
STA100 Papers_2019
Objective
1) A(4,3) B(10,7); find the mid point
2) 4[2 0 ]
4 −1
3) If b^{2}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( 180^{0}Cos30^{0})
By
applying angle rule Cos[ 2(90))^{0}Cos30^{0}]
Cos(30^{0})
Cos30
^{0} =  √3
2
3)
If f(x)=4x+1 and g(x)=x6 then find
f(x)g(x).(2 marks)
f.g(x)= f(x) × g(x)
f.g(x)= (4x+1)(x6)
f.g(x)= [4x(x)+4x(6)+1(2x)+1(6)]
f.g(x)=
[4x^{2}24x+2x6]
f.g(x)= (4x^{2}22x6)
4) If
f(x)= 3x1 and g(x)= 2x1 then find the product of i.e, f.g(x)
f.g(x)= f(x) * g(x)
f.g(x)= (3x1)(2x1)
f.g(x)= [3x(2x)+3x(1)1(2x)1(1)]
f.g(x)= [6x^{2}3x2x+1]
f.g(x)=
[6x^{2}5x+1]
9) Fg(x) fx()= x^{3}+1
g(x)= 3^{2}+1
Same method will be used as above;
10) Expand
the Sin(AB)
Sin(AB) = (SinA+(B))
Sin(AB) = SinA+Cos(B) + CosA+Sin(B)
Sin(AB) = SinA+Cos(B) +
CosA+Sin(B) Sin(AB) = 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 nonzero 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=2Bi find out Z.Z^{*}=?
Z=2Bi Z^{*}=2+Bi
Then,
Z.Z^{*}=
(2Bi)( 2+Bi)
Z.Z^{*}= [2(2)+1(Bi)Bi(2)Bi(Bi)]
Z.Z^{*}= [4+Bi2BiBi^{2}] Z.Z^{*}= [4+(12)BB(1)] Z.Z^{*}= [4+(1)B+B] Z.Z^{*}=
[4B+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 2x3y= 12
2x3y= 12
2x3y12 = 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 (x5)^{2}
(y7)^{2} = 4a
(x5)^{2} (y7)^{2} = 4a
Center equation of a circle (xk)^{2} (yh)^{2} = r^{2}
(x5)^{2} (y7)^{2}
= 7^{2}
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
A∩B
A∩B= {2,4,6,8,10,12,14,16} ∩ {12,14,16,20}
A∩B= {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 3–3! 0! 0! 1
24)x^{2}+6x+5= 0
x^{2}+6x+5=0 x^{2}+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 3^{rd} and 4^{th} terms of geometric
series are 12 & B respectively. Find out the sum to infinite.
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