Mathematics | Civil Engineering | TANCET Anna University Online Objective Test

TANCET Anna University Civil Engineering # Mathematics Probability Prepare / Learn

Q1. The conditional probability of an event E, given the occurrence of the event F lies between

A. 0 < P (E|F) ≤ 1

B. 0 < P (E|F) < 1

C. 0 ≤ P (E|F) ≤ 1

D. 0 ≤ P (E|F) < 1

Answer : Option C
Explaination / Solution:

As the probability of any event always lies between 0 and 1. Therefore , 0 ≤ P (E|F) ≤ 1.

TANCET Anna University Civil Engineering # Mathematics Inverse Trigonometric Functions Prepare / Learn

Q2. he value of

\tan 15^{0} + \cot 15^{0}

A. Not defined.

B. 4

23–√

D. 3–√2

Answer : Option B
Explaination / Solution:

TANCET Anna University Civil Engineering # Mathematics Principle of Mathematical Induction Prepare / Learn

Q3. The inequality

2^{n} + 1 < n!

is true for :

A. all n

B. all n > 3

C. None of these

D. all n > 1

Answer : Option B
Explaination / Solution:

When n = 1 we get

3 < 1

, and when n = 2 we get

5 < 2

,. when n = 3

9 < 6

, which are inavlid inequations. Only when n = 4 we get

17 < 24

, which is valid.

TANCET Anna University Civil Engineering # Mathematics Continuity and Differentiability Prepare / Learn

Q4. The function f (x) = [x] is

A. a constant function

B. continuous for all x

C. derivable for all x

D. discontinuous only for integral x

Answer : Option D
Explaination / Solution:

Case 1 Let c be a real number which is not equal to any integer. for all real numbers close to c the value of the function is equal to [c]; i.e., $lim_{x \to c} f (x) = lim_{x \to c} [x] = [c]$ . Also $f (c) = [c]$ and hence the function is continuous at all real numbers not equal to integers.

Case 2 Let c be an integer. Then we can find a sufficiently small real number $r > 0$ such that $[c - r] = c - 1 w h e r e a s [c + r] = c$

This, in terms of limits mean that $lim_{x \to c^{-}} f (x) = c - 1, lim_{x \to c^{+}} f (x) = c$

Since these limits cannot be equal to each other for any c, the function is discontinuous at every integral point.

TANCET Anna University Civil Engineering # Mathematics Conic Sections Prepare / Learn

Q5. The number of points on X-axis which are at a distance c units (c

<

3) from ( 2, 3) is

A. 3

B. 0

C. 2

D. 1

Answer : Option B
Explaination / Solution:

the shortest distance from x-axis to the point is 3.

TANCET Anna University Civil Engineering # Mathematics Differential Equations Prepare / Learn

Q6. General solution of a given differential equation

A. contains exactly one arbitrary constant

B. contains exactly two arbitrary constants

C. contains arbitrary constants depending on the order of the differential equation

D. does not contain arbitrary constants

Answer : Option C
Explaination / Solution:

The general solution of differential equation contains arbitrary constants equal to the order of differential equaition.

TANCET Anna University Civil Engineering # Mathematics Three Dimensional Geometry Prepare / Learn

Q7. Shortest distance between