FAISALABAD BOARD 2014
PAPER MATHEMATICS
PART-II
Time: 30 Min
(Objective Part)
Marks: 21

 Note: Four Answers are given against each column A, B, C & D, Select the write answer and only separate answer sheet. Fill the circle A,B,C or D with pen or marker in front of that question number.

(A)
(B)
(C) 1
(D) 180

• The value of  is 2 for all x, then=:

(A) -2
(B) –x+2
(C) 2
(D) x+2

• The notation used by Leibniz for derivative is :

(A)
(B)
(C)
(D) ƒ(x)

• The tangent to a curve us perpendicular to x- axis if:

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

• Differentiating x6 w.r.t. x3, we get:

5x⁴
3x²
2x²
2x³

(A)
(B)
(C)
(D) None of these

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

• The area between x-axis and curve y=sin2x form x=0 x= is:

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

• If ……………

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

(A)
(B) x+c
(C) –x2+c
(D) Lnx

(A)
(B) +c
(C)
(D)

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

(A)
(B)
(C)
(D) None of these

• The y-intercept of the line 2x+3y-1=0 is:

(A)
(B)
(C) 2
(D) 3

• A quadrilateral having two parallel and two non- parallel sides called:

(A) Square
(B) Rectanle
(C) Trapezium
(D) Paralelogram

• x=-1 is in  the solution of:

(A)
(B) 2x+3 < 0
(C) 3x+4 < 0
(D) X < 0

• The equation of a circle does not contain term involving:

(A)
(B)
(C) xy
(D) None of these

• Axis of parabola

(A) x = 0
(B) y = 0
(C) x = y
(D) x = -y

• The direction consines of a vector parallel to z-axis are:

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

• 2x2=:

(A)
(B)
(C)
(D) 0

Subjective Part II
Section –I

• Find the domain and range of the function
• Evaluate
• Find the derivative of the function  by definition
• Differentiate  w.r.t ‘x’
• Find if x=at² and y=2at
• If y=cos
• Find  if y=tanh(x²)
• If
• Find     (x≠0)
• Find y² if x²+y²=a²
• Prove that …………
• Define increasing and decreasing function

3. Attempt any Eight parts

• If  and dy when x changes from 3 to 3.02
• Evaluate
• Evaluate
• Evaluate
• Evaluate
• Evaluate
• Evaluate
• Evaluate
• Evaluate
• Solve the differential equation
• Graph the solution set of
• Define the feasible solution set

4. Attempt any nine parts

• Find the distance between the point. A
• Transform the equation 4x+7y-2 = 0 in normal form
• Find an equation of the line through (-4,7)parallel to the line 2x-7y+4 = 0
• Find the area of a triangular region whose vertices are A(5,3), B(-2,2), C(4,2)
• Find the point of intersection of the lines x-2y+1 = 0; 2x-y+2 = 0
• Find center and radius of the circle x²+y²-6x+4y+13 = 0
• Write down equation of tangent to the circle x²+y² = 25 at (4,3).
• Find the focus and vertex of parabola y² = 8x
• Find the foci, eccentricity of ellipse x²+4y² = 16
• Write the Vector    in the form  , when P(2,3) Q(6,-2)
• Find direction cosines of v=.
• Find a scalar α, so that the vectors 2i+aj+4k and3i+j+ak  are perpendicular.
• Find the constant α, such that the vectors i-j+k, i-2j+5kand 3i-aj+5k  are coplanar.r

Section-II

Note: Attempt any THREE questions. Each questions carries 10 Marks

5. (a) Evaluate
(b) Show that

6.(a) Evaluate
(b) Prove that the linear equation ax+by+c = 0 in two variables x and y represents a straight line.

7.(a) Solve the differential equation
(b) Maximize ƒ(x,y) = 3x+y, subject to the constraints x+6y>9,3x+5y>15,x>0,y>0.

8. (a) Find equation of tangent to circle x²+y² = 2perpendicular to line 3x+2y=6
(b) Prove that in any triangle ABC, b=c cosA+a cosC (By vectors method)

9. (a) Find an equation of ellipse whose focus is at (±3,0) and minor axis of length 10.
(b) Prove by vector method that sin(α + β) = sin α cos β - cos α sin β