Mathematics
(Objective)
Maximum Marks:- 20
Time Allowed:- 30 minutes
Note:-You have four choices for each objective type question as A, B, C and D. The choice which you think is covert; fill that circle in front of that question number. Use marker or pen to fill the circles. Cutting or filing two or more circles will result in zero mark in that question. Attempt as many questions as given in objective type question paper and leave other blank. Use of ink remover or white correcting fluid is not allowed.

Q. 1

• If z=3+4i , then |z| =________           
  

(A) 5            
(B) -5          
(C) 25         
(D) -25

• The power set of the empty set is_____

(A) Empty set          
(B) Non empty net               
(C) Proper set         
(D) Improper set

• Rank of matrix is______

(A) 1             
(B) 2            
(C) 3            
(D) 4

• The trivil solution of homogenous system of linear equation in three variables is____

(A) (0,0,1) 
(B) (0,1,0) 
(C) (1,0 0) 
(D) (0,0,0)

• An equation of the form ax²+bx+c =0 is called quadratic if

(A) a=0       
(B) a≠0
(C) b=0      
(D) b≠0

• If a polynomial f(x) is divided by x -, then remainder is_____

(A) f(-a)     
(B) f(-1/a) 
(C) f(1/a)  
(D) f(a)

• The fraction is_______    

(A) Proper fraction         
(B) Improper fraction
(C) Common fraction
(D) Irrational fraction

• 21st term of 2+4+6+--------is
  

(A) 40         
(B) 42         
(C) 44         
(D) -42

• If a, A, b are in A.P, then A=_______

(A)        
(B)         
(C)      
(D) 

• ⁶C₂=______
  

(A) 5
(B) 10
(C) 15
(D) 20

• The probability to get an odd number in a dice thrown once is____

(A)
(B) 1/6
(C) 2
(D) 1/3

• Middle term of (a+b)n, when n is even is_____
  

(A)     
(B)
(C)
(D)

• n₁>2^n-1is true for_____
  

(A) n>1
(B) n≥1
(C) n=1       
(D) n≥4

• 120°=______

(A)  
(B)
(C)
(D)  

• Cos²Ѳ=_______

(A)  
(B)
(C)
(D)  

• Range of Tan x is_____          
  

(A) -∞<y< ∞     
(B) -∞<y< 0       
(C) -∞ ≤ y ≤ ∞    
(D) 0<y<2π

• Circum radius of a circle is denoted by
  

(A) R
(B) r
(C) r₁
(D) r₂

• If in a triangle ABC, α=90°, then
  

(A) b²+c²=a²            
(B) c²+a²=b²             
(C) a²+b²=c²            
(D) b²- c² =b²

• Sin^-1(A +B)=______             
  

(A) Sin^-1A+Sin^-1B
(B) Sin^-1A – Sin^-1B 
(C) Cos^-1A+Cos^-1B 
(D) Cos^-1A-Cos^-1B 

• If SinX=andx є[0,2π],thenx____
  

(A) x/3, 2x/3             
(B) x/4, 3x/4             
(C) 5x/3, 4x/3           
(D) 1x/6, 5x/6

Mathematics
(Subjective)
Time Allowed: 2.30 hours

2. Answer briefly any Eight parts from the followings:

• What is multiplicative inverse of 2+i3.
  
• Factorize 3x²+3y²
  
• Define a set
  
• Write power set of set {a, b}
  
• If is singular what is value of K.
  
• Define a scalar matrix.
  
• Find transpose of A=    
  
• Find A-1 if A=
  
• What is quadratic equation whose root are α, β
  
• What is Discriminant of ax2+ bx + c = 0
  
• Show that =
  
• Evaluate (1+ω+ω²)⁸
  

3. Answer briefly any eight parts from the followings:-  (8 x 2 = 16)

• Resolve  in to Partial fraction.
  
• Resolve in to Partial fraction.
  
• How many terms of the series: (-7)+(-5)+(-3)+....amount to 65?
  
• Which term of the sequence: x2-y2,x+y, ,.....is
  
• Insert three G.Ms between 2 and 32.
  
• If 5 is the harmonic mean between 2 and b, Find b
  
• Write in to factorial form of n (n-1) (n-2)
  
• In how many ways can be letters of the word "MISSISSIPPI" be arranged when all the letters are to be used?
  
• Find the value of n, when “C10=
  
• If sample spaces = {1,2,3,...,9}, Event A= (2,4,6,8}and Event B={1,3,5} Find P(AB).
  
• Using binomial theorem expand 4
• If x is so small that its cube and higher power can be neglected, then show that  =1--  x2
  

4. Answer briefly any Nine parts from the followings: (9 x 2 = 18)

• A railway train is running on a circular track of radius 500 meters at the rate of 30 km/h. Through what angle will it turn in 10 sec.
  
• Prove that  = (CosecѲ+CotѲ)2
  
• Without using table find value of Sin(-780°)
  
• Prove that  =tanα
  
• Prove that Sin (Ѳ + ) +Cos (Ѳ +  = CosѲ
  
• Express Sin5x+Sin7x as product
  
• Find period of Cos  
  
• At the top of a cliff 80 m high, the angle of depression of a boat is 12° How far is the boat from the cliff.
  
• Solve the triangle ABC with a=7 , b=3, c=5
  
• Find the area of triangle ABC when α=35°17', y= 45°13', b=42.1
  
• Find 'R' and 'r' if a=13, b=14, c=15 are sides of triangle ABC.
  
• Find the solution of equation which lies in (0,2π) when CosecѲ=2
  
• Solve Sin x + Cos x=0 when xє[0,2π]
  

Section----ll

Attempt any three questions. (10 x 3 = 30)

5-(a) Show that the set {1,ω,ω²}when ω³=1 is an Abelian group w.r.t ordinary multiplication.
(b) Using Cramer's Rule solve system of equations
2x + 2y + z=3
3x - 2y - 2z =1
5x + y - 3z= 2 

6-(a) Show that the roots of x²+(mx+c)²=a²will be equal, if c²=a² (1+m²) 
(b) Resolve  in to Partial fractions

7-(a) Find the vulgar fraction of 1.53
(b) Find 6th term in the expansion of ()10

8-(a) Prove the result: =
(b) If α+β+ϒ = 180°, show that Cotα Cotβ + Cotβ Cotϒ+ Cotϒ Cotα=1

9-(a) Prove that r r₁ r₂ r₃=∆²
(b) Prove that Sin^-1 + Sin-1 = Sin-1