Inter (Part-I) Bahawalpur Board 2014
Mathematics
Part I (Objective Type)
Time Allowed: 20 Minutes 
Max. Marks: 17

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
Circle the correct option i.e. A/B/C/D. Each part carries one mark.

• The set  is called:

(a) Infinite Set
(b) Singleton Set
(c) Empty Set
(d) Set with two elements

• Which of the following is binary operation in positive integers:

(a) Addition
(b) Subtraction
(c) Square Root
(d) Divison

• i.14 equal to

(a) 1
(b) -1
(c) I
(d) –I

• If A=  then A32 equal to :

(a) 2
(b) 0
(c) -1
(d) -3

• If the root of the quadratic equation ax² + bx + c = 0 are complex, then:

(a) b² – 4ac < 0
(b) b²-4ac > 0
(c) b²-4ac = 0
(d) b²+4ac = 0

• If w is complex roots of unity then 1+w+w² equal to :

(a) 1
(b) 0
(c) -1
(d) –w²

• Transport of Diagonal Matrix is :

(a) Scalar Matrix
(b) Row Matrix
(c) Null Matrix
(d) Diagonal Matrix

• Partial Fraction of will be of the form:

(a) + 
(b)++ 
(c)++ 
(d)+

• ^pn_requal to : where n > 0, r > 0

(a)
(b)  
(c)  
(d)  

• Arithmetic Mean between a and b is :

(a)  
(b) ±
(c)  
(d)

• equal to :

(a)  
(b)  
(c)  
(d)

• If A and B are Mutually Exclusive Events then P (A U B) equal to

(a) P(A) +P
(b) P (A)-P
(c) P (AB)
(d) P(A)+.P(B)-P(A∩B)

• Sec²θ- Tan²θ  equal to =:

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

• The sum of odd coefficients in expansion of (1+x)4 is:

(a) 8
(b) 10
(c) 12
(d) 16

• If Tan x =-1 then general value of x is :

(a) {+nπ}
(b) {+nπ}
(c) {+nπ}
(d) {+nπ}

• Sin (90+θ) equal to :

(a) sin θ
(b) –sin θ
(c) Cos θ
(d) –cos θ

• Cos (2sin-1x) equal to :

(a)   
(b)  
(c)  
(d) 1- 2x²

• b²+c²-abc cosᵒ equal to :

(a) Δ
(b) 0
(c) a2²
(d) 1-2x²

• Period of Tanθ is :

(a) 4π
(b) 3π
(c) 2π
(d) π

• The number of terms in expansion of (a+b)⁸ is:

(a) 8
(b) 9
(c) 10
(d) 11

Inter (Part-I) Bahawalpur Board 2014
Mathematics
Part I (Subjective)
Time Allowed: 2.30 Hours 
Max. Marks: 80 

Section I

Q.No.2  

• Does the set (0, • 1) possess closure property with respect to addition and multiplication. Justify.
• Simplify   I101
• Define Binary Operation
• Define Group
• Show that p à( pvq ) is a tautology
• State Factor Theorem.
• If A = find At                
• Find  x if  
• Evalute ( 1 + w- w²)⁸.               
• Discuss nature of root of equation 2x2 + 5x -1= 0
• If A and B are non- regular matrices, then show that (AB) -1 = B-1 A-1

Q.No.3

• Define Partial Fraction.    
• Find two A.Ms between /2 and 3/2.
• Write first four term of a_n = n/(2n+1)
• Define G.M. Between any two number a and b.
  
• Verify G2 = AH, If a =2i, b = 4i
• How many diagonals can be formed in case of a polygon having 12- sides ?
• Determine the probability of getting 2- heads in two successive tosses of a balanced coin.
• Write the sample space of tossing of one dice.
• State the Principle  of Mathematical Induction.
• Check Divisibility of n² + n by 2 for n =12
• Expand (8-2x)-1 upto 4-term

Q.No.4

• Convert into Radian 105° , Convert into Degree
• Find the period of Cos²x.
• Verify sin + sin + Tan = 2
• Find the value of Cos15
• If ∞ ,β, γ be the angles of Triangle ABC, prove that cos =
• Find the value of cos2∞ when sin∞= ,∞ in I- Quad
• Express sums into product Sin 50 + Sin 30
• Find the area of the triangle ABC If b = 125, γ = 36ᵒ41, ∞ = 45ᵒ17
• Without using calculator show that Cos-  = cot
• Find the salution of equation ------------
• Solve the Trigonometric Equation Cosec2ᵩ = , ᵩ € (0, 2π)

Section-II

Question #5
(a) Find the inverse of A =  and show that -1   A    A = I³
(b) Show that the root of (mx + c)² = 4ax will be equal, If      c = : m ≠ 0

Question #6
(a) Resolve into Partial Fraction, 
(b) Sum to n terms the series    3+33 +333 + …………..

Question #7
(a) Prove that n-1cr + n-1cr-1 = ncr
(b) Show by Mathematical Induction.

For all n positive integers.

Question #8 
(a) Find the value of the remaining trigonometric functions when Cos =  and the terminal arm of the angle is in Quad- IV
(b) Prove that Cos20 + Cos100 + Cos140 = 0

Question #9  
(a) Solve the Triangle, in which  a=28.3, b = 31.7, c = 42.8           
(b) Prove that Cos -1 + 2 Tan -1  = Sin -1