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. Maximize Z = 3x + 2y subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.

A. Maximum Z = 18 at (4, 3)

B. Maximum Z = 22 at (4, 3)

C. Maximum Z = 20 at (4, 3)

D. Maximum Z = 24 at (4, 3)

Answer : Option A
Explaination / Solution:

Objective function is Z = 3x + 2 y ……………………(1).
The given constraints are : x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0. The corner points obtained by drawing the lines 3x+y=15 and x+2y=10 graphically are (0,0),(0,5), (5,0) and (4,3).

Corner points	Z = 3x + 2y
O(0 ,0 )	0
A(5,0)	15
B(0,5)	10
C(4,3)	18……………………..(Max.)

Here , Z = 18 is maximum at ( 4, 3 )

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

Q2. The values of ‘a’ for which the roots of the equation sin θ = a in A.P. are

A. 0, 1 and – 1

B. None of these

C. 0 and 1

D. - 1 and 1

Answer : Option A
Explaination / Solution:

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

Q3. If in moderately asymmetrical distribution mode and mean of the data are 6 μ and 9 μ respectively, then median is

A. 8 μ

B. 7 μ

C. 6 μ

D. 5 μ

Answer : Option A
Explaination / Solution:

median=mode+2mean3=6μ+2(9μ)3=24μ3=8μ

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

Q4.

R is a relation from { 11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation $R^{- 1}$ =

A. {(8,11),(10,13),(12,15)}

B. {(8, 11), (10, 13)}

C. {(8, 11), (9, 12), (10, 13)}

D. {(11, 8), (13, 10)}

Answer : Option B
Explaination / Solution:

R is a relation from { 11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation

R^{- 1}

is given by x = y + 3,from {8, 10, 12} to { 11, 12, 13}

\Rightarrow

relation = {(8,11),(10,13)}.

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

Q5.

is equal to

A. 0

B. a positive real number

C. None of these

D. a negative real number

Answer : Option A
Explaination / Solution:

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

Q6. The coordinates of the foot of perpendicular from ( 0 , 0 ) upon the line x + y = 2 are

A. ( 1, 2 )

B. ( - 1 , 2 )

C. ( 1, 1 )

D. None of these

Answer : Option C
Explaination / Solution:

The equation of the line perpendicular to the given line is x - y + k = 0

Since it passes through the origin,

0 - 0 + k = 0

Therefore k = 0

Hence the equation of the line is x - y = 0

On solving these two equations we get x = 1 and y = 1

The point of intersection of these two lines is (1,1)

Hence the coordinates of the foot of the perpendicular is (1,1)

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

Q7. Consider a function f(x) = 1 - |x| on -1 ≤ x ≤ 1. The value of x at which the function attains a maximum, and the maximum value of function are:

A. 0,-1

B. -1,0

C. 0, 1

D. -1, 2

Answer : Option C
Explaination / Solution: