Sargodha Board 2017
INTERMEDIATE PART-I (11th CLASS)
Mathematics (NEW SCHEME)
TIME ALLOWED: 20 Minutes 
 MAXIMUM MARKS: 15
OBJECTIVE|
Note: You have four chokes 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. Attempt as many questions as given in objective type question paper and leave others blank. No credit will be awarded in case BUBBLES are not filled. Do not salve question on this sheet of OBJECTIVE PAPER.

Q.No.1

•  belongs to the set of:

(A) Area 
(B) Complex    
(C) Prime
(D) Even

• The number of subsets of a set having 3 elements is:

(A) 4
(B) 6
(C) 8
(D) 10

• The value of determinant of a identity matrix is equal to:
  

(A) 0
(B) 1
(C) -1
(D) 2

•   A square matrix A is symmetric if A^t =
  

(A) A
(B) -A
(C) 2
(D) -A^t

• The product of all cube roots of unity is:
  

(A) 1
(B) 0
(C) 2
(D) -1

• If (x - a) is a factor of a polynomial ( then  equals to
  

(A) 1
(B) 0
(C) 2
(D) -1

• Partial fractions of   will be of the form:
  

(A)
(B)
(C) +
(D) 

• The A.M between andis:
  

(A)   
(B) 
(C) 
(D) 

• The Geometric means between 2 and 4 are
  

(A) ±8
(B) ±4
(C) ±2 
(D) ±3

• If A and B are independent events then P(AB).=
  

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

• For an Event E, the range of its Probability is
  

(A) 0 <P(E) <1 
(B) 
(C) 0P(E)1 
(D)

• If n is even, the Binomial expansion n will have
  

(A) One middle term
(B) Two middle term
(C) Three middle term
(D) No middle term

• The number of terms in the expansion of 10 is
  

(A) 10
(B) 11
(C) 12
(D) 9

• If Cot >0 and Sin <0 , then terminal arm of the angle lies in.
  

(A) I
(B) II
(C) III
(D) IV

• Sin  is equal to
  

(A)
(B)  
(C) 
(D) 

• Period of tan is
  

(A) π
(B) π/7
(C) 7π
(D) π+7

• Radius of escribed circle is:
  

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

• In an equilateral triangle with usual notations r:R:is
  

(A) 1:1:1 
(B) 2:1:2 
(C) 3:2:1 
(D) 1:2:3

•    is equal to:
  

(A)
(B) 60°   
(C) 30°   
(D) 2

•   If   the General Solution of the equation Sin  is:
  

(A)
(B) 
(C) 
(D) 

Sargodha Board 2017
INTERMEDIATE
PART-I (11th CLASS)
Mathematics
(NEW SCHEME)
TIME ALLOWED: 2.30 Hours
MAXIMUM MARKS: 80
SUBJECTIVE

2. Attempt any Eight of the following. All carry equal marks.
SECTION-I

1. Does the not {1, -1} posses closure property with respect to (i) addition (ii) Multiplication
2. Simplify (5,- 4):(-3,- 8)
3.  Write the converse and inverse of – p q
4.  Factorize 22
5.  If a, b are elements of a group. Show that -1 =-1 -1
6.  Define an onto function.
7.  If = and  = Find the values of  
8. Show that  
9.  Find the multiplicative inverse of  
10.  A number exceeds its square root by 56: Find the number.
11.  Show that (x-2) isa 'Actor of 4 -132 +36
12.  Prove that each complex cube roots of unity is square of the other.

3. Answer briefly any Eight parts from the followings:-

1. Resolve into Partial Fractions.
   
2. If 5, 8 are two A.Ms between a and b, find a and b
   
3. If and  are in G.P. Show that conunon ratio is ±
   
4. Define Harmonic Progression.
   
5. Insert two G.Ms between 2 and 16.
   
6. Write ………  in the factorial form.
   
7. Prove that  
   
8. Find the number of diagonals of a 6-sided figure
   
9. In how many ways can 4 keys be arranged on a circular key ring?
   
10. Stare Principle of Mathematical induction.
    
11. Expand to two terms.
    
12. Expand to two terms.

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

1. Show that 2 sin 45o+ cosec 45° =
   
2. Convert 18° 6’12n to decimal form   
   
3. Prove that2  
   
4. Find the value of cos
   
5. Show that cos  coscos2  sin2
   
6. (vi)   Prove that
   
7. Find the period of cot
   
8. In triangle ABC give that b=3,c=5,a=120° Find  and
   
9. Find area of triangle ABC when a = 4.8, = 83°42' , =32°12'
   
10. Prove that
    
11. Find the value of tan 
    
12. Solve the equation -1+cos x = 0,x 
    
13. Find the solution of the equation cot

Section —   II

Note: Attempt any three questions.
5. (a) Convert the given theorem to logical from and prove by constructing truth table.
(b) Use Cramer’s rule to solve the system of linear equations:-

6. (a) If the roots of 2 +qx+q =0 are then prove that
(b) Resolve the following into Partial Fractions:

7. (a) If S₂,S₃,S₆ are the Sums of 2n, 3n, 5n terms of an A.P. Show that S₅ = 5(S₃- S₂)
(b) Use mathematical Induction to prove the following formula for every positive Integer n ……………+

8. (a) Prove that sin6
(b)     Prove that

9. (a) Find the area of triangle ABC,given three sides: a = 32.65 , b = 42.81 c = 64, 92.
(b) Prove that cos^-1 A+cos^-1 B=cos^-1