Inter (Part-II)
Lahore Board 2013
Mathematics (New Scheme)
Time Allowed: 30 Minutes
OBJECTIVE
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.

• The area between the x-axis and the curve .y =cos  x from x = to x= is
  

(A) 1   
(B) 2
(C) 3   
(D) 4

• The ratio in which y-axis divides the line joining (2,-3) and (-5, 6) is:
  

(A) 2 : 3          
(B) 2 : 5
(C) 1 : 2          
(D) 3 : 5

• Foci of ellipse  =1 are:
  

(A) (± 1,0)      
(B) (0, ± 1)
(C) (± 2, 0)     
(D) (0, ± 2)

• Let f (x, y) = 0 and f (kx, ky) = kn f (x, y), then it is homogenous equation of degree:
  

(A) 1   
(B) 2
(C) 0   
(D) n

• If y = f (x) is a differentiable function, then differential of x is defined by the relation:
  

(A) dx =  y   
(B) dx = dy
(C)  x = dy   
(D) dx = x

• The non-negative inequalities are called:
  

(A) Parameters
(B) Constants
(C) Decision variables
(D) Vertices

•  is

(A) –sin²x        (B)sin²x
(C)-sin²x         (D) sec²x

• The area A of a circle as a function of its circumference 'C' is:
  

(A) A=     
(B) A=
(C) A=  C²  
(D) C²

(A)       
(B) nx+ex+c
(C) exnx +c   
(D) nx-ex+c

• If a is constant, then  = :
  

(A) sin x + c   
(B) — sin  + c
(C) y cot + c 
(D) x sin  + c

• Notation for derivative was used by Newton is:
  

(A)              
(B) D f (x)
(C) f(x)           
(D) f' (x)

The function f(x) =2+3x² has minimum value at:

(A) x = 3        
(B) x = 2
(C) x = 1         
(D) x = 0

•  (cosec²x — cot² x) is:

(A)cot²x + cosec²x
(B) -2 cosec x cot x + 2cot x cosec² x
(C) 0
(D)sec² x + tan² x

• Commutative Law holds in:
  

(A) Vector product
(B) Cross product in three vectori
(C) Inner product       
(D) None of these

• Centre of circle 4x² + 4y² — 8x + 16y — 25 = 0 is:
  

(A)      
(B)
(C) (1, -2)       
(D) (1, 2)

• is:

(A) Scalar product     
(B) Vector product
(C) Cross product      
(D) Meaningless

• The slope of tangent line to y = f(x) at (x1, y1) is:
  

(A) m             
(B)
(C) f’(x)          
(D)

Paper: II
Max. Marks: 20
Inter (Part-II)
Lahore Board 2013
Mathematics
Time: 2.30 Hours
Marks: 80
SUBJECTIVE
(Section — I)

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

• If f (x) = then find f (x2 + 4)
  
• Evaluate         
  
• Differentiate w.r.t. 'x'
  
• Differentiate  & w.r.t. 'x'.
  
• Find and when x = at2 , y = 2at.
  
• Differentiate n(x2 + 2x) w.r.t. 'x'.
  
• If y = x esinx then find  .
  
• Find the derivative of sin-1 w.r.t. 'x'.
  
• Find if y = tan h (x2).
  
• Find y1, if x3 - y3 = a3.
  
• State the Machlaurin's series expansion.
  
• Prove that =0

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

• Evaluate
  
• Use differentials. Find the approximate value of .
  
• Find
  
• Evaluate
  
• Evaluate
  
• Evaluate
  
• Find the area between x-axis and4he curve y = cos from x =
  
• Solve the differential equation
  
• Evaluate
  
• If , then evaluate the definite integral
  
• Define feasible solution set.
  
• Graph the solution set of the following linear inequality in xy-plane: 3x-2y 6.
  

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

• Find the points trisecting the join of (-1, 4) and (6 , 2).
  
• The coordinates of P are given in xy-coordinate system. Find the coordinates of P in xy-coordinate system P (8 , 10) , 0' (3 , 4).
  
• Find the slope and inclination of the line through A (-2 , 4) , B (5 , 11)
  
• Find the equation of a line bisecting second and fourth. quadrant.
  
• Find the equation of line having x-intercept — 3 and y- intercept 4.
  
• Find the centre of x2 + y2 + 12x-l0y = 0.
  
• Find the focus and vertex of parabola x2 = -16y.
  
• Define major and minor axis of ellipse.
  
• Define hyperbola.
  
• Find the magnitude of
  
• Find a so that |=3
  
• Find the projection of along along  for
  
• Define vector product of two vectors.

(Section — II)

Attempt any THREE questions.

5.a) If Discuss the continuity off (x) at x = 2 and x = -2.
b) If x = sin  and y = sin , show that (1 — x²) y₂— xy₁ m₂y = 0.

6.a) Evaluate .
b) Find the conditions that the lines y = m₁ x + C₂; y=- m₃x + c₃ are concurrent

7.a) Evaluate the definite integral
b) Graph the feasible region subject to the following constraints: 2x — 3y 6, ; 2x + y2 ; x  0 , y 0.

8.a) Find equations of the tangents to the circle x2 + y2 = 2 perpendicular to the line 3x +2y=6
b) Prove that the line segment joining the mid-points of two sides of a triangle is parallel to the third side and half as long.

9.a) Find the focus, vertex and directrix of the parabola y = 6x2-1   
b) Find the volume of tetrahedron with vertices (0, 1, 2) ,(3, 2, 1) , (1, 2, 1) and (5, 5, 6).