Mathematics
(Objective)
(Common for Old & New Scheme)
Paper (II)
Time Allowed:- 30 Minutes
PAPER CODE 4191
Maximum 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. Use marker or pen to fill the circles. Cutting or filling two or move circles will result in that questions. White Paper Code, which is printed on the question paper, on the both sides of the Answer sheet and fill bubbles accordingly, otherwise the student will be responsible for the situation. Use of link Remover or while correcting fluid is not allowed.

Q. 1

• If (x) = 2x + 1 then fof (x) =

(A) 4x+1                
(B) 4x+3                
(C) 4x-3                 
(D) 4x-1 

• xo  equals                                
  

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

•     equals

(A) 2                   
(B) 2                    
(C) 2                     
(D) n (ax+b)

•  =  ,  is Called

(A) Product rule                 
(B) Quoteient rule               
(C) Chain rule      
(D) Power rule

• ( Sin  equals

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

•    (Sec^-1 x) is equal
  

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

• f (x) is increasing if

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

• e^x (Cosx + Sinx ) dx is
  

(A) e² cos x +C     
(B) e² sin x+ C     
(C) –e² sin x +C   
(D) xe^sec  +C           

•  dx equals                                           
  
•   dx equals         
  

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

• 2 xdx equals

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

•  dx equals  
  

(A) 0                   
(B) 1                      
(C) 2                      
(D) ½

• Area bounded by Cos x from x=   to  is
  

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

• All Points (x ,y) with x<0, y<0 lies in Quadrant
  

(A) I                 
(B) II                      
(C) III                     
(D) IV    

• Slope of line parallel to line ax +by +C=0 is
  

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

• The Point (1,2) satisfy in quality

(A) x+2y>3      
(B)x-2y>3            
(C)x-2y 3           
(D)x+2y<3

• Vertices of hyperbola   ,  = 1 equals                    
  

(A) (a,0)           
(B) (-a,0)               
(C) (,0)              
(D) (0,)

• Eccentricity of ellipse   +  =1 equal

(A)5/4             
(B)                       
(C)5/3                   
(3)3/5

• The magnitude of dot and cross products of two vectors are 6 and 6respectively then angle between vectors is
  

(A) 90°                             
(B) 60°                             
(C) 30°                 
(D) 45°

• For two non zero vectors a and b   is equal to

(A) ab Cos θ         
(B) ab Sin θ           
(C) ab Cos θ n     
(D) ab sin θ n

Mathematics
(Subject)
(Common for Old & New Scheme)
( Session:- 2010-12 to 2013-15)
(Inter Part-II)
Time Allowed: 2.30 hours
(Session 2010-12 to 2012-14)
Maximum Marks: 80

Section-I

2. Answer briefly any Eight parts from the followings: (8 x 2 = 16)

• Define odd function with example.
• Prove that sinh 2x= 2 Sinh x Cosh x
• Differentiate x^-3+2x-^3/2+3 w.r.t x
• Differentiate tan³ Sec² w.r.t .
• Find f’(x) for f(x) = n(
• Find fro y=x² n
• Find for y = 5e^3x-4
• Find y₂ for y = 2x⁵ – 3x⁴ + 4x³+x-2
• Find y² for y = sin 3x
• Find f’ (0) for f(x) = sin x
• Define increasing function.
• Find the intervals for increasing and decreasing function f(x) = Cos x for (- )

3. Answer briefly any Eight parts from the followings: 16

• Computer dy if y=x^2­-1 and x changes from 3 to 3.02
• Evaluate dx
• Find value of
• Compute
• Determine the value of ³. nx dx
• Evaluate ^ax [aSec^-1 x+ ] dx
• Evaluate )dx
• Compute dx
• Find the area between x- anix and curve y=5-x² from x=1 to x=2
• Solve
• Shade the feasible region of 4x-3y 12
• Define optimal solution.

4. Answer briefly any Nine parts from the followings: 18

• Find an equation of the line having x-intercept -9 and slope -4.
• Find h such that the points A(h,1) , B(2,7) and C(-6,-7) are vertices of a right triangle with right angle at the vertex A.
• Find the equation of the straight line if its slope is 2 and y – intercept is 5
• Determine the value of such that the lines 2x-3y-1=0, 3x-y-5=0 and 3x+py+8y=0 meet at a point.
• Find the distance between the points A(3,1) and B(-2,-4)
• What are Conics ?
• Find an equation of circle with ends of a diameter at (-3, 2) And (5,-6)
• Check the position of the point (5,6) with respect to the circle 2x²+2y²+12x+8y+1=0
• Find focus and directrix of the parabola y²=8x
• Define position vector.
• Find direction cosines of the vector
• Find volume of the parallelepiped determined by =i-2 +3k’, -7 -4k
• Find a real number α so that the vectors αi+2α -k and ѵ=ΐ + α +3k are perpendicular.

Section-II

5-(a) If (x)= x 2

Find the value of k so that f (x) is continuous at x=2
(b) If x=a Cos³ θ, y=b Sin³θ then show that a +b tan θ=0

6. (a) Evaluate dx
(b) Find an equation line through (5,-8) and perpendicular to the join of (-15,-8),(10,7)

7. (a) Find the area bounded by the curve y = x³ – 4x and the x-axis.
(b) Minimize Z=2x+y subject to constraints
x + y ≥ 3
7x+5y ≤ 5
x ≥ 0
y ≥ 0

8. (a) Find the equation of the tangents to circle x²+y²=2 parallel to the line x-2y+1=0
(b) Prove that in any triangle ABC b²=c²+a² -2ac Cos B( by vector method)

9. (a) Derive the emotion of the ellipse in standard form.
(b) If
a = 4i+3j+ ķ
b = 2i-j+2k
Find a unit vector perpendicular to both a and b. Also find the sine of the angle between the vector a and b