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

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

Q1.

\int_{0}^{π / 2} \log

(tan x) dx is equal to

A. π2log2

B. −π2log2

C. 1

\int_{0}^{π / 2} \log

(cot x) dx

Answer : Option D
Explaination / Solution:

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

Q2. The unit vector in the direction of a given vector

\vec{a}

is denoted by

A. a...

B. a˙

C. a ¨

Answer : Option D
Explaination / Solution:

\hat{a} = \frac{\vec{a}}{| \vec{a} |}

, is called the unit vector of a given vector

\vec{a}

in the direction of

\vec{a}

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

Q3. If A and B are events such that P(A|B) = P(B|A), then

A. A ⊂ B but A ≠ B

B. P(A) = P(B)

C. A ∩ B = ∅

D. A = B

Answer : Option B
Explaination / Solution:

It is given that :

P (A / B) = P (B / A) \Rightarrow \frac{P (A \cap B)}{P (B)} = \frac{P (B \cap A)}{P (A)} \Rightarrow \frac{1}{P (B)} = \frac{1}{P (A)} \Rightarrow P (A) = P (B)

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

Q4. tan x is periodic with period

A. 3π2

B. π/2

C. π

D. 2π x/3

Answer : Option C
Explaination / Solution:

The values of tanx repeats after an interval of π.

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

Q5. If k be an integer, then

\underset{x \to k}{L t}

(x –[x])

A. is equal to – 1

B. does not exists.

C. 1

D. is equal to 0

Answer : Option C
Explaination / Solution:

\begin{matrix} lim_{x \to k^{-}} (x - [x]) = lim_{x \to k^{-}} x^{-} - lim_{x \to k^{-}} [x] \end{matrix}

= k - (k - 1) = 1 for all

x \in (k - 1, k), [x] = (k - 1)

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

Q6. The greatest positive integer, which divides

(n + 1) (n + 2) (n + 3) . . . . . . . . . . . . . . . . . . (n + r) \forall n \in W

, is

A. ( r + 1 ) !

B. n+r

C. r

D. r !

Answer : Option D
Explaination / Solution:

If n = 0 the given expression becomes 1.2.3.4........r = r! Also when n = 1 one more extra term will be there in the product 2.3.4........

(r + 1)

which is also divisible by r!.

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

Q7. The number of tangents to the circle

x^{2} + y^{2} - 8 x - 6 y + 9 = 0,

which pass through the point ( 3, - 2), is

A. 0

B. 1

C. None of these

D. 2

Answer : Option D
Explaination / Solution:

After completing the square,we get

so center is (4,3) and radius is 4.

Distance between center and given point which is greater than 4.

hence point lies outside the circle .

Since point lies outside of the circle there will be 2 tangents since two tangents can be drawn from external point to a circle.

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

Q8. Determine order and degree (if defined) of y’ + 5y = 0

A. 2, 1

B. 1, 2

C. 1, 1

D. 1,degree undefined

Answer : Option C
Explaination / Solution:

Order = 1 , degree = 1. Since the equation has the highest derivative as y' and its power is 1

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

Q9.

If 12C4 + 12C5 =nC5 ,then n is equal to

A. 11

B. 13

C. None of these

D. 12

Answer : Option B
Explaination / Solution:

We have nCr - 1 + nCr = n+1Cr

Hence 12C4 + 12C5 = 13C5 ................(i)

But given 12C4 + 12C5 =nC5 ................(ii)

Comparing (i) and (ii) we get n = 13