FEDERAL BOARD
MATHEMATICS HSSC-II (2015)
SECTION-A (Marks 20)
INTER PART-2
Time allowed: 25 Minutes
NOTE: - Section-A is compulsory. All parts of this section are to be answered on the question paper itself. It should be completed in the first 25 minutes and handed over to the Centre Superintendent. Deleting/Overwriting is not allowed: Do not use lead pencil,
Q1. Circle the correct option i.e. A/B/C/D. Each part carries one mark.

• What is the range of f-1, when f(x) = 2 +?

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

• lim =?

A.
B.
C.
D. None of these

• Ins (1 +x) =?

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

• If P is the perimeter of square and A its area then A=?

A.
B.
C.
D. 16P2

A.  
B.
C.
D.

• If 

A.   
B.
C.
D. None of these

•  are the parametric equation of:

A. Ellipse
B. Circle
C. Hyperbola
D. Parabola

A.
B.
C.
D. None of these

A. 28
B. 48
C. 58
D. 20

• Distance of the point (x,y) from x-axis is:

A. x
B. y
C.
D.

• The slope of the line 2x + 3y = 7 is:

A.
B.
C.
D.  

• The coordinates of the point that divides the join of A (-6, 3) and B (5, -2) in the ration 2:3,

A. (1,)
B.  
C. (
D. None of these

• The two lines 1 and 2 with respective slope m1 and m2 are perpendicular if:

A. m1 + m2 = 0
B. m1m2 = 1
C. m1m2 = -1
D m1- m2 = 0

• A region which is restricted to the first quadrant is called:

A. Maximum region
B. Minimum region
C. Feasible region
D. Objective function

• The centre of a circle x2 + y2 + 6x - 10y - 15 = 0 is:

A. (5 , 3)
B. (5, -3)
C. (-3, 5)
D. (3, 5)

• If e<1, the conic is called:

A. Parabola
B. Circle
C. Hyperbola
D. Ellipse

• The focus of a parabola x2 = -16y is:

A. (-4,0)
B. (0, -4)
C. (4, -4)
D. (0, ±4)

• If A =  + , then the unit vector A is:

A.  
B.
C.
D. None of these

• A vector perpendicular to 2 -  +  and 4 + 2 + 8 is:

A.    + 8
B.  + 8
C.   + 8
D.  -6 + 8

•  is :

A. 2 -
B. 2 -
C. 0
D. None of these

FEDERAL BOARD
MATHEMATICS HSSC-II (2015)
Time allowed: 2:35 Hours
Total Marks: 80
Note: Attempt any ten parts from Section 'B' and any five questions from Section 'C' on the separately provided answer book. Use supplementary answersheet i.e. Sheet-B if required. Write your answers neatly and legibly.

SECTION - B (Marks 40)

Q.2 Attempt any TEN parts. All parts carry equal marks.

• Evaluate Lim
• Graph the curve that has the parametric equations given below:
  X = t - 1,   y = 2t – 1,   - 1 < t <5
  where "t" is a parameter.
• Prove that y + x= 0 If
  X =  ,  y =
• If y = tan(p tan-1 x) show that:
  (1 + x2)Y1 – P (1 + Y2) = 0
• Find the point on the curve y = x2 + 1 that is closest to the point (18,1).
• Evaluate  dx?
• Evaluate  dx.
• Evaluate  sec x(secx +tanx) dx.
• Find an equation of the line through (5,-8) and perpendicular to the joint A (-15,-8) and B (10, 7).
• Find the point which is equidistant from the points A (5,3), B (-2,2) and C (4,2).
• Find centre and radius of circle with the given equation
  4x2+ 4y2 - 8x + 12y - 25 = 0
• Find an equation of the ellipse with foci (3,0) and minor axis of length 10.
• A parabolic arch has a 100 m base and height 25m. Find the height of arch at the point 30 m from the centre of the base.
• Prove that the altitudes of a triangle are concurrent.

SECTION — C

Q.3 if
Discuss continuity at x = 2 and x = -2
Q. 4 Solve the differential equation
Y – x  = (1 + x )
Q. 5 If y = acos(n x)+bsinin x Prove that  
X2     +   x   +  y =0
Q. 6 find the area of the region bounded by the triangle whose sides are
X - 2y-6 = 0,                        3x – y + 3 = 0, 2x + y – 4 = 0
Q. 7 maximize the function defined as;
f(x , y) = 2x + 3y  subject to the constraints, 2x + y ≤ 8; x + 2y≤ 14 x ≥ 0; y ≥ 0.
Q.8 Find the equation of the fangents to the ellipse +   Which are parallel to the line 3x + 8y+1=0, also find the points of contact.
Q. 9 A particle is displaced from the point A (5, -5, -7) to the point B (6, 2, -2)under the action of constant force define by 10 — + 11, 4 +5 + 9 and – 2 + - 9 show that the total work done by the force is 102 units.