Mathematics  I Mid  II, March  2015
1.The value of C in Rolls’s Theorem for f (x) = x^{3} − x^{2} − x in (0, 2) is

1/2

1

3/2

3/4

Answer: B
2.If f (x) = x and g(x) = x^{2} −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 e^{x} 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 − s^{2} > 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., where R is the region bounded by the parabola y^{2} = 4x and x^{2} = 4y
Answer: D
10. bounded by the positive coordinate axes and x^{2} + y^{2} = 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 = x^{2} + y^{2} ,v = 2xy , then ……………………
Answer: 4(x^{2}  y^{2})
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) = x^{2/3} and g(x) = 1/x^{1/3 }in (1, 8) is ……….
Answer: 3
15.The stationary point of x^{2} + y^{2} + 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 = x^{2} and y = x, the limits are …….
Answer: x = 0 to 1; y = 0 to x^{2} 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: a^{6}/48