RAWALPINDI BOARD 2012
PAPER Mathematics PART-I
(Objective Part)
Marks: 20

Note: You have four choice 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.

lim_x→1(x-1)cosec(x-1) = ?

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

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

d/dx (cosechx) = ?

(A) -cosechx, cothx
(B)
(C)
(D)

(A) -1/2x
(B)
(C)
(D)

d/dx [(ƒ(x)^-1g(x)] = ?

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

d/dx[1.secx]=?

(A) d/dx (cosx)
(B)
(C)
(D)

∫-cosec²xdx = ?

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

(A) ln|tanx| + c
(B)
(C)
(D)

∫5^5xdx=?

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

Order of

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

(A) -e^cosx + c
(B)
(C)
(D)

∫xe^x²dx = ?

(A) (1/2)e^x² + c
(B)
(C)
(D)

Distance of 4x + 3y -2= 0 from origin is

(A) 2/5
(B)
(C)
(D)

Equation of line perpendicular to x = 4 passing through (1,7) is:

(A) y =7
(B)
(C)
(D)

There are …….. feasible solutions in feasible solution region.

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

The equation ax² + by² + 2gx +2ƒy + c= 0 either a=0 or b=0 represents.

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

Eccentricity of 4x² -9y² = 36 is

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

x = acosθy = b sinθ are parametric equations of:

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

A force is applied at point "A" then moment of ? about "B" will be

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

A vector makes equal angles with three axes then that angle is:

(A) cos^-1
(B)
(C)
(D)

Inter (Part-I) Rawalpindi Board 2012
Mathematics
Part I (Subjective)
Time Allowed: 3.10 Hours
Max. Marks: 83

SECTION-I

2. Attempt any EIGHT short questions.

Find the domain and range of
Evaluate
Find the derivative of f(x) = c by definition.
Find the derivative of (2x + 3)5 by first principle.
Differentiate x^-3 + 2x(3/2) + 3 with respect to x.
Find dy/dx if x²+ y² = 4
Find d/dx if y = xcosy
Find ƒ(x) for ƒ(x) = ln(e^x + e^-x)
Find y² for y = sin 3x
Write down Maclaurin series formula.
Define stationary point.
Using differentials, find d/dx for xy + x =4

3. Attempt any EIGHT short questions.

Integrate: 1(2x + 3)Z x
integrate:
Evaluate: ∫xlnxdx
integrate: ∫e^x(cosx + sinx) dx
Evaluate:
Evaluate:
Evaluate:
Find the distance between A(3,1) and B(-2,-4).
Define the differential equation with an example.
Find the area between thex axisand the curve y = sin2x from x=0 to x=π/2
The two points P and O' are given in xy coordinate system. Find xy coordinates of P referred to O'x, O'y where P(-2,6), O' (-3,2).
Find the inclination and slope of the line joing of given A(-1,4), B(6, 2).

4. Attempt any NINE short questions.

Find the inclination and slope of the line joing of given A(-1,4), B(6,2).
2) Two points P and 0' are given in xy-coordinates system. Find the x,y coordinates of P referred to Coordinates axis O'X & O'y: P (3/2 , 5/2) , O'(-1/2 , 7/2)
3) What do you mean by constants used in xcosα+ysinα=p
5) Find the centre and radius of circle: x²+ y²+ 6x - 4y + 13 = 0
6) Write down the equation of tangent to the circle x² + y² = 64 at (4,3)
7) Define Hyperbola.
8) Find focus and vertex of parabola x² = 24
9) Find the centre and foci of ellipse x² + 9y² = 18
10) Find equation of hyperbola having Foci (0 , ±9) and Directories y=±4
11) Find , where = 2 - ,
12) Find the cosine of the angle between and where =
13) Find a unit vector ⊥ where = + , =

SECTION-II

Attempt any THREE questions.. (8 X 3 = 24)

Question #5
a) Find the
b) If y =x⁴ + 2x² + 2 ,prove that

Question #6
a) Evaluate:
b) Transform the equation 5x - 12y + 39 = 0 into two Intercept form and normal form.

Question #7
a) Evaluate: ² ² .
b) Minimize Z = 2x + y subject to constraints x + y ≥ 3, 7x + 5y ≤ 5 , x ≥ 0 , y ≥ 0

Question #8
a) Find the coordinates of the points of intersection of the line 2x + y = 5 and the circle x²+y²+2x-9 = 0
b) CFind a vector of length 5 in the direction opposite that
of î - 2ĵ + 3ǩ

Question #9
a) Show that the equation 9x² - 18x + 4y² + 8y - 23 = 0 represents an ellipse. Find its elements.
b) Prove that in any triangle ABC c² = a²+b²-2abcosc