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

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

Q1. Which of the following is not possible ?

\cos θ = \frac{1 + t^{2}}{1 - t^{2}}, t \neq 0

\cos θ = \frac{1 + t^{2}}{1 - t^{2}}, t \neq 0

B. secθ=52

C. tanθ=100

D. sinθ=57

Answer : Option A
Explaination / Solution:

he value of $\cos θ$ lies between - 1 and 1

But when t=2 the value of $\cos θ = \frac{1 + t^{2}}{1 - t^{2}}, t \neq 0$ is $\frac{5}{- 3}$ which is more than 1 , so it is not possible.

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

Q2.

\frac{d}{d x} (\tan^{- 1} (\sec x + \tan x)

is equal to

A. none of these.

B. -1/2

D. 1/2

Answer : Option D
Explaination / Solution:

\frac{d}{d x} (\tan^{- 1} (\sec x + \tan x))

= \frac{\sec x \tan x + \sec^{2} x}{1 + {(\sec x + \tan x)}^{2}} = \frac{\sec x (\sec x + \tan x)}{2 \sec x (\sec x + \tan x)} = \frac{1}{2}

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

Q3. A 3 × 3 matrix P is such that, P³ = P. Then the eigenvalues of P are

A. 1, 1, −1

B. 1, 0.5 + j0.866, 0.5 − j0.866

C. 1, −0.5 + j0.866, −0.5 − j0.866

D. 0, 1, −1

Answer : Option D
Explaination / Solution:

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

Q4.

\frac{3}{4} + \frac{15}{16} + \frac{63}{64} + . . . . . . . . . . .

to n terms is equal to

A. n+4n3−13

B. n−4n3−13

C. n+4−n3+13

D. n+4−n3-13

Answer : Option D
Explaination / Solution:

When n = 1 we get 3/4, and the subsequent terms when n is replaced by 2,3,4...

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

Q5. A fair coin is tossed a fixed number of times. If the probability of getting 4 heads is equal to the probability of getting 7 heads, then the probability of getting 2 heads is

A. 3/ 1024

B. 3/ 4096

C. 1/ 1024

D. 55/ 2048

Answer : Option D
Explaination / Solution:
No Explaination.

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

Q6. The foot of perpendicular from (α,β,γ) on Y axis is

A. ( 0 , α , 0 )

B. ( 0 , 0 , 0 )

C. ( 0 , β , 0 )

D. None of these

Answer : Option C
Explaination / Solution:

Let P( $α, β, γ$ ) be the point and Q (0,b,0) be any point on Y axis.

drs of PQ=( $α, β - b, γ)$

drs of y axis (0,b,0)

Since PQ perpendicular to y axis.hence a1a2+b1b2+c1c2=0

hence the foot of perpendicular will be $(0, β, 0)$

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

Q7.

A. diagonal matrix

B. none of these.

C. symmetric matrix

D. skew-symmetric matrix

Answer : Option D
Explaination / Solution:

The diagonal elements of a skew – symmetric matrix is always zero and the elements aij= - aji

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

Q8. The number of all odd divisors of 3600 is

A. 45

B. 9

C. 18

D. None of these

Answer : Option B
Explaination / Solution:

$w e h a v e 3600 = 2^{4} {. 3^{2} .5}^{2}$

To get the odd factors we will get rid of 2's

We will make the selection from only 3's and 5's

Number of ways 3 can be selected from a lot of two 3's= 3 ways ( one 3,two 3's or three 3's)

Number of ways 5 can be selected from a lot of two 5's= 3 ways ( one 5,two 5's or three 5's)

Therefore the number of odd factors is 3600= 3 X 3 =9

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

Q9. In vector form, if

θ

is the angle between the two planes

then

Answer : Option B
Explaination / Solution:

In vector form, if

θ

is the angle between the two planes

then, cosine of the angle between these two lines is given by :

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

Q10.

Forming a differential equation representing the given family of curves by eliminating arbitrary constants a and b from $y^{2} = a (b^{2} - x^{2})$ yields the differential equation

A. yy′′+y′2+1=0

B. yy′′−y′2+1=0

C. yy′′+y′2=0

D. yy′′+y′2−1=0

Answer : Option A
Explaination / Solution:

2yy′=−2xyy′=−xyy′′+y′2+1=0

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