MTH101 Midterm Solved Paper 3

MTH101 - Calculus And Analytical Geometry

x^2-9|=……….

1. |(x-3)^2|
2. |(x+3)^2|
3. |x-3||x+3|
4. |x+3||x+3|

Usually the number that signifies the idea of f(x) being as close to limit L as want to be must be a/an ……………

1. Integer
2. Natural number
3. Small positive number.
4. Small negative number.

A function f is said to be continuous on a closed interval [a, b] if f is continuous from the right at “a” and “f” is continuous from the left at “b” and “f” is continuous on

1. (a,b]
2. [a,b)
3. [a,b]
4. (a, b)

If f is continuous on [a, b], and if f(angel) and f(beer) have opposite signs, then there is …………………… one solution of the equation f(x) = 0 in the interval (a, b).

1. at most
2. exactly
3. at least
4. not more than

(epsilon) used in the definition of limit can be a negative number.

1. True
2. False

If a function is differentiable at a point then it is continuous at that point. The converse is

1. False
2. True

If the function f and g are continuous at c, then f + g is ………… at c.

1. Discontinuous
2. Continuous

If f is continuous on a closed interval [a, b] and C is any number between f(angel) and f(beer), inclusive, then there is at least one number x in the interval [a, b] such that ---------

1. f(x) is not equal to C
2. f(x) = C
3. f(x)>C
4. f(x)<C

|x-3| < 1 implies.....

1. -4 < x < 4
2. 2 < x < 4
3. -2 < x < -4
4. x-3 < 1

If for any positive number e(epsilon) we can find d (delta) such that| (3x-5) - 1| < e ,if x satisfies 0< |x-2| < d Then f(x) =…………

1. 3x-5- 1
2. x-2
3. 3x-5
4. None of these

A graph of an equation is the points on the xyplane that ………the equation.

1. Satisfy
2. Does not satisfy.

If two lines have same slope, say 1, then these two lines are

1. Parallel to each other
2. Parallel to x-axis
3. Parallel to y-axis
4. Perpendicular to each other

There is one-to-one correspondence between the points on coordinate line and ___________

1. Set of natural numbers
2. Set of integers
3. Set of irrational numbers
4. Set of real numbers

Which of the following is y-intercept of a line represented by equation, 5y = - 2x + 16

1. 2
2. 5
3. 8
4. 16 / 5

Does the point (1,2) satisfies the equation: 2y=x2−1

1. Yes
2. No

Let x is a real variable. The inequality -5 < x < 2 denote ________

1. Set of all rational numbers between -5 and 2
2. Set of all real numbers between -5 and 2.
3. Set of all natural numbers between -5 and 2
4. Set of all integers between -5 and 2

Which of the following option describes the graph of equation:(x2)+(y2)=1

1. A parabola whose vertex is at point (1, 0).
2. A straight line whose slope and y-intercept is 1.
3. A circle centered at origin and its radius is 1
4. None of these

Graph of the equation x2+y2=9 represents a.................

1. Circle not sure
2. Parabola
3. Ellipse
4. None of these.

Which of the following is distance between the points (2, 5) and (-1,

Q1. ?

1. Square root of (-7)
2. Square root of (37)
3. 25
4. 5

The inequality, {1 / x} < 1 can be simplified to which of the following?

1. (1 - x) / x > 0
2. (1 - x) / x < 0
3. (1 – x ) < 0
4. (1 – x ) > 0