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

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

Q1. If a line has the direction ratios – 18, 12, – 4, then what are its direction cosines ?

A. −911,611,-211

B. −911,611,211

C. −711,611,−311

D. 911,611,−211

Answer : Option A
Explaination / Solution:

If a line has the direction ratios – 18, 12, – 4, then its direction cosines are given by:

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

Q2. In any ΔABC,ΔABC, the expression (a + b + c) (a + b – c) (b + c – a) (c + a – b) is equal to

A. 3Δ2

B. 4Δ

C. 4Δ2

D. 16Δ

Answer : Option C
Explaination / Solution:

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

Q3. The number of significant numbers which can be formed by using any number of the digits 0, 1, 2, 3, 4 but using each not more than once in each number is

A. 356

B. 410

C. 260

D. 96

Answer : Option C
Explaination / Solution:

Case 1: for 5 digit numbers Ten Tens thousands place can be occupied in 4 ways since 0 cannot be suitable. For ones place remaining 4 numbers ( since repetition is not allowed ) can be occupied in 4 ways : and the tens place in 3 ways and hundreds place in 2 ways and the thousands place in 1 way. Hence the total number of ways is 4x1x4x2x3= 96.

t th	th	h	t	o
4	1	2	3	4

Case 2: for 4 digit numbers thousands place can be occupied in 4 ways since 0 cannot be suitable. For ones place remaining 4 numbers ( since repetition is not allowed ) can be occupied in 4 ways : and the tens place in 3 ways and hundreds place in 2 ways . Hence the total number of ways is 4x4x2x3= 96.

th	h	t	o
4	2	3	4

Case 3: for 3digit numbers hundreds place can be occupied in 4 ways since 0 cannot be suitable. For ones place remaining 4 numbers ( since repetition is not allowed ) can be occupied in 4 ways : and the tens place in 3 ways Hence the total number of ways is 4x4x3= 48

Case 4: for 2 digit numbers Tens place can be occupied in 4 ways since 0 cannot be suitable. For ones place remaining 4 numbers ( since repetition is not allowed ) can be occupied. Hence the total number of ways is 4x4=16.

Case 5: For single digit in 4 ways .

Hence 96 + 96 + 48+ 16+4 = 260

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

Q4. A point ( x , y , z ) moves parallel to X- axis . Which of the three variables x , y , z remain fixed ?

A. z and x

B. x and y

C. y and z

D. x

Answer : Option C
Explaination / Solution:

A point ( x , y , z ) moves parallel to X- axis then value of x will vary and remaining will be fixed

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

Q5. A square matrix

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

is called an upper triangular if

a_{i j} = 0

for

A. i is greater than j

B. i = j

C. none of these.

D. i is less than j

Answer : Option A
Explaination / Solution:

Upper Triangular matrix is given by :

[\begin{matrix} a_{11} & a_{12} & a_{13} \\ 0 & a_{22} & a_{23} \\ 0 & 0 & a_{33} \end{matrix}]

Here,

a_{i j} = 0

if i is greater than j.and

a_{i j} \neq 0

, if I is less than j.

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

Q6. If If

ω

is a non real cube root of unity and

{(1 + ω)}^{9} = a + b ω; a, b \in R,

then a and b are respectively the numbers :

A. 0 , 1

B. -1 , 0

C. 0 , -1

D. 1 , 0

Answer : Option B
Explaination / Solution:

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

Q7. If A and B are not disjoint Set , then n (A∪B) is equal to

A. n ( A ) + n ( B ) – n (A∩B)

B. n ( A ) + n ( B ) + n (A∩B)

C. n ( A )

D. none of these.

Answer : Option A
Explaination / Solution:

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

Q8. The number of terms in the expansion of

[(x + 4 y)^{3} (x - 4 y)^{3}]^{2}

A. 32

B. 8

C. 6

D. 7

Answer : Option D
Explaination / Solution:

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

Q9. The area bounded by the parabola y =

x^{2}

+ 1 and the straight line x + y = 3 is given by

A. 45/7

B. 9/2

C. 25/4

D. none of these.

Answer : Option B
Explaination / Solution:

The two curves parabola and the line meet where,
3 - x =

x^{2} + 1

\Rightarrow x^{2} + x - 2

= 0

\Rightarrow x = - 2, 1.

Required area ;

\int_{- 2}^{1} {3 - x - (x^{2} + 1)} d x

{[2 x - \frac{x^{2}}{2} - \frac{x^{3}}{3}]}_{- 2}^{1}

\frac{9}{2}

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

Q10. Given that x is an integer, find the values of x which satisfy both 2x + 3 > 7 and x + 4 < 10

A. 4

B. 4 , 5

C. 3 , 4 , 5

D. 3

Answer : Option C
Explaination / Solution:

Since x is an integer the solution set

Since x is an integer the solution set =

Hence the integer values which satisfy both the inequalities are

Mathematics - Online Test

Mathematics | Online Objective Test | Start Test

Prepare Before Start Test | Learn

UPSC Civil services Entrance exams | Online Test

GATE Exam | Online Test

Under Graduate Entrance Exams | Online Test

Problem Solving and Reasoning | Online Test

CAT Entrance Exams | Online Test

CLAT LAW Entrance exams | Online Test

Banking Entrance exams | Online Test

UGC NET Entrance exams | Online Test

TANCET Anna University | Online Test

TN State Board | Online Test