Inter (Part-I) Lahore Board 2014
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 or filling two or more circles will result in zero mark in that question.

•   belongs to set of :
  

(A) Real numbers       
(B) Prime number
(C) Even numbers      
(D) Complex numbers

• If A = {1 , 2 , 3 , 4 , 5 },B {,4,5,6,7,8,9,10}, then A - B is equal to :

(A) {6,7,8,9,10}         
(B) {4,5}
(C) {1,2,3}                 
(D) {4,5,6,7,8,9,10}

• The domain off = {(a, 1),(b,1),(c,1)} is equal to

(A) {a,b,c}                 
(B) {a}
(C) {1}                       
(D) {b,c}

• If A is non-singular square matrix, then AA-1 equals :

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

• If two rows of any square matrix are identical, then the value of determinant is:

(A) 1   
(B) -1
(C) 0   
(D) 2

• The sum of the four fourth roots of unity is

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

• The product of cube roots of unity is

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

• Partial fraction of is of the form .

  (A) 
  (B)
  (C) +
  (D)

• If an= (-1)n+1, then.26th term is :

(A) -1 
(B) 1
(C) 26 
(D) -26

• In geometric sequence nth term equal to :

  (A) al +(n -1)d            
  (B)  
  (C) a1rn-1
  (D)

• If nC8 = nC12,  then "n" equal" to :

(A) 4   
(B) 8
(C) 20 
(D) 12

• The factorial form of is :

(A)  
(B)  
(C)  
(D)

• The inequality 4n > 3n +4 is true for :

(A) n = 1        
(B) n a 2
(C) n = 0         
(D) n < 2

• The sum of all coefficients in the binomial expansion of (1+x)n is:

(A) 2n-1
(B) 2n+1
(C) 2n
(D) 0

• sin² θ + cos² θ

(A) -1
(B) 1
(C) 2
(D) 0

• The value of cos 315° is

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

• Period of sin 3 -x is :
  

(A) π 
(B) 3π 
(C)  
(D) 6π

• Angle below the horizontal line is called :
  

(A) Right angle
(B) Oblique angle
(C) Angle of depression
(D) Angle of elevation

• The value of cosec2
  

(A)  
(B) - 
(C)  
(D) -

• If cos x=, then reference angle is :
  

(A)  
(B)  
(C)  
(D)

Lahore Board 2014
Inter (Part -I)
Mathematics
Paper I (Essay Type)
Time Allowed: 2.30 hours
Max. Marks: 80
(Group-I)

(SECTION-I)

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

• Does { 1 } possess closure property w.r.t. addition and multiplication? Justify.
• Prove that z =,
• Define a set.
• Write converse and inverse of the conditional ~ p à?0 ^ q
• Define into function.
• If a, b are elements of a group, then show that (ab)-1 = b-1 a-1
• If A = then find adj A
• Define the terms symmetric and skew symmetric matrices.
• If A is symmetric or skew symmetric then A2 is symmetric?
• Prove that = x³ + y³ = (x + y)(x + ωy)(x + ω²y)
• By synthetic division show that x = 2 is solution of polynomial x3 - 7x+ 6 = 0
• (xii) If α,β are roots of 3x2 - 2x+ 4 = 0 . find value of

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

• Resolve into partial fractions
  
• Find indicated term of 2, 6, 11, 17, …………a7
  
• Find A.M. between 3 and 5 
  
• Find 5th term of G.P. , 3, 6, 12, .......
  
• Find 9th term of H.P, --------
• Find n , if ⁿC₅ = ⁿC₄
• If sample space, S = { 1, 2,------9 }, events B = 1 , 3 ,5 A= { 2, 4, 6, 8}, find P(A∪B)
• State "The laws of probability for addition".
• Check whether is an integer for n = 2,3
• Expand (4 - 3x)1/2 upto four terms.
• Write the binomial series with its condition on x

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

• Find θ when  = 1.5cm r = 2.5cm
  
• Verify the 2sin 45° + cosec45°
  
• If are angles of ΔABC then prove that tan (α +β) + tan  = 0
  
• Find the value of cos 105°
  
• Find the value of cos 2α , if cos α = , α in I quadrant.
• Express sums into product cos 6 θ+ cos 3 θ
• Find the period of sin x/3
• Solve the right ΔABC in which  = 90° b = 68.4 c = 96.2
• Solve the ΔABC in which b=14.8 c=16.1 , a = 42° 45'
• Find the area of ΔABC c = 32 α = 47° 24' β = 70° 16'
• Show that sin (2 cos-1 x)         
• Find the solution of cot θ = in [0,2π]
• Solve the trigonometric equation sec2 θ = 4 -2,  [0, 2π]

(SECTION-II)

Attempt any THREE questions.
5.(a) Use Crammer's rule to solve the system
(b) Solve the system of equations: x²+(y+1)2=18;(x+2)2+y²=21
6.(a) Resolve into partial fractions
(b) Find n so that  may be H.M. between a and b

7.(a) Find the value of n and r when ⁿC_r =35 and ⁿP_r =210   
(b) Find the coefficient of x5 in the expansion of

8.(a) Show that : sin⁶θ — cos⁶θ = (sin²θ - cos²θ) (1 - sin²θ cos²θ)
(b) If  are the angles of a triangle ABC, show that

9.(a) At the top of a cliff 80 m high, the angle of depression of a boat is 12°. How far is boat from the cliff?           
(b) Prove that sin^-1