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

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

Q1. The lines ix + my + n = 0 , mx + ny + l = 0 and nx + ly +m = 0 are concurrent if

A. l – m – n = 0

B. l + m + n = 0

C. I – m + n = 0

D. l + m – n = 0

Answer : Option B
Explaination / Solution:

The required condition for concurrency is a3(b1c2 - b2c1) + b3(c1a2 - c2a1) + c3(a1b2 - a2b1) = 0

Here a1 = l, a2 =m, a3 = n and b1 = m, b2 = n, b3 = l and c1 = n, c2 = l and c3 = m

Substituting the values we get

n(ml - n2) + l(nm - l2) +m(ln - m2) = 0

This implies l3 + m3 + n3 - 3lmn = 0

That is (l + m+ n)(l2 + m2 + n2 -lm -mn - nl) = 0

This implies l + m + n = 0

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

Q2. The contrapositive of the statement “ if

2^{2} = 5,

then I get first class” is

A. If I do not get a first class , then

2^{2} = 5,

B. none of these

C. If I do not get a first class , then

2^{2} \neq 5

D. If I get a first class , then

2^{2} = 5,

Answer : Option C
Explaination / Solution:

p: $2^{2} = 5$

q:I get first class

the contrapositive of $p \to q i s \sim q \to\sim p$ . hence the answer is If I do not get a first class , then $2^{2} \neq 5$

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

Q3.

\int \frac{f^{'} (x)}{\sqrt{f (x)}} d x

is equal to

A. f(x) + C

B. log ( f(x) ) + C

\frac{1}{2} \log | f (x) |

+ C

D. 2√f(x) + C

Answer : Option D
Explaination / Solution:

$\int \frac{f^{'} (x)}{f (x)} d x = \int {(f (x))}^{- 1 / 2} f^{'} (x) d x = \frac{{(f (x))}^{1 / 2}}{1 / 2} + C = 2 \sqrt{f (x)} + C$

$s u b s t i t u e f (x) = t^{2} t h e n f^{'} (x) d x = 2 t d t \Rightarrow \int 2 d t = 2 t + C = 2 \sqrt{f (x)} + C$

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

Q4. Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

A. −3√2i^−12j^

B. 3√2i^−12j^

C. −3√2i^+12j^

D. 3√2i^+12j^

Answer : Option D
Explaination / Solution:

Let

\vec{r} = x \hat{i} + y \hat{j}

be a unit vector in XY plane,making angle 300 with positive X axis,so we have the vector as

\vec{r} = \cos 30^{0} \hat{i} + \sin 30^{0} \hat{j}

x = \frac{\sqrt{3}}{2}; y = \frac{1}{2}, (∵ | \vec{r} | = 1) .

∴ \vec{r} = \frac{\sqrt{3}}{2} \hat{i} + \frac{1}{2} \hat{j}

is the required vector.

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

Q5.

\cos^{- 1} (\cos x) = x

is satisfied by ,

A. x∈[−1,1],

B. x∈[0,1]

C. x∈[0,π]

D. none of these.

Answer : Option C
Explaination / Solution:

\cos^{- 1} (\cos x) = x

if ,

0 ⩽ x ⩽ π

i.e. if ,

x \in [0, π]

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

Q6. Let the eigenvalues of a 2 x 2 matrix A be 1, -2 with eigenvectors x₁ and x₂ respectively. Then the eigenvalues and eigenvectors of the matrix A²− 3A + 4I would, respectively, be

Answer : Option A
Explaination / Solution:

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

Q7. The line 3x – 4y = 0

A. is a normal to the circle

x^{2} + y^{2} = 25

B. does not meet the circle

x^{2} + y^{2} = 25

C. does not pass through the origin

D. is a tangent to the circle

x^{2} + y^{2} = 25

Answer : Option A
Explaination / Solution:

$x^{2} + y^{2} = 25$

After completing the square,we get

$(x - 0)^{2} + (y - 0)^{2} = 5^{2}$

so center is (0,0) and radius is 5 units.

As the normal should pass through the centre of the circle, center should satisfy the equation of normal

so 3x – 4y = 0 is the equation of normal as (0,0) satisfy this equation.

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

Q8.

\frac{d}{d x} (\cos^{- 1} x) = - \frac{1}{\sqrt{1 - x^{2}}}

where

A. −1

B. −1⩽x⩽1

C. −1

D. −1⩽x<1

Answer : Option A
Explaination / Solution:

\frac{d}{d x} (\cos^{- 1} x) = - \frac{1}{\sqrt{1 - x^{2}}}

is valid only if ,

1 - x^{2} > 0,

i.e. if

x^{2} < 1 i . e . i f | x | < 1

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

Q9. The solution of tan 2 θ tan θ = 1 is

A. (2n±1)π6

B. (4n+1)π6

C. (2n+1)π3

D. (2n+1)π6

Answer : Option D
Explaination / Solution:

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Principle of Mathematical Induction Prepare / Learn

Q10. The sum of the terms in the nth bracket of the series 1 + (2+3+4) + (5+6+7+8+9) ….is

A. (n+1)3+8n2

B. (n+1)(n+2)6n

C. None of these

D. (n -1)3+n3

Answer : Option D
Explaination / Solution:

replace n = 1 we get the first term and n = 2 we get the sum of first two terms....

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