Mathematics - I Mid - II, March - 2015

1.The value of C in Rolls’s Theorem for f (x) = x3 − x2 − x in (0, 2) is
  • 1/2
  • 1
  • 3/2
  • 3/4
Answer: B
2.If f (x) = x and g(x) = x2 −1 then the value of C in [1, 4] in cauchy’s mean value theorem is
  • 2
  • 2.5
  • 3
  • 3.5
Answer: B
3.The expansion of ex in powers of (x −1) is
Answer: B
4.if  then  
  • 1
  • u
  • v
  • uv
Answer: B
5.If at ( a,b ) for f (x, y), rt − s2 > 0 and r > 0 then f has
  • maximum
  • minimum
  • saddle point
  • no stationary value
Answer: B
6.
Answer: D
7.
  • 1/8
  • 1/4
  • 1/2
  • 1/6
Answer: D
8.
Answer: A
9.http://i.imgur.com/bfWPIOI.gif, where R is the region bounded by the parabola y2 = 4x and x2 = 4y
Answer: D
10. bounded by the positive coordinate axes and x2 + y2 = 9 , After changing into polar coordinates is
Answer: A
11.If  in [1, 2] then the value of C in cauchy’s mean value theorem is …………………………………
Answer: 4/3
12.If u = x2 + y2 ,v = 2xy , then  ……………………
Answer: 4(x2 - y2)
13.The Taylor’s series for f(x ) in powers of x – a is………………………
Answer:
14.The value of C in Cauchy’s mean value theorem for f (x) = x2/3 and g(x) = 1/x1/3  in (1, 8) is ……….
Answer: 3
15.The stationary point of x2 + y2 + 6x +12 is…………….
Answer: (-3, 0)
16.(3, 3/2) = ..................
Answer: 32/105
17.In Evaluating ∫∫ xy(x + y)dxdy over the region between y = x2 and y = x, the limits are …….
Answer: x = 0 to 1; y = 0 to x2 or x = y to x = ; y = 0 to y =1
18.After changing the order of Integration , the limits are ……………………….
Answer: x= y to x=1; y =0 to y=1
19. ...............
Answer: 10
20. ................
Answer: a6/48