Inter (Part-I) Multan Board 2014
Mathematics
Part I (Objective Type)
Time Allowed: 30 Minutes 
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 in the answer-book. 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.

• 5! =

(a) 140
(b) 120
(c) 5
(d) 0

• The value of 10 P1 is :-

(a) 10
(b) 20
(c) 80
(d) 90

• The co-efficient of last term in expansion of (a-b)5 is :-

(a) 1
(b) 1
(c) 0
(d) 2

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

(a) -x
(b) 2x
(c) 3x
(d) 4x

• A right angle is equal to :-

(a) 90°
(b) 90’
(c) 90”
(d)60°

• cos(a- π/2) =

(a) -sin a
(b) cos x
(c) cos a
(d) sin a

• The period of sec x is :-

(a) π
(b) 2π
(c) 3π
(d) 4π

• In a right triangle , no angle is greater then:-

(a) 90°
(b) 80”
(c) 60°
(d) 45°

• tan-1 (-1) =

(a) π/6
(b)-π/4
(c) π/2
(d) -π

• If cos 2x = 0, then solution in 1st quadrant is :-

(a) 30°
(b) 45°
(c) 60°
(d) 15°

• -1/2 +   =

(a) 3
(b) 2
(c) 1 
(d) 0

• If A= {} then P(A) =

(a) { }
(b) {0}
(c) {Ø}
(d) {0,1}

• AUB =

(a) Bп U
(b) AпB
(c) Ø
(d) BUA

• If -1         3   = 0 then x =X        1

(a) 3
(b) -3
(c)1/3
(d)-1/3

• The additive inverse of matrix A is:-

(a) A
(b) -A
(c) A2
(D) A3

• The product of roots of 5x2 –x +2=0 is :-

(a) 5/2
(b)-5/2
(c) 2/5
(d) 2

• 1+ш +ш2 =

(a)ш
(b)1
(c)ш2
(d)0

• The improper fraction can be changed into proper fraction:-

(a) addition
(b) subtraction
(c) multiplication
(d) division

• The next term in 7,9,12,-------- is:

(a)16
(b)14
(c)15
(d)18

• The 5th term of a 8 = 2n + 3 is:-

(a)-13
(b)-7
(c)7
(d)13

Inter (Part-II) Faisalabad Board 2015
Mathematics
Part II(Subjective)
Time Allowed: 2.30 Hours 
Max. Marks: 80

Section I
2. Attempt any eight parts.                                                                                                    8 X 2 = 16

• name the properties used in : (a)4+9=9+4      (b)a-a=0
• express (2+ (3 +  in the form of a  +bi
• if B = {1,2,3} , then find power set of B.
• write converse and inverse of ~ p→q
• find the inverse of {(x,y)! y = 2x + 3, x,y Є R}
• define a semi group.
• find x and y if [x+3             1  ]     =    y         1  
                         -3             3y-4         -3       2x
• show that 2        3        0                    2        1        0
                  3        9        6       = 9        1        1        2
                  2       15      1                     2        5        1
• if A is symmetric or skew- symmetric matrix, show that A2 is symmetric.
• evaluate (1+ш –ш2)8
• State the factor theorem.
• if a, β are the roots of 3x2 -2x +4=0, find the value of 1/a2  + 1/β2

3. Attempt any eight parts.                                                                                               8 x 2 = 16

• resolve  7x +25/(x+3)(x+4) into partial fractions.
• find the indicated term of sequence 1,1 -3,5,-7,9------------a8
• if aa-3 = 2n -5 find nth term of the sequence
• find 5th term of the G.P      3,6,12,-----------
• find nth term of H.P,        1/3, 1/5,1/7,------------
  
• evaluate 12P5
  
• find the value of n when C12 =nC6
• a die is thrown, find probability that dots on the top are prime numbers or odd numbers.
  
• find the probability that sum of dots appearing in two successive throws of two dice is every time 7.
  
• state principle of mathematical induction.
  
• expand (2-3x)-2 up to three terms.
  
• if x is so small that its cube and higher powers can be neglected, then show that ~ 1-x/2 -9/8 x2

4. Attempt any nine parts.                                                                                                           9 x 2 = 18

• What is the circular measure of the angle between the hands of a clock at 4O’ clock?
• Verify sin60n cos30n – cos 60n sin 30n = sin 30
• Without using tables find the value of sec (-960°
• Prove that:- sin(θ +270°) = -cosθ
• Prove that:-  sin 2a/(1+cos2 a) = tan a
  
• Express product as sums cos(2x +30°) cos(2x - 30°)
  
• Find the period of  cosecx/2
  
• A vertical pole is 8m high and the length of its shadow is 6m. What is the angle of elevation of the sun at that moment.
  
• Solve the triangle ABC if β = 60°, y= 15° and b =
  
• Find the area of ΔABC for b=37, c= 45 and a = 30°50’
  
• Show that cos(sin-1 x) =
  
• Solve the trigonometric equation. Sec2θ=4/3, θЄ[0,2π]
  
• Define the domain of cos-1 x.

SECTION-II
NOTE:- ATTEMPT ANY THREE QUESTIONS.  (3 X 10 = 30)

QUESTION#5
(a) Solve the system of linear equations by cramer’s rule. 2x + 2y +z = 3,    3x-2y-2z =1  ,     5x +y – 3z = 2
(b) Prove that x2/a2 + (mx +c)2/b2   = 1 will have equal roots if c2 = u2 m2 + b2, , a = 0, b = 0

QUESTION#6
(a) Resolve (x-1)(x-3)(x-5)/(x-2)(x-4)(x-6)  into partial frations.
(b) Find three consecutive numbers in G.P whose sum is 26 and their product is 216.

QUESTION#7
(a) Find the values of n and r, when C: nCr : n+1Cr  = 3:6:11
(b) If x is very  nearly equal to 1 then prove that pxp – qxq = (p-q) xp+q
QUESTION#8
(a) Show that 1- sinθ/1+sinθ  = secθ –tan θ
(b) If a,β and y are the angles of ΔABC , prove that Tan a/2, tan β/2 +tan β/2. Tan y/2 + tan y/2. Tan a/2 =1

QUESTION#9

(a) Three villages A, B and C are connected by straight roads 6km, 9km,13km. what angles these roads make with each other?
(b) Prove that tan-1  ¼ + tan -1 1/5 = tan-1 9/10