Mathematics | ECE Electronics and Communication Engineering | TANCET Anna University Online Objective Test

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Linear Programming Prepare / Learn

Q1. Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs 60/kg and Food Q costs Rs 80/kg. Food P contains 3 units/kg of Vitamin A and 5 units / kg of Vitamin B while food Q contains 4 units/kg of Vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.

A. Minimum cost = Rs 180 at all points lying on segment joining

(\frac{8}{3}, 0) a n d (2, \frac{1}{2})

B. Minimum cost = Rs 160 at all points lying on segment joining

(\frac{8}{3}, 0) a n d (2, \frac{1}{2})

C. Minimum cost = Rs 180 at all points lying on segment joining

(\frac{8}{3}, 0) a n d (2, \frac{1}{2})

D. Minimum cost = Rs 170 at all points lying on segment joining

(\frac{8}{3}, 0) a n d (2, \frac{1}{2})

Answer : Option B
Explaination / Solution:

Let number of food type P = x
And number of units of food type Q = y
Therefore , the above L.P.P. is given as :
Minimise , Z = 60x +80y , subject to the constraints : 3 x + 4y ≥ 8, 5x + 2y ≥ 11, x,y ≥ 0.

The corner points can be obtained by drawing the lines 3x+4y=8 and 5x+2y=11 graphically.

The points so obtained are (8/3,0), (2,1/2), (0,11/2)

Corner points	Z = - x + 2y
D(8/3,0 )	160………………….(Min.)
A(2,1/2)	160………………(Min.)
B(0,11/2)	440

Here Z = 160 is minimum. i.e. Minimum cost = Rs 160 at all points lying on segment joining $(\frac{8}{3}, 0) a n d (2, \frac{1}{2})$ .

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Linear Inequalities Prepare / Learn

Q2. Solve the system of inequalities (x + 5 ) − 7 ( x − 2 ) ≥ 4x + 9 , 2 ( x − 3 ) − 7 ( x + 5 ) ≤ 3x − 9

A. − 4 ≤ x ≤ 1

B. − 4 ≤ x ≤ 4

C. − 9/4 ≤ x ≤ 1

D. − 1 ≤ x ≤ 1

Answer : Option A
Explaination / Solution:

Hence the solution set is $[- 4, \infty) ⋂ (- \infty, 1] = [- 4, 1]$

Which means $- 4 \leq x \leq 1$

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Sequences and Series Prepare / Learn

Q3. The 20th term of the series 2×4+4×6+6×8+... is

A. 1600

B. 420

C. 1680

D. 840

Answer : Option C
Explaination / Solution:

here,

$\begin{array}{l} a_{n} = 2 n (2 n + 2) \\ a_{20} = 2 (20) (2.20 + 2) = 40 (42) = 1680 \end{array}$

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Statistics Prepare / Learn

Q4. The median of the data 13,14,16,18,20,22 is

A. 19

B. 18

C. 17

D. 16

Answer : Option C
Explaination / Solution:

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Application of Integrals Prepare / Learn

Q5.

The area bounded by the curves $y^{2} = x^{3} a n d | y | = 2 x$ is given by

A. 2

B. 32/3

C. 32/5

D. none of these.

Answer : Option A
Explaination / Solution:

Both

y^{2} = x^{3}

and

| y | = 2 x

are symmetric about y – axis and on solving them we get :

x = 0, \sqrt{2}

required area :
=

2 \int_{0}^{\sqrt{2}} (2 x - x^{3}) d x = 2 {[x^{2} - \frac{x^{4}}{4}]}_{0}^{\sqrt{2}} = 2 s q . u n i t s

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Relations and Functions Prepare / Learn

Q6. A relation R on a set A is called an empty relation if

A. one element of A is related to all the elements of A

B. every element of A is related to one element of A

C. no element of A is related to any element of A

D. every element of A is related to any element of A

Answer : Option C
Explaination / Solution:

For any set A ,an empty relation may be defined on A as: there is no element exists in the relation set which satisfies the relation for a given set A i.e. let A={1,2,3,4,5} and R={(a,b): a,b ∈A and a+b= 10},so we get R={ } which is an empty relation.

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Determinants Prepare / Learn

Q7.

A. none of these.

B. 2(a+b+c)3

C. −2(a+b+c)3

D. 4(a+b+c)3

Answer : Option A
Explaination / Solution:

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Straight Lines Prepare / Learn

Q8. The lines x + 2y – 3 = 0, 2x + y – 3 = 0 and the line l are concurrent . If the line I passes through the origin, then its equation is

A. None of these

B. x + y + 0

C. x – y = 0

D. x + 2y = 0

Answer : Option C
Explaination / Solution:

Equation of a line passing through the intersection of two lies is given by ax1 +by1 +c1 + k(ax2 +by2 +c2) = 0

Hence x+2y-3 + k(2x+y-3) = 0

Since it passes through (0,0)

-3 -3k = 0

This implies k = -1

Sustituting for k we get,

x+2y-3 +(-1)(2x+y-3) = 0

-x +y =0 or x - y = 0

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Mathematical Reasoning Prepare / Learn

Q9. Which of the following is always true ?

A. (p→q)≅(∼q→∼p)

B. ∼(p∧q)≅(∼p∧∼q)

C. ∼(p→q)≅(p∨∼q)

D. ∼(p∨q)≅(∼p∨∼q)

Answer : Option A
Explaination / Solution:

$\sim q \to\sim p \equiv q \lor \sim p$ Since $p \to q \equiv\sim p \lor q$

$\sim p \lor q \equiv p \to q$

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