Mathematics | CSE, IT Computer Science Engineering and Information Technology | TANCET Anna University Online Objective Test

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Maths Sets Prepare / Learn

Q1. If A = { 0,1,5,4,7 }. Then the total number subsets of A are

A. 60

B. 40

C. 20

D. 32

Answer : Option D
Explaination / Solution:

in any set having n elements then Total no of subsets=2n

so total subset = 25=32

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Limits and Derivatives Prepare / Learn

Q2.

\frac{d}{d x} (\cos^{- 1} (\sqrt{1 - x^{2})})

is equal to

A. 11−x2√for0<|x|<1

B. 24−(2x)2√for|x|<1

C. 11+x2√for|x|<1

D. x|x|1−x2√for0<|x|<1

Answer : Option D
Explaination / Solution:

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Linear Programming Prepare / Learn

Q3. A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time. If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity?

A. Maximum profit = Rs 200

B. Maximum profit = Rs 210

C. Maximum profit = Rs 220

D. Maximum profit = Rs 230

Answer : Option A
Explaination / Solution:

Let number of rackets made = x
And number of bats made = y
Therefore , the above L.P.P. is given as :
Maximise , Z = x +y , subject to the constraints : 1.5x +3y ≤ 42 and. 3x +y ≤ 24, i.e.0.5x + y ≤ 14 i.e. x +2y ≤ 28 and 3x +y ≤ 24 , x, y ≥ 0.

Corner points	Z = x + y
O( 0 , 0 )	0
D(0,14 )	14
A(8,0)	8
B(4,12)	16…………………(Max.)

Here Z = 16 is maximum. i.e Maximum number of rackets = 4 and number of bats = 12.
Here , profit function is P = 20x + 10y
Profit is maximum at x = 4 and y = 12 .
Therefore , maximum profit = 20(4) + 10 ( 12) = 200.i.e. Rs.200.

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Linear Inequalities Prepare / Learn

Q4. Solve the system of inequalities − 2 ≤ 6x − 1 < 2

A. −16<x<32

B. none of these

C. −17≤x>12

D. −16≤x>12

Answer : Option D
Explaination / Solution:

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Application of Derivatives Prepare / Learn

Q5. The line

\frac{x}{a} + \frac{y}{b} = 1

touches the curve

y = b e^{- x / a}

at the point

A. (a,ab)

B. (a,-a)

C. (0,b)

D. ( – a ,ba)

Answer : Option C
Explaination / Solution:

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Sequences and Series Prepare / Learn

Q6. The sum of all 2-digited numbers which leave remainder 1 when divided by 3 is

A. 1600

B. 1610

C. 1616

D. 1605

Answer : Option D
Explaination / Solution:

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Statistics Prepare / Learn

Q7. If the two lines of regression are y = 3x – 5 and y = 2x – 4 , then ρ(X,Y) is equal to

A. 23−−√

B. 1

C. 32−−√

D. 16−−√

Answer : Option A
Explaination / Solution:

let us assume that y = 3x – 5 and y = 2x – 4 are lines of regression of x on y and y on x respectively,therefore

$\begin{array}{l} b_{x y} = 1 / 3 \\ b_{y x} = 2 \end{array}$

$ρ = \pm \sqrt{b_{x y} b_{y x}} = \pm \sqrt{2 / 3}$

but sign of $ρ$ is same as $b_{y x}$ and $b_{x y}$

therefore $ρ = \sqrt{2 / 3}$

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Application of Integrals Prepare / Learn

Q8. The positive value of the parameter a for which the area of the figure bounded by y = sin ax , y = 0 , x =

\frac{π}{a} a n d x = \frac{π}{3 a}

is 3 is equal to

A. 2+3√3

B. 1/2

C. None of these

D. 2

Answer : Option B
Explaination / Solution:

TANCET Anna University CSE, IT Computer Science Engineering and Information Technology # Mathematics Relations and Functions Prepare / Learn

Q9. Let A be the set of all students of a boys school. The relation R on A is given by R = {(a, b) : a is sister of b} is

A. Empty

B. Reflexive

C. Universal

D. Trivial

Answer : Option A
Explaination / Solution:

Because , the relation is defined over the set A be the set of all students of a boys school.

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