Sargodha Board
(Inter Part- I)
(Session 2015)
Mathematics
(Objective) Paper (1)
Time Allowed:- 30 minutes
Maximum Marks: 20
 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 will. Cutting or filling two or more circles will result in zero mark in that question. Write PAPER CODE, which is printed on this question paper, on the both sides of the Answer Sheet and fill bubbles accordingly, otherwise the student will be responsible for the situation. Use of Ink Remover or white correcting fluid is not allowed.

• For all a,b,c,a=b,b= c   a=c is called ____

(A) Transitive property
(B) Symmetric property
(C) Reflexive property
(D) Trichotomy props

• If 'A' is a subset of set B, then A____

(A) A^c
(B) B^c
(C) A
(D) B

• If 'A' and 'B' are disjoint sets, then n(AUB)=____

(A) n(A)
(B) n(B)
(C) n(A-B)
(D) n(A)+n(B)

• The matrix is a ___

(A) Rectangular matrix
(B) Diagonal matrix
(C) Scalar matrix
(D) Hermitian matrix

• Transpose of a row matrix is a

(A) Square matrix
(B) Column matrix            
(C) Symmetric matrix
(D) Skew-symmetric matrix

• Leading coefficient of the equation x²+2x² +3x +4 = 0 is__

(A) I 
(B) 2
(C) 3
(D) 4

• Roots of the equation ax² + bx+ c =0, a  0 are imaginary if

(A) b²- 4ac > 0 
(B) b²- 4ac =0
(C) b²- 4ac  0
(D) b²- 4ac  0   

• The partial fractions of    are of the form

(A)   +  
(B)   +  
(C)   +
(D)   +            

• The sequence 4,12,36……….. is

(A) A.P
(B) G.P
(C) H.P
(D) Series

• Sum of the convergent series  + r +  +…………infinity is

(A)  
(B)
(C)  
(D)

• Factorial form of 6x 5 x 4 is

(A)
(B)
(C)
(D)

• =

(A) 
(B) 
(C)  
(D)  

• Number of terms in the expansion of  is

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

• The expansion of is valid if  

(A) lxl>1
(B) |x| 
(C) |x|  
(D) |x|         

• If sin<0 and cos>0, then ‘ is in

(A) I quadrant
(B) II quadrant
(C) Ill quadrant
(D) IV quadrant

•  sin3α =

(A) 4sinα -3 
(B) 3sinα - 4  
(C) 4 -3cos α 
(D) 3cos α - 4α

• Domain of cos x is

(A) R-(1)
(B) R 
(C) [-1,1]
(D) R-(0)

• In a right angle triangle no angle is greater than
  
  (A) 30°
  (B) 45°
  (C) 60°
  (D) 90°.

•   Cos ()

(A)  
(B)  
(C)   
(D) 2

•  1f cos 2x=0, then solution in I quadrant is _

(A) 15°
(B) 30°
(C) 45°
(D) 60°

Mathematics (Subjective)
(Session 2015)
Paper (1)
Time Allowed: 2.30 hours
(Inter Part -I)
Group-I
Maximum Marks: 80
Section I

2.Answer briefly any Eight parts from the followings:• 8 x 2=16

• If z be the complex number then prove that = +
• Simplyfy in the form a+bi
  
  
• If A={1,2,3,4) ,B={3,4,5,6,7,8), C=(5,6,7,9,10} verify the Associativity of union
  
  
• If a, b are elements of a group G then show that =
  
  
• For A=(1 .2,3) find the relation ((x,y) I x + y < 5)
  
  
• Define Power set of a set.
  
  
• Find the value of if A = is Singular
• Without expansion verify that=0
  
  
• Solve the system of linear equation using Matrix
  
  
• Solve the equation x(x+7) = (2x-1) (x+4) by Factorization
  
  
• If are the roots of  3-2+4 = 0 find the values of
  
  
• For what value of m will the roots of the equation (m +I)2(m +3)x + m +8 = 0

3.Answer briefly any Eight parts from the followings:

• Resolve
  
  
• Write 1st 3 terms of = (2n -3)
  
  
• If ,,are in A.P then show that common difference is  
  
  
• If 5 and 8 are two A.Ms b/w a and b, find a and b.
  
  
• If  ,,are in G.P. Show that common ratio is
  
  
• Find the value of n when nP2 =30
  
  
• Find the number of diagonals of 6 sided figure.
  
  
• Find the value of n when ⁿC12= ⁿC6
  
  
• Determine the probability of getting two heads in two successive tosses of a coin?
  
  
• Verify the result 4n > 3n + 2n-1 for n = 2 , 3
  
  
• Find the 6th term in the expansion of (x2-)10
  
  
• Expand (1+2x)^-1 upto 4 terms.

4. Answer briefly any Nine parts from the followings:-

• Convert 150° into Radians.
  
  
• Find θ when I= 1.5 cm. r = 2.5 cm.
• Find the value of cos
  
  
• Without using table find value of tan (110°)
  
  
• Prove that sin (180°+ α)sin (90 - α). - sin α cos α
  
  
• Prove that = tan 56°
  
  
• Find the period of sin
• Show that r²=Stan
• Show that r = (S - a)tan
  
  
• State the Law of Sines
• Find the value of Sin-1  
  
  
• Solve 4 cos2 x -3 = 0 , x [0,2π]
  
  
• Solve sec2α=  in[0,2π]

Section ------ II

(b) Solve the equation 4x- 3.2x+3+128 = 0

6.(a) Resolve into Partial Fractions.
(b) If  S₂,S₃,S₅ are the sums of 2n, 3n, 5n terms of an A.P. show that S₅=5(S₃- S₂)

7.(a) Prove that  ⁿ⁺¹C_r + ⁿ⁺¹C_r-1 = ⁿC_r
(b) Find the term independent of x in the expansion10     

 8. (a) Prove that +=
(b) Prove that (without calculator) Sin  Sin Sin Sin=

9.(a) The sides of a triangle are x2 + x + I, 2x + I and x2 - I . Prove that the greatest angle of the triangle is 120°.
(b) Prove that sin-1+Cot-13=