission, Brokerage and Discount

If a random variable X follows Poisson distribution sucli that P(X = 1) = P(X = 2), find:

(a) the mean and

(b) P(X = 0). [Given: e^{-2} = 0.1353)

Chapter: [0.14] Random Variable and Probability Distribution

The probability of defective bolts in a workshop is 40%. Find the mean and variance of defective bolts out of 10 bolts.

Chapter: [0.14] Random Variable and Probability Distribution

Given the following table which relates to the number of animals of a certain species at age x . Complete the life table with dx, qx, Lx and Tx.

x | 0 | 1 | 2 | 3 | 4 | 5 |

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

Chapter: [0.14] Random Variable and Probability Distribution

Co-efficient of correlation between the variables X and Y is 0.3 and their covariance is 12. The variance of X is 9, find the standard deviation of Y.

Chapter: [0.14] Random Variable and Probability Distribution

Compute correlation coefficient for the following data :

X | 9 | 7 | 6 | 8 | 5 |

Y | 19 | 17 | 16 | 18 | 15 |

Chapter: [0.14] Random Variable and Probability Distribution

Surabhi, Simona and Shruti started a business in a partnership by investing ₹ 60,000, ₹ 40,000 and ₹ 75,000 respectively. At the end of the year they found that they have incurred a loss of ₹ 24,500. Find that how much loss each one had to bear?

Chapter: [0.08] Ratio, Proportion and Partnership

Three cars were sold through an agent for Rs 1,60,000, Rs1,48,000 and Rs 1,50,000 respectively. The rates of commission were 17 .5% on the first, and 12.5% on the second. If on the whole, the agent received 14% commission on the total sales, find the rate of commission paid on the third car.

Chapter: [0.09] Commission, Brokerage and Discount

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`

Chapter: [0.023] Linear Regression [0.13] Regression Analysis Introduction

If Σ_{x1} = 56 Σ_{y1} = 56, Σ`x_1^2` = 478,

Σ`y_1^2` = 476, Σ_{x1y1} = 469 and n = 7, Find

(a) the regression equation of y on x.

(b) y, if x = 12.

Chapter: [0.023] Linear Regression [0.13] Regression Analysis Introduction

Solve the following minimal assignment problem :

Machines | A | B | C | D | E |

M_{1} |
27 | 18 | ∞ | 20 | 21 |

M_{2} |
31 | 24 | 21 | 12 | 17 |

M_{3} |
20 | 17 | 20 | ∞ | 16 |

M_{4} |
21 | 28 | 20 | 16 | 27 |

Chapter: [0.027000000000000003] Assignment Problem and Sequencing [0.15] Management Mathematics

Solve the following L.P.P.:

Maximize Z = 4x + 5y

subject to 2x + y ≥ 4

x + y ≤ 5,

0 ≤ x ≤ 3,

0 ≤ y ≤ 3

Chapter: [0.15] Management Mathematics

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