RAWALPINDI BOARD 2017
INTERMEDIATE
PART-II (12th CLASS)
Mathematics
(NEW SCHEME)
Group-I
TIME ALLOWED: 20 Minutes
MAXIMUM MARKS: 15
OBJECTIVE
Note: You have four chokes 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. Attempt as many questions as given in objective type question paper and leave others blank. No credit will be awarded in case BUBBLES are not filled. Do not salve question on this sheet of OBJECTIVE PAPER.

Q.No.1

• The critical value of  equals:

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

• If  , then  equals.

(A)
(B)
(C)  
(D)

• equals:

(A)  
(B) 
(C)  
(D)  

•  is equal to:

(A)  
(B)  
(C)  
(D)  

• If  is continuous at point , then:

(A)  
(B)
(C)
(D)

•  is equal to:

(A)  
(B)  
(C)  
(D)  

• is equal to:

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

• is equal to:

(A)  
(B)  
(C)  
(D)  

• Let , then  equals:

(A) ay
(B) -ay
(C) a²y
(D) -a²y

• The co-ordinates of vertices of hyperbola  equals:

(A)  
(B)  
(C)  
(D)  

• The co-ordinates of centre of circle x² + y² - 6x + 4y + 13 = 0 is equal to:

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

• Vector triple product of three non zero vectors  , b and c is denoted by:

(A) a x (b x c)
(B) a. (b x c)
(C) a. (b + c)
(D) a. (b - c)

• [2 k j i] is equal to:

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

•  is equal to:

(A)  
(B)  
(C)  
(D)  

•  is equal to:

(A)  
(B)  
(C)  
(D)  

•  equals:

(A)  
(B)  
(C)  
(D)  

• Inclination of line joining two points (-2, 4) and (5, 11) equals:

(A) 3
(3) 4
(C) 6
(D) 2

• Two lines represented by ax² + 2hxy + by² = 0 will be perpendicular if:

(A) h² + ab = 0
(B) h² - ab 0
(C) a - b = 0
(D) a + b = 0

• Perpendicular distance of point P(6, -1) from line 3x + 4y + 1= 0 equals:

(A) 1
(B) 2
(C) 3
(D) 4

• (0, 0) lies in the solution set of inequality.

(A)  
(B)  
(C)  
(D)  

RAWALPINDI BOARD 2017
INTERMEDIATE
PART-II (12th CLASS)
Mathematics (NEW SCHEME)
TIME ALLOWED: 2.10 Hours
MAXIMUM MARKS: 60
SUBJECTIVE
SECTION-I

2. Attempt any Eight of the following. All carry equal marks.

• Evaluate  
  
• Differentiate  w.r.t. x.
  
• Find , when  
  
• Differentiate  w.r.t x.
  
• Find , 
  
• Find f'.
  
• Find .
  
• Find   
  
• Apply maclaurin's series expansion to prove that --------
  
• Discuss continuity of function  
  
• Determine the function  as an even or odd function.
  
• Determine the intervals in which  is increasing or decreasing function.

3. Write short answers to any Eight questions.

• Evaluate:.
  
• Evaluate:
  
• Evaluate .
  
• Evaluate: 
  
• Evaluate:
  
• Evaluate: .
  
• What is the linear programming?
  
• Solve the differentional equation  
  
• Using differentional find  in the equation x2+ 2y2 = 16
  
• Using differentional to find the value of.
  
• Find the area bounded  function from  
  
• Graph the solution set of the linear inequality x +y > 5 by shading.

4. Write short answers to any Nine questions.

• Find co-ordinates of the point that divides the join of A(-6 , 3) and B(5 , 2) in the ration 2: 3.
  
• Find the slope and inclination of the line joining the points (4, 6) and (4, 8).
  
• Convert 2x - 4y + 11 = 0 in normal form.
  
• Find and equation of the line through the point (2 , -9) and intersection of the lines 2x + 5y - 8 = , 3x - 4y - 6 = 0.
  
• Find whether the point (5 , 8) lies above or below the line 2x - 3y + 6 = 0.
  
• Find the centre and radius of the circle 5x2+ 5y2+ 14x+ 12y - 10 = 0.
  
• Determine whether the point P(-5 , 6) lies outside on or inside the circle x² + y² + 4x - 6y - 12 = 0.
  
• Find focus and vertex of parabola y² =  
  
• Find foci and eccentricity of the ellipse 25x² + 9y² = 225.
  
• Find direction cosines of the vector  
  
• Find a vector of length 5, in the direction opposite to the vector  
  
• If , then prove that
  
• Find the value of, so that the vectors  are coplanar.

SECTION-II

5. (a). Evaluate:
(b). If  then prove that  
6. (a). Evaluate
(b). Find equations of two parallel lines perpendicular to  such that the product of the x- and y- intercepts of each is 3.
7. (a). Evaluate:   
(b). Minimize  subject to the constraints  
8. (a). Show that the lines  and  are tangent to the circle  
(b). Prove that, by vector method  
9. (a). Find centre , foci and vertices of the hyperbola  
(b). Find volume of the tetrahedron whose vertices are A(2 , 1, 8) , B(3, 2 , 9), C (2, 1, 4) and D (3 , 3, 0)