MATHEMATICS HSSC—II
SECTION — A (Marks 20)
Time Allowed:25 Minutes
NOTE: Section-A is compulsory and comprises pages 1-2. All parts of this section are to be answered on the question paper itself. It should be completed in the first 25 minutes and handed over to the Centre Superintendent. Deleting/overwriting is not allowed. Do not use lead pencil.

• y=sinx is a _____________

(A) Linear function
(B) Constant function
(C) Rational Function
(D) Trigonometric Function

• x²+xy+y²=2 is a/an_________

(A) Implicit function
(B) Inverse function
(C) Explicit Function
(D) Constant Function

• If f(θ)=2sinθ+3cosθthen f(θ) is a /an________

(A) Odd function
(B) Even function
(C) Hyperbolic Function
(D) None of these

(A) na^n-1
(B)naⁿ
(C)naⁿ⁺¹
(D) none of these

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

• Equation of parabola is__________

(A) x²+y²=1
(B) x=y
(C) x²= 4ay
(D) None of these

• If f(x)=sinx and q(x)sin-1x then______________

(A) (gof)s=sin^-1(sinx)
(B) x
(C) sin x +sin^-1 x
(D) none of these

(A) Velocity
(B) Derivative
(C) Integration
(D) None of these

• If x=at and y=at² then  is

(A)
(B)
(C) 
(D) y

•  then

(A) extanx+c
(B) exsec2x+c
(C) excot-1x+c
(D) None of these

• Distance of the line –x+3y+1=0 from(0,2)is

(A)
(B)
(C) 
(D)

• If the lines ax-y-1=0 and x+y+1=0 are perpendicular to each other then value of “a” is __________

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

• A point solution region where two of its boundry lines intersect is called a

(A) Solution
(B) Corner point
(C) Open half
(D) Half Plane

• Which Unit vector is along y-axis?

(A)
(B)
(C)  
(D)

• Length of transverse axis of hyperbola is

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

• The value of c for y =mx+c touch the ellipse at (x,y) is

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

• If the vector  and  are perpendicular to each other then  is

(A)
(B)
(C) |a|2|b|2
(D) None of these

• If the vector  ,  and  are said to be coplanar if  is

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

• The co-ordinate of foci of an ellipse are

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

• The area of the triangle having   ,  as two sides is given by 

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

Time Allowed:2:35 Hours                
Total Marks Sections B and c:80

Note: Attempt any ten parts from Section ‘B’ and any five questions from Section ‘C’ on the separately provided answer book. Use supplementary answer sheet i.e. Sheet-B if required. Write your answer neatly and legibly

Section-B
(Marks-40)

2. Attempt any Ten parts. All parts carry equal marks

• Evaluate
  
• Find the values of m and n so that the given function f is continuous
  
• If y=, then show that
  
• Differentiate ab-ignition w.r.t. x if y=sin
  
• Prove that ex+h=ex
  
• Evaluate
  
• Write the equitation of the parabola with focus (-1,0) and nertex(-1,2)
  
• Solve
  
• Find an equation of an elipse with foci  and vertices
  
• Show that 10xy+8x-15y-12=0 represent a pair of straight lines
  
• Find the values of “a” and “b” so that the vectors  and  are parallel
  
• Find ‘k’ so that the line joining A(7,3); B(k,-6) and the line joining C(-4,5) and D (-6,4) are perpendicular
  
• Find measure of the angle between the lines represented by x2-xy-6y2=0
  

Section-C
(Marks 40)

Attempt any FIVE questions carry equal marks.

Q.3 Prove that

Q.4 Expand ax I the Maclaurin series

Q.5 Evaluate

Q.6 If x=a(); y=a(1-cos θ) then show that

Q.7 the points A(-1,2),B(6,3) and C(2,-4) are vertices of triangle. Show that the line joining the midpoint D of AB and mid point Eof Ac is parallel to BC and DE = BC

Q.8 Find the center, foci eccentricity and vertices of

Q.9 Find a vector perpendicular to each of the vectors