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Title Name Amity solve assignment for BSc. IT on Basic maths
University AMITY
Service Type Assignment
Course B.Sc-(IT)
Semester Semester-I Course: B.Sc-(IT)
Session
Short Name or Subject Code basic maths
Commerce line item Type Semester-I Course: B.Sc-(IT)
Product Assignment of B.Sc-(IT) Semester-I (AMITY)
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Questions:-


Basic Mathematics (ABI 105) - Semester I

Section A

Q.1 What is a set? Explain various methods to represent a set-in set theory.

Q.2.  Define the following with the help of suitable examples.          

 (i) Singleton Set                       (ii) Finite Set            (iii) Cardinality of a Set               (iv) Subset of a Set

Q.3. Differentiate between DFA and NFA

Q.4 Define the following concept with an example            

  1. a) Ambiguity in CFG b) Turning Machine

 Q.5 Distinguish between Mealy and Moore machine

Section B

QUESTION 1

QUESTION 2

QUESTION 3

Section C- Multiple Choice Question

QUESTION 1

f(x)= (x³/4)+2x² -6x .find f(-2)

   

18

   

-18

   

4

   

-4

10 points   

QUESTION 2

y=3x^3 +7x^5; then dy/dx at x =7 is

   

84467

   

84476

   

84477

   

84478

10 points   

QUESTION 3

If the order of matrix A is m * p. And the order of B is p*n. Then the order of AB is ?

   

m*n

   

m*p

   

n*m

   

p*n

10 points   

QUESTION 4

The number of non-zero rows in an echlon form is called ?

   

reduced echlon form

   

rank of a matrix

   

conjugate of the matrix

   

cofactor of the matrix

10 points   

QUESTION 5

Find lim x[integration]8 ( 5x + sin x ) /x

   

5

   

5+sinx

   

5/x

   

sinx/x

10 points   

QUESTION 6

"The smallest set A such that A ? {1, 2} = {1, 2, 3, 5, 9} is"

   

"{2,3,5}"

   

"{3,5,9}"

   

"{1,2,3,5,9}"

   

None of these

10 points   

QUESTION 7

A set consisting of a definite number of elements is called a?

   

Finite set

   

Infinite set

   

Null Set

   

Singleton set

10 points   

QUESTION 8

"The number of proper subsets of the set {1, 2, 3} is"

   

8

   

9

   

6

   

7

10 points   

QUESTION 9

Two finite sets have n and m elements. The number of elements in the power set of first set is 48 more than the total number of elements in power set of the second set. Then the values of m and n are

   

6 and 4

   

7 and 4

   

8 and 6

   

7and 6

10 points   

QUESTION 10

Find dy/dx of x^2+e^x+2x when x=3

   

3+e^3

   

5+e^3

   

9+e^3

   

8+e^3

10 points   

QUESTION 11

When we find maxima or minima then derivative of first order is equal to

   

1

   

-1

   

0

   

Cannot say

10 points   

QUESTION 12

"If n (A) = 115, n (B) = 326, n (A-B) = 47, then n (A U B) is equal to"

   

370

   

373

   

441

   

none of these

10 points   

QUESTION 13

Every set is a ___________ of itself

   

Proper subset

   

Compliment

   

Improper set

   

none of these

10 points   

QUESTION 14

integrate x^5 dx=

   

5x^4 +c

   

[x^6/6]+c

   

x^6

   

x^4+c

10 points   

QUESTION 15

integrate cotx dx

   

log|sinx| +c

   

log|cotx| +c

   

log|cotx| +c

   

tanx

10 points   

QUESTION 16

integrate (x+sinx)/(1+cosx)dx =

   

sinx

   

x cot(x/2) +c

   

x tan(x/2) +c

   

cosx

10 points   

QUESTION 17

integrate tanx dx

   

{-log|cosx|+c}

   

log|sinx|+c

   

log|cotx|+c

   

x cot(x/2)+c

10 points   

QUESTION 18

dy/dx of x(x-10) is

   

2x+10

   

2x-10

   

x-10

   

2x

10 points   

QUESTION 19

Matrix multiplication is

   

commutative

   

associative

   

both option i&ii

   

none of these

10 points   

QUESTION 20

Matrix addition is

   

commutative

   

associative

   

both option i&ii

   

none of these

10 points   

QUESTION 21

A matrix whose inverse exists is known as

   

transpose matrix

   

invertible matrix

   

both option i&ii

   

none of these

10 points   

QUESTION 22

If a and b are two given vectors. Then |a+b| is

   

less than or equal to |a|+|b|

   

more than or equal to |a|+|b|

   

equal to |a|+|b|

   

none of these

10 points   

QUESTION 23

If a and b are two given vectors. Then |a-b| is

   

less than or equal to |a|-|b|

   

more than or equal to |a|-|b|

   

equal to |a|+|b|

   

none of these

10 points   

QUESTION 24

Integrate sin^2(x)dx=

   

(x/2)+1/8(sin4x)+c

   

(x/2)+1/8(sin2x)+c

   

(x/2)-1/4(sin2x)+c

   

none of these

10 points   

QUESTION 25

Integrate cos^2(2x)dx=

   

(x/2)+1/8(sin4x)+c

   

(x/2)+1/8(sin2x)+c

   

(x/2)-1/4(sin2x)+c

   

none of these

10 points   

QUESTION 26

Integrate sec x dx =

   

log|sinx|+c

   

log|sec x+tanx|+c

   

(x/2)-1/4(sin2x)+c

   

none of these

10 points   

QUESTION 27

Integrate cosec x dx =

   

log|sinx|+c

   

log|sec x+tanx|+c

   

log|cosec x-cotx|+c

   

none of these

10 points   

QUESTION 28

A matrix in which number of rows equal to the number of columns is known as

   

Column matrix

   

Square matrix

   

Row matrix

   

Scalene matrix

10 points   

QUESTION 29

"The solution of the equations 3x + y + 2z = 3 ,2x 3y z = 3, x + 2y + z = 4 by Matrix method is"

   

"x = 1, y = 2, z = 1"

   

"x = 1, y = 2, z = 1"

   

"x = 1, y = 2, z = 1"

   

"x = 1, y = 2, z = 1"

10 points   

QUESTION 30

A__________ is a diagonal matrix whose elements in the diagonal are all ones.

   

null matrix

   

unit matrix

   

diagonal matrix

   

rectangular matrix

10 points   

QUESTION 31

The order of the matrix [4 7 3] is__________

   

3 *3

   

1*3

   

3*1

   

1*1

10 points   

QUESTION 32

Find the second derivative of y = x-2 at x = 2

   

0.375

   

0.367

   

0.96

   

-0.25

10 points   

QUESTION 33

Find the partial derivatives with respect to x of the function: xy2  5y + 6

   

y2

   

y2 -5

   

xy-5

   

2xy

10 points   

QUESTION 34

f(x)= x+1 and g(x) =2x+3 then fog(x) =

   

2x+3

   

2x+5

   

2x+4

   

2x+1

10 points   

QUESTION 35

f(x)= x+1 and g(x) =2x+3 then gof(x) =

   

2x+3

   

2x+5

   

2x+4

   

2x+1

10 points   

QUESTION 36

Find lim x?8 [ 1 + a/ x ] ^x

   

a^e

   

e^a

   

a^x

   

x^a

10 points   

QUESTION 37

x(dy/dx)+3/(dy/dx)=y^2 . Find order and degree

   

"order=1, degree=2"

   

"order=2, degree=2"

   

"order=2, degree=1"

   

"order=1, degree=1"

10 points   

QUESTION 38

Gauss elimination method is used

   

to solve the system of equations

   

to make the equations

   

to find determinant value

   

none of these

10 points   

QUESTION 39

Matrix equations solution is given by

   

Cramer´s rule

   

Gauss elimination method

   

matrix inverse method

   

all of these

10 points   

QUESTION 40

What is the first derivative dy/dx of the expression (xy)x = e?

   

y(1 + ln xy) / x

   

0

   

y(1 ln xy) / x2

   

y/x


Questions:-



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