Faisalabad Board 2017
Mathematics
(Objective Type)
Inter (Part-1)
Allowed: 15 minutes Note: Four possible answers A, B, C and D to each question are given. The choice which you think is correct that circle in front that question with Marker or Pen ink. 'Lining or filling two or more circles 'will result in zero mat k in that question. Write the letter A, B. C or D in the column. (Write correct "option) against each question also. If there k a contradiction in the bubble and hand written answer, bubble option will be considered correct.
Note:   Section I is compulsory. Attempt any three questions from Section II and any two parts from Section III.
SECTION-I

• ⁿP_r=(Where n >0,>0)

  A)
  B)
  C)
  D)

• Geometric mean between -2 and 9:

A)
B)
C)
D)

• If a=1, b= then A x H=:

A) 5
B) -5
C) -
D)

• (x+3)(x+4)=x2+7x+12 is:

A) Equation
B) Function
C) Identity
D) Conditional equation

• Product of all cube roots of units is:

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

• If 4x=then x=:

A)
B) 2
C)
D)

• If A=then cofactor of 6 is:

A) 1
B) -1
C) -6
D) 3

• If A and B are non-singular matrices, then (AB)-1=

A)
B) A-1B-1
C) BA
D) B-1 A-1

• A(AB)=

A) B
B) A AB
C)
D) A

• Modulus of 5-3i is:

A) 4
B) 16
C) 34
D)

• If sin x =cos x then x=:

A) 45o
B) 30o
C) 0o
D) 60o

• Sec =:

 A)
B) 2
C)
D)

• With usual notation =:

A) r
B) 2r
C) R
D) 1

• 22

A) δ
B) 0
C) a2
D) 1

• The period of sec x is:

A) Π
B) 2 Π
C) 3 Π
D) 4 Π

• Sin  

A) secα
B) –cosα
C) cos α
D) –sinα

•  radius equals:

A) 360_o
B) 335_o
C) 270_o
D) 225_o

• The number of terms in the expansion of8 is:

A) 8
B) 9
C) 10
D) 11

• The 2nd terms in the expansion of (is:

A) x
B)
C)
D) 4x

• 5 persons can be seated at a round table in how many ways?

A) 23
B) 24
C) 25
D) 26

SUBJECTIVE PART
     SECTION II

2: Write short answers to any eight questions.

• Prove that  by principle equality of fractions,
• Simplify (-1).
• Simplify Express complex number 1 + in polar form.
• Write two proper subsets of set
• Define Tautologies and absurdity.
• If a b are elements of a group G, show that -1 b-1a-1
• A=find A22 A32
• A = Show that (A-1)t = (At)-2
• If A is symmetric or skew-symmetric show that A2 is symmetric.
• If  are roots of , show that (1 + ) (1 +)=1-c
• Prove that (-1 +)4 + (-1 -)4=
• Find values of and b if -2 and 2 are roots of polynomial x3 - 4x2 + ax + b.

3.  Write short answers to any eight questions.

• Resolve  into partial fractions.
• Find the next term of the sequence ….
• In an A.P, a1 = 11, an = 68 d = 3, find n.
• Insert two G.Ms between 1 and 8.
• If the numbers,, are in harmonic sequence , find k.
• A die is rolled, find the probability that the top shows 3 or 4 dots.
• How many arrangements of the letters of the word "PAKISTAN" taken all together, can be made?
• Find the value of n, when 11Pn = 11 x 10 x 9.
• Convert n (n —1) (n - 2) (n —r+ 1) in factorial form.
• If x is so small that x2 and higher powers can be neglected, then show tha 
• Calculate (2.02)4 by binomial theorem.
• Expand (2 — i)5  

4.  Write short answers to any eight questions.

• Convert 120’40” into radian measure.
• Verify sin2+sin2+tan=2
• Prove the identity 2 cos2-1=1-2sin2
• Show that sin
• Prove that tan(45o+A)tan(45o-A)=1
• Express cos 6 product.
• Find the period of tan 4x.
• Define the terms, angle of elevation and angle of depression.
• In a triangle ABC, a=7,b=7,c=45 and
• Find the area of , if b=37, c=45 and =30o50’
• What is the domain and range of sin x?
• Find the solutions of sin x= in [0,2]
• Solve the trigonometric equation tan2

SECTION II

Q.5.
(a)Let G be the set of all 2 x 2 Non-Singular Real Matrices. Then under the usual Multiplication of Matrices G is a non-abelian group.
(b) Show that the set (1,) when  = 1 is an abelian group with respect to ordinary multiplication.

Q.6.
(a) If  are the roots of equation  Form the equation whose roots are    (and (
(b) Resolve into partial fractions

Q.7.
(a) Sum to n terms the series: 3 + 33 + 333 +………
(b) Identify the series: 1 +................ As a binomial expansion and find its sum.

Q.8.
(a) Prove that:  = tan
(b) Prove that: 

Q.9.
(a) Prove that in an equilateral triangle 1 =  
(b) Prove that sin-1  + sin-1  cos-1