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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

 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

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January 29, 2015
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08-May, 2019
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