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
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 Accounts 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. 

Assignment C
Question 1
By selling an article for Rs. 1900 a man suffers 5% loss. What is the cost price of the article?
a) Rs. 1000
b) Rs. 2000 
c) Rs. 1002
d) Rs. 2003

Question 2
An article was sold at a profit of 15% on the C.P. what is the percentage profit on S.P.?
a) 13(1/23)% 
b) 13(2/53)%
c) 13(4/23)%
d) (1/23)%

Question 3
What is the market value of 300 shares of Rs. 15 each if each share is sold at a premium of
Rs. 3?
a) Rs. 5200
b) Rs. 4500
c) Rs. 5400 
d) Rs. 5500

Question 4
What will be the income from investment of Rs. 13950 at 8% yielding stock of Rs 93?
a) Rs.1200 
b) Rs.1301
c) Rs.1400
d) Rs.1103

Question 5
"Find the interest on Rs. 10,200 for 7 years and 6 months @6% per annum?"
a) Rs. 4500
b) Rs. 4520
c) Rs. 4540
d) Rs. 4590 

Question 6
In what time will Rs. 1250 amount to Rs.1400 at 6% per annum?
a) 1 years
b) 2 years 
c) 3 years
d) 4 years

Question 7
An Annuity payable for a fixed number of years is called -----.
a) Annuity certain 
b) perpetual annuity
c) immediate annuity
d) unpaid annuity

Question 8
Mark the best possible term you can use for the given expression 
∫ f ( x ) d x
a) Derivative dx
b) Indefinite integral 
c) Definite Integral
d) even function

Question 9
The empty set  is the subset of ________
a) Every set 
b) only universal set
c) only power set
d) no set

Question 10
Express exponential relation 6^(-1) =1/6 in logarithmic form.
a) -1 = log6
b) -8 = log6 (1/6)
c) -1 = log6 (17/6)
d) -1 = log6 (1/6) 

Question 11
Solve: 2x-y = 5; x-4y= -1
a) "x=3, y=0"
b) "x=3, y=2"
c) "x=3, y=1" 
d) "x=3, y=4"

Question 12
Suppose the marginal cost of a product is given by 25+3x-9x^2 25 + 3 x − 9 x 2 and
fixed cost is known to be 55 then its average cost function is given by _______
a) 25+15x-3x^2+55/x 
b) 25+15x-3x^2+55
c) 25+5x-2x^2+55/x 
d) 25+25x-3x^2+55/x^2

Question 13
The first term of an A.P. series is 2 and the common difference is 1/2. Find the 20th term?
a) 11
b) 12
c) 11.5 
d) 13

Question 14
"If A= {1,2} and B={3,7}, then A∩B ="
a) {0}
b) {2}
c) {3}
d) {φ} 

Question 15
An annuity is called --------- if the first payment is made after a certain period from the
beginning of the annuity.
a) Deferred annuity
b) Annuity certain 
c) perpetual annuity
d) immediate annuity 

Question 16
Solve: x^2 +35 =11x +5
a) "roots 5,6" 
b) "roots 5,7"
c) "roots 3,8"
d) "roots 5,9"

Question 17
"Find the 8th term of the series 2,4,8,16?"
a) 256 
b) 250
c) 253
d) 252

Question 18
The value of a determinant remains unaltered if rows and colums are?
a) increased by 2
b) decreased by 3
c) same
d) interchanged 

Question 19
A set is said to be ------ if no elements belong to it.
a) null set 
b) no set
c) free set
d) none

Question 20
"If A= {1,2,3,4,7} and B ={2,6,8}, then A LaTeX: \cup ∪ B"
a) "{1,2,3,4,7,6}"
b) "{1,2,6,8}"
c) "{1,2,3,4,7,6,8}" 
d) "{1,2,3,4,7}"

Question 21
"For any subset A and B of U, ( A ∪ B ) c ?"
a) A n B
b) A ∪ B
c) 
d) A c ∩ B c 

Question 22
4/3 is an example of?
a) prime numbers
b) whole numbers
c) irrational numbers
d) rational numbers 

Question 23
Set of vowels in English alphabet contains elements
a) "{a, b, c, d, e, f}"
b) "{a, e, i, o, u}" 
c) "{p, q, r, s, t}"
d) "{l, m, n, o, p}"

Question 24
Set {x: x is an odd number between 10 and 18}
a) "{11, 12, 13, 15, 17} "
b) "{12, 16, 15, 13}"
c) "{11, 13, 15, 17}" 
d) "{12, 14, 16, 18}"

Question 25
A set consisting of only one element is called a ?
a) null set
b) singleton set 
c) no set
d) free set

Question 26
Integrating the following function we will get
f(x)=(√x-1/√x)^2
a) (x^2/2)-2x+log x 
b) -2x-(x^2/2)+log x
c) (x^3/3)-(2x^2)+log x
d) none of these 

Question 27
Find the Limit of (2x^2 -7x +6) / (5x^2 -11x +2) when x→2
a) 2x 
b) Infinity
c) 5x
d) none 

Question 28
Two matrices A and B can multiplied to get AB if?
a) both are rectangular
b) both have same order
c) no of columns of A is equal to columns of B 
d) no of rows of A is equal to no of columns of B

Question 29
"If U= {1,2,3,, .,8,9} be the universal set, A= {1,2,3,4} and B= {2,4,6,8}. Find 
( A ∩ B ) c
a) "{1,2,3,4,5}"
b) "{2,4,6,8}"
c) "{1,2,3}"
d) "{1,3,5,6,7,8,9}" 

Question 30
“If A is a symmetric matrix, then A' =?"
a) A 
b) |A|
c) 0
d) diagonal matrix

Question 31
The maximum and minimum values of a function are together called its?
a) extreme values 
b) good values
c) full values
d) null values

Question 32
The sum of two numbers is 24. Find the numbers if the sum of their squares is to be
minimum.
a) "11,11"
b) "11,12"
c) "12,12" 
d) "11,14"

Question 33
Find the maximum value of the function 2x^2-x^3 ( no answer is correct)
a) at x=4/3 is 4/3 
b) at x=4/3 is 4/4
c) at x=4/3 is 4/5
d) at x=4/3 is 4/6 
Question 34
Find the Differential coefficient of the function x^2 using the first principle
a) dy/dx =3x
b) dy/dx =4x +7
c) dy/dx =3x+8
d) dy/dx =2x 

Question 35
If log7 2401=x, then the value of x is ___
a) 2
b) 3
c) 4 
d) 5

Question 36
Arithmetric Progression is a?
a) Sequence 
b) equation
c) function
d) surd

Question 37
Integrate the function 1 x
a) 2x^(1/2) 
b) 2x
c) x
d) none

Question 38
Find the Characterisitc of the Logarithm of 196.458?
a) 0
b) 1
c) 2 
d) 196

Question 39
An equation of form a x^2+ bx + c = 0, a ≠ 0 is
a) Quadratic Equation 
b) cubic equation
c) linear equation
d) polynomial of degree n

Question 40
Dimension of matrix which consists of 3 rows and 4 columns is written as?
a) 3/4
b) 3x4 
c) 3+4
d) 3-4