SAHIWAL BOARD 2016
PAPER MATHEMATICS PART-I
Time 30 Minutes
(Objective Part)
Marks:20
Note: Four Answers are given against each column A,B,C&D. Select the write answer and only separate answer sheet, fill the circle A,B,C or D with pen or marker in front of that question number.

•  +  +……………  is equal to:

(a) n(n+ I)             
(b) n (n +1)(2n +1)

(c)  
(d) n  

• A.M between  and - is equal to

(a)       
(b)       
(c)     
(d)  

• Partial fraction of  is of the form:

(a)       
(b) 1+

  
(d)

• The degree of constant polynomial is:

(a) 0              
(b) 1            
(c)  2                  
(d) 3

• If = 1/2 then x is equal to:

(a) -1/2       
(b) -2         
(c) 1/2                 
(d) 1/4 

• If A and B are non-singular matries, then is equal to:

(a)        
(b) 
(c)       
(d) BA

• If A is singular matrix, then  is equal to:

(a)        
(b)        
(c) |A| adj A
(d) Does not exist

• The proposition p →q^q→p is written as:

(a) p^q 
(b) p →q     
(c) q→p 
(d) pq

•  has factors:

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

• The solution of equation cos x = -1 in [0,2π].

(a) π        
(b) -π/2        
(c) 2π       
(d) π/2 

• is equal to:

(a)    
(b)
(c)  
(d)

• Radius of escribed circle opposite to the vertex C is equal to:

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

• Area of triangle ABC is equal to:

(a) 1/2 ab
(b)  1/2 bcsinα
(c) 1/2 acsin      
(d) 1/2 absinα

• Range of cot x is equal to:

(a) R           
(b) Q           
(c) Z           
(d) N

•  is equal to:

(a) cos2α  
(b) sin2α   
(c)   
(d)

•  is equal to:

(a) -1      
(b) +1               
(c) 0           
(d) None of these

• If  > n +3 then it is true for

(a) n= 0   
(b) n< 1        
(c) n  2     (d) n  3

• Range of the probability of an event E is:

(a) (0,1)        
(b) [0.1]       
(c) [0,1)         
(d) (0,1]

• In the expansion of, number of terms is equal to:

(a) n + 1       
(b) 2n + 1    
(c) n + 2   
(d) 2n + 2

• r! nCr is equal to:

(a) nCr+1           
(b)   n+1Pr      
(c) nPr+1    
(d) nPr

Time. 2:30 Hours
Subjective part
Marks:80
SECTION-I

• Define rational numbers.
  
• Simplify .
  
• Simplify (5,-4)(-3,-8) .
  
• Define the power set of a set.
  
• Write the converse and invers of the.
  
• If a,b G , solve the equation, ax = b.
  
• Define the scalar matrix.
  
• Find x and y if +2=
  
• Without expansion show that =0
  
• Solve the equation by quadratic formula 16 + 8x +1 = 0 .
  
• Show that - = (x-y)(x-y)(x-y) .
  
• Find the nature of the roots of the equation. -5x+6=0

 3. Attempt any Eight Parts.

• Define proper and improper rational fractions.
  
• Write first four terms of an = (—On (2n - 3).
  
• If 1,1 and -1 are in A.P. Show that b = 2ac a b c a + c
  
• Find G.M of -2 and 8.
  
• Find the 9th term of 19191  3 5 7
  
• Evaluate  6!  and 8! 3!3! 4!2!
  
• Prove that "C, =" Ch_r,
  
• Define sample space.
  
• Find the value of n when "P2 = 30 .
  
• Prove that formula, 1+3+5+7+ + (2n -1) = n2 , for n = 1,2.
  
• Calculate by means of binomial theorem (0.97)3.
  
• Expand (4-3x)Y2 up to 2 terms.

4. Attempt any Nine Parts. (18)

• What is the circular measure of the angle between the hands of a watch at 4.0' clock. fr
  
• Verify that sine ir. - :sine - : sine fr - : sine fr - =1: 2 : 3 : 4 . 3 6 4 2
  
• Prove that  2tan0 1+ tan' 0= 2 sin 0 cos 0 .
  
• Prove that 0+11 +cos 9+ 5- = cos 9 . 6 3
  
• Prove that sin (a + f) sin (a - fl)=sin2 a - sin2 /3 = cos' ft - cost a
  
• Prove that sin π - 0) sin (5- + 0) = 1 cos 20 . 4 4 
  
• Find the period of tan % .
  
• At the top of a cliff 80m high, the angle of depression of a boat is 12°. How far is the boat from the cliff?
  
• Find the greatest angle of AABC whose sides are 16, 20, 33.
  
• With usual notations show that rrir2r3 = A' .
  
• Show that sin" (-x) = -sin" x .
  
• Solve sinx + cosx = 0.
  
• Solve see 0 =  ,0 E [0,2x].

SECTION-I

Attempt any THREE guestions:Each questions carries 10 marks.

5. (a) Use Cramer's rule to solve the system.
2x + 2y + z = 3
3x - 2y - 2z = 1 5x+ y-3z= 2
(b) Solve the system of equations x y = a+ b;-a +-b = 2.xy

6. (a) Resolve into partial fractions 1- x4
(b) Find the five numbers in A.P whose sum is 25 and the sum of whose squares is 135.

7. (a) Find the values of n and r when "C, = 35 and "P, = 210
(b) Find term independent of x in the expansion , x + 2x2

8. (a) Prove that sin' 0 - cos' 0 = (sin2 0 - cos' 0)(1 - sin' 0 cos2 0)
(b) Reduce cos° 0 to an expression involving only function of multiples of 0 , raised to the first power.

9. (a) Find the area of triangle ABC, in which a = 18, b = 24, c = 30
(b) Prove that sin^-13/5+ sin^-18/17 = sin^-1 77/85.