MATHEMATICS HSSC—I
SECTION — A (Marks 20)
Time Allowed:25 Minutes
NOTE: Section-A is compulsory and comprises pages 1-2. All parts of this section are to be answered on the question paper itself. It should be completed in the first 25 minutes and handed over to the Centre Superintendent. Deleting/overwriting is not allowed. Do not use lead pencil.

• The Multiplicative inverse of complex number (a,b) is

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

• If z = -2 - 3i then z- is  

(A) -4
(B) -61                                
(C) 6i                    
(D) 4

• The contra-positive of pà q is__________

(A)
(B)               
(C)
(D) None of These

• The set {1,-1,1-i}A posseses Closure Property with respect to____

(A)  Addition           
(B) Multiplication
(C) Division          
(D) Subtraction

• If all the elements in a square matrix A= [au] below the principal diagonal are zero i.e. [aij] =0i > j its called 

(A)Upper Triangular Matrix  
(B) Triangular Matrix
(C) Lower Triangular Matrix                               
(D) None of these

• In a square matrix A= [aij] ,if aij = ij and aij =K, then matrix A is called

(A) Diagonal matrix                                             
(B)  Scalar matrix
(C) Unit matrix         
(D) Null matrix

• 1(-1)(-i)=___________

(A) 1                     
(B) i
(C) --i                                   
(D) -1

• If Discriminant = b² - 4ac is a perfect square, then roots are       

(A) Irrational             
(B)  Rational
(C) Imaginary           
(D) Repeated equal

• If a_n - a_{n._}, = n + 2, a₁ = 2 then a₃ =_____

(A) 6                     
(B) 4                     
(C) 11
(D) 17

• The positive G. Mean of -2 and 8 is__

(A) 4i
(B) -41                  
(C) 4                     
(D) -4

• If  a die is rolled, then the probability of the dots on the top are greater than 4 is

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

• The sum of co-efficient in the binomial expansion is

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

• cos θ <0 and tan θ <0 lie in ________ quadrant

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

• Value of sin²+sin2+tan2 is

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

• The angles associated with basic angles of the θ to a right angle or its multiple are __angles

(A) Supplementary
(B) Complementary                 
(C) Obtuse            
(D) Allied

• sin+cos=______

(A) cos θ
(B) sin θ
(C) sec θ               
(D) cosec θ

• The period of trigonometric function 3cos  is ________

(A) 2π
(B) 10π 
(C) 5π
(D) None of these

• In any triangle ABC r₁r₂r₃

(A) rs²
(B) s²
(C)
(D)

• The value of sin

(A)
(B)  
(C)
(D)

• The solution set of trigonometric equation 1+cosx = 0 is 

(A) {2nπ}
(B) {π + 2nπ}
(C) {2π + nπ}
(D) None of these

Time Allowed:2:35 Hours
Total Marks Sections B and C: 80

Note: Attempt any ten parts from Section ‘B’ and any five questions from Section ‘C’ on the separately provided answer book. Use supplementary answer sheet i.e. Sheet-B if required. Write your answer neatly and legibly

Section-B
(Marks-40)

2. Attempt any Ten parts. All parts carry equal marks

• Simplify
  
• Give logical proof of  = where A and B are any sets
  
• Fix x and y
  
• If  are the roots of ax2+bx+c=0, then prove that and
  
• Resolve into Partial Fraction
  
• Determine whether -19 and 2 are then terms of A.P. 17,13,9,…. or not
  
• Find the values of ‘n’ and ‘r’ when ⁿC_r =35 and ⁿP_r =210 
  
• Prove Mathematical induction 2+6+18+………..+23n-1-3n-1
  
• Prove that
  
• Without using calculator and tables, find the values of all trigonometric functions of 75o
  
• The area of triangle is 121.34 if  then find c and angle
  
• Show that cos (2sin-1x)=1-2x2 without using calculator and table
  
• Solve trigonometric equation tan2
  
• Prove that R= using half angle formulas
  

Section-C
(marks-40)

Attempt any five questions. All parts carry equal marks
Q.3 find the value of ‘λ’ for which the syste, has non-trivial solution. Also solve the system for the value of

Q.4 Solve the equations (x2+6x+8)(x2+14x+48)=105

Q.5 if the numbers 1,4 and 3 are subtracted from three consecutive terms of an A.P the resulting numbers are in G.P. Find the numbers if their sum is 21

Q.6 show that   where ‘n’ and ‘N’ are nearly  equal

Q.7 prove that sin

Q.8 Prove that in an equilateral triangle ABC,rE:r₁=1:2:3

Q.9 Solve the trigonometric equation sinx+sin3x+sin5x=0