STA100 Past Paper


              STA-100 Paper 2019

General Mathematics & Biostatistics



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 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

Egg Chicken                               Mango, Orange                                    Orange

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.


Thank You !


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