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

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

Q2. Different calendars for the month of February are made so as to serve for all the coming years. The number of such calendars is

A. 7

B. 2

C. 14

D. 8

Answer : Option C
Explaination / Solution:

The month of February has either 28 days (non-Leap Year) or 29 days(Leap Year).

Thus there are 2 possibility for the number of days in February.

Also the first day of the month of February can be any of the 7 days in a week.

So total number of February calendars = 2 * 7 =14

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

Q3. Two lines

are coplanar if

A. (a2→−a1→).(−b1→×−b2−→−)=0

B. (a2→−a1→).(b1→×−b2→)=0

C. (a2→−a1→).(−b1→×b2→)=0

(\vec{a_{2}} - \vec{a_{1}}) . (\vec{b_{1}} \times \vec{b_{2}}) = 0

Answer : Option D
Explaination / Solution:

In vector form:

Two lines

are coplanar if (

(\vec{a_{2}} - \vec{a_{1}}) . (\vec{b_{1}} \times \vec{b_{2}}) = 0

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

Q4. To form a differential equation from a given function

A. Differentiate the function successively as many times as the number of arbitrary constants inthe given function and eliminate the arbitrary constants.

B. Differentiate the function once and eliminate the arbitrary constants

C. Differentiate the function once and add values to arbitrary constants

D. Differentiate the function twice and eliminate the arbitrary constants

Answer : Option A
Explaination / Solution:

We shall differentiate the function equal to the number of arbitrary constant so that we get equations equal to arbitrary constant and then eliminate them to form a differential equation

TANCET Anna University ECE Electronics and Communication Engineering # Mathematics Complex Numbers and Quadratic Equations Prepare / Learn

Q5.

If $α$ is a complex a number such that $α^{2} + α + 1 = 0$ then $α^{31}$ is

A. α2

B. 1

C. α

D. 0

Answer : Option C
Explaination / Solution:

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

Q6.

{(\sqrt{5} + 1)}^{4} + {(\sqrt{5} - 1)}^{4}

A. a negative integer

B. a negative real number

C. an irrational number

D. a rational number

Answer : Option D
Explaination / Solution:

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

Q7. Which set is the subset of all given sets ?

A. { }

B. { 1,2,3,4 }

C. { 1 }

D. { 0 }

Answer : Option A
Explaination / Solution:

{ } denoted as null set. and Null set is subset of all sets.

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

Q8.

\frac{d}{d x} (\cos e c^{- 1} x)

is equal to

A. 1xx2−1√for|x|>1

−1|x|x2−1√for|x|>1

C. 1xx3−2x√;for|x|>1

D. −12xx2−1√for|x|>1

Answer : Option B
Explaination / Solution:

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

Q9. A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines tomanufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs 10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximize his profit? Determine the maximum profit.

A. 32 packages of screws A and 22 packages of screws B; Maximum profit = Rs 414

B. 30 packages of screws A and 20 packages of screws B; Maximum profit = Rs 410

C. 32 packages of screws A and 20 packages of screws B; Maximum profit = Rs 412

D. 30 packages of screws A and 22 packages of screws B; Maximum profit = Rs 412

Answer : Option B
Explaination / Solution:

Let number of packages of screws A produced = x
And number of packages of screws B produced = y
Therefore , the above L.P.P. is given as :
Maximise , Z = 7x +10y , subject to the constraints : 4x +6y ≤ 240 and. 6x +3y ≤ 240 i.e. 2x +3y ≤ 120 and 2x +y ≤ 80 , x, y ≥ 0.

Corner points	Z =7 x +10 y
O( 0 , 0 )	0
D(40,0 )	280
A(0,40)	400
B(30,20)	410…………………(Max.)

Here Z = 410 is maximum.
i.e 30 packages of screws A and 20 packages of screws B; Maximum profit = Rs 410.

Mathematics - Online Test

Mathematics | Online Objective Test | Start Test

Prepare Before Start Test | Learn

UPSC Civil services Entrance exams | Online Test

GATE Exam | Online Test

Under Graduate Entrance Exams | Online Test

Problem Solving and Reasoning | Online Test

CAT Entrance Exams | Online Test

CLAT LAW Entrance exams | Online Test

Banking Entrance exams | Online Test

UGC NET Entrance exams | Online Test

TANCET Anna University | Online Test

TN State Board | Online Test