STA100 Midterm Past Papers Set 4

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

Q1. 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

Q2. 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

Q3. If f(x)=4x+1 and g(x)=x-6 then find f(x)-g(x). (2 marks)

f.g(x)= (4x+1)(x-6)

f.g(x)= (4x2-22x-6)

Q4. Write the equation in complete square form , x2 +4x+2 . (3 marks)

x2 +bx+ b +2b

x2 +bx+ 16 +24

x2 +4x+ 16 +2-(2) ( 4 ) 0 ] −4 [ 8 x2 +4x+4 (x+2)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

6) .a=3000, r=

2 find the a10

2(3+5i)-4i)(3+5i)

.a=3000, r= 2 find the a10 = a1r10-1

a10 = (3000)(r9)

a

10 = (3000)( )

a

3000 10 = (

Q7. 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)

rP = 2P = 2! = 2! = 2∗1 = 2 = 2 s 2–2! 0! 0!

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

f.g(x)= (3x-1)(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

Example; [0 1 2]

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

Example; [0 1 0]

Q12. 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

Q13. 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