MTH101 Final Term Solved MCQs by VU Topper RM

What does it mean for an improper integral to converge?

1. The integral has a well-defined upper and lower bound.
2. The function f(x) is always positive.
3. The limit of the integral approaches a finite value.
4. The limit of the integral approaches infinity.

Correct answer: The limit of the integral approaches a finite value.

If a flat surface of area A is submerged horizontally in fluid at a depth h then the fluid exerts a force F perpendicular to the surface this force F is defined as A. F =A ρh

B. F = ρhA

C. F =ρha D. F = ρh

If a function is constant over an interval, what can be said about its arc length on that interval?

1. The arc length is proportional to the slope.
2. The arc length is equal to the width of the interval.
3. The arc length is infinite.
4. The arc length is zero.

Correct answer: The arc length is equal to the width of the interval.

If [-8,8] is subdivided into ‘16’ equally spaced subintervals, then the RIGHT end point of 13th sub-interval will be--------. A. 2 B. 4 C. 3

D. 5

Which of the following statements is true regarding the ARC LENGTH PROBLEM?

1. It only deals with straight lines.
2. It is applicable only to polynomial functions.
3. It focuses on finding the area under a curve.
4. It addresses the challenge of determining the length of curved lines.

Correct answer: It addresses the challenge of determining the length of curved lines.

The volume V of a cylinder with base area A and height h is calculated by ---------. A. V = A h^2

B. V = A h

C. V = A h^3 D. V = 2A h

A. 600 ft. Ibs

B. 3000 ft. Ibs

C. 300 ft. Ibs D. 500 ft. Ibs

Distance between the points (-2,-3) and (-4,-1) using the distance formula is......... A. Sqrt(10)

B. Sqrt(8)

C. 0 D. None of these

1. If Sin(3x^2) / 6 + C is the anti–derivative of a function f(x), then f(x) = __________. x^2 Cos(3x^2).

x Cos(3x^2). x Cos(3x). none

2. Which of the following is the integral of Sin(3x+5) with respect to x ? -1/3[-Cos(3x+5)]

1/3[-Cos(3x+5)]

1/15[-Cos(3x+5)] -Cos(3x+5)

3. If ‘n’ goes from 1 to 3 and the summation of ‘na’ = 6a, then the value of ‘a’ is ----------

-6

undetermined

4. If ‘n’ goes from 1 to any large ODD number then the summation of ‘(-1)^n’ = ---------

-1

that specific large ODD number

5. 1+2+3………+t equals

n(n+1)/2

t(t+1)/2

n(n+1)(2n+1)/6 none

6. If definite integral of f(x)=Sinx over [a,0] is equal to ‘-2’ then the value ‘a’ is--------- pi/2

pi

-pi

7. If the definite integral of f(x)=3 over [1,x] is greater than ‘12’ then -----

x>12 x>5