RAWALPINDI
BOARD 2014
PAPER MATHEMATICS
PART-ITime: 30 Min.
(Objective Part1)
Marks: 20
Note: Four Answers are given against each column A,B,C & D. Select the write answer and only separet answer sheet, fill the circle A,B,Cor D with pen or marker in front of that question number.

• For quadratic equation ax²+bx+c=0, the sum of its roots is:

(a)  
(b)  
(c)
(d)

• Partial fraction of   will be:

(a)
(b)
(c)  
(d) 1+

• Common difference of A.P. 17, 13, 9, ………….  is:

(a) 4    
(b) -4  
(c) 30  
(d) 15

• Arithmetic Mean between  and 3 is:

(a)  
(b) 2           
(c) 6    
(d) 3

• The multiplicative inverse of non-zero real No. is:

(a) 0    
(b) a    
(c) -a   
(d)

• If A = {}, the P(A) is equal to:

(a) Infinite set
(b) Singletion set
(c) Empty set  
(d) Null set

• The additive inverse of a matrix A is:

(a) A   
(b) -A 
(c) A2  
(d)         

• │1  2│ is equal to:│3  4│

(a) -2   
(b) 2    
(c) 0    
(d) 3

• If x²+ 3x+ 7 is divided by x + 1, remainder is:

(a) -5   
(b) 11  
(c) 5    
(d) -11

• Area of a triangle in terms of its sides is:

  (a) 
  (b) bcsina
  (c)
  (d) ac

• In-radius r of a triangle is:

(a) s∆
(b)     
(c)     
(d)     

•  sec(cos-1 ) is equal to:

(a)     
(b) 2    
(c)     
(d)     

• 1 + Cot²θ  is equal to:

(a) sec²θ
(b)           
(c) tan²θ         
(d)

• ⁿP₄ is equal to:

(a) 36  
(b) 360
(c) 6    
(d) 4

• The value of ⁶P₁ is:

(a) 18  
(b) 12  
(c) 6    
(d) 0

• The inequality n!> 2"-1 is valid if:

(a) n = 3          
(b) n ≤ 3         
(c) n< 4           
(d) n ≥ 4

• Which angle is quadrantal angle?

(a) 120o           
(b) 270o          
(c) 60o 
(d) 45o

• If sinɵ=, then ɵ is:    

(a) 30°
(b) 45°
(c) 90°
(d) 120°

• sin319° is equal to:

(a) -cos 33°
(b) sin 41°       
(c) -sin 41°
(d) sin 16°

• The period of cot 3x is:

(a)
(b)
(c)
(d) π

Time: 2:30 Hours
(Subjective Part)
Marks: 80
SECTION-I

2. Attempt any Eight Parts.

• Show that Ѵz € c, z.z=│z│²
• Define the terms proper subset and improper sub set.
• What is the diagonal matrix?
• Solve by using quadratic formula 15x² + 2ax – a² = 0
• Verify without expansion│α β + γ 1│ = 0
  │β γ + α 1│
  │γ α + β 1│
• Evalualte(1+w+w²)8:-
• Does the set (1,-1} possess closure property w.r.t. addition and multiplication?
• Find thy inverse and tell whether inverse is a function or not, if           
  A={(2,1),(7,8),(8,7),(4,3)}.
• A number exceeds it square root by 56, find the number.
• Define the terms upper triangular and lower triangular matrix.
• Check whether the given martrix is singular or not, if:-
  A=
• If α, β are roots of equaiton 3x²- 2x + 4 = 0, find  +

3. Attempt any Eight Parts.16

• Define the rational fraction.
• Resolve  into partial fraction.
• Define Hamonic Mean between "a" and "b".
• Insert four real geometric mean between 3 and 96.
• Find "n", if ⁿP₂ = 30.
• Evaluate 3  correct to three places of decimals.
• If the 5th term of an A.P. is 13 and 17th term is 49, find a13.
• If 5,8 are two A.M. between "a" and "b", find "a" and "b".
• In how many ways can a necklace of "8" beads of different colours be made?
• How many diagonals can be formed by joining the vertices of a polygon having 8
  sets?
• Find the probability if there are 5 green and 3 red bails in a box, one ball is taken out
  and ball is green.
• Determine the middle term in the expression of

4.Attempt any sine Parts.18

• Prove that  = (cosecɵ + cotɵ)²
• Prove that  = tan37o
• Find the period of cos
• Find the value of sin²α, if cosα= , where 0 < α <
• Prove that R=.
• Solve the equation sinx=
• Solve for solution set, if the equation is sinx + cos 3x = cos5x.
• If tanɵ = and the terminal arm of the angle is not in the III quadrant, find the value
  of  
• Express product as sum or differences of  sin(x+45o)sin (x-45o).
• At the top of a cliff 80m high, the angle of depression of a boat is 12o. How far is the
  boat from the cliff?
• Solve the triangle ABC in which: b = 95;c = 34;α = 52o.
• Find the measure of the greatest angle, if sides of the triangle are 16,20,30.
• Without using the table and calculator, find the value of tan (-135o)

SECTION-II:

Attempt any THREE questions. Each question carries 10 marks.
Q.5
(a) Prove that set of a 4 fourth roots of unity {1,-1,i,-i} is a group with respect to
multiplication.
(b) Solve the matrix equation 3x-2A= B, if:


Q.6
(a) lf the roots of px²+ qx +q= 0 are α and β, then prove that:

(b) Resolve into partial fraction  

Q.7
(a) If H.M. and A.M. between two numbers are 4 and that   respectively.Find the
numbers.
(b) Use binomial theorem to show that:
1+  ++  + ……….. =

Q.8
(a) Prove the identity =tanɵ+secɵ

(b) Prove that  +  = 2cot²ɵ.

Q.9
(a) Solve the trianle ABC if α = 53, β = 88o36, γ= 31°54'.
(b) Prove that: 2tan-1 + tan-1+ =+