Inter (Part-II) Bahawalpur Board 2014
Mathematics
Part I (Objective Type)
Time Allowed: 20 Minutes 
Max. Marks: 17

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.

• f(x) = Cosx+Sinx is ……….. function

(a) Even
(b) Odd
(c) Both Even and Odd
(d) Neither Even or Odd

• (2) Lim x>2  …………….

(a)  
(b) 2
(c)
(d) 0

• If f (x) = , then f(8) = …………..

(a)
(b)
(c)
(d) 3

•  (Log) = …………..

(a)
(b)    
(c)   
(d)

• It y = ,the n y3 is :

(a)    
(b)   
(c)   
(d)

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

(a) f (c)=0 
(b) f(c) > 0 
(c) f(c) < 0
(d) f (c) > 0

• Maclaurins Expansion of in (i=x) is :

(a) x-+ 
(b) 1-++
(c) -x 
(d) x-

• Differential of x is :

(a) 2x 
(b) 2xdx
(c) 2x
(d) 2x

• ∫dx =

(a)  +c
(b) +c
(c) +c
(d) +c

• ∫cos5xdx =

(a) 5Sin5x+c
(b) sin5x
(c) -5Sin5x+c
(d) -sin5x + c

• ∫dx =

(a) +c
(b) inx + c
(c) (inx+c
(d) in(inx) +c

• ∫dx =

(a) In (ax-1) +c
(b) aln (ax-1)+c
(c)  
(d)

• The solution of the differential equation ydx+ xdy = 0 is :

(a) in(xy) = 0
(b) in  
(c) xy = c
(d) in=c

• The lines a1x +b1y+c1 = 0 and a2x + b2y + c2 = 0 will be perpendicular if:

(a)  
(b) =  
(c) +=0
(d) = 0

• The perpendicular distance of the line 12x +5y =7 from origion is :

(a) 13 
(b)  
(c)  
(d)

• (1,3) is in the solution region of :

(a) x+y > 0
(b) (6, -4)
(c) (3, -2)
(d) x-y = 0

• The centre of the circle +-6x+4y+13 =0 is :

(a) (-6, 4)
(b) (6,-4)
(c) (3,-2)
(d) (-3, 2)

• The vertex of the parabola  = 4ay is :

(a) (a, 0)
(b) (-a,0)
(c) (0,0)
(d) (0, -a)

• If P= () then PQ is :

(a) ()i+()j 
(b) ()i+()j
(c) ()i+()j
(d) ()i+()j

• 2i x 2j . k :

(a) -4   
(b) 4
(c) 1
(d) 0

Inter (Part-II) Bahawalpur Board 2014
Mathematics
Part II (Subjective)
Time Allowed: 2.30 Hours 
Max. Marks: 80 

Section I

Q.No.2

• (i) Without finding inverse state domain and range of f-1 (x) where f(x) = 2 +
• Evalute (1+) 
• Find Maclaaurin Series for Sinx
• Find  if y = Cosh^-1 (Sec x)
• Find y² if x = at², y - bt⁴
• Differentiate Cot w.r.t “x”.  
• Prove (Cosec x) = -Cosec Cot x
• Find derivative of y = (2 )(x-) w.r.t “x”
• Find derivative of x (x-3) w.r.t “x” by definition.
• Find  if x = ⱺ +  and y = ⱺ + 1
• Find the extreme values for the function f(x) = 3x² -4x +5
• Find two positive integers whose sum is 30 and their product will be maximum.

Q.No3 

• Evaluate ∫(+dx
• Evaluate ∫ Sixdx
• Evaluate ∫x lnx dx
• ∫ dx
• Evalute  
• Define Optimal Solution.
• Solve different equation  for xy+x=4 by differentials
• Prove that (x)dx = (x)dx + (x)dx
• Find the area between x-axis and the curve u +1 from x=-1 to x=2
• Write associated equations 2x + 5y < 30, 5x + 4y < 20

Q.No.4

• Find the distance between point A (3, 1) : B (-2, -4)
• If P (x, y) = (5,3) and axes are rotated through angle ⱺ = 45ᵒ, find P (x,y)
• Reduce 5x -2y + 39 = 0 into slope Intercept form.
• Find centroid of triangle ABC whose vertices are A(-2,3): B(-4,1) and (3.5)
• Define Homogeneous Equation of Degree 2
• Find Centre and circle ++12x-10y = 0
• Find vertex and directrix of parabola =-8 (x-3)
• Compute eccentricity of ellipse 9+=18
• Find equation of Hyperbola with foci (+5,0): vertices (+3,0)
• Find direction cosines of v = i-j-k
• If u = [3,1,-1] and v [2,-1,1], find u   ‘   v
• Prove that a x (b+c) + b x (c+a) + c x (a+b) = 0
• Find the value of 2i x 2j  ‘ k

Section-II

Question #5
(a) For the real valued function f, defined below find:
(i)     
(ii) (-1) and verify f(f(x)) = x f(x) = (-x+09)³
(b) If y = aCos (lnx) + bSin(inx), prove that + x +y = 0

Question #6
(a) Evaluate ∫x xdx
(b) Find the equation of line through the point (2, -9) and the intersection of the lines 2x + 5y -8 = 0 and 3x -4y -6 = 0

Question #7
(a) Evaluate dx
(b) Maximize (x,y) = 2x+3y subject to the constraints 2x+y < 8
X + 2y < 14, x > 0 , y > 0

Question #8
(a) Find equation of the circle pssing through A (3, -1) B (0, 1) and having centre at 4x-3y -3 =0
(b) Prove that angle in a semi circle is a Right Angle.

Question #9
(a) Show that the equation 9x2 -18x + 4y2 + 8y = 0 represents an ellipse Find in centre foci vertices and co-vertices
(b) Prove that Sin (∞-B) = Sin∞ CosB -Cos∞ SinB by vector method