Federal Board HSSC-I (2012)
    MATHEMATICS
Time: 25 Minutes  
Marks: 20
    SECTION — A (Marks 20)

Q.1     Circle the correct option i.e. A/B/C/D. Each part carries one mark.

•  = ___________ .
  (A) 3        
  (B) 2
  (C) 1                                       
  (D)      -1
  
•    is :
  (A) 1 + i
  (B) 1 - i
  (C) 2(1 + i)
  (D) 2(1 – i)
  
• (xc  yc) = ___________ .
  (A)  x y                    
  (B) x  y
  (C)  (x  y)c                  
  (D) None of these
  
  
• If   X =  then X = _________
  (A)           
  (B)              
  (C)                               
  (D)
  
  
• (v)        For what value of m, the roots of the equation (m+1)x2+2(m+3)x + m + 8=0 are equal?
  (A)                  
  (B)  
  (C)                                      
  (D) None of these
  
  
• If  is the cube roots of unity, then a quadratic equation whose roots are 2 and 22 is :
  (A) x2 + 2x + 4 = 0           
  (B) x2 - 2x + 4 = 0
  (C) x2 + x + 4 = 0               
  (D) x2 + 2x - 4 = 0
  
• If degree of P(x)=3 and degree of Q(x) = 4, then  will be __________
  (A) Proper Rational FractionB.       
  (B) Improper Rational Fraction
  (C) Polynomial
  (D) None of these
  
  
• If a, b, c are in G.P and a > 0, b > 0, c > 0, then the reciprocals of a, b, c form
  (A) A.P      
  (B) G.P
  (C) HP                            
  (D) None of these
  
  
• If , ,   are in    A.P then the common difference is ________
  (A)                                           
  (B)
  (C)                                
  (D)
  
  
• A card is drawn from a pack of 52 cards at random. What is the probability that it is either a heart    or a king?
  (A)                                                 
     (B)
  
  (C)                                            
          (D)
  
  
• The middle terms in the expansion of  will be
  (A) 5th term  
  (B) 7th term
  (C)  8th term                          
  (D) 6th term
  
  
• Circular measure of the angle between the hands of a watch at a 4'0 clock is
  (A)   radians                          
  (B)  radians            
  (C)    radians                        
  (D)   radians
  
  
• If tan  =  and 0 < θ <   then  = __________
  (A)                                       
  (B)
  (C)                                       
  (D)      None of these
  
  
• (xiv)     The angles 90°  θ.180° ± θ,270°  0,360° ± 0 are the______ angle.
  (A) Composite                       
  (B) Half
  (C) Quadrantal                        
  (D) Allied
  
• The period of 3cos is  is _______________
  (A) 5 π                                                
  (B) 2π
  (C) 10                                               
  (D) 6π
  
• The in-radius r of a triangle is given by _______________
  (A)                                               
  (B)
  (B)                                  
  (D)      None of these
  
•    sin  = ___________________
  (A) 0                                      
    (B)
  (C)                                         
  (D)
  
  
•   If α and β are the roots of the equation x2 - (p - 1)x + c = 0 then (1 + α)(1 + β) = ___________
  (A) 1 - c                                             
  (B) c - 2
  (C)  -c                                                 
  (D) None of these
  
  
•    Which term of 64, 60, 56, 52, ………. is zero?
  (A) 16th                                               
  (B) 17th
  (C) 14th                                               
  (D) 15th
  
• Multiplicative inverse of 1 - 2i is = __________
  (A)                                    
  (B)  
  (C)                                    
  (D) None of these

  MATHEMATICS HSSC-I
Time allowed: 2:35 Hours      
    Total Marks = 80

Note:   Attempt any ten parts from Section 'B' and any five questions from Section 'C' on the separately provided answer book. Use supplementary answer sheet i.e.Sheet-B if required. Write your answers neatly and legibly.
SECTION - B (Marks 50)
 Q.2     Attempt any TEN parts. All parts carry equal marks.                                  (10 x 4 = 40)

• Simplify
  
• Without expansion verify that  = 0                                            
  
• Find the condition that  +  = 5 may have roots equal in magnitude but opposite in signs.
• Find the SUM of 20 terms of the series whose rth term is 3r + 1
  
• Resolve into Partial Fraction  
  
• Show that 16C11+ 16C10  = 17C11
  
• Find the term independent of x in the expansion of
  
• If cotθ =  and 0 < θ <  find the value of remaining trigonometric ratios.
  
• If sinα = , then find the values of sin2α and cos2α, where 0 < α <
  
• Draw the graph of y = tan x, x[-π,π] Graph paper should be given to the candidates.
  
• Solve the triangle ABC if
  
  α = 35°17' , β = 45°13', b, = 421         
  
• Show that cos-1 (-x) = π –cos-1x
  
• Solve 2x - y = 4 and 2x2 - 4xy – y2 = 6
  
• Show that the statement q  (p  q)   q  is a tautology.
  

SECTION - C (Marks 40)
Note:   Attempt any FIVE questions. All questions carry equal marks.                               (5 x 8 = 40)
Q.3      Prove that  is an irrational number.
Q.4      Find the value of A for which the system has non-trivial solutions. Also find solution for
the value of 𝞴
x + y + z    = 0
2x+y- 𝞴z    = 0     
x + 2y - 2z = 0
Q.5      Show that roots of the equation
(x-a)(x-b) + (x-b)(x-c) + (x-c)(x-a) = 0
are real and will be equal only if a=b=c
Q.6      If m and n are nearly equal show, that (    +
Q.7    If , β, γ are the angles of a triangle ABC, then show that
Cot  + Cot  + Cot  = Cot  Cot  Cot
Q.8     Prove that r1 =   with usual notation. Also show that r1 = s tan
Q.9     Solve the equation sin2x + cosx = 1