SAHIWAL BOARD 2014
PAPER MATHEMATICS
PART-I
Time: 30 Min.
(Objective Part)
Marks: 20
Note: Four Answers are given against each column A, B, CandD. 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.

• The degree of the polynomial 7x⁵+ 5x²+ 9 = 0 :

(a) 2
(b) 6    
(c) 5
(d) 7

• The rational fraction  is :  

(a) Proper fraction
(b) lmproper fraction
(c) Both
(d) None of these

• The H.M. between a and b is :

(a) a + b
(b) a - b
(c)
(d) ab

• The rational fraction  :         

(a) Proper fraction
(b) Improper fraction
(c) Both
(d) None of these

• The next term of G.P. 1,2,4,8,16,……….. is:

(a) 15
(b) 19  
(c) 21
(d) 32

• A =  is matrix of order:

(a) 2x3
(b) 2x4
(c) 4x2
( d) 0

• If a, β are the roots of ,x2 + x + 1= 0 then a + β  = :

(a) -1
(b) 2    
(c) I
(d) 0

• A = :

(a) A
(b)    
(c) 3
(d) B

• If A = , B =  then A + B = :

(a)
(b)
(c)
(d)

• If Z = 20+15i then |z| =

(a) 20
(b) 15  
(c) 25
(d) 30

• If X, y  R then X + iy is pure imaginary if:

(a) x # 0, y= 0
(b)) x = 0, y = 0
(c) x = 0,y # 0
(d) x; 0,y # 0

• In the expansion of (x — y)" then terms are alternatively + Ve and

(a) Negative
(b) Undefined
(c) Absurd
(d) None of these

• sin 2θ=

(a) 2sin θ.cos θ
(b) 2 tan θ       
(c) sec² θ
(d) 2sin θ

• If sin θ < θ ,cosθ < θ then θ lies in quadrant.

(a) I
(b) II   
(c) III
(d) IV

• sin 390' =

(a)
(b)   
(c) -
(d) 1

• tan (450 - θ) =

(a)
(b)        
(C)  
(d)        

• The range of COS X is:

(a) R
(b) [-1, 1]        
(c) [-3, 3]
(d) [0,3]

• r²  =

(a)  
(b)              
(c)  
(d)

• The number of terms in the binomial expansion of (a +6)15 are:

(a) 15
(b) 14  
(c) 16
(d) 13

• | =

(a) 24
(b) -24
(c) 0
(d) None of these

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

Q.2
Attempt any Eight Parts. (2×8 =16)

• Define irrational number.       
• Find modulus of I -j
• Define an Onto function.
• Write down power set of {+,-}
• Define semi-group.
• Let P  q be a conditional, find converse and inverse.
• Define a square matrix.
• If  is singular matrix. Find K.
• If A and B are symmetric matrices and AB=BA. Show that AB is symmetric.
• Evaluate  +  + 1, is complex cube root of unity.
• State Remainder theorem.
• Find equation whose roots are 2 and 2 where  is cube root of unity.

Q.3
Attempt any Eight Parts. (2×8 = 16)

• Define partial fraction.
• Find the number of terms in A.P if ; a1 = 3, d = 7 and a,, = 59.
• Find the 5th term of the G.P. 3,6,12 …………
• Prove that G2 = Ax H for two positive numbers a and b.
• Find the next two terms of the sequence 1,6,20,56……       
• How many signals can be given by 5 flags of different colors, using 3 flags at a time?
• Find n, if ⁿC₁₂  = ⁿC₆ ..
• A die is rolled. What is the probability that the dots on the top are greater than 4?
• If x is so small that its square and higher powers can be neglected
  then show that  = 1 -  x .
• Calculate (2.02)4 by means of binomial theorem.
• Expand (I+2x)-1 uptu 4 terms. 
• Prove that ⁿC_r x r ! or | = ⁿP_r

Q.4
Attempt any Nine Parts.(9×2 =18)

• Prove that I +cot²θ = cos ec²θ
• Show that (secθ + tanθ)(secθ - tanθ) = 1.
• If cos a = , Find cos2’a where 0 < a <  .
• Show that :-    sin(450 + a) =  (sin α + cos α) .
• Pnove that:- sin (1800 + α) sin (900 -α) =  -sin α cos α .
• Find the period of sin .
• Define the angle of Depression.
• Define an oblique triangle.
• If in a triangle ABC, β =  600,  γ = I50,  b = . Find a.
• In triangle ABC a=13,  b=14,  c=15, Find R.
• Evaluate without using table sin-1 (1).
• Solve the equation 1 +COS x = 0  X  [0,2π] .
• Find solution of equation sec x = -2 in [0,2π].

SECTION-II

Attempt any THREE questions. Each questions carries 10 marks.

Q.5
(a)show that:-  = (a – b) (b – C) (c – a).

(b)Solve the equation: - 3 – 4 = 0

Q.6
(a)Resolve  into partial fractions.
(b)Find n so that  may be H.M. between a and b.

Q.7
(a) Prove that ⁿC_r +ⁿC_r-1 = 11+1C_r .
(b)Find the term involving x-2 in the expansion of    

Q.8
(a)Find the values of remaining trigonometric functions
sin θ = -   and the terminal arm of the angle is not in quad.
(b)Prove that sin 100 sin 300 sin 500 sin 700 =  .

Q.9
(a)With usual notation show that:-
r= 4R sin  cos  cos
(b)Prove that
Sin^-1 A – sin^-1  B = sin^-1  .