Inter (Part-II) Bahawalpur Board 2016
Mathematics
Part I (Objective Type)
Time Allowed: 30 Minutes 
Max. 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 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.

• If 3x+4y-7=0, then  =:

(a)
(b)
(c)
(d)     

• :

(a) 40
(b) 3e
(c) 2e
(d) e                      

• Sech² x =:

(a) Cosh2 x
(b) 1+tanh2x
(c) 1-tanh2x
(d) tanh2 x-1      

• If = y, then =:

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

• f (x) = -3x2 has maximum value at:

(a) x=-2
(b) x=-1
(c) x=0
(d) x=1

•      (Cosechx) =:

(a) Cosechx Cothx
(b) Senchx tanhx
(c) – Cosechx Cothx
(d) Cosech2 x

•      (Inx)

(a)
(b) x
(c) –x
(d)

• e Thanx Sec2 x dx=

(a) eTanx
(b) e-Tanx
(c) eCotx
(d) e-Cotx

• cx (-) dx=

(a)
(b) xex
(c)
(d)

• (2dx) =:

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

• Cot3x(-Cosec2x) dx=

(a) (2x+1
(b)  (2x+1
(c)  (2x+1
(d)  (2x+1

•  dx=:

(a)
(b)
(c)
(d) π

• Mid point A(2,0),B(0,2) is:

(a) (0,2)
(b) (2,0)
(c)(2,2)
(d) (1,1)

• Distance of point (1,-2) from Y-axis is:

(a) 2
(b) 1
(c) 3
(d) 4

• Slope of Y-axis is:

(a) 0
(b) 1
(c)-1
(d) Undefined

• Which one of the following points satisfies x+2y<6:

  (a) (4,1)
  (b) (3,1)
  (c)(1,3)
  (d) (1,4)

• If v=2 I + j – k, v=I + j + 4 k are perpendicular, then =:

(a)
(b)
(c)  
(d) 3

• Directrix of Y2=8x is:

(a) x+2=0
(b) x-2=0
(c)y+2=0
(d) y-2=0

• Equation of tangent to circle x2+y2=a2 at P(x1,y1) is:

(a) xx₁ + yy₁=a²
(b) xx₁-yy₁=a²
(c) xy₁+yx₁=a²
(d) xy₁-yx₁=a²

• Which one of the following points satisfies x+2y<6:

(a) (4,1)
(b) (3,1)
(c)(1,3)
(d) (1,4)

Inter (Part-II) Bahawalpur Board 2016
Mathematics
Part II (Subjective)
Time Allowed: 2.30 Hours 
Max. Marks: 80 

Section I

2. Write short answers to any EIGHT questions:                                     (2x8=16)

• Find fog(x), when f(x) = ; g(x) =; x
• Find  where y=(3x2-2x+7)6
• Evaluate
• Find  if x=1-t2,y=3t2-2t3
• If y = , find
• Find  if y= xeSinx
• Find  if 3x+4y+7=0
• Differentiate x-3+2 +3t2-2t3
• Find the derivative of f(x )=c by definition.
• Define continues Function.
• Define Paint of Inflexion.     
• Differentiae Sin2x w.r.t. Cos4x

3. Write short answers to any EIGHT questions:               (2x8=16)

• Find Sy if y= and x changes from 4 to 4.41
• Evaluate ( dx
• Evaluate dx
• Evaluate tan2xdx
• Evaluate x5Inx dx
• Evaluate ex( dx
• Compute  dx
• Solve the equation =
• Evaluate  Cos2θ.Sinθ dθ
• Graph the solution region of 3x+7y21
• Define the corner points.
• Find  the area between x-axis and the curve y=Cosx from x=- to x=

4.  Attempt any NINE parts.                                                                (2x9=18)

• In the triangle A (8,6). B ( -4, 2), C (-2,- 6 , find the slope of any two altitudes.
• Find an equation of the line through (-4, 7 ) and parallel to the line 2x-7y+4=0
• The points A (-5, - 2) and 0 (5,-4 ) are ends of a diameter of a circle. Find its Centre and Radius.
• Find the distance of P(6,-1 ) from line 6x - 4y + 1 = 0
• Find separate equations of the lines represented by 9x2 +24xy + 16y2
• Find equation of a circle  with ends of a diameter at ( -3, 2 ) and ( 5, -6 ).
• Find equations of tangent to the circle x2+ y2 = 2 perpendicular to the line 3x+2y=6
• Find the equation of parabola with focus (1, 2 ), vertex (3,2).
• Find Foci , Ecentricity of ellips: x2 + 4y2 = 16
• Find the vector from the print A to me origin where i-2j and B is a point (-2,5).
• Find a vector of magnitude 4 and la parallel to 2i – 3 j+6 k.
• Find  so that vector u   =a I + 2 j – k, v = I +  j + 3 k are perpendicular.
• A force F=4 I-3 k   passes through the point. A (2, - 2. 5 ). Find moment of F about the point B (1,-3,1 )

SECTION-II

NOTE: - Attempt any three questions. 10 x3=30

Question #5
(a) Discuss the continuity at x = 2 if  f(x)= (5)
(b) Show that =, if = tan-1      (5)

Question #6

(a) Evaluate  dx  (5)

(b) Find the angles of the triangle whose vertices are A(-5,4),B(-2,-1),C(7,-5). (5)

Question #7
(a) Evaluate                                                    (5)
(b) Maximize f (x,y)= 2x + 5y subject to the constrains                        (5)
2y-x8; x-y4
x0;y0

Question #8
(a) Write the equation of circle passing through the given points A(-7,7),B(5,-1),C(10,0). (5)
(b) Find the magnitude of the vector   and write the direction Cosines of .=+            (5)

Question #9
(a) Find an equation of the Hyperbola with given data Centre (0,0), Focus (6,0),Vertex(4,0). (5)
(b) Find a unit vector perpendicular to the plane  and  given below. Also find sine of angle between them, where =2 – 6 – 3,  = 4  + 3 - . (5)