MATH101 Quiz #3 Solved 2016

MATH101 Quiz #3 Solved 2016

If x = 3 + 4 + . . . + 20, then x = ________. Select correct option

·         210.

·         207.

·         250.

·         None of these

Integral of 5^2 is

NOTE: x^n means ‘x’ to the power ‘n’ Select correct option

·         (1/3)5^3

·         10

·         25x

·         None of these

Integration of “cosecx.cotx” with respect to x is ----- Select correct option

·         -Cosecx

·         Tanx

·         Cosecx

·         Cotx

For any continuous function on the interval [0,1], if the area under this curve is divided into ‘5’ equal rectangles ,then the length of each rectangle will be……… Select correct option

·         1/4

·         1/5

·         ½

·         1

Which of the following is the value of definite integral of 5+5x , where the lower limit is -1 and upper limit is 1 ? Select correct option

·         12

·         10

·         14

·         16

If x =(1+2+3+...+10)+{(1^3)+(2^3)+(3^3)+...+ (10^3)}, then x = _______. Select correct option

·         110.

·         55.

·         3025.

·         3080

If the value of definite integral of a function f(x) taken from 1 to 3 is 9 then its value taken from 3 to 1 is Select correct option

·         9

·         0

·         -9

·         None of these

Which of the following is the value of definite integral of f(x)=(x-1), where the lower limit is 0 and upper limit is -1? Select correct option

·         2/3

·         0

·         3/2

·         1

Which geometrical figure is used for approximating the area under the curve? Select correct option

·         Circle

·         Right angled triangle

·         Pentagon

·         None of these

Summation of ‘kx’ where k goes from 1 to 5 equals Select correct option
15x

15k

55

None of these

If f(x) = Cos(x) + Sin(x) + x, then which of the following is NOT true about it. Select correct option Its anti – derivative is Sin(x) – Cos(x) + x^2/2 + 4. Its anti – derivative is -Sin(x) – Cos(x) + x^2/2 + 4. Its anti – derivative is Sin(x) – Cos(x) + x^2/2 + 5. None of these.

If x = 5 + 6 + . . . + 40, then x = ________. Select correct option 820. 850. 810. None of these.

If f(x) = Sin(x) + x, then which of the following is true about it Select correct option Its anti – derivative is –Cos(x) + x^2/2 + 10.

Its anti – derivative is Cos(x) + x^2/2 + 10.

Its anti – derivative is Cos(x) + 1.

None of these.

Sum of n-terms of a series whose nth term is ‘n’ = 1/n+1.then what is the sum of the first two terms is ----- Select correct option 5/6 6/5 6 6/4

Let f(x)=x^3 and a= -5 ,b=5 and n= no. of partition of [-3,3]=4 Let the widths of first, second, third and fourth intervals are 3,0,1,2 respectively. Then the “Mesh size” of partition is……………

0 3 1 2

If ‘n’ goes from 1 to 4 and the summation of ‘na’ =Maxima of (e^x) in the interval[-e,0], then the value of ‘a’ is ----------- Select correct option 10

-10

1/10

-1/10

Integration of 4Cosx with respect to x is……….. Select correct option 4Sinx - 4Sinx

If ‘k’ goes from zero to ‘n’ in the summation of ‘Sink’ then which of the following will be other expression for this given summation such that its lower limit changes to ‘5’? Select correct option Summation ‘Sin(k+5)’ while ‘k’ goes from ‘5’ to ‘n+5’ Summation ‘Sin(k-5)’ while ‘k’ goes from ‘5’ to ‘n-5’ Summation ‘Sin(k-5)’ while ‘k’ goes from ‘5’ to ‘n+5’ Summation ‘Sin(k+5)’ while ‘k’ goes from ‘5’ to ‘n-5'

(1^2)+(2^2)+(3^2)+……………..+(50^2) equals-------- NOTE: x^n means ‘x’ to the power ‘n’ Select correct option 42925 55227 6373 None of these

The area between f(x)=-x and the closed interval [-1,0] on x-axis is ----------

1

2

1/2

-1/2

Integral of x^101 is

NOTE: x^n means ‘x’ to the power ‘n’

102x^102+C

(1/102)x^102+C

101x^100 +C

None of these

Integral of x^(-10) is

NOTE: x^n means ‘x’ to the power ‘n’

-10x^(-11)+C

1/(9x^9)+C

- 1/(9x^9)+C

None of these

Summation of 2 where sum ranges from 0 to 10 equals 20.

True

False

If integral of ‘f(x)’ from [-1,2] = 4 and integral of ‘g(x)’ from [-1,2] = 8 ,than integral of (2f(x) +3g(x)) from [-1,2] =……..

30

36

32

38

If the closed interval [-10,x] is divided into ‘20’ equally spaced subintervals each of which having the width equals to ‘1’ unit then the value of ‘x’ is --------

20

10

0

30

Integral of (1-2x) from [0,1] is ………..

1

2

0

3

The estimated area under f(x) = x from x = 0 to x = 3 with right end points for n = 3 is ________.

7

5

6

None of these

How many subintervals of length ‘2’ will be formed for the interval [4,16] ?

4

5

6

7