Federal Board 2014
MATHEMATICS
HSSC-I
Time allowed: 25 Minutes
Marks: 20

SECTION — A
                                                                                       
NOTE: Section-A is compulsory. 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.

• ∀a, b R, a = b b= a, this property is called

(A) Transitive        
(B) Symmetric
(C) Reftexive          
(D) Additive

• i²² =

(A) i                  
(B) -i
(C) -1                
(D) 1

• If A Bthen A ∪ B =

(A) A                 
(B) B
(C) Φ                 
(D) X

• If order of a matrix A it 2 x 3 and of matrix B Is 3x 3 the order of 'AB' is

(A) 3x2               
(B) 2x2
(C) 3x3                
(D) 2x3

• The discriminant for equal roots is

(A) >0                
(B) <0
(C) =0                
(D) Perfect square

• If a_n-3 = 2n - 5 , its nth term is

(A) 2n+1              
(B) 2n+3
(C) 2n-2              
(D) 2n - 8

• If a, A, b are in A.P. then 2A=

(A) a - b             
(B)     
(C) a + b             
(D) a x b

• The number of terms in the expansion of (a +x)ⁿ

(A) n + 1             
(B) n-1
(C) n                  
(D) 2n

• n! > n2 is true for integral value of n=

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

• If  are the angles of a triangle than tan() + tan =

(A) 0                   
(B) 1
(C) 2               
(D) None of these

• =

(A) tan 11°            
(B) cot 11°
(C) tan 56°            
(D) cot 56°

• Sine is a periodic function and its period is

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

• Geometric Means between -2 and 8 is
  

(A) 2                 
(B) 8
(C) ±4                
(D) None of these

• All trigonometric functions are positive in quadrant

(A) I                  
(B) II
(C) III                  
(D) IV

• In a triangle ABC, the measures of the three sides opposite to three angles are denoted by

(A) 1,2,3             
(B) A, B, C
(C)           
(D) a, b, c

• r. r₁. r₂. r₃ =

(A) S                   
(B) s-a
(C) Δ                  
(D) Δ²

• tan^-1(1) =

(A)               
(B) π/2
(C)                
(D) π

• The graph of y = sin^-1 x is along the

(A) x-axis
(B) y-axis
(C) Both A and B
(D) None of these

• In the binomial expansion of (a + b)n is called

(A) Root
(B) Element
(C) Index
(D) None of these

• If r = 1,then 'P. =

(A) n!                
(B) n
(C) (n -1)            
(D) None of these

MATHEMATICS HSSC-I
Section - B
(Mark 40)

2. Attempt any TEN parts. All parts carry equal marks.

• Show that (z - )² is real number  z  C.
  
• Define Group. Also give one example.
  
• Show that =9
  
• Find the condition that one rot of x² + px + q = 0 is Multiplicaticative inverse of the other
  
• Find the values of 'a' and 'b' if' - 2' and '2’ are the roots of the polynomial x³ - 4x² + ab + b  
  
• Resolve  into Partial Fractions.
  
• If the H.M and A.M between two numbers are 4 and respectively, find the numbers.
  
• Write (n + 2)(n + 1)(n) , in the factorial form.
  
• If x is so small that its square and higher powers may be neglected, show that x.
  
• If cot =  and the terminal arm of the angle is in the 1st quadrant 0 <θ<, find the value of
  
• Prove that tan is a periodic function of π
  
• If the measures of the sides of a triangle ABC are 13, 14, 15, find 'r'.
  
• Prove that tan-1(-x)= -tan-1 x
  
• The Sum of a positive number and its reciprocal is  .Find the number.

Section - C (Mark 40)

Note: Attempt any FIVE questions. All questions carry equal marks.

Q.3 Simplify (-- i)

Q.4 Use matrices to solve

Q.5 If ω is a root of x2 + x + 1 = 0, show that its other root is ω² and prove that ω² and prove that ω³ = 1

Q.6      Solve the system of equations

3x + 4y = 25 ,

Q.7  If 2y =  then prove that 4y2 + 4y - 1 = 0

Q.8    Reduce cos⁴ θ to an expression involving only function of multiples of θ, raised to the first power.