Inter(Part 11)
Gujranwala 201 4
Mathematics
Paper II (Objective)
Time: 30 Minutes
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 with marker or pen on the answer book provided. Cutting or filling two or more circles will result in zero mark in that question. Attempt as many questions as given in objective type question paper and leave others blank.

Q.1

• j x i =

(A) j  
(B) i
(C) -i
(D) -j

• Vector product of two vectors is a

(A) scalar quantity
(B) unit vector
(C) vector quantity
(D) null vector

• The eccentricity "e" of parabola is

(A) 0 < e < 1
(B) e = 1
(C) e > 1         
(D) e = -1

• The condition that the line y = mx + c is a tangent to the circle x² +  y² = a² is

(A) c² +  a²  (1 + m²)     
(B) c² =  a²  (1 - m²)
(C) c²=  a²  (m² -1)
(D) c +  a²  (1 + m²)

• Which one satisfies the inequality x + 2y < 6?

(A) (1,4)
(B) (1,3)
(C) (1,4)
(D) (3,1)

• Which one is equation of straight line perpendicular to x- axis?

(A) x  = k
(B) y = k
(C) x + y = k  
(D) x-y=k

• Number of straight lines passing through one point is

(A) one
(B) finite
(C) infinite
(D) three 

• = _________________

(A) | +c
(B) |x| +c
(C)  +c
(D) -1x^-2 +c

•   dx = --------------

(A)
(B)  +c
(C)  +c
(D)  +c

• secxdx = ------------------

(A) sec x tanx +c
(B)
(C)
(D) secx + tanx +c

• n     f’ (x) dx =--------------

(A) [f(x)]ⁿ+1+c
(B)  +c
(C) [f(x)]ⁿ⁺¹+c .(n+1)+c
(D) n[f(x)]ⁿ⁺¹+c

• -1f’(x) dx=---------------

(A)
(B)
(C)
(D)

• If f(x)dx = 5,  f(x) dx =---------

(A) -5
(B) 5
(C) 0
(D) 1

•   (

(A)
(B) 2x
(C)
(D)

• x (a , b), a function f(x) is said to be increasing in (a,b) if

(A) 
(B) f’ (x)< 0
(C) f’ (x) > 0
(D) f’ (x) =0

• If f(x) = sinx, then slope of tangent line at.x =0 is

(A) 0
(B) 1
(C) -1
(D) does not exist

• Which one is Leibniz notation for derivative of f(x)?

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

•  (2x2+3)5= --------------

(A) 5 (2x2 +3)4
(B) 5(2x2 + 3)4 .4
(C) 5 (2x2 +3)4 .3
(D) (2x2+3)4 .20x

• f(x) = x is a/an

(A)  even function
(B) odd function
(C) neither even nor odd        
(D) cubic function

• cosh²  x – sinh²x=----------

(A) -1
(B) 1
(C) 2
(D) 0

Inter(Part-lI)
Gujranwala Board 2014
Mathematics Time: 2:30 hours
Paper r II
(Subjective) Marks: 80
(SECTION-2)

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

• Define the left hand limit,
• If f(x) =[find “c” so that Lim f(x) exists.
• Differentiate  w.r.t.x
• Find derivative of f(x) – x² by definition
• Find  if  =  
• Differentiate sinx w.r.t. x
• Differentiate  sin^-1 w.r.t. x
• Prove that = ax (). If y = ax
• Find f’ (x) if f(x) =  (
• What is stationary point?
• State Tailor Series of f(x_) at x =a
• Find  if x = y sin y

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

• Find and dy if y = x²?
• Evaluate  dθ
• Evaluate
• Find  dx
• Find
• Find  
• Find  
• Find
• Solve the differential equation  =
• Find the area between the x-axis and the curve y = x² +1 from x = 1 to = 2
• Define optimal solution.
• Graph the solution linear inequality 3x -2y  6

Q.4
Write short answers to any NINE question : (2x9=18)

• Find the points of trisection of the line segment joining the points A (-1,4) and B (6,2)
• Find the equation of a line bisecting 2nd and 4th quadrants.
• Find an equation of a line through (-4 , 7) and parallel to the line 2x -7y +4 = 0.
• Find the angle from the line with slope  to the line with slope
• Find a family of lines through the intersection of the lines 3x -4y -10=0 and x+2y -10 = 0
• Find the equation of the circle whose ends of diameter are at (-3,2) and (5,6)
• Check the position of the point (5,6) w.r.t the circle 2x² +2y² + 12x – 8y+1=0
• Find focus, vertex, axis and directory of the parabola, x² = -16y
• Find the equation of the ellipse whose foci are (,-1) and (0,-5) and length of major axis is 6.
• Find the work done by a force F =4i +3j +5k  in moving an object from P1(3, 1,-2) to P2 (2,4,6)

(SECTION –II)

Q.5
(a) Find the values m and n, so that function f(x) is continuous at x=3 where . (5)
F (x) =  
(b) If y = a cos (+b sin ( prove that:(5)
X²+ x +y=0

Q.6
(a) Evaluate I = sin x dx  (5)         
(b) Find an equation of the line through the intersection of the lines x+2y +3=0, 3x +4y +7 = 0 and making equal intercepts on axes. (5)

Q.7
(a) Evaluate  dθ  (5)         
(b) Maximize f(x,y) = x+3y subjected to constraints 
2x +5y  30; 5x +4y  20; x  0;y  (5)

Q.8
(a) Find the equation of a circle passing through the points A4,5) B(-4,-3), C(8,-3) (5)
(b) Find two vectors of length 2 parallel to the vector v =2i -4j +4k. (5)
Q.9
(a) Find the centre, foci, eccentricity and vertices of hyperbola =I (5)
(b) Use vector method to prove that sin (a-) = sin a cos cos a sin.  (5)