Inter (Part-I)
Lahore Board 2013
Mathematics (New Scheme)
Time Allowed: 30 Minutes
OBJECTIVE
Max. Marks: 20
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 or filling two or more circles will result in zero mark in that question.

• The number of term in the expansion of (a + b)⁷ is:
  

(A) 4   
(B) 6
(C) 7   
(D) 8

• Sin ( -300°) =
  

(A)  
(B) 
(C)  
(D) 0

• If a, b, c are sides of a triangle then
  

(A) cos         
(B) cos
(C) cos          
(D) sin

• The period of tan - is:

(A)   
(B) 2
(C) 3
(D) None of these

• The 3rd term of sequence an = (-1)n (n - 7) is:

(A) 8   
(B) 4
(C) -4  
(D) -8

• A right triangle is in which one angle = :

(A) 45°
(B) 90°
(D) 360°
(C) 270°

• If 4x =
  

(A)    
(B) 
(C) 2   
(D) -2

(A)        
(B) 
(C)           
(D)

• If n is odd, then the expansion of (a + x)n has:
  

(A) Two middle terms
(B) 3 middle terms
(C) 4 middle terms     
(D) 0 middle term

• rad

(A) 360°
(B) 335°
(C) 270°
(D) 225°

• The A.M between x-3and x+5 is
  

(A) x + 1
(B) x-1
(C) x - 3
(D) x + 5

• If Matrix is singular, then x is
  

(A) 3
(B)2
(C) 4
(D) 6

• Partial fractions of  are
  

(A)  
(B)  
(C) 
(D)

• 1+=

(A)
(B) –
(C)
(D)

• Range of function y=cos-1 x is
  

(A) [-1,1]
(B) [-1,1)
(C)[0,π]
(D)[0,π)

• Circle passing through three vertices of a triangle is called
  

(A) Circumcircle
(B) In-circle
(C) E-circle
(D) Semicircle

• Solution set of 1+cos x =0 is
  

(A) {2nπ}
(B) {π +2nπ}
(C) {π}
(D) {2π +nπ}

• The Matrix is
  

(A) Diagonal
(B) Scalar
(C) triangular
(D) Singular

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

(A)         
(B)         
(C)  
(D) (n+2)!

• Multiplicative inverse of (1,0) is
  

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

Inter (Part-I)
Lahore Board 2013
Mathematics
Time: 2.30. Hours
Paper: I
Marks: 80
SUBJECTIVE
(Section - I)

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

• Name the properties used in the following equations:
  (a) 4 + 9 = 9 + 4 (b) . 1000 x 1 = 1000
• Factorize : 9a² + 16b²
• What is the difference between {a , b} and { { a , b}?
• Write the two properties of binary operation, when "S" is a non-empty set.
• If A = and A2 = find the values of a and b.
• Solve the matrix equation for X ; 3X - 2A = B if A = and B =
• State the two properties of A square matrix when |A| =0'
• If A is symmetric or skew-symmetric matrix, show that A² is symmetric matrix?
• Solve for x : x (x + 7) = 2x - 1) (x + 4).
• What are the reciprocal equations?
• Evaluate : (1+) ()
• If the roots of the equation x² - px + q = 0 differ by unity, prove that p² = 4q + 1.

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

• Resolve into partial fraction.
  
• Resolve into partial fraction with unknown constant
• Which term of A.P.5, 2, - 1, is - 85?
• Find three A. Ms between and  and
• If y= +-------- and if 0<x<2 then prove that x =
• If first term of an H.P is -   and fifth term is , find 9th term ?
• Prove that ⁿP_r=n^n-1P_r-1
• In how many ways can '5' persons be seated at round table?
• Find the value of ‘n’ if ⁿC₁₀=
• Pakistan and India play a cricket match, what is the probability that Pakistan wins.
• Find the coefficient of x5 in the  upto three decimal places.

4. Write short answers to any NINE (9) questions:  (18)

• Prove that sin3+ cos3=(sin)(1-sin)
  
• Prove that cost2 - sin2 + =
  
• Expression sin 5x+xin3x as product
  
• Prove that cost3a=4cos3-3cos
  
• Prove that =tan56o
  
• Prove that (270o-)=cot
  
• Find the period of tan
• Define Hero's formula.
• Define escribed circle.
• Prove that R=abc
• The area of triangle is 2437 if a =79,c=97, find
• Solve the equation 1+cosx=0
• Find the solution of cosec =2 in [0,2]

Section (II)

Attempt any THREE questions
5. a) Show that the set {1,} when  is an abelian group w.r.t. ordinary multiplication
b) Find inverse of the matrix, A=

6. a) Show that (1+) () () ()---- 2n-factor =1 where  is cube root of unity
b) Resolve into partial fractions

7.a) Find n so that  may be H.M between a and b
b) If y =-------then prove that

8.a) If cos, find value of remaining trigonometric functions?
b) Prove that sin 10osin 30osin 50osin 70o =

9.a) Prove that in an equilateral triangle r:R:r1:r2=1:2:3:3:3
b) prove that sin-1 A+sin-1 B=sin-1