Mathematics Paper I
(Objective) Group-1
Time Allowed.- 30 minutes
Maximum Math:- 20

Note: You have four choices for each objective type question as A, B, C and D. The choice which you think is correct; fill that circle in front of that question number. Use marker or pen to fill the circles, Cutting or filling two or more circles will result in zero mark in that question, Attempt as many questions as given in objective type question paper and leave others blank. Write the letter A, B, C or D in the column (write correct option) against each question. If there is a contradiction in the bubble and hand written answer, bubble option will be considered correct.

• If 2=--x + iy then tan  is
  

A.                                      
B.                                       
C. x+y                                                   
D. xy

• The multiplicative inverse of (1,2) is
  

A.  i                         
B.  I                               
C.                                
D. None of these

• If K is any real number then K(a,b)=
  

A. (Ka, Kb)                     
B.  ()                             
C. (a,b)                              
D. ()

• If set AB then
  

A. A                    
B. A                 
C. A                     
D. A

• If  then |A|
  

A. 34                                   
B. -14                                   
C. 14                                      
D. -34

•  is equal to
  

A. 0    
B. 1 
C.                                 
D.

• The fourth tern of an  is

A.                                  
B.                                   
C.                                    
D.

• The relation -called A
  

A. Number                  
B. Integer                              
C. Equation               
D. Fraction

• The harmonic Mean between two was a and b is  
  

A.                            
B.                                      
C.                              
D.

• 6P3=
  

A. 36                             
B. 360                                     
C. 6                                            
D. 120

• For an event A, the range of its probability is
  

A. -1<PA. <1           
B. 0<PA. <1                               
C. 0<PA. <1                                        
D. 0<PA. <1

• n!>2n-1
  

A. n>4                       
B. n > 2                                       
C. n < 4                               
D. n < 2

• In the expansion of  the co-efficient of x2 is a
  

A.-(2)⁶a⁵ 
B. (2)⁶a⁵
C. a⁵                                    
D. -a⁵

• If |x|< I then the expansion of (1-x)1/2up to two terms is
  

A.                  
B.                                     
C. 1-x                                     
D. 1+x

• The 60th part of one minute is called one
  

A. Minute              
B. Radian                                      
C. Degree                        
D. Second

A. tan                  
B. -tan                                            
C. -cot                          
D. cot 

• The range of cos x is
  

A. [-1, 1]               
B. R     
C. =(2n+1) 

D. R-{x/x=n

• A triangle in which two sides are equal is called

A. Isosceles         
B. Right                            
C. Equilateral                                  
D. None of them

• ) is equal to
  

A.                      
B.                            
C.                                      
D.

•   then
  

A.                     
B.                                                
C.                                                      
D.

Mathematics (Subjective)
Time Mowed: 2.30 hours   
Maximum Marks: 80
Group -I SECTION

2. Answer briefly any Eight parts from the followings:-

• Name the property used in a(b - c) = ab – ac
• Show that 2 is a real number,  
  
• Verify associativity of union for the sets A,B &C A={1,2,3,4}B={3,5,6,7,2} C={5,6,7,9,10}
  
• Write the converse and contra positive of the conditional
  
• For A={1,2,3,4} find the relation in A:  R={(x,y)ly=x)
  
• Show that S={ 1,), where = 1 is an abelian group w.r.t multiplication
  
• Solve the system of linear equation: 2x₁3x₂=5; 5x₁+x₂=4
  
• Find the value of x ;
  
• If A is a square matrix of order 3. Show that (A -A') is skew-symmetric
  
• Solve the equation by completing square x²+6x-567=0
  
• If are roots of 3x²-2x+4=0, find the-value of  
  
• Solve the system of equations: 3x+2y=7    ; 3x²=25+2y2

3. Answer briefly any eight parts from the followings:

• Define improper Rational Fraction.
  
• Resolve  into Partial fraction.
  
• Write formula for finding sum of n terms of A.P.
  
• If y=1+2x+4x²+8x³…………,then show that x=
  
• Find the 9th term of H.P. ………..
  
• State Fundamental principle of counting.
  
• How many arrangements of letters of word `Pakistan' can be made.
  
• A fair coin is tossed four times. Find the probability that top shows 2 heads and 2 tails.
  
• Let S={1,2,……..9}. Event A={2,4,6,8} and Event B={1,3,5} Find P(A
  
• Using mathematical induction, prove that 12+32+52 +…..+ (2n -1)2= for n=1 and n=2   
  
• Calculate ‘r’ for finding term independent of x tile expansion of ( )10
  
• If x is so small that its square and higher powers be neglected, then prove that 

4. Answer briefly any Nine parts from the followings:-

• Convert the system into Radian 154
  
• Prove that Sin 60° Cos 30° Cos60° Sin30° =Sin30°
  
• If are the angle of triangle ABC prove that tan() + tan 
  
• Prove that Cos( +45°) = (Cos )
  
• Prove that 1+tan tan2 = Sec2         
  
• Express the sum or difference as product is to
  
• Find the Range of Cot  
  
• Find the period of 3 Cos
  
• Solve the right triangle ABC in which  =90°   = 62° 40'  b=796
  
• Solve the triangle ABC in which a=3  c = 6     =36° 20'
  
• Show that r = 4R Sin-Sin Sin
  
• Find the solution of the equation lie in [0,2] Cot  
  
• Solve the trigonometric equation Cot2

SECTION ---- 11

Note: Attempt any three questions.

5 A. If h is a group under the operation * and a, b  h then find the solution of the equations
(i) a* n b                                              (ii) n * a = b

B. Solve the system
x -2y +z =-1
3x+y-2z =4
y z = 1
6. A. If are roots of px2+qx+q=0 then prove that
(b.) Find n so that may be H.M. between a and b

7. A. Two coins are tossed twice each find the probability that the head appears S on the first toss and the same faces appears in the two tosses.
B. For y = …….show that 5y²+10y-4=0

8.A. Find x if tan2 45 - Cos2  = xsin45 45
B. If are the angle of a tringle ABC. Prove that sin (

9 .A. Prove law of cosine of a triangle ABC b2=a2+c22ac CosB
B. Prove (without using calculator)