STA100 All Paper Mid Term
STA100 All Paper Mid Term
STA100 All Paper Mid Term
STA-100
Prepared by:
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STA-100 Papers_2019
Objective
1) A(4,3) B(10,7); find the mid point
2 0
2) 4[ ][8 0]
4 −1 16 −4
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
Cos[ 2(90))0-Cos300]
-Cos(-300)
√3
-Cos30 0 = -
2
5) .(2-4i)(3+5i)
2(3+5i)-4i)(3+5i)
6+10i-12i-20i2
6-2i-20(-1)
6-2i+20
26-2i
1
6) .a=3000, r=
2
find the a10
2(3+5i)-4i)(3+5i)
1
.a=3000, r= find the
2
a10 = a1r10-1
a10 = (3000)(r9)
a10 = (3000)( 1) 9
2
a10 = (3000
9
)
2
7) A club has five seniors and three junior players . For and upcoming tournament they have to make
a team of two juniors and two seniors. how many possible number of teams they can make (this
question is from combinations ) (5 marks)
r 2!
P = 2P = =
2! 2∗1 2
= = =2
s 2
2–2! 0! 0! 1
8) If f(x)= 3x-1 and g(x)= 2x-1 then find the product of i.e, f.g(x)
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
A= {a,b,c,d,……,z}
C= {4,6}
(x-k)2- (y-h)2 = r2
(x-5)2- (y-7)2 = 72
.x2+3 =
7
tt
3 2 7 3 2
2 3
.x +2 +( ) = +( )
2t 2t t 2t
3 2 7 9
(x + ) = +(4t2)
2t t
3 2 28t+9
(x + ) =( )
2t 4t2
2
J(x + 3 ) =J( 28t+9)
2t2 4t
.x+ 3 = 28t+9
± (J 2
)
2t 4t
3 –3±√28t+9
.x+ =
2t 2t
20) A= {2,4,6,8,10,12,14,16}
B={12,14,16,20}
find A∩B
22) 1 2 1 2 2 3
A=[2 1 2] B=[ ], is multiplication possible
2 1 1
3 1 3
Order of A= 3 × 3
Order of B=2 × 3
For the multiplication
Number of Columns in A = Number of rows in B
Here,
3≠2
SO, multiplication is not possible.
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.
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 !