Paper Multan
2015(A)
INTERMEDIATE
PART-I (11th CLASS)
MATHEMATICS
PAPER-I
GROUP-I
TIME ALLOWED: 30 Minute
OBJECTIVE
MAXIMUM 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 circle. Cutting or filling two or more circles will result in zero mark in that question. Attempt as many Questions as given to objective type question paper and leave others blank. No Credit will be awarded In case bubbles are not filled. Do not solve question on this sheet of OBJECTIVE PAPER.

Q.1

• If S is sample space and E  is an event, then:

(A) 0<P (E) <1
(B) -1<P (E) <1
(C) 0P (E) 1
(D) 1P (E) 1

• If And B are independent events,then P(AB)=

(A) P(A)+P(B)
(B) P(A)-P(B)
(C) P(A).P(B)
(D) P(A)+P(B)- P(AB)

• If n is even,then middle term in the expansion of (a+x)n is:

(A)
(B) th
(C)  th
(D) th

• ++++----+th:

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

• The area of the sector of circular region of radius r is given by:

(A) r²θ
(B) 2r²θ
(C)  r²θ
(D)  r²θ

• 2Sin²θ/2 equals:

(A)1+cosθ
(B) 1-cosθ
(C) 1+sinθ
(D) 1-sinθ

• The period of cot 8x is:

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

• With usual notations,R=

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

• The value of sec=

(A)
(B) 2
(C)
(D)

• If sinx=,then x=

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

• If n is prime number,then is:

(A) rational
(B) irrational
(C) prime number
(D) complex number

• If Ac is complement of a set A,then AAc is equal to:

(A) A
(B) A^c
(C) U
(D)

• If G equal{1,-1,I,-i} is a group under multiplication,then inverse of –I is:

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

• If order of a matrix A is mxn and order of Bis nxp,then order of AB is :

(A) m x n
(B) m x p
(C) p x m
(D) n x p

• is :

(A) null matrix
(B) idsentify matrix
(C) diagonal matrix
(D) scalar matrix

• For ax²+bx+c=0,if b²-4ac<0,then roots are:

(A) real
(B) imaginary
(C) equal
(D) rational

• Equation 2^2x-3.2^x+32=0,is _____equation.

(A) reciprocal
(B) radical
(C) exponential
(D) linear

• Partial fraction of  is of the from:

(A) 1+ +
(B)  +
(C)
(D)  +

•  =

(A)
(B)
(C)
(D) 2

• No term of geometric sequence can be:

(A) 0
(B) 1
(C) 2
(D) 3

INTERMEDIATE
PART-I (11th CLASS)
MATHEMATICS
PAPER-I
GROUP-I
TIME ALLOWED: 2.30 Hours
 SUBJECTIVE
MAXIMUM MARKS: 80 
Note: Write same question number and its part number on answer book, as given in the question paper.
SECTION-I

2.Attempt any eight parts.(8x2=16)

• simplify by justifying each step  +    /   -
• find modulus of 1-i
• define tautology and absurdity.
• find inverse and range of  f={(2,1),(3,2),(4,3)}
• show that N(pàq)àP is a tautology.
• if a and b are elements of a group ‘G’ then show that (ab)-1 =b-1a-1
• find x and y if  =
• find the inverse of
• define symmetric and skew symmetric matrix.
• evaluate (-1+)5 +(-1-)5
• sum of positive number and its reciprocal is 26/5.find the number.
• find four fourth roots of unity.

3.Attempt any eight parts.(8x2=16)

• Resolve into partial fraction of
• If a,b,c,d, are in G.P, prove that a2-b2,b2-c2,c2-d2 are in G.P.
• Sum the series  +2 +  +------+a13.
• Which term of the  A.P -2,4,10,------ is 148?
• If 5 is the H.M between 2 and b, find b.
• Find the number of diagonals of 12-dided figure.
• How many arrangements of the letter of the word mathematics can be made?
• Define circular permutation.
• Prove that nC^r=nC^n-r
• Expand (1-x) up to three terms.
• State the binomial theorem.
• Write the formula for finding the middle term the expansion of (a + x)n ,if n is even.

4.Attempt any nine parts.(9x2=18)

• With usual notations if θ=65020,r=18mm,=?
• Prove that Cot²θ- Cos²θ= Cot²θ Cos²θ
• Write the fundamental law of trigonometry.
• Prove that  sin+ cos = cosθ
• Prove that  = tan
• Express cos120 + cos48o as product.
• Write the domain and range of y=
• Define the angle of elevation.
• solve if 0,=0, b=
• find the smallest angle of  when a=37.34,b=3.24 ,c=35.06
• show that cos-1  = sin-1 
• Solve sin x = 1        in [0,2π]
• Solve sec2  θ=     in [0,2π]

Section-II

Note-Attempt any three questions.3x10=30

5.(a)Salve by  Crammer’s rule  2x +2y+z=3, 3x-2y-2z=1, 5x+y-3z=2 (5)

(b)show that (1+w)(1+w²)(1+w⁴)1+w⁸)------------2n factors=1 (5)
6.(a)Resolve into partial fraction.   (5)

(b) Sum the series 3+5-7+9+11-13+15+17-19+-----up to 3n terms, (5)

7.(a)How many numbers greater than 1000,000 can be formed from the digits0,2,2,2,3,4,4? (5)

(b) If y=+ ()2  +   ()3 +----------------then prove that y2+2y-2=0 (5)

8.(a)Prove that sin³θ +cos³θ =(sinθ-cosθ)(1+sinθ cosθ) (5)

(b) Prove that   (5)

9.(a)Solve the triangle in which a=7,b=7,c=9 (5)

(b) Prove sin-1      =cos-1     (5)