(12th CLASS-2013)
MATHEMATICS
GROUP FIRST
OBJECTIVE
TIME: 30 MINUTES
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. 

Q. NO. 1

• Lt (1+ x)^1/x equals
  

(A) e^-1
(B) e   
(C) e²  
(D) e³

• If f(x) = 2x + 1 then fof(x) equals
  

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

• d/dx (Cosechx) ?
  

(A) sech x tanhx
(B) -Cosechx
(C) -Cosechx cothx
(D) -Coth²x

• If f(x) =x^2/3 then f:(8) equals
  

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

•  (xⁿ) = ?
  

(A) –nx^n-1
(B) nx^n-1          
(C) (n-1)x^n-1    
(D)

•  (f(x))n = ?
  

(A) n(f(x))^n-1
(B) (f’(x))ⁿ
(C) n(f(x))^n-1f’(x)
(D)

• (e^f(x)) = ?
  

(A) e
(B) e^x
(C)  
(D) e^f(x)f’

• for n # -1, ʃxn dx = ?
  

(A)  
(B)
(C) nxn-1
(D)  + c

• ʃ e^ax {af(x)+f’(x)} dx = ?
  

(A) ae^ax f(x) + c
(B) e^ax f’(x) + c
(C) e^ax f(x) + c
(D) ae^ax f’(x) + c

(A) 0   
(B) -1  
(C) 1   
(D) ∞

(A) 0   
(B) 6   
(C) 8   
(D) 16

• ʃ ef(x)f’(x) dx equals
  

(A) In/f(x)/+ c
(B) In/f’(x)/ + c
(C) ef’(x) + c
(D) ef(x) + c

• Solution of differential equation ydx + xdy = 0 is
  

(A) xy = c
(B) In/xy/= c  
(C) In│x/y│= c          
(D) x/y = c

• Slope of the line through the points (x1, y1) and (x2, y2) is 
  

(A)  
(B)          
(C)
(D)

• Intercept form of the equation of a straight line is
  

(A) x/a – y/b = 0
(B) x/a + y/b = 0
(C) x/a – y/b = 1         
(D) x/a + y/b = 1

• x = 0 is not in the solution of the inequality
  

(A) 2x+ 3 > 0
(B) 2x+3 < 0
(C) x+ 4 > 0
(D) x+5 > 0

• The centre of the ellipse (x-1)² /a²  + (y-1)² /b²  = 1 is
  

(A) (-1, -1)      
(B) (-5, -3)      
(C) (0, 0)
(D) (1, 1)

• Vertices of Hyperbola x²/a² – y²/b² = 1 are
  

(A) (±a, 0)      
(B) (0, ±a)
(C) (0, ±ae)     
(D) (±ae, 0)

• The projection of b along a is
  

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

• If the vectors 2i + 4 j - 7k and 2i + 6 j + xk are perpendicular then x equals 
  

(A) 5   
(B) 4   
(C) 2   
(D) 1

(12th CLASS 2013)
MATHEMATICS
SUBJECTIVE
GROUP FIRST

SECTION-I

2. Attempt any eight (8) short questions (16)

• Find  if f(x) = x3 + 2x2 - 1
  
• Find f-1(x) if f(x) = ; x > 1
  
• Differentiate by 1st principle if f(x) = x
  
• If y=    find dy/dx
  
• Find dy/dx if  x2+ y2=4
  
• If y=sin-1  find dy/dx
  
• If y = cos h-1(x2) find dy/dx
  
• If y =In (x2-9) find y2
  
• Find extreme value of (x)= 3x2 -4x + 5
  
• If x = y siny find dy/dx
  
• If y= x esinx find dy/dx
  
• Find dy/dx if x2- 4xy - 5y = 0    

3. Attempt any eight (8) short questions (16)

• Evaluate ʃ(+ ) dx
  
• Evaluate ʃsin2 x dx
  
• Evaluate ʃ dx
  
• Find the anti-Derivative of
  
• Evaluate ʃ x2 Inx dx
  
• Evaluate ʃ xTan-1x dx
  
• Evaluate  ʃex(1/x + Inx) dx
  
• Evaluate ʃdx 
  
• Evaluate -2ʃodx       
  
• Solve the differential equation dy/dx = -y         
  
• Graph the solution set of the linear inequality 2x + y ≤ 6          
  
• Define feasible region

4. Attempt any Nine (9) short question: (18)       

• Find the mid point of lire segment joining the points A (-, -1/3) and B(-3,5)        
  
• Find the slope and incliration of the joining the points (-2 , 4) and (5, 11)
  
• Find an equation of horizontal line through (7, -9)
  
• Find an equation of line through (8, -3) slope undefined
  
• Find the point of intersection of the lines x-2y+1=0 and 2x-y+2=0
  
• Find an equation of circle with centre (5, -2), radius= 4
  
• Find the equation of tangent to x²+y²=25 at (4, 3)
  
• Find the vertex and directrex parabola x²=4(y-1)
  
• Find the vertices of the ellipse 9x²+y²=18
  
• Find the sum of the vectors AB and CD given the four points A(1,-1), B(2,0), C(-1, 3) D(-2,2)     
  
• Find a vector of magnitude 4 and parallel to the vector 2i -3j + 6k
  
• Determine whether the triple 45°, 45°, 60° are direction angles of single vector
  
• Define vector product of two vectors

Note: Attempt any three questions from this section                                 3 x10=30

5.(a) Show that
(b) Differentiate    w.r.t, from first principles

6 (a) Evaluate ʃdx     
(b) Find the equation of the line through the point (2, 9) and the intersection of the lines 2x + 5y – 8 =0 and 3x - 4y - 6 =0

7.(a) Evaluate
(b) Maximize f(x, y)= 2x+5y subject to the constraints         
2y – x ≤ 8
X – y ≤ 4
X ≥ 0
Y ≥ 0

8.(a) Write an equation of circle that passes through points A(4,5) , B(-4,-3), C(8,-3) 
(b) Define direction cosines of a vector and prove Cos2 α + Cos2 β + Cos2 γ = 1

9.(a) Show that the parabola (x Sinα - y Cosα)2=4a (x Cosα - y Sinα) has focus at (aCosα, aSinα) and the directrix xCosα + ySinα = 0
(b) Find volume of tetrahedron whose vertices are A(2,1,8), B(3,2,9), C(2,1,4) and D(3,3,10)