Gujranwala Board 2012 Inter Part-I)
Mathematics
OBJECTIVE Paper:
Time Allowed:- 30 minutes
Maximum Marks: 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 will. Cutting or filling two or more circles will result in zero mark in that question. Write PAPER CODE, which is printed on this question paper, on the both sides of the Answer Sheet and fill bubbles accordingly, otherwise the student will be responsible for the situation. Use of Ink Remover or white correcting fluid is not allowed.

• The solution of the equation sec x = -2 in the interval[0, 2xj is:

A.    

B.   
C.        
D.

• Radius of e-circle r² is given by:
  

A.                     
B.          
C.             
D.     

• If  are angles of a triangle then tan (+ tan

A. 0
B. 1
C. 2
D. -1

• The expansion of is valid if:

A. |x|> 
B. |x|<1

C. |x|< 

D. |x|<2

• The inequalities n is true for integral values of n:

A. n < 4 
B. n < 1 
C. n > 2
D. n >4 

• Factorial form of (n+2) (n + 1) (n) is:

A.                       
B.  
C.              

D.

• If 5 is A.M. between -5 and b, then b is equal to:
  
  A. 0                               
  B. 15                
  C. -5                  
  D. 10
• The product of the roots of equation ax2+ bx – c=0 is:
  

A.                            
B.   
C.                            
D.

• The set of second elements of the ordered pairs forming a relation is called

A. subset                    
B. domain
C. range                      
D. power set

• (z +)2 is:

A. complex number     
B. real number    
C. rational number      
D. irrational number 

• The value of cos  is:  

A.                       
B. 1  
C.               
D.  

• Cosine is periodic function of period:

A. 2                     
B.            
C.                       
D.

• If sin  > 0 and sec  then terminal arm of the angle  lies in  

A. 1st quadrant      
B. 2nd quadrant    
C. 3rd quadrant    
D. 4th quadrant                                                                                                               

• General term of the expansion(a+x)n is given by 

A. nC,anxn+r           
B. nC,an-rxn       
C. nC,anxr                 
D. nC,an-rxr 

• Probability of an impossible event is:

A. P(E) = 1               
B. P(E)= 2        
C. P(E)= 0        
D. P(E)=                                         

• G. M. between -2 and S is:

A. 4           
B. +4i       
C. +6           
D. +i                

• Partial fractions of will be;

A.             
B.          
C.    

• If order of a matrix A is m x n, they order of At is:

A. m x n               
B. n x n                     
C. n x m                   
D. m x m 

• If A B, then A B is:

A. A                       
B.  
C. AB   
D. B

•   is:

A. real number
B. natural number
C. rational number
D. imaginary number 

Inter (Part-I) Gujranwala Board 2012
Mathematics
SUBJECTIVE Paper: 1

Note: Section 1 is compulsory. Attempt any three (3) questions from Section II

(Section - 1)

Write short answers to any EIGHT questions:

• Prove that  Explain each step.
• Simplify
• Write two proper subsets of (a, b,c)
• Show that the statement  is a tautology
• For A = {1, 2, 3, 4}, find the relation {(x, y) |x+ y <5}
• Define ‘Monoid’.
• If A and B are square matrix of the same order, explain why in general (A + B)2 A²+2AB + B²
• Without expansion show that
• If A=
• Define the radical equation with example.
• Evaluate
• Show that the roots of the equation px2-(p-q)x-q=0 will be rational

3. Write short answers to any EIGHT questions:

• Define partial fraction resolution.
• Resolve into partial fraction
• Which term of A.P; 5, 2, -1 ... is -85?
• Define geometric mean
• Find the 88th term of H.P;,……………           
• Find n when 11Pn=11.10.9
• In how many ways can 4 keys be arranged on a circular key ring?
•  A fair coin is tossed three times. Find the probability that it shows one tai
• Write the formula for product of probabilities of two events.
• Using mathematical induction, prove that ………..+ for n=1 and n=2
• Find the term independent of x in the expansion of (
• If x is so small that its square and higher powers be neglected, then prove that

4.Write short answers to any EIGHT questions:

• Convert the angle  radian into degree.
• Find r if
• Prove that 2 sin 45° ÷  cosec 45° =
• Show that
• Prove that
• Express sin5 as a sum or difference.
• Draw the graph of sin x from 0 to 180°.
• State any two laws of cosines in a triangle
• Find area of the triangle ABC when a = 35° 17',
• With usual notations prove that
• Show that
• Prove that
• Solve the equation 1+cosx=0

Section-II

5 (A).Show that the set consisting of elements of the form a+ b(a,b being rational), is an abelian group w.r.tt addition.
(B). Show that

6 (A). Find the values of a and b if -2 and 2 are the roots of the polynomial x³ - 4x²+ ax+b
(B) For what value of n is positive G.M between a and b.

7 (A).Find the number of 5-digit numbers that can be formed from the digits I, 2, 4, 6, 8 when no digit is repeated) but the digits 2 and 8 are next to each other.
(B) If x is so small that its square and higher powers can be neglected, then show that

8 (A). If cosec, find the value of remaining trigonometric ratios.
(B) Prove that 1+tan

9(A). Using usual notations, prove that r=s tan  tan
B. Without using calculator/table, show that