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

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

Q1. For the curve

x = t^{2} - 1, y = t^{2} - t

tangent is parallel to X – axis where

A. t=13√

B. t=−13√

C. t = 0

D. t=1/2

Answer : Option D
Explaination / Solution:

dydx=0⇒dydt=0⇒2t−1=0⇒t=12.

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

Q2. The area bounded by the curves y =

| x |

- 1 and y = -

| x |

+ 1 is

A. 2

B. 4

C. 2√2

D. 1

Answer : Option A
Explaination / Solution:

The graph of modulus function is V-shaped graph. Therefore , from graph , the area is = √2 × √2 =2.

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

Q3. Given that x is an integer , find the values of x which satisfy the simultaneous linear inequalities 2 + x < 6 and 2−3x < − 1.

A. 1 , 2, 3, 4.

B. 1 , 2 , 3

C. 2 , 3, 4,

D. 2 , 3

Answer : Option D
Explaination / Solution:

We have $2 + x < 6$

$\Rightarrow 2 + x - 2 < 6 - 2$

$\Rightarrow x < 4$

Now $2 - 3 x < - 1 \Rightarrow 2 - 3 x - 2 < - 1 - 2 \Rightarrow - 3 x < - 3 \Rightarrow \frac{- 3 x}{- 3} > \frac{- 3}{- 3} \Rightarrow x > 1$

Hence the solution of the given system of equations is given by $1 < x < 4, x ϵ Z \Rightarrow x = 2, 3$

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

Q4. If a is a real number, then

\underset{x \to a}{L t} \frac{| x - a |}{x - a}

A. is equal to 0

B. is equal to – 1

C. does not exist

D. is equal to 1

Answer : Option C
Explaination / Solution:

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

Q5. Minimize Z = 3x + 5y such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.

A. Minimum Z = 7 at

(\frac{3}{2}, \frac{1}{2})

B. Minimum Z = 10 at

(\frac{3}{2}, \frac{1}{2})

C. Minimum Z = 8 at

(\frac{3}{2}, \frac{1}{2})

D. Minimum Z = 9 at

(\frac{3}{2}, \frac{1}{2})

110 V 60 Hz

Answer : Option A
Explaination / Solution:

Objective function is Z = 3x + 5 y ……………………(1).
The given constraints are : x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0 .

The corner points obtained by drawing the lines x+3y=3 and x+y=2 are (0,0), (3,0),(0,2) and (3/2,1/2)

Corner points	Z = 3x + 5 y
A(3 , 0 )	9
B ( 0 ,2 )	10
C( 3/2 , 1/2 )	7………………..( Min. )

Here Z = 7 is minimum at ( 3/2 , ½ ) .

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

Q6. The values of x for which the solutions of the equation cos θ=x,θ≥0 form an A.P. are

A. None of these

B. - 1 and 1

C. 1,0 and – 1

D. 0 and 1

Answer : Option C
Explaination / Solution:

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

Q7. Which of the following is not a measure of central tendency :

A. median

B. mode

C. range

D. mean

Answer : Option C
Explaination / Solution:

meausre of central tendencies give the middle most or average value whereas range gives the difference between highest and lowest value.

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

Q8. To evaluate the double integral