Federal Board (2015)
MATHEMATICS
SECTION-A
(Marks 20)
Time allowed: 25 Minutes
Note: Section-A is compulsory and comprises pages 1-2.All parts of this section are to be answered on the question paper itself. it should be completed in the first 25 minutes and handed over to the centre superintendent. Deleting/overwriting is not allowe(D) Do not use lead pencil.

Q1. Circle the correct option i.e. A/ b/ C/ (D) Each part carries one mark.

• Real part of  is:
  

(A)
(B)            
(C)                            
(D) None of these

• Number of elements in the set {{a,b},{b,c},{c,d}} is:
  

(A) 3
(B) 5
(C) 4
(D) None of these

• The set {1, ω, ω2}, Where ω3= 1is an abelian group under:
  

(A) Addition
(B) Multiplication
(C) Division
(D) None of these

• ||= α  || then α =
  

(A) 3
(B) 6
(C) 9
(D) 12

• For a square matrix A,A-At is:
  

(A) Symmetric
(B) Hermitian
(C) Skew Hermitian
(D) Skew Symmetric

• (-1+)5 + (-1-)5=
  

(A) 16
(B) 48
(C) -32
(D) -1

• The formation of partial fractions of  =
  

(A)  +
(B)  +
(C)  +  +
(D) None of these

• If   ,   ,  are in A.P, then b =
  

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

• The sum of infinite geometric series  +   + +………=
  

(A) 1
(B) 14
(C) 12
(D) None of these

• Factorial form of n (n-1) (n-2)….. (n – r + 1)=
  

(A)
(B)
(C)
(D) None of these

• If P2=30 then n=
  

(A) 15
(B) 6
(C) 10
(D) 15

• In the expansion of ( x -  )11,the sixth term from the end is:
  

(A) 5th term
(B) 7th term
(C) 4th term
(D) None of these

•  +  =
  

(A) 2
(B) 0
(C)
(D) None of these

•  =
  

(A) 300
(B) 1200
(C) 450
(D) 600

• tan(2π+Ѳ)=
  

(A) cot Ѳ
(B) - Cot Ѳ
(C)
(D) -

• cos3α =
  

(A) 4sin3 α-3sin α
(B) 2 cos  sin
(C) 2 cos2  sin2
(D) None of these

• Period of 3 cos  =
  

(A) 2π
(B) 6 π
(C) 30 π       
(D) 10 π

• sin^-1 x =
  

(A)  + cos-1 x
(B) cos-1 x -
(C) tan-1 x -
(D)  - cos-1  x

• sin  =
  

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

• Solution set of sin x = -  is
  

(A) { + 2nπ} U {  +2nπ}  
(B) { + 2nπ} U {  +2nπ}    
(C) {  +2nπ} U { + 2nπ}

Time allowed: 2:35 Hours
Total Marks section B & C: 80
NOTE: Section-'B' and 'C' comprises pages 1-2 and questions therein are to be answered on the separately provided answer book. Answer all questions from Section 'B' and Section 'C'. Use supplementary answer sheet i.e. Sheet-B if require(D) Write your answers your neatly and legibly.

SECTION – B
(Marks 40)

2. Attempt any TEN parts. All parts carry equal marks.  (10x4=40)

• Show that ∀Z  C,Z² + Z^-2 is real number.
  
• Construct the truth table of [(p q) ^ p] 4 q
  
• Show that
  |a+1      a              a  |
  |  a       a+1           a  |= ι²(3a + ι)
  |  a         a           a+1|
  
• Show that the roots of the (mx + c)2 = 4ax will be equal if c =  ; m # 0
  
• Resolve into partial fractions
  
• How many terms of the series (-7) + (-5) + (-3)….amount to 65?
  
• How many arrangements of the letters of the given word, taken all together, can be made "PAKISTAN".
  
• Find the term independent of x, in the expansion of (x -  )10
  
• What is the circular measure of the angle between the hands of a watch at 4 o'clock?
  
• Prove that (sec 0 + tan Ѳ)2 =
  
• Prove that:  = tan 5 6°
  
• Find the area of the triangle ABC, given three sides a = 524 , b = 276 c = 315
  
• Show that  =  +  +
  
• Prove: thn-1  + thn-1  = thn-1  + thn-1
  

SECTION — C
(Marks 40)

Attempt any FIVE questions. All questions carry equal marks. (5x8=40)

Q.3 Use matrices to solve the system:
x₁ – 2x₂+x₃ =-4
2x₁-3x₂+2x₃=-6
2x₁+2x₂+x₃=5

Q.4 If  x + 1, x - 2 are the factors of x3 + px2 + qx + 6 by use of synthetic division find the values of p and q.

Q.5 Sum to n terms of series 3 + 33 + 333 +……   

Q.6 Prove that    +          =
Q.7 Find the values of remaining trigonometric function, sin Ѳ = -   and the terminal arm of the angle is not in the quadrant III.

Q.8 Draw the graph of cos x from 0° tO 360°

Q.9 Solve the equation 2x = cos x