Basic Mathematics

Assignment A
On selling a pen drive for Rs 708.50, a man gains 9%. For how much should he sell it to gain 11%? 

3.  Explain De Morgan’s Law with examples. 

4.  How we find maxima by derivatives? 

5. If 4 times the 4th term of an A.P. is equal to 9 times the 9th term of the A.P., what is  the 13th term of this A.P.?   

Assignment B

In a survey of 400 students of a college it was found that 240 study mathematics, 180 study Statistics and 140 study Accounts, 80 study mathematics and Statistics, 60 study Statistics and Accounts, 100 study Accounts and mathematics and 40 study none of these subjects. On the basis of this information answer the following questions.
Q No 1:  Find the number of students who study Acconts only.

No 2:  Find the number of students who study at least one of these subjects

No 3: Find the number of students who study all of these subjects. 

SECTION C

QUESTION 1

"Find the 8th term of the series 2,4,8,16?"
        
256

250

253

252

QUESTION 2

A set consisting of only one element is called a?
        
null set

singleton set

no set

free set

QUESTION 3

Integrate the function 1/√x
        
2x^(1/2)

2x

x

none

0.75 points   

QUESTION 4

In what time will Rs. 1250 amount to Rs.1400 at 6% per annum?
        
1 year

2 years

3 years

4 years
QUESTION 5

Find the Differential coefficient of the function x^2 using the first principle
        
dy/dx =3x

dy/dx =4x +7

dy/dx =3x+8

dy/dx =2x

QUESTION 6

The value of a determinant remains unaltered if rows and colums are?
        
increased by 2

decreased by 3

same

interchanged

QUESTION 7

Express exponential relation 6^(-1) =1/6 in logarithmic form.
        
-1 = log6

-8 = log6 (1/6)

-1 = log6 (17/6)

-1 = log6 (1/6)

QUESTION 8

What will be the income from investment of Rs. 13950 at 8% yielding stock of Rs 93?
        
Rs.1200

Rs.1301

Rs.1400

Rs.1103

QUESTION 9

What is the market value of 300 shares of Rs. 15 each if each share is sold at a premium of Rs. 3?
        
Rs. 5200

Rs. 4500

Rs. 5400

Rs. 5500

QUESTION 10

An equation of form a x^2+ bx + c = 0, a ≠ 0 is 
        
Quadratic Equation

cubic equation

linear equation 

polynomial of degree n

QUESTION 11

"If A= {1,2} and B={3,7}, then A∩B ="
    
0

 ∅

2

3

QUESTION 12

am x an = ?
        
a(m+n)

am-n

amn

am

QUESTION 13

An annuity is called --------- if the first payment is made after a certain period from the beginning of the annuity.
        
Deferred annuity

Annuity certain

perpetual annuity

immediate annuity

QUESTION 14

solve: 2x-y = 5; x-4y= -1
        
"x=3, y=0"

"x=3, y=2"

"x=3, y=1"

"x=3, y=4"

QUESTION 15

Two matrices A and B can multiplied to get AB if?
        
both are rectangular

both have same order

no of columns of A is equal to columns of B

no of rows of A is equal to no of columns of B

QUESTION 16

Find the Limit of (2x^2 -7x +6) / (5x^2 -11x +2) when x→2

        
2x

Infinity

5x

none

QUESTION 17

"0,1,2,3,4, .are called"
        
prime numbers

whole numbers

irrational numbers

none

QUESTION 18

Set {x: x is an odd number between 10 and 18}
        
"{11, 12, 13, 15, 17} "

"{12, 16, 15, 13}"

"{11, 13, 15, 17}"

"{12, 14, 16, 18}"

QUESTION 19

Express log subscript 5 625 = 4 in exponential form.
        
5^4 =625

5^5 =625

5^6 =625

5^7 =625

QUESTION 20

Solve: x^2 +35 =11x +5
        
"roots 5,6"

"roots 5,7"

"roots 3,8"

"roots 5,9"

QUESTION 21

The first term of an A.P. series is 2 and the common difference is 1/2. Find the 20th term?
        
11

12

11.5

13

QUESTION 22

Determine log subscript x 2401 when x³ = 7

16

14

12

10

QUESTION 23

The sum of two numbers is 24. Find the numbers if the sum of their squares is to be minimum.
        
"11,11"

"11,12"

"12,12"

"11,14"

QUESTION 24

"If U= {1,2,3,, .,8,9} be the universal set, A= {1,2,3,4} and B= {2,4,6,8}. Find left parenthesis A intersection B right parenthesis to the power of C.

"{1,2,3,4,5}"

"{2,4,6,8}"

"{1,2,3}"

"{1,3,5,6,7,8,9}"

QUESTION 25

Set of vowels in English alphabet contains elements
        
"{a, b, c, d, e, f}"

"{a, e, i, o, u}"

"{p, q, r, s, t}"

"{l, m, n, o, p}"

QUESTION 26

" If A is a symmetric matrix, then A' =?"

A

|A|

0

diagonal matrix

QUESTION 27

4/3 is an example of ?
        
prime numbers

whole numbers

irrational numbers

rational numbers

QUESTION 28

"Find the interest on Rs. 10,200 for 7 years and 6 months @6% per annum?"
        
Rs. 4500

Rs. 4520

Rs. 4540

Rs. 4590

QUESTION 29

Find the maximum value of the function 2x^2-x^3

at x=4/3 is 4/3

at x=4/3 is 4/4

at x=4/3 is 4/5

at x=4/3 is 4/6

QUESTION 30

Arithmetric Progression is a?
        
sequence

equation

function

surd

QUESTION 31

Dimension of matrix which consists of 3 rows and 4 columns is written as?

3/4

3x4

3+4

3-4

QUESTION 32

"For any subset A and B of U, (A∩B) ͨ ?”
A n B

A ∪ B

π

A  ͨ ∩ B ͨ  

QUESTION 33

An Annuity payable for a fixed number of years is called -----.
        
Annuity certain

perpetual annuity

immediate annuity

unpaid annuity

QUESTION 34

By selling an article for Rs. 1900 a man suffers 5% loss. What is the cost price of the article?
        
Rs. 1000

Rs. 2000

Rs. 1002

Rs. 2003

QUESTION 35

"If A= {1,2,3,4,7} and B ={2,6,8}, then A union B"

"{1,2,3,4,7,6}"

"{1,2,6,8}"

"{1,2,3,4,7,6,8}"

"{1,2,3,4,7}"

QUESTION 36

An article was sold at a profit of 15% on the C.P. what is the percentage profit on S.P.?
        
13(1/23)%

13(2/53)%

13(4/23)%

(1/23)%

QUESTION 37

A set is said to be ------ if no elements belong to it.
        
null set

no set

free set

none

QUESTION 38

The maximum and minimum values of a function are together called its?
        
extreme values

good values

full values

null values

QUESTION 39

Find the Characteristic of the Logarithm of 196.458 ?
        
0

1

2

196

QUESTION 40

Integers between -3 and 2 includes?

"0, -2, -1, 1"

"-2, -1, 0, 1"

"-1, -2, 0, 1"

"0, 1, -1, -2"

Assignment C
 
1.      
 
(A): a=2,b=4 
 (B): a=4,b=2 
 (C): Both Options i & ii 
 (D): None of these 

2. Square Matrix =
 (A): Symmetric Matrix + Skew-Symmetric Matrix 
 (B): Symmetric Matrix -Skew-Symmetric Matrix 
 (C): Symmetric Matrix *Skew-Symmetric Matrix 
 (D): Symmetric Matrix /Skew-Symmetric Matrix 

3. The system of liner equations AX = B said to be : Consistent (with unique solution) if
 (A): |A|?0 
 (B): |A|=0 
 (C): (adj A )B =0 
 (D): (adj A )B =1 

4. The system of liner equations AX = B said to be : Inconsistent i.e.has no solution if
 (A): |A|?0 
 (B): |A|=0 
 (C): (adj A )B =0 
 (D): |A|=0and (adj A)B is a non null matrix 

5. The set of intelligent students in a class is
 (A): Null set 
 (B): Finite set 
 (C): Not a well defined collection 
 (D): Singleton set 

6. A square matrix whoose all the elements exept the diognal elements zeroes is called a
 (A): Scalar Matrix 
 (B): Diagonal Matrix 
 (C): Row Matrix 
 (D): Square Matrix 

7. If n (A) = 115, n (B) = 326, n (A-B) = 47, then n (A U B) is equal to
 (A): 370 
 (B): 373 
 (C): 441 
 (D): none of these 

8. The complement of the union of two sets is the intersection of their complements and the complement of the intersection of two sets is the union of their complements. These are called.
 (A): Union laws 
 (B): De Morgan’s laws 
 (C): Associative laws 
 (D): Commutative laws 

9. If we differentiate y=(x³/4)+2x² -6x we get:
 (A): 3x²/4 - 4x 
 (B): 3x²/4 + 4x -6 
 (C): 3x³/4 + 4x +6 
 (D): 3x²/4 + 4x+6x 

10. ∫sin^2 x   dx   =
 (A): x /2 -(sin2x/4)+c 
 (B): x /4 -(sin4x/8)+c 
 (C): x /3 -(sin2x/4)+c 
 (D): x /8 -(sin2x/4)+c 

11. If A, B, C be three sets such that A ? B = A ? C and A n B = A n C, then
 (A): B=C 
 (B): A=C 
 (C): A=B 
 (D): A=B=C 

12. If A and B are any two sets, Then A ? (A n B) is equal to.
 (A): B 
 (B): A 
 (C): BC 
 (D): AC 

13. y= x(x-1) then dy/dx is
 (A): 2x+1 
 (B): 2x-1 
 (C): x(x+1) 
 (D): x 

14. f(x)= x3+6x-17 , find f(-2)
 (A): 37 
 (B): 3 
 (C): -37 
 (D): 0 

15. 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
 (A): 6,4 
 (B): 7,4 
 (C): 8,6 
 (D): 7,6 

16. For a square matrix A, A-A' is
 (A): Symmetric Matrix 
 (B): Skew-Symmetric Matrix 
 (C): Row Matrix 
 (D): Null Matrix 

17.  ∫log x   dx   =
 (A): x (logx-1)+c 
 (B): x (logx-1) -c 
 (C): x (logx+1)+c 
 (D): x (logx-x)+c 

18.  ∫1/(a^2 +x^2)   dx   =
 (A): (1/a) [tan^-1(x/a)]+c 
 (B): (2/a) [tan^-1(x/a)]+c 
 (C): (3/a) [tan^-1(x/a)]+c 
 (D): (1/a) [tan^-1(x/a)]-c 

19. ∫1/x   dx=
 (A): log x / c 
 (B): log x - c 
 (C): log x + c 
 (D): log x c 

20. ∫e^x  {f(x)+f' (x)} dx   =
 (A): e^x f(x)+c 
 (B): e^x f(x)-c 
 (C): e^x f' (x)+c 
 (D): e^2x f(x)+c 

21. F(-x) = F (x) This Function is known as
 (A): Step Function 
 (B): Even Function 
 (C): Inverse Funtion 
 (D): Rational Function 

22. y=x^4- 3x^2+x; then dy/dx is
 (A): 4x^3 /6x/1 
 (B): 4x^3 +6x+1 
 (C): 4x^3 -6x+1 
 (D): 4x^3 -6x-1 

23. Base of natural log is
 (A): 10 
 (B): 100 
 (C): 2 
 (D): e 

24. Classify the differential equation e^x dy/dx+3y=x2 y
 (A): Linear and not separable 
 (B): Both separable and linear 
 (C): Separable and not linear 
 (D): Neither separable nor linear. 

25. Suppose y is a function of x. Which of the option is d(x^3y)/dx?
 (A): 3x^2y+x^3dy/dx 
 (B): 3x^2y 
 (C): 3x^2y+x^3 
 (D): 3x^2dy/dx 

26. For a square matrix A, A+A' is
 (A): Symmetric Matrix 
 (B): Skew-Symmetric Matrix 
 (C): Row Matrix 
 (D): Square Matrix 

27. Classify the following differential equation: dx/dt = x+2xt+cost/(1+t^2)
 (A): Linear and not separable 
 (B): Both separable and linear 
 (C): Separable and not linear 
 (D): Neither separable nor linear. 

28. F(x) = a^x where a is positive constant This Function is known as
 (A): Step Function 
 (B): Even Function 
 (C): Inverse Funtion 
 (D): Exponential Function 

29. If x=1-t^2/1+t^2 and y= 2t/1+t^2, then dx/dy=
 (A): (t^2-1)/2t 
 (B): 2t / (t^2-1) 
 (C): t 
 (D): t^2-1 

30. A matrix of order p*q change in a new matrix of order q*p then new matrix is called
 (A): Transpose 
 (B): Inverse 
 (C): Symmetrical 
 (D): Adjoint 

31. ∫ x log  x dx=
 (A): x^2/2  log x-x^2/4-c 
 (B): x^2/2  log x+x^2/4+c 
 (C): x log x 
 (D): x^2/2  log x-x^2/4+c 

32. (0.04)-1.5 = ?
 (A): 125 
 (B): 130 
 (C): 135 
 (D): 150 

33. Discriminant of quadratic equation ax2 +bx +c = 0 is
 (A): b2 - 4ac 
 (B): 4ac-b2 
 (C): a2 - 4bc 
 (D): b2 + 4ac 

34. Two matrices A and B are multiplied to get AB if
 (A): both are rectangular 
 (B): both have same order 
 (C): no of rows of A is equal to no of columns of B 
 (D): no of columns of A is equal to columns of B 

35. (1000)9 ÷ 1024 = ?
 (A): 10000 
 (B): 100 
 (C): 1000 
 (D): 1000000 

36. If the cost price is 25% of selling price. Then what is the profit percent.
 (A): 100% 
 (B): 200% 
 (C): 250% 
 (D): 300% 

37. If A = {1, 2, 3, 4} and U = {1, 2, 3, 4, 5, 6, 7, 8} then find A complement (A’).
 (A): {1, 2, 3, 4} 
 (B): {1, 2, 3, } 
 (C): {1, 2, 3, 4,5,6,7,8} 
 (D): {5,6,7,8} 

38. A diogonal matrix whoose all elements are same is
 (A): Scalar Matrix 
 (B): Diagonal Matrix 
 (C): Row Matrix 
 (D): Square Matrix 

39. y=(x³/4 ) + 2x² -6x find y' when x= 4
 (A): 24 
 (B): 22 
 (C): 16 
 (D): 48 

40. ∫ x log? x dx=
 (A): x^2/2 log? x-x^2/4-c 
 (B): x^2/2 log x+x^2/4+c 
 (C): x log x 
 (D): x^2/2 log? x-x^2/4+c 

Question 1. 
Mark the best possible term you can use for the given expression 
∫ f ( x ) d x
a) Derivative dx
b) Indefinite integral (right answer)
c) Definite Integral
d) even function