Mathematics
(Objective)
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 more circles will result in zero mark in that question Attempt as many questions as  given in objective type question paper and leave other blank. Use of ink remover or white correcting fluid is not allowed.

Q.1

(A) 7/5
(B) 5/7
(C) 2
(D)

• If f(x) is a function such that f(-x) = f(x) than f(x) is said to be
  

(A) Odd function             
(B) Even function            
(C) Constant function
(D) Linear function

• Derivative of x³ with respect to x²is
  

(A) 0     
(B) Undefined  
(C)
(D) 3x²

• Derivative of  w. r. t. 'x' is
  

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

•  (Tan^-1x +Cot^-1x) =
  

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

• If f(x) = then f'(-1)=

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

• Differential of y is

(A) dy'  
(B)    
(C) dx   
(D) dy

•  x dx = 
  

(A) In|Cos x|+c
(B) In|Sec x|+c
(C) In|Cosec x|+c           
(D) In|Cot x|+c

• ( +  ) dx=

(A) In |x tan2x|+c          
(B) In |x Sin2x|+c            
(C) In |x Cos2x|+c           
(D) In |x Cot2x|+c

•  dx= 
  

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

• x  dx=

(A) . + c  
(B)  + c
(C)   + c
(D) 2 +c

• The area of curve y = Cos x from x= -  to x = is 
  

(A) 1     
(B) 2      
(C) 3
(D) 4

• The general solution of differential equation = is
  

(A) y = tan-1x+c
(B) y = In(x +  )+c
(C) Y = Cosh-1x+c             
(D) y = Cot-1x+c

• The distance of the point (1,1) from origin is
  

(A) 0     
(B) 1      
(C)   
(D) 4

• The point P(x1, y1) and the origin are on the same side of ax+by+c=0 if "ax1,+by1,+c" and 'c' have the  (A) c=0               
  

(B) Same sign    
(C) Opposite sign            
(D) does not possible

• The solution of ax + by < c is
  

(A) Closed half plane
(B) Open half plane        
(C) Parabola      
(D) Hyperbola

• Radius of circle 4x2+4y2 +8x+8y - 68=0 is
  

(A) 4
(B)
(C) 5      
(D) 12

• The length of latus rectum of ellipse  + =1
  

(A) 1     
(B) 2      
(C) 4      
(D) 8

• The magnitude of vector is also called its
  

(A) Parameter  
(B) Variable       
(C) Point             
(D) Norm

• The area of triangle whose adjacent sides are 3 +4j, and 12i 9j is
  

(A)
(B) 55/2               
(C) 65/2               
(D) 75/2

Mathematics
(Subjective)
Time Allowed: 2.30 hours
Maximum Marks: 80

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

• Let f(x) = , Find the Domain and Range of f
  
• The real valued function f and g are defined below. Find fog(x) =? If f(x) =2x+1; g(x)= , x≠1
  
• Find by definition, the derivative w.r.t x of the function x3/2
  
• Find  if y =  
  
• Find , if y2+x2-4x=5
  
• If y = , Find by making suitable substitution.
  
• Differentiate (1+x2)nw.r.t.x2.
  
• Prove that  [Sin-1x ]= ,x є(-1,1)
  
• Find if y= x Cos y.
  
• Find  If y =
  
• Find  if y = log10 (ax2+bx+c)
  
• Find  if y = Cos h 2x.                                                          
  

3. Answer briefly any Eight parts from the followings:- (8 x2=16)

• Using differentials find  and  in the equation xy - lnx = c
  
• Evaluate  dx   
  
• Evaluate  dx
  
• Evaluate x2nxdx
  
• Find  dx
  
• Evaluate  (asec-1x+         
  
• Evaluate
  
• Find 2nx dx
  
• Find area between x-axis and curve y = 4x-x2.            
  
• Solve differential equation  =
  
• Define objective function and optimal solution .
  
• Graph the solution set of  5x - 4 y ≤ 20
  

4. Answer briefly any Nine parts from the followings:-  (9 x 2 =18)

• The point C (-5, 3) is the centre of the circle and P(7,-2 ) lies on the circle. What is the radius of the Circle?
  
• Find h such that the points A (-1, h), B (3, 2) C (7, 3) are collinear.
  
• Find an equation of the line through A (-6, 5) having slope 7.
  
• Check whether the point (5, 8) lies above or below the line 2x - 3y+6=0)
  
• Find the lines represented by 10x2 - 23xy - 5y2=0
  
• Find the centre and radius of the circle 5x2+5y2+14x+12y -10=0
  
• Check the position of the point (5, 6) with respect to the circle 2x2+2y2+12x - 8y+1=0
  
• Write an equation of the parabola with focus (-3 ,1) and directrix x=3
  
• Find the centre and Focii of the ellipse 9x2+y2=18
  
• Find the direction cosines of the vector 6i- 2j+ k
  
• Find a scalar α so that the vectors 2i+ aj +5k and 3i+ j+αk are perpendicular.
  
• Prove that the vectors i- 2j + 3k , -2i. +3j - 4k and i-3j + 5k are coplaner.
  
• A Force F =7i+ 4j -3k is applied at P(1,-2,3). Find its moment about the point Q(2,1,1)
  

Attempt any three questions.
5-(a) Discuss the continuity of f(x) at x=2
(b) Differentiate with respect to x Sec-1

6-(a) Evaluate dx
(b) Find the interior angles of the triangle whose vertices are A(- 2 ,11) , B(-6,-3) , C(4,-9) 

7-(a) Evaluate dx
(b) Minimize f(x, y) = 3x+y subject to the constraints
3x + 5Y ≥ 15
X + 3y ≥ 9             x ≥ 0, y ≥ 0

8-(a) Show that the line 2x+3y-13 = 0 is tangent to the circle x2-y2+6x-4y=0
(b) Find a vector whose magnitude is 4 and is parallel to 2i -3j+ 6k

9-(a) Prove that the latus rectum of ellipse  +  =1  is
(b) Prove that in a triangle ABC a = b Cos C + C Cos B (By vector method)