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. If (x-a)2 + (y-b)2 = c2 represents a circle, then

A. a = b = 0

B. a = 0

C. b = 0

D. c ≠ 0

Answer : Option D
Explaination / Solution:

(x-a)2 + (y-b)2 = c2 here (a,b) is center and c is the radius

and radius cannot be zero because if radius is zero it will become a point or degenerate circle so c $\neq$ 0.

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

Q2. The number of arrangements of n different things taken r at a time which exclude a particular thing is

A. P(n.r)

B. None of these

C. P(n-1,r)

D. P(n-1,r-1)

Answer : Option C
Explaination / Solution:

The number of arrangements of n different things taken r at a time which exclude a particular thing is n-1Pr = P(n-1,r)

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

Q3. Find the order and degree of

y''' + y^{2} + e^{y'} = 0

A. 3, degree undefined

B. 4, degree undefined

C. 1, degree undefined

D. 2, degree undefined

Answer : Option A
Explaination / Solution:

Order = 3 ,Since the highest order derivative is

y'''

but degree cannot be defined ,because the deriative term y’ is present in exponential form.

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

Q4. Angle between skew lines is

A. the angle between two intersecting lines drawn from any point parallel to each of the skew lines

B. the angle between two intersecting lines drawn from any point perpendicular to each of the skew lines

C. the angle between two non intersecting lines drawn from any point parallel to each of the skew lines

D. the angle between two non intersecting lines drawn from any point anti – parallel to each of the skew lines

Answer : Option A
Explaination / Solution:

Angle between skew lines is the angle between two intersecting lines drawn from any point parallel to each of the skew lines .

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

Q5. In a triangle ABC,

\tan \frac{A + B}{2} \cot \frac{A - B}{2}

is equal to

A. none of these.

B. a−ba+b

C. a+ba-b

D. a−bc

Answer : Option C
Explaination / Solution:

$A + B + C = 180^{\circ} \Rightarrow \frac{C}{2} = 90^{\circ} - (\frac{A + B}{2})$

$∴ t a n (\frac{A - B}{2}) = \frac{a - b}{a + b} . c o t [90^{\circ} - (\frac{A + B}{2})] \Rightarrow t a n (\frac{A - B}{2}) = \frac{a - b}{a + b} . t a n (\frac{A + B}{2}) \Rightarrow t a n (\frac{A + B}{2}) . c o t (\frac{A - B}{2}) = \frac{a + b}{a - b}$

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

Q6. The area bounded by the curve y =

x^{3}

, the x – axis and two ordinates x = 1 and x = 2 is

A. 17/4 sq. units

B. 15/4 sq. units

C. 15/2 sq. units

D. 17/2 sq. units

Answer : Option B
Explaination / Solution:

\int_{1}^{2} | y | d x = \int_{1}^{2} {{| x |}^{3} d x = \int_{1}^{2} x^{3} d x = [\frac{x^{4}}{4}]}_{1}^{2} = [\frac{16}{4} - \frac{1}{4}] = \frac{15}{4}

sq.units.

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

Q7. If the direction cosines of a straight line are < k , k , k > , then what will be the value of k

A. k = 1

B. k=13√ork=−13√

C. k > 0

D. 0 < k < 1

Answer : Option B
Explaination / Solution:

We know that if l , m , n are direction cosines of a lines then l2+m2 +n2= 1

so, k2 + k2 +k2 = 1

3 k2 = 1

k2 = 1/3

taking squareroot on both sides , we have $k = \frac{1}{\sqrt{3}} o r k = - \frac{1}{\sqrt{3}}$

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

Q8. A square matrix

A = {[a_{i j}]}_{n \times n}

is called a diagonal matrix if

a_{i j} = 0

for

A. I = j

B. I ≠ j

C. I < j

D. I > j

Answer : Option B
Explaination / Solution:

In a diagonal matrix all elements except diagonal elements are zero.i.e.

a_{i j} = 0, i f f i \neq j .

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

Q9.

The function f (x) = $x^{2}$ , for all real x, is

A. neither decreasing nor increasing

B. Increasing

C. Decreasing

D. none of these

Answer : Option A
Explaination / Solution:

f(x) = x2

\Rightarrow

f'(x) = 2x for all x in R.
Since f ‘(x) = 2x > 0 for x >0, and f ‘ (x) = 2x< 0 for x < 0 ,therefore on R , f is neither increasing nor decreasing . Infact , f is strict increasing on [ 0 ,