Multan board Mathematic 2016
(Inter part-1)
(Mathematic)
(GROUP-1)
Note: Pour 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.

• Range of tan x is equal to:

1. Q
2. IR
3. Z 
4. N

• If ABC be any triangle and  then,

• Angle below the horizontal line is called:

1. Right angle
2. Oblique angle
3. Angle of Elevation
4. Angle of Depression

• Cos ( ) is equal to:

• If Cos x + 1 = 0. Then:

1. {}
2.  
3.  
4. 

• The modulus of 1-i is equal to:

1. - 2
2. 2
3. - 
4. 

• Tabular form of a set   is equal to:

• If =  then det A is equal to:

1.  0
2. 1
3.  (a - b)(c - a)
4.  

• The cofactor of an element   denoted by   is equal to.

• A quadratic equation , becomes liner equation if:-

1. a = 0
2. b = 0
3. c =0
4. a=b

• Complex cube roots of -1 are:

• Panel fractions of  is equal to:

• If a, G, b be the G.P where a, b are numbers then G.M is equal to:

• Reciprocal term of A.P:

1. A.P.
2. G.P.
3. H.P.
4. None of these

• If S is a sample mace and E = S is on event then P (E) is equal to,

1.  
2. 0
3. 1
4. (0.2)

• If  =  which of the following mat he true?

1.  
2. r + q=n
3. r – q + n
4. q  = 0

• 1+2x+3+------ is the expansion of:-

• Sum of exponent of a end b in  in every term is:

1.  
2. 2 
3.  
4. 

• The 60th part of 1- degree is called one:-

1. Second
2. Minute
3. Degree
4. Radian

•  is equal to,

SUBJECTIVE PART
(Group 1)
(Section-I)
NOTE: Write same question number and its part number on answer book, as gives in the question paper.

Q2: Attempt any eight parts.

1. Simplify by expressing in the form a + bi
2. Write in descriptive and tabular form.
3. Factorize a²+4b²
4. Define Group.
5. Write Reflexive Property of Equality of Real Numbers.
6. Construct the truth table of of two statements p and q.
7. Discuss the nature of the roots of equation x²+2x+3=0
8. Find two consecutive numbers whose product is 132.
9. Write any two properties of determinants of square matrices.
10. Find the matrix X if X=X=
11. Find the value of k if the polynomial has a remainder of - 4 when divided by (x + 2).
12. If the matrices A and B are symmetric and AB = BA, show that AB is symmetric.

Q3. Attempt any eight parts.

1. Resolve into partial fractions  
2.  Write the 1st three terms of the sequence if an = 
3.  Find A.M between  and.
4. Find the 12thterm of G.P if 1+ i, 2i, -2 +2i,-----
5.  Find the 9thterm of the H.P------
6.  Write in factorial form
7.  Find the value of n when
8.  Show that  
9.  Expand up to three terms  
10.  Using Binomial theorem find the value up to three place of decimals of 
11.  Expand and simplify  
12. Define Mutually Exclusive Events.

Q4. Attempt any nine parts.

1. Find r when  radian.
2. Prove that  
3.  Prove   
4.  If  are the angles of a triangle ABC , then prove that Cos( 
5.  Prove that Cos( 
6.  Express Sin5 Cos2as sum or difference.
7.  Find the period of Cot8x
8.  Solve the right triangle, in which y=  a = . , a  243
9.  With usual notations. prove that R = 
10.  Show that
11.  Without using calculator, show that  
12.  Find the solutions of in  
13. Find the solutions of in

SECTION-II
NOTE: Attempt any three questions.

Q5:

1. Solve the followings system of linear equation by Cramer’s rule: 2x + 2y + r=3, 3x – 2y -2z = 1, 5x +y -3z=?
2. Show shot the roots of the following equation:- (x-a) (x-b) + (x-c)(x-a) are equal.

 
Q6:

1.  Resolveinto partial fraction.
2.  Find four terms of A.P whose sum is 32 and sum of whose squares is 276.

Q7:

1.  In how many ways can be letters of the word MISSISSIPPI be arranged when all the letters are to be used?
2.  if x is very nearly equal to 1. then prove that p 

Q8:

1. Prove that  
2. Prove that sin10 sin30 sin50 sin70= 

Q9:

1. Prove that
2. Prove that

Multan board
Mathematic 2016
Inter part-1
(GROUP 2)

Note:Pour 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.

• Range of   = Cos x is:-

1.  R
2. 
3. 
4. 

•  With usual  notations area of triangle ABC is:

1. )
2. 
3. 
4. 

• With usual notation Iris 

•  Solutions of the equation 1 + Cos = 0 are in quadrants:-

1. I and IV
2.  II and III
3.  II and IV
4.  None of these

•  Modulus of  is:

1.  4
2.  16
3.  34
4. 131

• Drawing conclusions from peruses  believed to be true is called

1.  Induction
2. Deduction
3.  Proposition
4.  Contradiction

1. 1
2. 2
3. 3
4. -3

• Every Diagonal matrix is also:-

1.  Triangular Matrix
2.  Scalar Matrix
3.  Rectangular Matrix
4. Symmetric Matrix

1. Recipmen1 Equation
2.  Transcendental Equation
3.  Quadratic Equation
4.  identity

• If the roots of  are real and unequal then:

•  Any improper rational fractional can be reduced to a mixed form by:

1. Addition
2. Multiplication
3. Factorization
4. Division

• With usual notations, the product of n Geometric Means between a and b is

• -------

• If A and B are independent events then probability=

• ------= 

• There is no integer  for which  is:-

1. Odd
2.  Even
3.  Prime
4.  Complex  

• Expansion of is valid if:

• An angle is said to be in standard position if its vertex is at:-

• =

SUBJECTIVE PART
Mathematic
(Group 2)
(Section I)

Q2: Attempt any eight parts.

1. Name the property used in  
2.  Separate into real and imaginary pans.
3.  Simplify.
4. Write  in the descriptive and tabular forms.
5.  Show that is a tautology.
6.  Define a Group.
7.  Find the value of  is singular.
8.  Without expansion verify that
9. If  is symmetric. Show that is symmetric.
10. Prove that
11. If  are the roots of prove that 
12.  Show that the roots of   are rational.

Q3: Attempt any eight parts.

1. Resolve  into Partial Fractions.
2.  Find the next two terms of 7. 9, 12. 16,
3.  If  and  are in A.P. show that  
4. Find the sum of infinite geometric series -----
5.  If 5 is H.M. between  and , find
6.  Evaluate  
7. How many 3 - digit number can be formed by using each one of the digits 2. 3, 5, 7, 9 only once?
8.  Find the value of /n, when
9.  A die is rolled. What is the probability that the dots on the top are greater than 4?
10.  Prove ---- 
11.  Find the 60thterm in the expansion of
12.  If  so small that its square and higher powers can be neglected. then show that

Q4. Attempt any nine parts.

1.  Verify = I - 2 when  =
2.  Verify
3.  Prove that  
4.  If  are the angles of a triangle ABC, then prove that
5.  Prove that  
6. Prove that Cos2+= 
7.  Find the period of 
8. Define in-circle.
9.  Prove that 
10.  Find, if measures of the sides of triangle  are 
11.  Show that  
12.  Find the solution of
13. Solve

SECTION-II
NOTE: - Attempt any three questions.

Q5:

1. Show that,=
2. Prove that  =1 will have equal roots if = 

Q6:

1. Resolve into partial fractions.
2. For what value of is the positive geometric mean between  and ?

Q7:

1. Prove that
2.   If .-------- then prove that

Q8:

1. Prove the identity
2.  Prove that  

Q9:

1.  The sides of a triangle and  Prove that the greatest angle of the triangle is  
2.  Prove that