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. The equations

x = a t^{2}, y = 4 a t; t \in R

represent

A. a hyperbola

B. a parabola

C. an ellipse

D. a circle

Answer : Option B
Explaination / Solution:

$y = 4 a t$

Squaring both sides,we get

$y^{2} = 16 a^{2} t^{2}$

Putting the value of at2 i.e. $a t^{2} = \frac{y^{2}}{16 a}$ in x = at2 we get,

$16 a x = y^{2}$

or $y^{2} = 4 (4 a) x$

which is nothing but equation of parabola.

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

Q2. If sin x - cos x =

\sqrt{2}

, then x = ( n is any integer)

A. ( 2 n + 1)

π

B. 2 n π

2 n π - \frac{π}{4}

D. 2nπ±π−π4

Answer : Option D
Explaination / Solution:

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

Q3. 23n-1 is divisible by

A. 3

B. 7

C. 6

D. None of these

Answer : Option B
Explaination / Solution:

If n = 1 we get 7. n = 2 we get 63 which is divisible by 7........

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

Q4. If

E_{1}

and

E_{2}

are two independent events, then P

(E_{1} \cap E_{2})

is equal to

A. P(E1)+P(E2)+P(E1+∪E2)

B. P(E1)P(E2)

C. None of these

D. P(E1) +P (E2)

Answer : Option B
Explaination / Solution:
No Explaination.

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

Q5. The locus of a first degree equation in x, y, z is a

A. None of these

B. sphere

C. plane

D. straight line

Answer : Option C
Explaination / Solution:

first degree equation in x, y, z can be written in the form Ax+By+Cz+d=0 Which represent a plane Where A,B and C are the direction ratios of normal to the plane

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

Q6. The system of equations, x + y + z = 6, x + 2 y + 3 z = 14, x + 3 y + 5z = 20 has

A. no solution.

B. only finitely many solutions

C. infinitely many solutions

D. a unique solution

Answer : Option A
Explaination / Solution:

The given system of equations does not has a solution if :

| \begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 5 \end{matrix} | = 0 \Rightarrow 1 (10 - 9) - 1 (5 - 3) + 1 (3 - 2) = 0 \Rightarrow 1 - 2 + 1 = 0

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

Q7. The total number of numbers from 1000 to 9999 (both inclusive) that do not have 4 different digits

A. 4536

B. None of these

C. 9000

D. 4464

Answer : Option D
Explaination / Solution:

First we will find the number of four digit numbers that can be formed using the digits 0,1,2,3,4,5,6,7,8,9 with repetition .

The first place can be filled by any of the 9 digits other than 0, and the second, third and the fourth places each can be filled by any of the ten digits

Hence the total number of ways of forming a four digit number = $9 \times 10 \times 10 \times 10 = 9000$

Now we will find the number of four digit numbers in which nall the digits are distinct

The first place can be filled by any of the 9 digits other than 0, and the second, can be filled by any of the remaining 9 digits since repetition is not possible

Similarly third and the fourth places each can be filled by 8 and 7 digits respectively

Hence the total number of ways of forming a four digit number with distinct digits b= $9 \times 9 \times 8 \times 7 = 4536$

The total number of numbers from 1000 to 9999 (both inclusive) that do not have 4 different digits= $9000 - 4536 = 4464$

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

Q8.

Derivative of $\sin^{3} x w . r . t . \cos^{3} x i s$

\sin^{3} x w . r . t . \cos^{3} x i s

A. – tan x

B. tan x

C. cot x.

D. tan3x

Answer : Option A
Explaination / Solution:

L e t y = s i n^{3} x a n d z = c o s^{3} x,

then ,

\frac{d y}{d z} = \frac{\frac{d y}{d x}}{\frac{d z}{d x}} = \frac{3 \sin^{2} x \cos x}{3 \cos^{2} x (- \sin x)} = - \tan x

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

Q9. The expression ((x + Y) - |x - y|)/2 is equal to

A. the maximum of x and y

B. the minimum of x and y

C. 1

D. none of the above

Answer : Option B
Explaination / Solution:

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

Q10. Equation of a plane perpendicular to a given line with direction ratios A, B, C and passing through a given point (x1, y1, z1) is

A. A (x + x1) + B (y – y1) + C (z – z1) = 0

B. A (x - x1) + B (y – y1) + C (z – z1) = 0

C. A (x – x1) + B (y – y1) + C (z – z1) = 1

D. A (x – x1) + B (y + y1) + C (z – z1) = 1

Answer : Option B
Explaination / Solution:

In Cartesian co – ordinate system Equation of a plane perpendicular to a given line with direction ratios A, B, C and passing through a given point (x1, y1, z1) is given by : A (x – x1) + B (y – y1) + C (z – z1) = 0 .

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