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. If a line is drawn through the origin and parallel to the line x – 2y + 5 = 0 , its equation is

A. x – 2y – 5 = 0

B. none of these

C. 2x + y = 0

D. x = 2y

Answer : Option D
Explaination / Solution:

If the line is parallel to the given line x-2y + 5 =0,

then the required line will have same slope

Hence the equaion of the given line is x-2y+k=0

since it passes through the origin,

0+0+k=0

Therefore k=0

Hence the equation of the required line is x-2y=0 or x=2y

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

Q2. ∼(p∨q)∨(∼p∧q) is logically equivalent to

A. ∼p

B. p

C. q

D. ∼q

Answer : Option A
Explaination / Solution:

$(\sim p \land \sim q) \lor (\sim p \land q)$

$\sim p \land (\sim q \lor q)$ distributive law

$\sim p \land T$ since $\sim q \lor q \equiv T$

$\sim p$ since $\sim p \land T \equiv\sim p$

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

Q3.

\int_{0}^{2} \sqrt{\frac{2 + x}{2 - x}} d x

is equal to

A. π+32

B. π+1

C. π+2

D. π2+1

Answer : Option C
Explaination / Solution:

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

Q4. Negative of a Vector

\vec{a}

is a

A. A vector whose magnitude is the same as that

\vec{a}

of but direction is 120° to that of

\vec{a}

B. A scalar whose magnitude is the same as that

\vec{a}

C. A vector whose magnitude is the same as that

\vec{a}

of but direction is opposite to that of

\vec{a}

D. A vector whose magnitude is the same as that

\vec{a}

of but direction is perpendicular to that of

\vec{a}

Answer : Option C
Explaination / Solution:

egative of

\vec{a}

is equal to -

\vec{a}

, i.e. A vector whose magnitude is the same as that of

\vec{a}

,but direction is opposite to that of

\vec{a}

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

Q5. If P(A) =

\frac{6}{11}

, P(B) =

\frac{5}{11}

and P(A ∪ B) =

\frac{7}{11} .

find P(A∩B)

A. 4/11

B. 4/13

C. 5/11

D. 5/17

Answer : Option A
Explaination / Solution:

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

Q6. The period of the function f(x)=cos 4x + tan 3x is

A. none of these

B. π2

C. π3

D. π

Answer : Option D
Explaination / Solution:

f(π)=(cos4π+tan3π)gives the same value as f (0) .Therefore,the period of the function is π

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

Q7. The inequality

n! > 2^{n - 1}

is true

A. for no n ∈ N

B. for all n > 1

C. for all n> 2 ,n∈N

D. for all n ∈ N

Answer : Option C
Explaination / Solution:

Since when n = 1 , we get the inequality as 1>1, which is not true. also for n = 2 , we get 2>2, which is false. Hence the given statement is true for n>2

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

Q8. The function f (x) = 1 + | sin x l is

A. differentiable nowhere

B. differentiable everywhere.

C. continuous nowhere

D. continuous everywhere

Answer : Option D
Explaination / Solution:

f (x) = 1 + | s i n x |

is not derivable at those x for which

x f o r w h i c h s i n x = 0, h o w e v e r, 1 + | s i n x |

is continuous everywhere (being the sum of two continuous functions)

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

Q9.

$x^{2} + y^{2} - 6 x + 8 y - 11 = 0$ is a circle. The points (0, 0) and ( 1, 8) lie

A. one on the circle and the other outside

B. one outside the circle and one inside

C. both inside the circle

D. both outside the circle

Answer : Option B
Explaination / Solution:

so the center is (3,-4) and radius is 6 units.

distance between center and (0,0) is

units which is less than the radius so it lies inside the circle

whereas the distance between center and (1,8) is

which is greater than the radius so it lies outside the circle

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

Q10. What is the order of differential equation :

\frac{d^{3} y}{d x^{3}} + \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{2} = e^{x}

A. 2

B. 1

C. 0

D. 3

Answer : Option D
Explaination / Solution:

Order = 3.Since the third derivative is the highest derivative present in the equation. i.e.

\frac{d^{3} y}{d x^{3}}

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