(12th CLASS - 2014)
MATHEMATICS
CROUP SECOND
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 m front of that question number. Use mites or pen to fill the circles. Cutting or filling two or more circles will result in zero mark in that question.

Question#1

• Which of the following is an odd function
  
  (A) Coax
  (B) Coshx
  (C) Sinhx
  (D) Sin2
  
  
• Lim el/x = ......... , x<0
  
  (A) -1
  (B) 0
  (C) 1
  (D) ∞
  
  
• The notion use  by Lagrange for derivative is
  
  (A) df/dx
  (B) f(x)
  (C) f(x)
  (D) Df(x)
  
  
• If  y = dy/dx   
  
  (A) 2,
  (B)
  (C)
  (D)
  
  
• If f(x) =  Sinx , then (π) =……
  
  (A)-1
  (B) 0
  (C) 1
  (D) ∞
  
•  is derivative of
  
  (A) Sin-1x
  (B) Sec-1
  (C) Tan-1x
  (D) Cot-1x
  
  
• If y= ex  then y3 = ……
  
  (A) e^x
  (B) e^2x
  (C) e^3x
  (D) e^-x
  
  
• 
  
  (A) 0
  (B) 2
  (C) 4
  (D) 6
  
  
•  dx =
  
  (A) Inx +C
  (B) Inx²+C
  (C) -1/x +C
  (D)
  
  
• (Cos²  x + Sin² x) dx =
  
  (A)Sinx + Cosx+ C
  (B) 2Sinx + 2Cosx+ C
  (C) -Sinx + Cosx +C
  (D) x+C
  
• The order of differential equation -2=0 is
  
  (A) 1
  (B) 2
  (C) 3
  (D) 4
  
  
• Secx tanx dx =
  
  (A) sec² + c
  (B) tanx+  c
  (C) secx² + c
  (D) None of these
  
  
•  dx =
  
  (A)  +C
  (B)  + C
  (C)  nx n+1+C
  (D)  nx + C
  
  
• The coordinate axes divide the plane tinto ……………… equal parts
  
  (A) 2
  (B) 3
  (C) 4
  (D) 5
  
  
• The centroid of a triangle divides each median in the ratio
  
  (A) 2:1
  (B) 1:2
  (C) 3:1
  (D) 1:3
  
  
• A vertical line divides a plane into .. ........... half planes
  
  (A) upper and lower               
  (B) upper and right
  (C) left and right                     
  (D) left end lower
  
  
•  Asymptotes are very useful in graphing
  
  (A) Circle
  (B) parabola
  (C) ellipse
  (D) hyperbola
  
  
•  A circle is called a point circle if  
       
  (A) r = I
  (B) r =0             
  (C) r = 2
  (D)  r = 3
  
  
• The vector   lies in the plane of the vectors  and  then .  x .=………
  
  (A) 0 
  (B) 1
  (C) – 1
  (D) 2
  
  
• If  a,  ,  are the direction angles of a vector then Cos2 a + Cos2   + Cos²   = ........
  
  (A) 0 
  (B) 1
  (C) 2 
  (D) 3

(I2th CLASS 1214)
TIME 2.38 HOURS
SUBJECTIVE MARKS: 80
SECTION-I

2. Attempt any eight (8) short questions

• Let f : R→R be the function defined by f(x) = 2x+1 Find f-1 (x)
  
• Evaluate Lim  
  
• Find the derivative of x2 w.r.t ‘x' by ab.initio
  
• Find dy if xy + y2 =2 dx
  
• Differentiate  w.r.t ‘x’
  
• Find  if x = y Sin  y   dy
  
• If y= in (x2 -9) find y2
  
• If y = xesinx find dy/ox
  
• If = (x) if f(x) =
  
• Find extreme value of f(x) 3x2
  
• Differentiate Sinx w.r.t Cot x
  
• Find dy/dx if y = Sinhl (x/2)

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

• If xy+x use diffrentials find dy/dx
  
• Evaluate  dx
  
• Evaluate dx
  
• Evaluate  dx
  
• Evaluate C    dx
  
• Evaluate x3 In x dx
  
• Evaluate   dx
  
• Evaluate  dx
  
• Evaluate  dx
  
• Solve the differentia equation xdy + y(x-I) dx = 0
  
• Graph the solution of 2x-3y ≤ 12
• Define the vertex of the solution region

4. Attempt any Nine (9), questions 18

• Find doe coordinates of the point that divides the goal of A (-6.3) and B(5,2) in the  I ratio 2:3 internally
  
• Cheek whether the point (.  is  at a distance of 15 units from origin
  
• Find the slope and indication of the line joining the points (3, - 2) and (2,7)
  
• Cheek whether the lines, 4y – 2x -1 = 0 and x- 2y -7 = 0 are parallel or perpendicular?
  
• Find the distance of the point P (6.-1) to the line 6x -4y + 9 = 0
  
• Find an equation of the circle with none at () and radius 2
  
• Cheek the position of the point (5,6)  with respect to circle 2x2 + 2y+ 2y2 + 12x -8y + 1=0
  
• Find IM Focus and vertex of parabola x2 =5y 
  
• Find Foci, eccentricity of ellipse 25x29y2 =225
  
• Let A (2,5),B (-1,1), C(2,6) Find  -  
  
• If u = 2.i + 3j +k , v = 4 I +6 j +2k , w = 06i -9j-3k.. Find  | u –v-w|
  
• Find the projectin of b along a when a = 3i +j –k, b = .2i –j + k
  
• Find the volume of the parallelepiped determined  by u=I +2.j –k,v=i-2j+3k, w=i-7j -4k

SECTION-III

Note: Attempt any three questions from this section
Question#5
(a). Prove that Lim loge a
(b) Show that y=x has a minimum value at x =1/e

Question#6
(a) Evaluate  x tan2 dx
(b)  Find the area Or the triangular n glen whose vertices are A(5.3) ,B(- 2,2) , C(4,2)

Question#7
(a) Solve the differential equation (Siny + y Cosy) dy = [x (2 In,x+1)] dx.
(b) Maximize f (x,y) = 3x+4y≤ 12, 2x +y ≤ 4, 4x -y ≤4x≥ 0 , y ≥0

Question#8
(a) Find equation of circle passing thmugh A(3,- I) , B(0,I) and having centre at 4x - 3y - =0
(b) Prove Cos (a + ) = Cos a Can  - Sin a Sin  by vectors raethod

Question#9
(a) Find the equation of parabola Eying focus at (2,5) and directix y =1
(b) Find the area of thc triangle by -.actor method if 1(0,0,0), Q(2,32) ,12(- l,),41