«MATHEMATICS»
Inter (Part. 1)
Paper: Objective Type  Time: 30 Min
Marks: 20
Session (2011 - 2013)
Note: Write answers to the question on the objective answer sheet provided. Four possible answer A, B, C, D to each question are given which answer is correct, fill the relevant circle with pen ink to each question on the answer sheet provided.

• Name the property which is used in the inequality -3 < -2 à0 < 1 :

A. Additive Property
B. Multiplicative Property
C. Both A & B
D. Reflexive

Modules of complex number -5i is :

A. + 5
B. -5
C.  
D. 5

• According to Demerger’s Law (AÚB) =

A. AÚB
B. A∩B
C. A∩B
D. A∩B

• A and B are overlapping sets:

A. A∩B = ⱺ
B. A∩B = ⱺ
C. A∩B = B
D. A∩B = A

• Let A be a square matrix then =

A.
B. A
C.
D.

• Let ∞, ß be the roots of  ax²+bx + c = 0 : a  = 0 then ∞ß is :

A.
B. c/a
C.
D.

• The General Term of the G.P is:

A. an = a₁+(a-1)d
B. a₁ = an+(n-1)d
C. an=a₁rn-1
D. an = d+(n-1)a₁

• The relation of the form  : Q (x) = 0 is called a :

A. Number
B. Integer
C. Equation
D. Fraction

• The nth term of an A.P. is (3u) the first three terms are

A. 3,2,1
B. 1,2,3
C.
D.

• 9.8.7.6 = :

A.
B. 51/91
C. 51
D. 31

• P (E) – E is event, S is sample space:

A. E
B.
C. S
D.

• If a is any positive integer then 4n > 3n + 4 is true for all values of n.

A. n >2
B. b > 2
C. n < 2
D. n < 2

• In the expansion of ()6 the coefficient of x3 is :

A.
B.
C. -3
D. -8

• If  < 1 then the expansion of (i-x)^1/2 4P to the terms is

A. 1+1/2x
B. 1-1/2x
C. 1-x
D. 1+ x

• Angel 275ᵒ lies in :

A. I Quadrant
B. II Quadrant
C. III Quadrant 
D. IV Quadrant

• Sin(-∞) = :

A. See∞
B. –Sin ∞
C. Sin ∞
D. –Cos ∞

• The domain of tanx is :

A. [-1,1]
B. R
C. R- {x/x = (2n+1), n εz3}
D. R- {x/x= nπ. Nεz}

• The sum of three angles of triangle is :

A. 360ᵒ
B. 270ᵒ
C. 225ᵒ
D. 180ᵒ

• Cos (Sin-1()) is equel to :

A.
B. 1/
C. 2
D.

• If See2ⱺ =  then tan2ⱺ = :

A.  
B. -2/3
C.
D.

«MATHEMATIES»
(Subjective)
Inter-A-2012
Inter Part I  
 Total Marks :80
Time : 2 : 30 Hours

NOTE : It it Compulsory to attempt (C18) path; lean fin= Q.No.2. and 3 while attempt any (09 ) parts from Q_No.4 and attempt any (03) questions from Part II_ Write same questions no and its part no as given in the question paper.
Part I

Q.No.2

• Does the set {1,-1} possess Closure Property w.r,i. Multiplication? 
• Factorize   3x² + 3y²
• Write power set of A = {9,11}         
• Write Converse and Contrapositive of q —>  p
• Define Function.
• In group (Z,+) write inverse of 2 and -3
• If A =           Show that A4 = I2
  
• Show that  = ⱺ
  
• Show that B =  is skew symmetric
  
• Solve 4x² + 7x – 1 = 0 by Quadratic Fomula
  
• Evaluate w28 + w29 +1
  
• If ∞ , ß are root of x2 – px – P –c = 0 Prove that (1+ ∞)(1+ß) = 1-c

Q.N0.3

• Resolve the  expression  into partial fraction.
  
• Define the proper Rational Fraction
  
• Find two Geometric means between I and 8
  
• If 5, 8 are two arithmetic means between a and b find a and b.
  
• How many diagonals can be formed by joining vertices of polygon having 5 sides.
  
• A die is thrown what is the probability that number is prine.
  
• If x is so small that its square and higher powers may be neglected then show that
  
  
  
  

Q.No 7 (a) Prove that  n-1 cr + n-1cr-1   = ncr
(b) Prove by mathematical induction that (x+y) is a factor of x2n-1 + y2n-1 for all positive value of n.

Q.No8 (a). Find the value of the Trignometric Function of