Mathematics 

Assignment A  

                                         
1. Write De-Morgan laws with examples

2. Write Leibnitz theorem with examples

3. Find dy/dx, given y=log(tanx/2) - cotx log(1+sinx)-x

4. Find the general solution of differential equation:- dy/dx +2y=6e^x

5. Prove that addition of vectors is (i) commutative (ii) associative.

6. Integrate 1/(sinx+tanx)

7. Solve the system of equations by matrix method
  

8. Find derivative of     e^x/x^2

Assignment B
Case Study
Of the 400 candidates who were interviewed for a position at a call centre, 200 had a laptop, 140 had a calculator and 280 had a mobile phone. 80 of them had both, a laptop and a calculator, 60 had both, a calculator and a mobile phone and 120 had both, a laptop and mobile phone and 20 had all three.
On the basis of above information answer the following questions:
QUESTION 1
a. How many candidates who attended the interview had at least one of the three gadgets?    

QUESTION 2
b. How many candidates had none of the three?

QUESTION 3
c. How many candidates have only laptops?

Assignment C
QUESTION 1
f(x)= (x³/4)+2x² -6x .find f(-2)        
18
-18
4
-4

QUESTION 2
y=3x^3 +7x^5; then dy/dx at x =7 is        
84467
84476
84477
84478

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
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

QUESTION 5
Find limx
        
5

5+sinx

5/x

sinx/x

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

QUESTION 7
A set consisting of a definite number of elements is called a?
        
Finite set

Infinite set

Null Set

Singleton set

QUESTION 8
"The number of proper subsets of the set {1, 2, 3} is"

8

9

6

7

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

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

QUESTION 11
When we find maxima or minima then derivative of first order is equal to
        
1

-1

0

Cannot say

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

QUESTION 13
Every set is a ___________ of itself
        
Proper subset

Compliment

Improper set

none of these

QUESTION 14
Integrate x^5 dx=
        
5x^4 +c

[x^6/6]+c

x^6

x^4+c

QUESTION 15
Integrate cotx dx
        
log|sinx| +c

log|cotx| +c

log|cotx| +c

tanx

QUESTION 16
Integrate (x+sinx)/(1+cosx)dx =
        
sinx

x cot(x/2) +c

x tan(x/2) +c

cosx

QUESTION 17
Integrate tanx dx
        
{-log|cosx|+c}

log|sinx|+c

log|cotx|+c

x cot(x/2)+c

QUESTION 18
dy/dx of x(x-10) is
        
2x+10

2x-10

x-10

2x

QUESTION 19
Matrix multiplication is
        
commutative

associative

both option i&ii

none of these

QUESTION 20
Matrix addition is
        
commutative

associative

both option I & ii

none of these

QUESTION 21
A matrix whose inverse exists is known as
        
transpose matrix

invertible matrix

both option i&ii

none of these

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

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

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

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

QUESTION 26
Integrate sec x dx =
        
log|sinx|+c

log|secx+tanx|+c

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

none of these

QUESTION 27
Integrate cosec x dx =
        
log|sinx|+c

log|secx+tanx|+c

log|cosec x-cotx|+c

none of these

QUESTION 28

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

Square matrix

Row matrix

Scalene matrix

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"
QUESTION 30

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

unit matrix

diagonal matrix

rectangular matrix

QUESTION 31

The order of the matrix [4 7 3] is__________
        
3 *3

1*3

3*1

1*1

QUESTION 32

Find the second derivative of y = x-2 at x = 2
        
0.375

0.367

0.96

-0.25

QUESTION 33

Find the partial derivatives with respect to x of the function: xy^2 -5y + 6
        
y2

y2 -5

xy-5

2xy

QUESTION 34

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

2x+5

2x+4

2x+1

QUESTION 35

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

2x+5

2x+4

2x+1

QUESTION 36

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

e^a

a^x

x^a

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"

QUESTION 38

Gauss elimination method is used
        
to solve the system of equations

to make the equations

to find determinant value

none of these

QUESTION 39

Matrix equations solution is given by
        
Cramer's rule

Gauss elimination method

matrix inverse method

all of these

QUESTION 40

What is the first derivative dy/dx of the expression (xy)x = e?
        
y(1+ lnxy)/x

0

y(1 lnxy) / x2

y/x