Inter (Part-I) Lahore Board 2016
Mathematics
Part I (Objective Type)
Time Allowed: 30 Minutes 
Max. Marks: 20

Note: You have four choices 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.

Question #1
Circle the correct option i.e. A/B/C/D. Each part carries one mark.

• If z = 1 - i then |z| =:

(A) 2
(B) -2
(C) –
(D)

• The conjunction of two statements p and q is denoted by:

(A) p v q
(B) p → q
(C) q → p
(D) p Ʌ q

• The (0, 0) solution of the system a¹x + b¹y = 0 and a²x + b²y = 0 is called:

(A) Consistent
(B) Inconsistent
(C) Non-trivial
(D) Trivial

• (A-1)t is equal to:

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

• If one solution of the equation x2 + ax + 2 = 0 is x = 1 then a = :

(A) -7
(B) 7
(C) -3
(D) 0

• If w is the cube root of unity then w =

(A) w2
(B) 1
(C) W-2
(D) 1+W2

•  = +:

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

• The harmonic equal two mean between two numbers a and b is equal to:

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

• If a =1,b =5 then A x H is equal to:

(A) 5
(B) -5
(C)
(D)

• If A and B are independent events and P(A) = 0.8, P(B) = 0.7 then P(AB) equals:

(A) 0.56
(B)
(C)
(D) 0.1

• If n P2 = 30 then n is equal to:

(A) 6
(B) 5
(C) 4
(D) 10

• The rth term in the expansion of (a+b)n is

(A)  an-r xr
(B)  an xn-r
(C)  ar xn-r
(D)  an+r xr

• The sum of odd coefficients in the expansion of (1 + x)n is:

(A) 2n-1
(B) 2n+1
(C) 22n
(D) 2n-2

• One degree is equal to

(A)
(B)
(C)  radian
(D) 180°

• Cot (90-a) equals:

(A) –tan a
(B) tan a
(C) cot a
(D) –cot a

• Period of tan x is equal to:

(A) 2
(B)
(C)
(D) -3

• For any  ABC, c2  =:

(A) a2 +c2 – 2ac cos
(B) a2 + b2 – 2ab cos Y
(C) b2 + c2 – 2bc cos a
(D) a2 –c2 2ac cos Y

• In any  ABC, cos  is equal to:

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

• y = cos x is one to one in interval:

(A) [0]
(B) [0,]
(C) [0,∞]
(D) [0,]

• If y= cos-1 x then its domain is :     

(A) - x
(B) -1 x 1
(C) 0
(D) -∞ < x < + ∞

Inter (Part-I) Lahore Board 2016
Mathematics
Part I (Subjective)
Time Allowed: 2.30 Hours 
Max. Marks: 80 

Section I

2. Write short answers to any Eight (8) questions: 16

• State transitive property of inequalities.
• Show that  z  C, z2 + z2 is a real number.
• Find modulus of the complex number 1 –i
• Write the power set of {a , {b, c}}
• Write inverse and contrapositive of conditional p → q.
• Define finite and infinite group.
• If   and A2= fine values of a and b
• Find the values of x if                  
• Without expansion show that    
• Solve the equation x2 - 7x +10 = 0 by factorization.
• A number exceeds its square root by 56. Find the number.
• If a,  are roots of 3x2 - 2x + 4 = 0, find the value of a2  2?

3.Write short notes on any EIGHT (8) questions: 16

• (i) Define proper rational fraction.
• (ii) If an-3 = 2n - 5, find the nth term of the sequence?
• (iii) If  and  are in G.P show that the common ratio is
• (iv) Find 12th terms of harmonic sequence  
• (v) Find A.M between 1 - x + x2 and 1 + x + x2
• (vi) Write (n + 2)(n + 1) (n) in factorial form. 
• (vii) Find value of n when nC10 =
• (viii) Find value of n when 11Pn = 11.10.9 
• (ix) A die is thrown. Find probability that the dots on top are prime numbers or odd numbers.
• (x) Calculate (0.97)3 by binomial theorem.
• (xi) Expand (1 + 2x)-1 upto four terms.
• (xii) Evaluate  correct to three places of decimal.

4. Write short answers to any NINE (9) questions:                                                    18

• (i) Convert 54°45' into radians. •
• (ii) If cot  and the terminal arm of the angle is not in 8 quadrant I, find the values of cos e and cosec 8?
• (iii) Prove that  + cot  = cos ec
• (iv) Without using the table and calculator, find the value of cos 315°.
• (v) Prove that    = tan 37°
• (vi) Express 2 sin 7 sin 2 as a sum or difference. (vii) Find the period of sec 9x.
• (viii) Solve the right triangle ABC, in which =  90°, = 50°10', c = 0.832
• (ix) Find the area of the triangle ABC, in which b = 37 , c = 45 , a =30°50'.
• (x) Prove that rr1r2r3= 2
• (xi) Show that cos (2sin-1 x) = 1 - 2x2.
• (xii) Find the solution of the equation 1 + cosx = , which lie in [0, 2-]
• (xiii) Find the solution of the equation tang  - sec  - 1 = 0 which lie in [0, 2]

SECTION-II

NOTE: - Attempt any three questions. 10 x3=30

Question #5
(a) Use adjoint method to solve the system x1 - 2x2 + X3 = -4
2x2 3x2 + 2x3 = -6
2x1 + 2x2 + x3 =5
(b) Solve the system of equations       3x + 4y = 2
 +   = 2
Question #6
(a) Resolve   into partial fractions                                                    5
(b)The sum of 9 terms of an AP is 171 and its eighth term is 31. Find the series.     5
Question #7.
(a) How many 6-digit numbers can be formed from the digits 2,2 3, 3, 4, 4? How many of them will lie between 400,000 and 430,000?                                   5
(b) If x is nearly equal to 1, prove that pxp - qxq  (p - q)xp+q                                  5         

Question #8
(a) Find the value of the trigonometric functions angle                                 5
(b) Reduce cos4 to an expression involving only function of multiples of 8, raised to the first power.                                                                                                   5
Question #9
(a) Show that r1 =4 R sin  cos  cos                                                                  5         
(b) Prove that sin-1 +cot-l x =                                                                             5