Inter (Part-I) Bahawalpur Board 2016
Mathematics
Part I (Objective Type)
Time Allowed: 30 Minutes
Max. 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. Cutting or filling two or more circles will result in zero mark in that question.

Question #1
Circle the correct option i.e. A/B/C/D. Each part carries one mark.

• Which of the following is not a Binary Operation:

(A) Division              
(B) Addition       
(C) Multiplication   
(D) Square root

• Which Symbol is used for the Membership of a set:

(A) ^               
(B) V              
(C) ɛ               
(D) ~

• A Matrix of Order 1x m is called:

(A) Row matric      
(B) Column matric         
(C) Null matric 
(D) Diagonal matric

• (AB)t = :

(A) AB              
(B) BA           
(C) At  Bt             
(D) Bt At              

• What is degree of x 3 -2 x 4 y2 +7 y5 :

(A) 3         
(B) 4    
(C) 5                
(D) 6

• For real and repeated roots b2-4ac will be:

(A) Positive                
(B) Negative 
(C) Zero         
(D) Imaginary

• The Conditional Equation x-1/3=2 holds if x is equal to:

(A) 8             
(B) 7                 
(C) 6               
(D)5

• Which of the given can not be any term of G.P. :

(A) -1        
(B) 0       
(C) 1   
(D) 5

• For any two members a and b,G2   is equal to (with usual notation):

(A)A x H               
(B) A ÷ H           
(C) A - H              
(D) A + H

• 6!  +  0! Is equal to

(A) 719           
(B) 720           
(C) 721           
(D) 722

• If r = n , then nCr is equal to

(A) 0               
(B) 1   
(C) n!  
(D) (n-1)!

• Number of term in the expression of (2x-y) 9 is:

(A) 8               
(B) 9    
(C) 10 
(D) 11

• The expansion of (1+3x) ½  is valid only when: For (int x=0; x<=2: x++)

(A) ǀxǀ < 1/2     
(B) ǀxǀ < 1/3     
(C) ǀxǀ <1     
(D) ǀxǀ =1        

• Which of the following is not Quadrantal Angle:

(A)9/2д                         
(B) 13д  
(C) 4/3д                                  
(D) д /2

• Sin (3д /2-Ѳ) is equal to:

(A) SinѲ        
(B) –SinѲ       
(C) CosѲ        
(D) - CosѲ

• The domain of Cosx is: 

(A) [-1,1]         
(B) (-π /2, π /2)
(C) rI              
(D) Δ

• Notation of Radius of In-circle is:

(A) r                 
(B) R
(C) rI           
(D) Hewlett

• Circumradius R is equal to=

(A) π /4                            
(B) - π /4     
(C) - π /2          
(D) π /2          

Solution of the equation Cos =-1 in [0,2 π]  is:

(A) 0, π          
(B) 0, 2π       
(C) π   
(D) 0

Inter (Part-I) Bahawalpur Board 2016
Mathematics
Part I (Subjective)
Time Allowed: 2.30 Hours
Max. Marks: 80 

Section I

2. Write short answers to any EIGHT questions:  (2x8=16)

• Name the property used in a ( b-c ) = ab-ac          
• Define a Function           
• Show that V2ɛC,z2 +̅z2 is a real number.
• Define Hermitian Matrix            
• Find Multiplicative inverse of (√2, -√5)
• Write down power set of {9,11}
• Write Converse,Inverse of Conditional q→p    
  
• RTate remainder Theorem.       
• Discuss the nature of roots of equation x2 +2x+3 = 0
• Evaluate (1+w-w2) 8
• Find values of x if
  │1       2          1│
  │2       x          2│       =          0
  │3       6          x│
• Find Inverse of
  │-2      3│
  │-4      5│

3. Write short answers to any EIGHT questions:               (2x8=16)

• Define improper Rational Fraction.
• How many diagonal of 8 sided figure?
• If an-3 =2n-5,find nth term of the sequence.
• If 1/1+√x+1/1-x+1/1-√x+ ------ n term, find “d”.
• Convert 2.33 into an equivalent Common Fraction.
• Write the Sample Space for tossing a coin three times.
• In H.P.  a1 =-1/3, a5 =1/5 find a9       
• Show that 2+6+8+------ + 2x3n-1 =3n-1 is true for n=1,n=2
• Find 6th term in the expansion of (x2 -3/2x) 10
• Write Tr +1 term of Binomial Theorem in the expansion of (a + x) n             
• How many numbers can be formed from the digits 2,2,3,3,4,4?
• Find the value of n, when n P2  = 30

4.  Attempt any NINE parts.                                                                (2x9=18)

• Prove that 2Sin 45° +1/2 Cos 45° =3/√2     (Without Calculator)
• Find l when Ѳ =65° 20ﹶ    r=18mm
• Prove that SinѲ/1+ CosѲ+ CotѲ = CosecѲ
• Without using tables/calculator,
• Prove that Cos 306° + Cos 234°  + Cos 162° + Cos180 =0
• Prove that Tan(45°  + A) Tan(45°  + A) = 1      
• Define the period of a Function.
• State the law of Cosines (any two)       
• Solve Sin 2x + Cos x = 1 where xɛ[0,2π]
• Find the value of Sin (tan -1 (-1)) (without calculator)
• Find the solution of CotѲ = 1/√3 where Ѳ ɛ [0,2π]
• Find the value of Cos 2α when Cosα=3/5 where 0<α< π/2
• The area of triangle is 2437, if a=39 and c=97 then find Angle β.
• Show that r₂ =  sTan β/2 (with usual notation)