MATHEMATIC
(Inter-A-2012)
Paper II
Time: 30Min
Marks: 20
Session (2010 - 2012)

Note: Write answer 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.

Q.No1

• The area A of a circle as a function of its circumference C :

A. A=
B. A= 
C. A= 
D. A=

• =

A. 9(
B. 9( 
C. 2(
D. (

•  =

A.
B.  
C.  
D.

•  =

A.
B.
C.
D.

A.
B.  
C.
D.

• If f( c) = 0 then f has relative maximum at x = c if :

A. f(C ) > 0
B. f (c) < 0
C. f (c) = 0
D. f (c) > 0

• ∫ =

A.  
B.  
C.  
D.

• ∫ , f(x)dx =

A. In f (x) + c
B. in f (x) + c
C.
D.

• ∫

A. Co
B. Si 
C. Si 
D. Co

• σ∫2xdx =

A. 9
B. 7
C. 4
D. 0

• -∞∫
  

A.
B.  
C.  
D.

• σ∫ Sin2xdx =

A.
B.  
C.  
D.

• The distance between the point (1,2), (2,1) is :

A. 1
B.  
C. 2
D.

• The slop of the linc with inclination  is :

A. 0
B.
C. 1
D.

• X+2y > 6 is not satisfied by :

A. (2,3)
B. (2,2)
C. (3,2)
D. (3,3)

• Equation of circle with centre at origin and radius  is :

A. =  
B.  
C.  
D.

• Equation of the parabola is :

A. y = 4ax
B. x = 4ay
C.  
D.  4a

• The end points of the minor axis of the ellipse are called its:

A. Foci
B. Vertices
C. Co-vertices
D. Directrix

• The numbers Cos∞,  Cosβ , Cos Y are called:

A. Constant Numbers
B. Direction Angles
C. Direction Cousines
D. None of these

• (i-j)-(j-k) x (k-i) = :

A. I
B. (0)
C. i-k
D. j-k

810-8150+1100
Subjective
Mathematics 
Inter-A-2012
Inter Part-II
Time: 2 : 30 Hours
Session (2010- 12 ) 
Total Marks: 80

Note: It is compulsory to attempt (08) parts each from Q.No.2 and 3 While attempt any (09) from parts from Q.No.4 and attempt any (03) question from Part- II. Write same question no. and its part no. as given in the question paper.

Part II 25x2=50

Q.No.2

• Evaluate
• Define Continuity of a Function.
• Find derivative of , at x=a from first principal.
• Provo that  [ c f (x) ]=c [f(x)]
• Differentiate w.r.t. x
• Find  if x =  1 - t², y= 3t²-2t.
• Differentiate Sin-1  w.r.t. x.
• Find  if y=Sinh-1()
• Find y₂ if x³-y³=a³.
• Prove by Mauclarin’s Series cosx = 1-+++________
• Define Stationary Point.
• Divide 20 into two parts so that sum of  their squares will be minimum.     

Q.No.3

• Find  and dy if y=x²-1,x charges from 3 to 3.02
•  Evaluate
• Find the value of
• Find the Secx dx
• Compute the  x Inxdx by parts.
• Evaluate [-Sinx+2Cosx]dx
• Find dx
• Evaluate (x-
• Solve the differential question equation =.
• Find the area bounded by Cos function from x = - to x=
• Define Corner Point of a Solution.    
• Graph the linear inequality 3x - 2y  6         

Q.No.4

• Find points trisecting the join of A(-1,4) and B(6,2).
• Define the Trapezium.
• Using slopes show that triangle with its vertices A(6,1),B(2,7) and C(-6,-7) is right triangle.
• The vertices of a triangle are A(-2,3),B=(-4,1) and C(3,5). Find coordinates of Centroid.
• Find equation of circle with centre ( 5 , - 2 ) and radius 4.
• Find vertex and focus of parabola x²  4x = 3y + 13 = 0        
• Find equation of parabola with focus ( -3,1 ) and directrix x = 3.
• Find equation of ellipse having Foci ( + 3  , 0 ) and vertices ( + 6 ,0 ).
• Prove latus rectum of ellipse +=1 is
• Find equation of  hyperbola whose foci are (+ 4,0) and vertices (+2,0).
• Write two properties of Cross Product.
• Find vector whose magnitude is “2” and parallel to (-i+j+k).
• Prove Cos(-β)=CosCosβ + sinSinβ vectorially.

Part-II

Q.No.5 (a) Prove that =n where n is an integer and    a> 0.    (5)
(b) if   y ( Cos^-1x)², prove that(1- x²) y² – xy₁ - 2 =0        (5)

Q.Ne.6 (a) Evaluate    tan4xdx     (5)
(b) Derive the normal form of the equation of a Straight Line.      (5)

Q.No.8 (a) Find an circle passing through A(1,4); B (-1,8) and Tangent to the line x+3y-3=0 (5)
(b) If B,C and D are respectively ( 4 , 1 ) , { -2 , 3 ) and ( - 8,0 )use vector method
To find the coordination of the point A if ABCD  is a parallelogram.   (5)

Q.No.9 (a) Find the Centre, Foci , Eccentricity , Veritces and Directrices of the ellipse.+=1               (5)
(b) Find a unit vector perpendicular to the plane containing  & . Also find the  Sine of the angle between  &  , where
=2i-2j+4k, =-i+j-2k