Questions:
Basic Mathematics (ABI 105)  Semester I
Section A
Q.1 What is a set? Explain various methods to represent a setin 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
 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)
10 points
QUESTION 2
y=3x^3 +7x^5; then dy/dx at x =7 is
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 ?
10 points
QUESTION 4
The number of nonzero 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
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"
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
10 points
QUESTION 11
When we find maxima or minima then derivative of first order is equal to
10 points
QUESTION 12
"If n (A) = 115, n (B) = 326, n (AB) = 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


logsinx +c



logcotx +c



logcotx +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


{logcosx+c}



logsinx+c



logcotx+c



x cot(x/2)+c

10 points
QUESTION 18
dy/dx of x(x10) is
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 ab is


less than or equal to ab



more than or equal to ab



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 =


logsinx+c



logsec x+tanx+c



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



none of these

10 points
QUESTION 27
Integrate cosec x dx =


logsinx+c



logsec x+tanx+c



logcosec xcotx+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__________
10 points
QUESTION 32
Find the second derivative of y = x2 at x = 2
10 points
QUESTION 33
Find the partial derivatives with respect to x of the function: xy2 5y + 6
10 points
QUESTION 34
f(x)= x+1 and g(x) =2x+3 then fog(x) =
10 points
QUESTION 35
f(x)= x+1 and g(x) =2x+3 then gof(x) =
10 points
QUESTION 36
Find lim x?8 [ 1 + a/ x ] ^x
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
