Rawalpindi board (2016)
Mathematics (objective Type)       
Time: 30 Minutes
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,C or D  with pen or marker in front of that question number.

• If Z is a complex number, then |Z|² is:

(a) Z²
(b) ()²
(c) Z
(d)

• For any two sets A and B, (A∩ B)’ is equal to:

(a) A'
(b) B'
(c) A'U B’
(d) A ∩ B

• The multiplicative identity in the set of real numbers is:

(a) Zero
(b) 1
(c) 3
(d) 2

• A square matrix A =[aij] with complex entries is called skew Hermitian if ()t is equal to:

(a) A
(b) -A
(c)|A|
(d) -|A|     

• If A and B are any two non singular matrices such that (AB)-1 is equal to:

(a) A^‑1 B^-1
(b) B^-1 A^‑1
(c) BA
(d) AB

• A reciprocal equation remains unchanged when variable x is replaced by:

(a)  
(b)  
(c)
(d) –x

• The roots of equation  - 5x + 6 = 0 are:

(a)2. -3
(b) -2 , 3
(c) 2, 3
(d) -2 , 3

• (x -1)2 = x2 – 2x +1 is called:

(a) Equation
(b) Conditional
(c) Identity
(d) Fraction

• A.M between  and 5:

(a) 4
(b) 5
(c) 10
(d) 2

• ntn term of G.P is:

(a) a1yⁿ
(b) a1y^n-1
(c)
(d)

• If n = 1, then value of n|n –1 is

(a) Zero
(b) 1
(c) 2
(d) -1

•  equals :

(a) 1
(b) n
(c) Zero
(d) 2

• General term of expansion (a + x)" is:

(a) a^n-r x^r
(b) a^n-r x^r
(c)   a^r x^n-r
(d)  a^n-r x^r

• The sum of binomial co -efficients in the expansion of (1 + x)4 is:

(a) 8
(b) 10
(c) 16
(d) 32

• cos²2 + sin² 2 is equal to:

(a) 1
(b) Zero
(c) sec2 0
(d) 2

• cos (π/2- β) is equal to:  

(a) sin β
(b) - sin β
(c) cos β
(d) - cos β

• Period of cosec 10x is:

(a)   
(b)  
(c)  
(d)

• For any triangle ABC, with usual notations r2 is equal to:

(a) 
(b)   
(c)
(d)    

• tan (sin-1 x) is equal to:

(a) 1+ 2x²
(b) 1–x²
(c)
(d)

• The solution of equation –2+ sin  = 0 are in quadrant.

(a) I &IV
(b) I & III
(c) III & IV
(d) II & IV

Rawalpindi board (2016)
part I
Mathematics (Subjective type)       
Time: 2:30 Hours
Section-I
Marks: 80

2. Attempt any Eight Parts.16

• Find the multiplicative inverse of (-4  7)
• Find real and imaginary parts of ()³.
• Define equivalent sets.
• Define monoid.
• Find the inverse of the matrix A =.
• Show that   = 0 without expansion.
• Find the value of λif A =  is singular.
• Define exponential equation.
• If U = {1,2,3,…….10} , A = {2,4,6……..20} and  B = {1,3,5……. 19} , prove that (AUB)’= A’ ∩B’
• Write converse and contrapositive of the conditional Nq  Np.
• Find there cube-cube roots of unity.
• If a, β are the roots of 3x2-2x+4= 0, find the values of  + .

3.Attempt any Eight Parts. 16

• Resolve into partial fractions.
• Which term of the A.P 5,2,-1....is -85.
• Find the value of n if nP4 : P = 9 :1.
• Find the number of diagonals of 12 sided figure.
• Find the first four terms of (1 + 2x)-1.
• Find the 6th term in the expansion of 10
• Find the next two terms of the sequence 1,-3,5,-7,9,-11,…….
• If 5,8 are two A.Ms between a and h find a and b.
• Convert the recurring decimal 2. into the equivalent common fraction.
• Convert n(n –1)(n – 2)…..(n – r + I) in the factorial form.
• How many numbers greater than 1000,000 can be formed from digits 0, 2, 2, 2, 3, 4, 4.
• Show that inequality 4n > 3n + 4 is true for n = 2,3.

4. Attempt any Nine Parts.18

• Verify 2 sin 45° +  cosec 45° =
• Prove that: cot2  - cos2  = cot2  cos2
• Find the value of tan 75° (without calculator).
• Prove that: cos 306° + cos 234° + cos 162° + cos 18° = 0.
• Prove that  =
• Prove that: sin sin =  cos2.
• Find the period of cos ec x/4 .
• Show that: tan (sin-1 x) = .
• Prove that abc (sin a + sin β + sin ) = 4S .
• Define trigonometric equation.
• Find the area of triangle ABC, if a = 524, b = 276, c = 315.
• Find the smallest angle of the triangle ABC, when a = 37.34,b= 3.24, c = 35.06.
• Find the solution of secx=-2 which lies in [0,2].

SECTION-11

Attempt any THREE questions. Each questions carries 10 marks.

5.(a) Use Cramer's rule to solve the system:
2x + 2y + z = 3 ; 33x – 2y -2z = 1 ; 5x +y – 3z = 2

(b) If a and β are the roots of x2-3x+5 = 0 from the
equation whose roots are  and  .
6.(a) Resolve into partial fractions.
(b) For what value of n is G.M between a and b.

7.(a) How many arrangements of the letters of the word ATTACKED can be made if each arrangement begins      with and ends with K.
(b) Find the co-efficient of x5 in the expansion of 10

8.(a) Prove the identity
sin6  – cos6  = (sine2 –cos2 )(1–sine2 cos2).
(b) If sin a= and cos=  where 0 < a < π/2 and
0<β< show that sin (a-β) =

9.(a) The sides of a triangle are x2+ x +1,2x +1 and x2 -1 prove
that the greater angle of the triangle is 120°.
(b) Prove that tan-1  + tan-1  = tan-1  + tan-1  .