Mathematics | CSE, IT Computer Science Engineering and Information Technology | TANCET Anna University Online Objective Test

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Conic Sections Prepare / Learn

Q1. The eccentricity of

3 x^{2} + 4 y^{2} = 24

A. 14

B. 12

C. 74

D. 74−−√

Answer : Option B
Explaination / Solution:

Given equation is 3x2 + 4y2 = 24

dividing throught by 24 we get,

$\frac{x^{2}}{8}$ + $\frac{y^{2}}{6}$ = 1

This implies a2 = 8 and b2 = 6

e = $\frac{\sqrt{a^{2} - b^{2}}}{a}$ = $\frac{1}{2}$

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Differential Equations Prepare / Learn

Q2. The number of arbitrary constants in the general solution of a differential equation of fourth order are:

A. 2

B. 3

C. 4

D. 1

Answer : Option C
Explaination / Solution:

4 , because the no. of arbitrary constants is equal to order of the differential equation.

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Three Dimensional Geometry Prepare / Learn

Q3.

If a line makes angles

90^{\circ}, 135^{\circ}, 45^{\circ}

with the x, y and z – axes respectively, find its direction cosines.

A. 0,−12√,15√

B. 1,−13√,12√

C. 0,−12√,13√

D. 0,−12√,12√

Answer : Option D
Explaination / Solution:

If a line makes angles

90^{\circ}, 135^{\circ}, 45^{\circ}

with the x, y and z – axes respectively, then the direction cosines of this line is given by :

\cos 90^{\circ} = 0, \cos 135^{\circ} = \cos (180^{\circ} - 45^{\circ}) = - \cos 45^{\circ} = - \frac{1}{\sqrt{2}}, \cos 45^{\circ} = \frac{1}{\sqrt{2}}

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Trigonometric Functions Prepare / Learn

Q4. ABC is an equilateral triangle of each side a (> 0). The inradius of the triangle is

A. a3

B. a/2√3

C. 3√a3

D. a2

Answer : Option B
Explaination / Solution:

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Permutations and Combinations Prepare / Learn

Q5. In how many ways can a mixed doubles tennis game be arranged from a group of 10 players consisting of 6 men and 4 women

A. 90

B. 120

C. 180

D. 48

Answer : Option C
Explaination / Solution:

A team of 4 players are to be selected.

2 out of 6 men can be done in 6C2 ways. 2 out of 4 women can be done in 4C2ways.

So the number of ways to select 4 players is 6C2x 4C2= 90.

Now we can arrange these people to form mixed doubles.

If M1,M2,W1,W2, are the 4 members selected then one team can be chosen as $(M_{1} {, W}_{1}) o r (M_{1} {, W}_{2})$ in 2 different ways

Therefore the required number of arrangements= 90x2 = 180.

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Introduction to Three Dimensional Geometry Prepare / Learn

Q6. The equation ( x – 1 ) ( x – 2 ) = 0 represents , in three dimensional space , a

A. pair of straight lines

B. sphere

C. pair of parallel planes

D. an empty set

Answer : Option C
Explaination / Solution:

The equation ( x – 1 ) ( x – 2 ) = 0 represents , in three dimensional space , a pair of parallel planes

( x – 1 ) ( x – 2 ) = 0 => ( x – 1 )=0 , ( x – 2 ) = 0

x =1 and x=2

According to the equation ax +by +cz = d and by the formula $\frac{a 1}{a 2} = \frac{b 1}{b 2} = \frac{c 1}{c 2}$ we have both the planes represent pair of parallel planes

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Matrices Prepare / Learn

Q7.

A square matrix A = ${[a_{i j}]}_{n \times n}$ is called a lower triangular matrix if $a_{i j} = 0$ for

A. i is less than j

B. i = j

C. is greater than j

D. none of these.

Answer : Option A
Explaination / Solution:

Lower triangular matrix is given by : $[\begin{matrix} a_{11} & 0 & 0 \\ a_{21} & a_{22} & 0 \\ a_{31} & a_{32} & a_{33} \end{matrix}]$ Here, $a_{i j} = 0$ , if i is less than j.and $a_{i j} \neq 0$ , if i is greater than j.