Inter (Part-II) Faisalabad Board 2015
Mathematics
Part II (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.

• =.

(a) sin-1
(b) sin-1
(c) sin-1
(d) sin-1

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

• dx=:

(a)   
(b) ax
(c)   
(d) axlan

• )

(a) cosh^-1x
(b) sinh^-1x
(c) tanh^-1x
(d) sech^-1x

•  |χ|atχ = 0 is : 

(a) 1    
(b) -1   
(c) 0    
(d) None

•  =

(a)          
(b) sec2 x
(c)           
(d)

• If  = lne^x, then  = 

(a) e^x   
(b)    
(c) 1    
(d) e^x-1

• If y = e^{cos x} then dy = :

(a) e^{cos x}
(b) e^{sin x}
(c) e^{-sin x}
(d) –sin xe^{cos x}

•            is _____ function

(a) Even
(b) odd
(c) Both even and odd
(d) Neither even nor odd

• Lim :

(a) 0    
(b) 2a  
(c) a²
(d) Undefined

• 2=:

(a) 0    
(b)
(c) -6
(d) None

• Co-vertices of the ellipse  =1 are       

(a)
(b)
(c)         
(d)

• Center of the circle 5x2 + 5y2 + 14x + 12y – 10 = 0 is

(a) (7,6)           
(b) (-7, -6)       
(c) (-14, -12)   
(d)

• The point (1, 3) lies in the solution region of the inequality

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

• The pair of lines represented by ax² + 2hxy + by² = 0 will be orthogonal if

(a) a + b > 0     
(b) a + b = 0     
(c) h²-ab<0      
(d) h² – ab = 0

• Equation of the line bisecting 2nd and 4th quadrant is

(a) y = x 
(b) y = -x         
(c) y =          
(d) y = mx       

(a) 0    
(b) 1    
(c) -2   
(d) 2

• =:

(a) 0
(b) x
(c)     
(d)

• (x+1)dx=:

(a) e^x   
(b) xe^x 
(c) e^x
(d) None

• Angle between the vectors +&+      is:

(a) 0    
(b) π
(c)
(d)

Inter (Part-II) Faisalabad Board 2015
Mathematics
Part II(Subjective)
Time Allowed: 2.30 Hours 
Max. Marks: 80 

Section I

2. Attempt any Eight Parts

• Evaluate
•    Discuss continuity
• Find domain and rang of
• If y =    -                 , find
• Differentiate sin³ x with respect to cos² x
• Prove that  (cos-1x) = -
• If y = in (ex+e-x), find
• Find derivative of
• Evaluate (sinh-1x)
• Find  if x = y sin y
• Find y² if x³-y³=a³
• Expand (1+x)ⁿ in maclaurin series

3. Attempt any Eight Parts

• Evaluate
• Find
• Find
• Evaluate
• Evaluate
• Find
• Evaluate  =
• Evaluate
• Evaluate
• Define feasible region and feasible solution
• Define optimal solution

4. Attempt any Nine Parts (18)

• Describe the location in the plane of the point p (x, y) for which |x|3
• The xy-coordinate axes are rotated the origin through an angle of 45° The new axes are OX and OY. IS the (X, Y) coordinates of P(5, 3).
• Using slopes, show that the points A (1 , 1), 8 (4 , 5) and C (12, -1) are the vertices of a right angle triangle.
• Find the distance between the parallel lines 3x - 4y + 3 = 0 and 3x -4 y+ 7=0
• Check whether the given lines are concurrent or not?  4x - 3y – 8 = 0,3x - 4y – 6 = 0, x - y - 2 = 0.
• Find and equation of the ellips with foci (±3,0) and minor axis of length 10.
• Find the equation of the circle with ends of its diameter at (-3, 2) and (5, -6).
• Find the focus and directrix of the parabola y² = -l2x.
•  Prove that the equation 25x2 -16y2 = 400 represents hyperbola. Find its foci.
• If 0 is the origin and = . Find point P, where A and B are (-3, 7)and (5 -6).
• Find the direction consines of the vector
• Find , so that the vectors  are coplanar
• Find  so that the |a|=3

(Subjective Part)
SECTION-II

Question #6
(a) Evaluate  
(b) Find the equation of line passing through the point of intersection of lines x-y-4 = 0and 7x + y + 20= 0 and perpendicular to line 6x + y - 14 = 0.

Question #7
(a) Evaluate                                                     .
(b) Graph the fesible region and find the corner points for the following system of inequalities subject to constraint:
x- y 3 ; x + 2y  6     

Question #8
(a) Find equation of tangent to circle x² +y² =2 and perpendicular to line 3x+ 2y =6.
(b) Prove that angle in a semi circle is a right angle.

Question #9
(a) Find focus, vertex and directrix line of the parabola x² = 5y
(b) Find the value of a so that ai +j, +3k and 2i + j – 2k are coplanar