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

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

Q1. The equation

a x^{2} + b y^{2} + 2 h x y + 2 g x + 2 f y + c = 0

represents a circle only if

A. a = b

\neq

0, h = 0,

g^{2} + f^{2} - c > 0

B. a = b , h = 0

C. a = b ≠ 0, h = 0

D. a = b

\neq

0, h = 0,

g^{2} + f^{2} - c > 0

Answer : Option D
Explaination / Solution:

recalling the general form of a circle as

(i) It is a quadratic equation in both x and y.

(ii) Coefficient of $x^{2}$ = Coefficient of $y^{2}$ .

(iii) There is no term containing xy i.e., the coefficient of xy is zero.

(iv) radius is $\frac{1}{a} \sqrt{g^{2} + f^{2} - c a}$

To satisfy (i) and (ii) condition we have $a = b \neq 0$

To satisfy (iii) condition we have $h = 0$

To satisfy (iv) and as we cant have neagtive sign in root so $g^{2} + f^{2} - a c > 0$

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

Q2. Determine order and degree (if defined) of

\frac{d^{2} y}{d x^{2}} = c o s 3 x + s i n 3 x

A. 3,1

B. 2,1

C. 1,2

D. 1,1

Answer : Option B
Explaination / Solution:

Order = 2 , degree = 1 .Since the highest derivative term is

\frac{d^{2} y}{d x^{2}}

and its power is 1

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

Q3. The sum of all the numbers which can be formed by using the digits 1 , 3 , 5 , 7 ,9 all at a time and which have no digit repeated is

A. 666660

B. 33333000

C. 600

D. 266664

Answer : Option A
Explaination / Solution:

First we will fix any one digit in a fixed position .Then we have the remaining 4 digits can be arranged in 4! different ways.

Which means each of the five digits can appear in each of the five places in 4! times.

Hence the sum of the digits in each position is $4! (1 + 3 + 5 + 7 + 9) = 25 \times 4!$

Now to find the sum of these numbers formed we have to consider the place values for these digits

So the sum of all the numbers which can be formed by using the digits 1 , 3 , 5 , 7 ,9= $25 \times 4! \times (1 + 10 + 100 + 1000 + 10000) = 25 \times 4! \times 11111 = 666660$

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

Q4. Vector equation of a line that passes through two points whose position vectors are

Answer : Option D
Explaination / Solution:

Vector equation of a line that passes through two points whose position vectors are

is given by:

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

Q5.

$b c \cos^{2} \frac{A}{2} + c a \cos^{2} \frac{B}{2} + a b \cos^{2} \frac{C}{2} i s$ $b c \cos^{2} \frac{A}{2} + c a \cos^{2} \frac{B}{2} + a b \cos^{2} \frac{C}{2} i s$ equal to

A. (s−c)2

B. (s−b)2

C. (s−a)2

D. s²

Answer : Option D
Explaination / Solution:

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

Q6. The area bounded by the curve

| x | + y = 1

and the x –axis is

A. 4

B. 1

C. 2

D. 1/2

Answer : Option B
Explaination / Solution:

The given curve consists of two straight lines x + y = 1 ( x ≥ 0 )and -x + y = 1 ( x < 0 )
Required area :
=

2 \int_{0}^{1} y d x

2 \int_{0}^{1} (1 - | x |) d x

2 \int_{0}^{1} (1 - x) d x

2 {[x - \frac{x^{2}}{2}]}_{0}^{1}

= 1sq.unit

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Introduction to Three Dimensional Geometry Prepare / Learn

Q7.

The graph of the equation

x^{2} + y^{2} = 0

in the three dimensional space is

A. Y - axis

B. Z - axis

C. XY – plane

D. X - axis

Answer : Option B
Explaination / Solution:
No Explaination.

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

Q8. If

[\begin{matrix} a & b \\ c & - a \end{matrix}]

is a square root of the

2 \times 2

identity matrix, then a, b, c satisfy the relation

A. 1+a2+bc=0

B. a2+bc=1

C. 1+a2−bc=0

D. 1−a2+bc=0

Answer : Option B
Explaination / Solution:

⎡⎣⎢⎢⎢acb−a⎤⎦⎥⎥⎥⎡⎣⎢⎢⎢acb−a⎤⎦⎥⎥⎥=⎡⎣⎢⎢⎢1001⎤⎦⎥⎥⎥⇒a2+bc=1

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

Q9.

At (0, 0) the curve

y^{2} = x^{3} + x^{2}

y^{2} = x^{3} + x^{2}

A. makes an angle of

60^{o}

with OX

B. none of these.

C. touches X – axis

D. bisects the angle between the axes

Answer : Option D
Explaination / Solution:

{(\frac{d y}{d x})}_{(0, 0)} = 1

and hence the tangent to the curve at ( 0 , 0 ) makes an angle of

\frac{π}{4}

with +ve X-axis.

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Complex Numbers and Quadratic Equations Prepare / Learn

Q10. Distance of the representative of the number 1 +i from the origin ( in Argand’s diagram ) is

A. 2

B. √2

C. 1

D. None of these

Answer : Option B
Explaination / Solution:

Let P(x,y) represent the complex number Z=x+iy in the complex plane(Argand plane) and let O(0,0) be the origin

Then we have OP= $\sqrt{x^{2} + y^{2}}$

Here Z=1+i so that P(x,y)=P(1,1)

Hence OP= $\sqrt{1 + 1} = \sqrt{2}$

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