INTERMEDIATE (12TH CLASS-2014)
PART-I
MATHEMATICS
GROUP-I
TIME ALLOWED:30
MAXIMUM MARKS:20
OBJECTIVE
Note: You have four choices for each objective type question us 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 mull in zero mark in that question. Attempt as many questions   as given in 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.No.1

• The anti derivative of   equals:

A. ln(tan-1 x)+c
B. Ln(tanx)+c
C. Tan-1x+ c
D. Tanx +c

• dx is equal to

A.
B. 
C.
D.

• (cosx-sinx)dx equals  to:

A.
B.
C.
D.

• If two lines are parallel,then:

A. M₁.m₂ = -1
B. M₁-m₂ = 1
C. M₁+m₂ = 0
D. M₁-m₂ = 0

• The point of intersection of two lines x+y=2 and 2x-y =1 is:

A. (1,2)
B. (-1,2)
C. (-1,-2)
D. (1,1)

• The inequality 2x+3y<5 is satisfied by point:

A. (1,1)
B. (-2,1)
C. (1,2)
D. (-2,3)

• X²+y²+2gx+2fy+c=0 is the equation of: Line Ellipse Hyperbola Circle The focus of the Parabola y²=4ax is:

A. (0,a)
B. (0,-a)
C. (a,0)
D. (-a,0)

• The work done by a force F during displacement d is equal to:

A.  x
B.  x
C.  .
D.  .

• i.( x ) is equal to:

A. 0
B. 1
C. -1
D. 2

• If f(-x) =f(x),then  f(x) is called:

A. Odd function
B. Even function
C. Explicit function
D. Implicit function

•  Equal to:

A. 0
B. -1
C. 1
D. 3

• (a²) is equal to:

A. x
B.
C. a\ln a
D. ax/lna

• The derivative of f(x) = equals:

A.
B.
C. 
D. 

• (sin ) is equal to:

A. Cosx³
B. -Cosx³
C. X²Sin x³
D. 3 X² Cosx³

• The derivative of   equals:

A.
B.
C.
D.

•  is equal to:

A. Sinx + Cosx
B. (Sinx + Cosx)²
C. Sinx-Cosx
D. (Sinx-Cosx)

•  is equal to:

A. -Cosec²x + c
B. Cosec² x+c
C. ln Cosx+c
D. ln Sinx+c

A.
B.
C.
D.

A.  +c
B.  +c
C.  +c
D.  +c

INTERMEDIATE (12TH CLASS-2014)
PART-I
MATHEMATICS
GROUP-I
TIME ALLOWED:2:30
MAXIMUM MARKS:80
Subjective

NOTE:write same question number and its part number on answer book,as given in the question paper.

SECTION-I

2. Attempts any eight parts.8x2=16

• State the sandwhich theorem
• If f(x) =, find fog(x).
• Differentiate x²-  w.r.t  x⁴.
• If y= tan(pTan^-1 x) show that (1+x²)y1 –p(1+y²)=0
• Find  if x=y sin y.
• Find  if y=
• Define increasing function.
• Find f’(x) if f(x) =ln (+).
• Find  if y=Cosh2x.
• Differentiate Sin-1
• Find extreme values of the function f(x) =3x²

3. Attempts any eight parts.     8x2=16

• Find dy of the function y=x²-1 when x changes from 3 to 3.02.
  
• Evaluate
  
• Evaluate
  
• Evaluate
  
• Evaluate dx
  
• Evaluate .
  
• Evaluate  dx.
  
• Evaluate
  
• Find they are between the x-axis and the curve u=Cos1/2x from x= -π to π.
  
• Solve the differential equation y dx + xdy =0
  
• Graph the inequality x+2y<6.
  
• Define an objective function and optimal solution.

4. Attempts any nine parts.

• Find equation of line with x- intercept :-9 and slope -4.
  
• Using slopes, shows that the triangle with its vertices A(6,1),B(2,7), and C(-6,-7) is aright triangle.
  
• Find an equation of the line through (-4,7) and parallel to the line 2x-7y+4=0.
  
• Find an equation of vertical line through (-5,3).
  
• Find p so that the lines 2x-3y-1=0,3x-y-5=0 and 3x+py+8=0 meet at a point.
  
• Find the center and radius of the circle with ends of a diameter at (-3,2) and (5,-6).
  
• Find the focus and directrix of parabola y²= -12x.
  
• Find foci and eccentricity of the elipse 9x²+y²=18.
  
• Find a vector whose magnitude is 4 and is parallel to 2i-3j+6k.
  
• If AB = CD ,find the coordinates of the point A when B(1,2),c(-2,5)  and D(4,11) are given.
  
• Show that the vectors 3i-2j+k,  i-3j+5k, 2i+j-4k from a right triangle.
  
• Find a vector perpendicular to the vectors a=I + j , b= I  - j.

SECTION-II

Note: Attempts any three questions. 3x10=30

5.(a) Discuss the countinuity of f(x) =at c = 1
(b) if x= Sinθ, y= Sinmθ,Show that (1-x²)y₂-xy₁+m₂y=0

6.(a) Evaluate dx
(b) Find the points trisecting the joints of A(-1,4) and B(6,2).

7.(a) Evaluate dx
(b) Graph the feasible region and fid the corner points of the following system of in equalities(subject to the constraint)
x-y ≤3,  x+2y≤6, x≥0,y≥0

8(a) Show that the circles x2+y2+2x-8=0 and x2+y2-6x+6y-46=0
(b) by using vector ,prove that the mid point of hypotenuse of a right triangle is equidistant from its vertices.

9.(a) Find the center ,foci ,eccentricity vertices and equation of directories of  - = 1
(b) Prove that four points  A(-3,5,-4) ,B(-1,1,1), C(-1,2,2) and D(-3,4,-5) are coplanar.

Paper Code
Number:4195
2014(A) ROLL.NO: ____________
INTERMEDIATE PART-II (12TH CLASS)
MATHEMATICS PAPER –IIGROUP-II TIME ALLOWED:30 minutes
MAXIMUM MARKS:20
OBJECTIVE

Note: You have four choices for each objective type question us 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 mull in zero mark in that question. Attempt as many questions   as given in 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.No.1

• dx =
  

A. +C
B. +C
C. +C
D. +C

• dx
  

A.
B. ln+c
C. lnf’(x)+c
D. f’(x)lnf(x)+c

• =
  

A.
B. 4
C. 2
D. 1     

A.
B.
C.
D. -

• The solution of differential equation  =-y is:

A. Y= x
B. Y= c
C. Y=
D. Y= c

• The slope of line with inclination 90” is:
  

A. 0
B. 1
C.
D.

• The distant of the point (-2,3) from y-axis  is:
  

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

• X=0 is in the solution of the inequality:
  

A. 2x+1>0
B. 2x+1<0
C. 2x+10
D. 2x-1 > 0

• _______ is equation of point circle.
  

A. X²-y² =7
B. X²+ y² =7
C. X²+ y²=0
D. X²+ y² =1

• The center of the ellipse  1 is:
  

A. (h,k)
B. (-h,-k)
C. (-h, k)
D. (h, -k)

• If the vectors 2+4-7and 2+6+x are perpendicular than x=
  

A. 8
B. 2
C. 1
D. 4

• If P=(2,3) and Q=(6,-2) then =
  

A. 4i+5j
B. -4i+5j
C. 4i-5j
5i-4j

• The function is said to be  an even function if f(-x) =_____
  

A. -f(x)
B. F(-x)
C. F(x)
D. None of these

• =
  

A. F’(x)
B. F’(a)
C. F’(2)
D. F’(0)

• =______
  

A. 0
B. 1
C. E
D.

• If f(x) =x100 then f’(1) =_____
  

A. 100
B. 90
C. 50
D. 0

•  is the derivative of:
  

A. x
B. x
C. x
D. x

• If f(x) =tan-1x then f’(Cotx) =______
  

A. -
B. Sin2x
C. Cos2x
D. Sec2x

• 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. Cosx+c
B. -Cosx+c
C. Sinx+c
D. -Sinx+c

INTERMEDIATE PART-I
(11TH CLASS-2014)
MATHEMATICS
GROUP-II
TIME ALLOWED:2:30
MAXIMUM MARKS:80
Subjective

NOTE:write same question number and its part number on answer book,as given in the question paper.

SECTION-I

2. Attempts any eight parts.    8x2=16

• Find fog(x) ,given that f(x) =2x+1 and g(x) =,x
• Evaluate 
• Find  if y² +x²-4x=5
• If y=, show 2x
• Find  if y=
• Find  if y=xcosy.
• Differentiate  sin-1  w.r.t x.
• Find  if y= Sin2x.
• Find  if y=x.
• Find y²if x² +y² =a².
• Prove =1+x+++ ____
• Find extreme value of f(x) =x²-x-2.

3. Attempts any eight parts. 8x2=16

• Find y in y=x² +2x,when x changes from 2 to 1.8.
• Using differentials find  in the equation x⁴+y²=xy²
• Evaluate the integral dx.
• Evaluate the integral dx.
• Evaluate the integral dx.
• Evaluate the integral x.
• Evaluate lnxdx.
• Evaluate  dx.
• Evaluate dx.
• Find the area below the curve y=3 and above the x-axis between x=1 and x=4.
• Solve the differential equation  =  
• Graph the solution set opf the linear inequality 3x+7y ≥21 in xy-plane.
• Define convex region.

4. Attempts any nine parts.

• Find
• Find an equation of line whose slope =-4 and x-intercept =-9.
• Find an equation of the line through (-4,7) and parallel to the line 2x-7y+4=0
• Find the distance  from the point P(6,-1)  to the line 6x-4y+9=0
• Find the angle from the line with slope  to the slope of line .
• Find the length of the tanget drawn from the point (-5,4) to the circle 5x²+5y²-10x+15y-131 =0
• Write an equation of the parabola with Focus = (-3,1);directrix x=3
• Define Ellipse.
• Find an equation of the hyperbola with foci (.
• Find the condstant  a so that the vectors = -3-+4 and  =-9-12 are parallel .
• If =  =0,=  =0, =  =0, find .
• Find a unit vector perpendicular to the plane containing =  + and =   -
• Prove that .(  x )+.( x)+.( x)= 3.( x )

SECTION-II

Note: Attempts any three questions.    3x10=30

5.(a) Show that the parametric equations x=a Cos θ, y=b Sin θ represent the equation of ellipse  =1
(b) Differentiate  w.r.t  .

6.(a) Evaluate xdx
(b) Determine the value of P ,such that the lines 2x-3y-1=0,3x-y-5=0 nad 3x+py+8=0 meet at a point.

7.(a) Solve (sin y +cos y)dy =[x(2lnx+1)]dx
(b) Maximize the function defined  as f(x,y) =2x+3y subject  to the constraints 2x+y≤8,    x+2y≤14 x≥0,y≤0

8.(a) Find an equation of the circle passing through the points A(4,5),B(-4,-3),C(8,-3)
(b) Prove by vector method that Cos ()=CosCos-SinSin.

9(a) Find the equation of an ellipse with Foci (±3,0) and minor axis of length 10.
(b) a A force of magnitude ‘6’ units acting parallel  to 2-2+ displaces, the point of application from (1,2,3) to(5,3,7).Find the work done.