D.G KHAN BOARD 2014
Inter Part I 
Mathematics
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

• The Additive inverse of 2 is:
  
  (A) 0
  (B) 1
  (C) -2
  (D) 1/2
  
  
• The no. of subsets of a set of 4 elements is:
  
  (A) 16
  (B) 18
  (C) 4
  (D) 6
  
  
• The disjunction of P and c is denoted by:
  
  (k) P ↔ q
  (B) P→ q
  (C) P← q
  (D) PV₁q
  
  
• P: 4 < 7 q : 7 < 11 then P ^ q is
  
  (A) False
  (B) True
  (C)Not valid
  (D) Unknown
  
  
• If A  then |A| =
    
  (A) 1
  (B) 0
  (C) -1
  (D) 12
  
  
• [0] is a:
  
  (A) Square matrix
  (B) Unit matrix
  (C) Scalar matrix  
  (D) Null matrix
  
  
• The discriminant of x2 + x+1 =0 is:
  
  (A) 3
  (B)  2
  (C) -2
  (D) -3
  
  
•  is :    
  
  (A) Propel fraction
  (B) Improper fraction
  (C) Decimal
  (D) Equation
  
• The 4th term of sequence an =  is:
  
  (A) 4
  (B) 3
  (C) 4/3
  (D) 4/9
  
  
• The Geometric Mean between 4 and 16 is:
  
  (A) ± 4
  (B) ±6
  (C) ± 8
  (D) ± 16
  
  
•   =
  
  (A)1/65
  (B) 65
  (C) 56
  (D) 1/56
  
  
• ⁶P₄
  
  (A) 36
  (B) 360
  (C) 6
  (D) 4
  
  
• In expansion of (a+b)7, he 2nd  term is: 
  
  (A) a⁷
  (B) 7a⁶b
  (C) 7ab⁶
  (D) ab
  
  
• If n is positive integer then 4n > 3n +4 is true for:
  
  (A) n>0
  (B) n≥2
  (C) n<2
  (D) n ≤ 2
  
  
• 1/4 Rotation (Anti Clock wise):
  
  (A) 45°
  (B) 90°
  (C) 180°
  (D) 360°
  
  
• Tan(α -π 1/2)=  
  
  (A) Sec α
  (B) Cot α
  (C) - Cot α]
  (D) Tan α
  
  
• The period of Cosec x is
  
  (A) π
  (B) 2 π
  (C) 3 π
  (D) 4 π
  
  
• For any triangle  =
  
  (A) Cos α
  (B) Cos β
  (C) Cos γ
  (D) Sin β
  
  
• If Cos x = √3/2 then reference angle of Cos x=
  
  (A) π /3
  (B) π /4
  (C) π /6
  (D) - π /6
  
  
• Tan^-1 (-1)=
  
  (A) π/6
  (B)-V/4
  (C) V/2
  (D) - π

SUJECTIVE TYPE

2. Attempt any 8 short questions:(8x2=16)

• Simplify by justifying each step of
  
  
• Find the multiplicative inverse of   (√2, √5)
  
• If A = (1,2,3,4,5) B = {4,5,6,7,8,9,10} , then find B-A.
  
• Define conjunction and disjunction of two statements P and q.
  
• Find the inverse of {(x y)!y2  =4ax, x, y ϵ R, x, y > 0}
  
• Show that the set {1, w w2}, when w3 = 1 is an Abelian group w.r.t ordinary multiplication.
  
• Solve dc matrix equation for x: 2x - 3A B if
  A =   and B=
• Without expansion show that
   = 0    
  
• Evaluate (-1+ √-3)5 + (-1- √-3)5
  
• If w is a cube root of unity, form an equation whose roots are 2w and 2w2
  
• State the Remainder theorem.
  
• Discuss the nature of the rows of equation 9x2 – 12x + 4=0
  
  

3. Attempt any 8 short questions:(8x2=16)

• Resolve   into partial fractions.
  
• Find the indicated term of sequence 1, 3, 12, 60…….a6
  
• Define Arithmetic Mean.
  
• Find G.M between -2i and 8i.
  
• If 5 is H.M between 2 and b . Find b
  
• Find value of n when nP2 = 30
  
• If nc10=  Find value. of n
  
• A die is thrown twice. What is the probability that sum of dots shown is 3 or 11.
  
• TWO dice are thrown twice, Find the probability that sum of dot shown in the first throw is 7 and that of second throw is 11
  
• State principle of extended mathematical induction.
  
• Using Binomial theorem Expand ( 3a -  )4
  
• Expand (4 - 3x)1/2 up to four terms.

4. Attempt any (9) short questions:

• Find θ when 1= 1.5 Cm, γ = 2.5 Cm.
  
• Verify  2 Sin 45° + 1/2 Cosec 45° = 3/√2—
  
• Sin (180° + α ) sin(90°-α) = - Sin α Cos α , Prove!
  
• Prove that Sin (180° θ) - Sin θ
  
• Prove that (1 — Cos α)/ Sin α = tan α/2
  
• Express the Product as sum 2 Sin 7 θ Sin 2 θ
  
• Find the Period of Cot 8x
  
• Solve the ∆ ABC in which  γ= 90° α = 37°20, a = 243
  
• State the “Law of sires”
  
•  Find the area of ∆ ABC for a = 200, b= 120, γ =150°
  
• Show that Sin-1(-x) = -Sin -1 x
  
• Find the solution of the equation Cot θ=    if θ ϵ [0,2 π].
  
• Find the solution of Sin x= -√3/2 in [0,2 π]

SECTION II

Note: Attempt any three questions from this section:
Question#5
(a) If A=  Show that A- (A)^t is Skew Hermitian.
(b) If α and β be the roots of x2 -3x +5 =0 from the equation whose roots are
 and

Question#6
(a) Resolve  into partial fractions.
(b) If y= ……… and if 0< x < 2,
then prove that x=

Question#7
(a) Find the values of n and r ⁿ C_r =35 and  ⁿP_r, = 210
(b) Find the coefficient of x⁵ in the expansion of (x²— 3/2x)10

Question#8
(a) Solve that (Sec θ - tan θ)2 =
(b) Show that  = 4 Cos 2 θ

Question#9
(a) Solve the following triangle in which a = 28.3          b = 31.7           c =42.8
(b) Prove that  2 Tan-1 1/3 + tan-1 1/7 = π/4