Inter (Part-II) Lahore Board 2012
Mathematics    Paper II (Objective Type)
Time Allowed: 30 Minutes     Max. Marks: 20
(Group-I)

Note: Four possible answers A, B, C and D to each question are given. The choice which you think is correct, fill that circle in front of that question with Marker or Pen ink. Cutting or filling two or more circles will result in zero mark in that question. Write the letter A, B, C or D in the column (write correct option) against each question also. If there is a contradiction in the bubble and hand written answer, bubbleoption will be considered correct.

Q1.1.

• f(x)=  is discontinuing at x = 3 because:

A.  
B. f(3) does not exist
C.  
D. None of these

A. cf'
B. c'f'
C. [cf(x)']
D. All of these

A.  
B.  
C.  
D.

A. 33xn3
B. 33xn9
C. 33xn27
D. 33xn18

• If f (x) = then f'(sin x)

A. sec-1    
B.             
C.             
D. tan-1 x

• If y = cos x then :

A. y₄+ y = 0
B. y₄- y = 0
C. y₂- y = 0
D. y₃- y = 0

A.         
B.  
C.  

A. sec2x+c    
B. n|cos x|+c           
C. n|sec x|+c
D. nx|sin x|+c

A. xnx-x+c 
B. xnx-x+c+c          
C. nx-x+c    
D. nx+x+c

A. 0         
B. 2   
C.
D. 1

• Degree of differential equation

A. 3
B. 1
C. e²
D. 5

A. e^-x sin x + c
B. -e^-x sin x + c
C. -e^-xsin x + c
D. e^-x sin x + c

• Distance of (-3, 7) from x-axis is:

A. 3
B. -3
C. 7
D. 10

• Centroid of triangle with vertices A (2,1), B(-1, 3) and C (-1, -4) is:

A. (3, 1)
B. (0, 0)
C. (2, 2)
D. (-2, -5)

• The inequality ax + by  c when a = 0 represents________ half plane:       

A. Left OR right
B. Upper OR lower
C. Open
D. None of these

• Centre of the circle x²+ y²+ 8x - 6y + 37 =0

A. (4, 3)
B. (-4, 3)
C. (-4, -3)
D. (4, -3)

• Length of Latus rectum of 9x²+ 4y² = 36 is:

A.  
B.  
C. 3/4
D.

• []

A. 1
B. 3
C. 0
D. 2

• For hyperbola:

A. c²= a²- b²
B. c²= a²+ b²
C. b²= a²+ c²
D. a²= b²+c²

• |cos +sin+0|

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

Inter (Part-II) Lahore Board 2012
Mathematics                           
Time Allowed: 2.30 Hours
(Group-I)
SECTION-I

2.Write short answers to any EIGHT (8) questions:   16

• Define the terms even and odd function.
• Evaluate the
• Let y = 2x² + 1 find y
• If y = (3t + 2)^-2 then find y
• Differentiate  w.r.t. x
• Find  if x =  and y =  +1
• If y = cot-1, find
• Fin if y =
• If y = sin 3x, fmd y₂
• What is Taylor theorem for expansion of a function f(x)
• What is 2nd derivative test for extreme value of a function?
• Divide 20 into So parts, so that the sum of their squares will be minimum.

3.Write short answers to any EIGHT (8) questions:   16

• Find ay and dy in y = x² - 1 when x changes from 3 to 3.02
• Find
• Find
• Find
• Evaluate
• Find is       
• State two properties of definite integral.
• Find
• Find area bounded by curve y = 4 - x² and the x-axis.
• Solve differential equation (e^x+ e^-x) =(e^x-e^-x)
• Define convex region.
• Graph solution region for x 2y  6

4. Write short answers to any NINE (9) questions:  18

• Find h such that A(-1, h), B (3, 2) and C (7, 3) are collinear.
• The xy - coordinates of P (5, 3) are rotated about the origin through angle 8 = 45° Find the XY - coordinates of the point P.
• Find an equation of the vertical line,through (-5, 3)
• Find the angle from the line with Slope  to the line with slope  
• Write the general form of an equation of a circle. What is its centre and radius?
• Find the length of the tangent drawn from the point (-5, 4) to the circle 5x²+ 5y² - 10x + 15y - 131 = 0
• Define chord and diameter of a circle.
• Find the focus and directrix of the parabola y² = 8x
• Show that the equation 9x² - 18x + 4y² + 8y - 23 = 0 represents an ellipse.
• Find and equation of hyperbola with foci (±5, 0); vertex (3, 0)
• Find a vector whose magnitude is 2 and is parallel to –i +j+k
• Find a vector perpendicular to each of the vectors a = 21-j+k and b=41+ 21-k
• A particle acted by constant forces 4i +1-  3k and 3i – j - k is displaced from A (1, 2, 3) to B (5, 4, 1). Find the work done.

(SECTION –II)

Note: Attempt any THREE questions.

5.A. Find the
B. Prove that =0 if

6.A. Evaluate
B. Find an equation of the perpendicular bisector joining the points A (3, 5) and B (9, 8).

7.A. Evaluate
B. Graph the solution region of the following system of linear inequalities and find the corner points:  3x+ 7y21 ; 2x-y-3 ;y0

8.A. Write an equation of the circle that passes through the points: A (a, 0) , B (0, b) , C (0, 0)     
B. If = 3i - j - 4k , = -2i -4j-3k ,  = + 2j- k , find a unit vector parallel to -3 + 2+ 4

9.A. Find an equation of the parabola with focus (1, 2) and vertex (3, 2)     5
B. A force  = 4 -3 passes through the point A (2, -2, 5). Find the moment of the force about the point B (1, -3, 1)