# STA-100 Paper 2019

General Mathematics & Biostatistics

|

STA-100 Papers_2019
Objective

1) A(4,3) B(10,7); find the mid point 2)  4[2       0 ]
4     −1
3) If b2-4ac<zero then there will be No Solution

## Subjective

1)     You have 5 chess cards named A,B,C,D,E . In how many ways you can arrange them to make a word from them (in this question we have to find possible number of permutations ) (2 marks)
5! = 5×4×3×2×1 = 120

2)     Find the exact value of Cos150 without using calculator. (3 marks)
Cos( 1800-Cos300)
By applying angle rule Cos[ 2(90))0-Cos300]
-Cos(-300) -Cos30 0 = - √3
2

3)     If f(x)=4x+1 and g(x)=x-6 then find f(x)-g(x).(2 marks)

f.g(x)= f(x) × g(x)
f.g(x)= (4x+1)(x-6)
f.g(x)= [4x(x)+4x(-6)+1(2x)+1(--6)]
f.g(x)= [4x2-24x+2x-6]
f.g(x)= (4x2-22x-6)

4)     If f(x)= 3x-1 and g(x)= 2x-1 then find the product of i.e, f.g(x)

f.g(x)= f(x) * g(x)
f.g(x)= (3x-1)(2x-1)
f.g(x)= [3x(2x)+3x(-1)-1(2x)-1(-1)]
f.g(x)= [6x2-3x-2x+1]
f.g(x)= [6x2-5x+1]
9)       Fg(x) fx()= x3+1 g(x)= 32+1
Same method will be used as above;

10) Expand the Sin(A-B)
Sin(A-B) = (SinA+(-B))
Sin(A-B) = SinA+Cos(-B) + CosA+Sin(-B)
Sin(A-B) = SinA+Cos(B) + CosA+Sin(-B) Sin(A-B) = SinA+CosB - CosA+SinB

11) Write down the properties to reduce a metric to reduce echelon form.
Definition:
“A matrix is in echelon form if it has the following properties”
o   Every non-zero row begins with a 1 (called a leading 1)
o   Every leading one in a lower row is further to the right of the leading one above it.
o   If there are zero rows, they are at the end of the matrix
 1 2 3 Example; [0 1 2] 0 0 1
Definition:
A matrix is in reduced echelon form if in addition to the above three properties it also has the following property:
o   Every other entry in a column containing a leading one is zero

 1 0 0 Example; [0 1 0] 0 0 1
12) If Z=2-Bi find out Z.Z*=?
Z=2-Bi         Z*=2+Bi
Then,
Z.Z*= (2-Bi)( 2+Bi)
Z.Z*= [2(2)+1(Bi)-Bi(2)-Bi(Bi)]
Z.Z*= [4+Bi-2Bi-Bi2] Z.Z*= [4+(1-2)B-B(-1)] Z.Z*= [4+(-1)B+B] Z.Z*= [4-B+B]
Z.Z*= 4

13) What is the cardianality of Sets? A= set of English alphabets B= set of integers
C= set of even number between 3 and 7

A= {a,b,c,d,……,z} Caridanility of set A is |A|= 26 B= {0,±1, ±2, ±3,…..}
(Set B is a infinite there for its caridanility can’t be counted)
Caridanility of set B is |B|= is uncountable

C= {4,6}

Caridanility of set C is |C|= 2

14) Find the slope of 2x-3y= 12
2x-3y= 12
2x-3y-12 = 0 Slope = - a
b

### = -2=2  –3        3 Intercept= - C
b

= - –12 –3

= - 12 3

15) Find Domain & Range for f(n)= 5n+2
Domain = {x ϵ R | x ≥ 2} R, Range= R

16)   Radius of Circle (x-5)2- (y-7)2 = 4a
(x-5)2- (y-7)2 = 4a
Center equation of a circle (x-k)2- (y-h)2 = r2
(x-5)2- (y-7)2 = 72

17) Find the slope of (2, -1) and (-5, 3) m= y2–y1
s2–s1
3–(–1) m=
–5–2

3+1 m=
–7

4 m=
–7

20) A= {2,4,6,8,10,12,14,16} B={12,14,16,20}
find AB

AB= {2,4,6,8,10,12,14,16} {12,14,16,20}
AB= {12,14,16}

23)A local family Restaurant have special breakfast and a customer choose one of them each day

#### EggChickenMango,OrangeOrange

Egg mutton                               Apple fruit Slice                                  Rasberry
Egg beef                                   Cup fruit juice                                    Tomato
Find the possible combination without meet.

Since we have to make combination without meet,
 3

P  =   3!     = 3!  = 3∗2∗1  = 6    3     3–3!        0!           0!           1

24)x2+6x+5= 0
##### x2+6x+5=0 x2+1x+5x+5=0 x(x+1)+5(x+1)=0 (x+5)+(x+1)=0
(1+x)+(1+5)=0

(x+1)=0                                                                   (x+5)=0
x=-1                                                                         x=-5
S.S={-1, -5}

25)If 3rd and 4th terms of geometric series are 12 & B respectively. Find out the sum to infinite.