Multan Board 2017
Mathematics
PART-I
Time: 30 Minutes 
Group 1
Note: Write answers to the questions on the objective answer sheet provided. Four possible answers A, B, C and D to each question are given. Which answer you consider correct, fill the corresponding circle  A, B, C and D given in front of each question with Marker or pen ink on the answer sheet provided.

• If ⁿC _s = ⁿC₁₂ then ⁿn_n equals to:-

1. 4
2. 8
3. 20
4. 12

• 2^nd term in (1 - x)^-1 is:-

1. 1
2. X
3. 2X
4. 3X

• If n²>n+3, then it is true for:-

1. n = 0
2. n< 1
3. n2
4. n2

•  tr radian equals to:-

1. 110°
2. 130°
3. 45o
4. 54o

• sin(a-) =____:

• The period of sin 2x is:-

• With usual notations 2s - b =

1. a – c
2. a + c
3. a+2b-c
4. a + b

• cos =____

• Tin-1(-1) =_____.

• Cos x=, then reference angle is:-

•  i14 equals to:-

1.  1
2. -1
3. I
4. -i

•  p  q is called converse of:-

•  If A = then adj. (A) = ____.

• The rank of the matrix  is :-

1. Zero
2. 1
3. 2
4. 3

• Four fourth roots of unity are:-

1. ±1. ±i
2. ±2, ±2i
3. ±3, ±i
4. ±4, ±4i

• If  is the complex cube roots of unity, then  =________.

1.  
2.  -1
3. 
4. 

• Partial fractions of   are of the form:-

• The fifth term of the sequence an = 2n + 1 is:-

1. 7
2. 9
3. 11
4. 13

• Geometric mean between -2i and 8i is:

1. ±3
2. ±2
3. ±1
4. ±4

• The value of 5p2 is:-

1. 5
2. 10
3. 15
4. 20

SUBJECTIVE PART
SECTION B

Q 2. Attempt any eight parts.

1. Simplify by justifying each step  
2. Simplify (5, -4)  (-3, -8)
3. Simplify   by expressing in the form a + bi.,
4. Write down power set of the set
5. Construct truth table for statement.
6. Show that the set N with respect of  is a semi-group where N is natural number.
7. Solve the systems of linear equations 3x1  x2 = 1 and x1 +x2 = 3
8. Without expansion verify that
9. Define rank of a matrix.
10. If is a root of x2+x+1 = 0 show that its other roots is.
11. If  are roots of ax2 + bx + c = 0, a  O. Then find the values of  
12. Show that roots of the equations px2  will be rational.

Q 3. Attempt any eight parts.

1. Define Partial fractions.
2. If  =, b = then find the arithmetic mean A and the geometric mean G.
3. Show that the reciprocals of the terms of G.P, a1, a1r2, a1r4._____form another G.P.
4. Find A.M between 1 - x + x2 and 1 +x +x2.
5. Write the next term of the sequence I, 6, 20, 56,
6. Convert  in the factorial form.
7. Prove that n. n-1Pr-1 =NPr.
8. A die is rolled. Find the probability of the event when number of dot on the top is less 5.
9. Find the value of n when nC10 = 
10. State Binomial Theorem.
11. if x is ,0 small that its square and higher powers can be neglected then show that
12. Expand the varies  up to 3 terms.

Q 4. Attempt any six parts.

• Find  when = radian, r= 6cm.
• Verify  + =  
• Prove the identity   Sing Cos= 1
• Prove that Sin (180o +a) Sin (90o-a) =-.
• Show that Sin Sin = Cos.
• Express  as product.
• Find the period of.
• A vertical pole is Sin-1 high and the length of its shadow is 6m. What is the Angle of Elevation of the Sun at that moment?
• Find the smallest angle of the ABC if a=37.34 b = 3.24 c=35.06
• In a triangle ABC,= 60o, =  and b  then find a. c.
• Show that Sin-1 (-x) =-Sin-1 x
• Solve the equation Sin2 x +  = 1 when x  
• Find solution of 4Cos2 x-3 = 0 when x   

SECTION-C

NOTE: - Attempt any three questions.
Q 5.

1. Consider the set S = set up the multiplication table and show S is an abelian group under multiplication.
2. Solve the systems of linear equations

Q 6.

1. When the polynomial2 is divided by  the remainder is 14. Find the value of k.
2. Resolve into Partial Fractions.

Q 7.

1. Insert seven A.Ms between 4 and 8.
2. Find the coefficient of xn in the expansion of

Q 8.

1. If  =  and find the values of the remaining trigonometric functions.
2. Prove the following identity

Q 9.

1. Prove that in tan equilateral triangle  
2. Prove that Sin-1 Sin-1 = Cos-1