Inter (Part-I) Lahore Board 2012
Mathematics    Paper I (Objective Type)
Time Allowed: 30 Minutes  
Max. Marks: 20
(Group-I)

Note: Four possible answers A, B, C and D to each question are given. The choice which you think is correct, fill that circle in front of that question with Marker or Pen ink. cutting ear filling two or more circles will result in zero mark in that question. Write the letter A, B, C or D in the column (write correct option) against each question also. If there; is a contradiction in the bubble and hand written answer, bubble option will be considered correct.

Q1.

A. Natural number
B. Whole number
C. Rational number
D. Irrational number

• Multiplicative inverse of - 3i is:
  

A. 3i
B.  
C.  
D. -3i

• If A and B are Disjoint Sets then A n B = :
  

A. 0
B. 1
C. 2
D.

• Number of identity elements in any group is:
  

A. 1
B. 2
C. 3
D. -4

• A square matrix A is symmetric if At =

A -A
B. A
C. A^t
D. A²

• When 3x4 + 4x3 + x -5 is divided by x + 1 then remainder is:

A. 7
B. 6
C.-6
D. 7

• Partial fractions of will be of the form:

A.   
B.           
C.  
D.

• If a, A, b are in A.P, then 2A = :

A.  
B. a + b
C. a-b
D.

• If y = - - - - then interval of convergence is:

A. 0<x<  
B.   
C. 1/2< x <-1/2
D. 0<x<

• nPn

A. n!
B. (n+1)!
C. 0
D. n

• A die is rolled, the probability that the dots on the top are greater than.4 is:

A.  
B. 1/3
C.
D.

• 2n-1<! Is true  for

A.
B.  
C.  
D.

• The middle term in the expansion of(3 2x)¹⁰ is:

A. T⁴
B. T⁵
C. T⁶
D. T⁷    

• 2nd term in the expansion of (1- 2x)^1/3 is:

A. 
B.  
C.  
D.

• If the length of arc is equal to radius of circle then angle subtended at the centre is equal to:

A. one degree
B. one radian
C. 180°
D. radians

•  = :

A.
B.   
C.  
D.

• The period of tan is:

A.  

B. 7  
C.   
D.

• In any triangle ABC with usual notation

A. cos  
B. cos  
C. cos
D. sin

• The value of sin

A.
B.
C. 1
D.

• Solution of equation tan x = lie in:
  

A. I and II quadrant
B. I and III quadrant
C. H and IV quadrant 
D. I and IV quadrant

Inter (Part -I) Lahore 2012
Mathematics    Paper I (Essay Type)
Time Allowed: 2.30 Hours     Max. Marks: 80
(Group-I)
SECTION-I

Write short answers to any EIGHT (8) questions: 16

• Name the property used in: 4 (58) = (45)8
• Prove that
• Verify distributivity of union over intersection for the sets A,B and C. A={1,2,3,4}, B={3,4,5,6,7,8}, C={5,6,7,9,10}
• Write the converse and contrapositive of the conditional qàp
• For A ={,1,2,3,4}, find the relation in A.R={(x,y)|x+y<5}
• Define semi group
• Solve the system of linear equations 3x-5y=1;-2x+y=-3
• If A=
• If A and B are symmetric and AB=BA, show that AB is symmetric?
• Solve the equations by completing x²-2x-899=0
• if  are roots of 3x²-2x+4=0, fins the value of
• Solve the system of equations 2x-y=4;2x²-4xy-y²=6

3. Write short answers to any EIGHT (8) questions

• Resolve into partial fractions
• Resolve into partial fractions
• Which term of the A.P -2, 4, 10----is 148
• If a, b, c, d in G.P, prove that a - b, b c, c d, are in G.P?
• If 5 is the H.M. between 2 and b, find b?
• Find the value of n,nP4:n-1P3=9:1
• Find the inverse of A= and show that A^-1A=I₃

6.A. Use synthetic division to find the values of p and q if x + 1 and x - 2 are the factors of the polynomial x³ + px² + qx + 6                (5)
B. Find the 18th term of the A.P. if its 6th term is 19 and the 9th term is 31.               (5)

7.A. Show that 16_c11+16_c10= 17_C11 (5)
B. Find the coefficient of x5 in the expansion of       (5)

8.A. If  is arc length of a circle central angle of an arc is  radian and r is radius of a circle then prove   = r.       (5)
B. Prove that (without using calculator) cos 20° cos 40° cos 60° cos 80° =          (5)

9.A.Solve the triangle ABC,in which a = 7, b = 7, c = 9 .  (5)
B. Prove that (without using calculator)