FAISALABAD BOARD 2012
PAPER MATHEMATICS PART-I
Time: 30 Min.
(Objective Part) 
Marks: 20

Note: Four Answers are given against each column A.11, C&D. Select the write answer and only separet answer sheet, fill the circle A, B, C or D with pen or marker in front of that question number.

• General solution set of the eq 1 + Cos x = 0
  (a) {2n}; n𝜀 Z                 
  (b) {n};n𝜀 Z
  (c){+2n}= n𝜀 Z
  (d) { +2n}; n𝜀 Z
  
  
• (   ) is equal to:
  (a) Tan-1 A + Tan-1 B                                     
  (b) Tan-1 A - Tan-1B
  (c)Cot -1 A + Cot-1 B                                  
  (d) Cot-1 A - Cot-1B
  
  
• Value of circum radus R is:
  (a)                     
  (b)
  (c)
  (d)
  
  
• The range of Cot x is:
  (a) IR                                           
  (b)[ -1 ,1 ]
  (c) IR – {x |x = n}
  (d) IR-{x|x= (2n+1)}
  
  
• If = 150°, then its reference angle is:
  (a)  15°
  (b)  30°                  
  (c)  45°
  (d)  60°
  
  
• Cot2  - cos ec2 is equal to:
  (a)  -1      
  (b)  0                    
  (c)   0         
  (d)   2
  
• The second term in the expansion of (1 +  x)-1 is:
  (a)                  
  (b)  2x
  (c)                        
  (d)
  
  
• The general term of the binomial expansion of (a+ x) n ,n𝜀N is:
  (a)  nCranxr
  (b) nCrarxr
  (c)  nCr(ax)n-r      
  (d)  nCran-rxr
  
  
• n2 > n+3 for all integral values of :
  (a)  n  3
  (b)  n  3                       
  (c)   n  2
  (d)   n  2       
        
  
• The probability that an event E does not occur is:
  (a) P(E)=
  (b) P()=
  (c)  P()= P(E) -1    
  (d)  P()= 1-P(E)    
  
  
• The number of ways in which 5 person can be seated at a round table are:
  (a) 2!       
  (b) 3!                   
  (c) 4!         
  (d) 5!
  
  
• If "a" and "b" are two positive distinct real numbers, then:
  (a) A> G                                    
  (b) A <G
  (c) A = G                                    
  (d) A  G
  
  
• The sum of n terms of an A.P. is n2. Then its common difference is:
  (a) 4       
  (b) 2      
  (c) -2      
  (d) 1
• The partial fractions of      will be of the form:
  (a) +  +
  (b) +  
  (c)+  +
  (d) +
  
  
• The degree of constant polynomial is:
  (a)         0        
  (b)         1        
  (c)         2          
  (d)        3
  
  
• If A = [] and B = [5 0] is  equal to
  (a)
  (b) []
  (c) [0 0]
  (d) []
  
  
• A function  is called onto, if:
  (a) Dom f = X                               
  (b) Range f = Y
  (c) Range f = X
  (d) Domain f= range f
  
  
• If A = {0}, then P(A) (power set of set A) is:
  (a)  {0}                           
  (b) {0,𝜙}
  (c) {𝜙,(0)}                      
  (d) {(0),( 𝜙)}
  
  
• Conjugate of - 2 + 3i is:
  (a) -2-3i                        
  (b) 2-3i
  (c) 2 + 3i                         
  (d) - 2 + 3i
  
  
• The set 10,11 is closed under:
  (a) Addition                      
  (b) Multiplication
  (c) Subtraction
  (d) Division

Time: 2:30 Hours 
      (Subjective Part)           
Marks: 80
SECTION-1

• Simplify: (a + bi)3
  
• Define the difference of two sets.
  
• Show that the statement P (Pq) is a tautology.
  
• Find the inverse of the relation {(x,y)|Y2 = 4ax,x  0}.
  
• Show that the set of natural numbers w.r.t. addition is not group.
  
• What is the transpose of a matrix?                          
  
• Without expansion show that               = 0             
  
• If the matrices A and B are symmetric and AB = BA, show that AB is symmetric.
  
• Define radical equation with example.
  
• Evaluate: (1 +  2)8   
  
• Discuss the nature of the root of the equation x2 + 2x +3 =0.
  
• 3.Attempt any Eight Parts.     16
  
• Resolve into partial fractions:
  
• Resolve into partial fractions:
  
• Which term of A.P. -2, 4, 10,….. is 148 ?
  
• Find the sum of infinite geometric series: + +1+…..
  
• Find the 9th, Term of harmonic sequence: -  , -  ,-1…
  
• Evaluate: 10P7
  
• Find the values of n & r, when rCr = 35,n Pr = 210.
  
• A coin is tossed four times. Find the probability to get two heads and two tails.
  
• A natural number is chosen out of first fifty natural numbers. What is the probability
  that chosen number is multiple of 3 or 5?
  
• Prove by induction that formula is true for all positive integer 'n' 1+5+9+……
  +(4n-3)=n(2n-1).
  
• Find the term involsing y3 its the expansion of (x -  )11
  
• If x is so small that its square and higher powers can be neglected then show that:
    4(1- )
  

4.          Attempt any Nine Parts.     18

• Convert the radian into the degree   .
  
•  Prove that Sin2   + Sin2  + Tan2  = 2
  
•   Prove that Sin(180o +α).Sin(90° - α) = SinαCosα .
  
•  Prove that       = tan 56°
  
•  Express the product as sum or difference 2Cos5 Sin3
  
•  Find the domain of tan .
  
•  Find the period of Sin3x.
  
•  Solve the right triangle ABC in which  90o , α = 37°20' , α = 243.
  
• Solve the triangle ABC in which β =125  =53°, α= 47°.
  
•  Find the area of ABC if α = 200 , β =120  = 150°.
  
•  Find the solution of equation lie in (0,2) Sinx =
  
• Solve the trigonometric equation, tan2 =
  

SECTION-II:Attempt any THREE questions. Each questions carries 10 marks.
5. (a) Let "G" be a group and a,b,c G. Then prove that
(i) ab = ac  b = c (ii) ba = ca  b = c holds in G.
(b) Solve the matrix equa ion for matrix A when A

6. (a) Show that the roots of the equation
(a2 - bc)x2 + 2(b2 - ca)x + c2 - ab = 0 will be equal if either a3 +b3 +c3 = 3abc or b = 0.
(b) The nth term of the series is 3n2 + 2x +1 . Find the sum to 2n terms.
7. (a) Prove that n-1Cr + n-1Cr_1 = nCr.
(b) If A and B are square matrices and AB = Ba, then show by mathematical induction that ABn = Bn A for any positive integer n.
8. (a) Find the values of all trigonometric functions of -  .
(b) Prove that Cos20°Cos40° Cos60° Cos80° = 16 without use of calculator.
9.(a) Prove the law of sines of a triangle ABC. ==
(b) Prove that (without using calculator),
Sin-5 ()+ Sin-1 ( )= cos-1 (