Calculus And Analytical Geometry (MTH101)

1. If \( f(x) = sin \; x \) and \( g(x) = x^2 \), then the derivative of \( f(x) \over g(x) \) is

   1. \( |x^2 cos(x) - 2x \; sin(x)|/x^4 \)
   2. \( |x^2 cos(x) + 2x \; sin(x)|/x^4 \)
   3. \( |x^2 cos(x) - 2x \; sin(x)|/x^2 \)
   4. None of the given

2. Let \( f(x) = \sqrt {x + 1} \) then \( f(-2) = \) ________.

   1. −1
   2. 0
   3. 1
   4. Not defined in R

3. At a corner a tangent line does not exist because the slopes of the secant lines do not have a (two sided) limit.

   1. True
   2. False

4. Which of the following is radius of a circle represented by equation: \(x^2 + y^2 = 25\)?

   1. 25
   2. 5
   3. 1
   4. 0

5. Graphically the function y = c represents ________ line.

   1. Horizontal
   2. Vertical

6. Let \(f(x) = {3 \over x}\), then which of the following is domain of f(x)?

   1. \((- \infty, 0)\)
   2. \((0, \infty)\)
   3. \((- \infty, \infty)\)
   4. \((- \infty, 0) U (0, \infty)\)

7. If f(x) = (107)^2 then f'(2) =
   NOTE: x^n means 'x' to the power 'n'

   1. 214
   2. 4
   3. 0
   4. None of the given

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

   1. True
   2. False

9. If \( f(x) = sec \; x \) and \( g(x) = csc(x) \), then the derivative of \( f(x) × g(x) \) is

   1. \( - sec \; x \; csc \; x \; cot \; x + csc \; x \; sec \; x \; tan \; x \)
   2. \( sec \; x \; csc \; x \; cot \; x + csc \; x \; sec \; x \; tan \; x \)
   3. \( - sec \; x \; csc \; x \; cot \; x - csc \; x \; sec \; x \; tan \; x \)
   4. None of the given

10. The derivative of ( sin(cos x)) is ________.

    1. cos(cos x)
    2. cos(sin x)
    3. −sin(cos x).sin x
    4. −cos(cos x).sin x

11. The derivative of \( {1 \over -x+1} \) with respect to x is

    1. \( (1-x)^2 \)
    2. \( 1/(1+x)^2 \)
    3. \( 1/(1-x) \)
    4. \( 1/(1-x)^2 \)

12. Which of the following is slope of a line segment joining the points (4, 3) and (−2, 3)?

    1. 0
    2. 3
    3. 5
    4. 1/7

13. The cotangent function is defined by Cot x = cos x/sin x

    1. True
    2. False

14. If f(x) = 8x, then f'(2) is ________.

    1. 4
    2. 2
    3. 3
    4. 8

15. If \( f(x) = ax + bx + c \), then its derivative with respect to x is ________.

    1. a + b
    2. b + c

16. If "f" is a continuous function on [a, b] then \( \int_a^b f(x) \,dx= \) ________

    1. \( \int_b^a f(x) \,dx \)
    2. \( -\int_a^a f(x) \,dx \)
    3. \(- \int_b^a f(x) \,dx \)
    4. \(- \int_b^b f(x) \,dx \)

17. Which of the following is midpoint of the line segment joining points (1, 3) and (1, 5)?

    1. (0, −1)
    2. (0, 2)
    3. (2, 8)
    4. (1, 4)

18. 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

19. Let \( f(x) = x - 3 \) and \( g(x) = x^3 \) then \( (f + g)(x) = ? \)

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

20. The derivative of composition of functions can be found by using ________.

    1. Power rule
    2. Chain rule
    3. Generalized derivative formula
    4. None of the given

21. Let \(f(x) = {1 \over x + 3}\), which of the following is domain of f(x)?

    1. \((- \infty, \infty)\)
    2. \((- \infty, 3)\)
    3. \((3, \infty)\)
    4. \((- \infty, -3) U (-3, \infty)\)

22. If (x approaches to 2) lim 3x-5=1. In this statement the limiting value of 3x-5 is ________.

    1. 1
    2. 2

23. If \(y = f(sin t) \) and \(y = t \) then \( ( {df \over dy} ) \)

    1. − sec y
    2. sec y
    3. cos y
    4. − cos y

24. Log with base 'e' is called ________ log.

    1. Natural
    2. Anti
    3. Inverse
    4. All of the given

25. Graph of \(y = f(x)\) and \(y = f(-x)\) are reflection of one another about the ________.

    1. y-axis
    2. x-axis

26. Is the graph of equation
    \(y = 4x + 1\)
    symmetric about x-axis?

    1. True
    2. False

27. If \( y = 9 \; cos(3x) \) then value of y at \( x = π \) is

    1. 9
    2. − 9
    3. 3
    4. 0

28. Let \(f(x) = x^2 + 1\) and \(g(x) = 2x\) then \(f(g(x)) =\)?

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

29. If \(g(X) = 3x^2 \) then \( g'(2) \) will be ________?

    1. 18
    2. 15
    3. 12
    4. −12

30. Which of the following is x-intercept of a parabola represented by the equation : \( y = x^2 + 2x \)

    1. 0 and −2
    2. 1 and 2
    3. 0 only
    4. 1 only

31. Does the point (1, 2) satisfies the equation: \(2y = x^2 -1\)?

    1. Yes
    2. No

32. The inequality,
    \( 6 < -2x < 4 \)
    can be simplified to which of the following?

    1. \( -3 > x < -2 \)
    2. \( -3 < x > -2 \)
    3. \( -3 > x > -2 \)
    4. \( -3 < x < -2 \)

33. Graph of the equation \(y = x + 3\) represents a ________.

    1. Circle
    2. Line
    3. Parabola
    4. Ellipse

34. Let \( f(x) = x - 3 \) and \( g(x) = 2x \) then f(g(x)) =?

    1. \( 2x - 3 \)
    2. \( 2x + 3 \)
    3. \( 2x - 1 \)
    4. \( -2x - 3 \)

35. If \( y = 2x \) then instantaneous rate of change of 'y' w.r.t. 'x' at 'x = −2' is ________.

    1. 2
    2. 1
    3. 3
    4. −1

36. Average rate of change in 'y' w.r.t. 'x' represents the slope of ________ line on the graph.

    1. tangent
    2. secant
    3. circle
    4. parabola

37. Let \( f(x) = \sqrt {x + 1} \) then \( f(-1) = \) ________.

    1. − 1
    2. 0
    3. 1
    4. Not defined

38. Which of the following is equation of a line whose slope is -4 and y-intercept is 2?

    1. \( -4y = x + 2 \)
    2. \( y = -4x + 2 \)
    3. \( y = 2x - 4 \)
    4. \( 2y = x - 4 \)

39. Graph of \(y = x^2 + 4\) is same as ________ but it has been translated 4 units up in the y direction.

    1. \(y = x^2 + 2\)
    2. \(y = x^2 - 2\)
    3. \(y = x^2\)
    4. None of the given.

40. If a secant line is drawn between two points P and Q on a curve, then the slope of this secant line is ________.

    1. f(x2) − f(x1)
    2. f(x2) − f(x1)/x2
    3. {f(x2) − f(x1)}/(x2 − x1)
    4. f(x1) − f(x2)/x2 − x1

41. The function f(x) = |x| is differentiable at x = 0

    1. True
    2. False

42. Which of the following is equation of a line whose slope is 7 and y-intercept is 3?

    1. \( 7y = x + 3 \)
    2. \( y = 3x + 7 \)
    3. \( y = 7x + 3 \)
    4. \( 3y = x + 7 \)

43. Which of the following is equation of a line that passes through the point (1, 7) and whose slope is 1?

    1. \( y = x + 6 \)
    2. \( y = x − 6 \)
    3. \( y = 7x + 1 \)
    4. \( 7y = x + 1 \)

44. Which of the following is y-intercept of equation \(2x = -5y + 3\)?

    1. −5
    2. 2
    3. 4
    4. 3/5

45. What is the derivative of \( cosec(x^4) \)?

    1. \( -cosec(x^4) \; cot(x^4) \)
    2. \( -4x^3 \; cosec(x^4) \; cot(x^4) \)
    3. \( cosec(x^4) \; cot(x^4) \)
    4. None of the given

46. Let \( f(x) = 4x + 1 \) then
    f(2) = ________.

    1. 6
    2. 7
    3. 9
    4. Not defined

47. Velocity is the rate of change of position w.r.t. ________.

    1. time
    2. force
    3. acceleration
    4. displacement

48. \( g(x) = |x + 3| \) is the composition of two functions, one is \( (x + 3) \) and the other is ________.

    1. x
    2. |x|
    3. 3
    4. 0

49. Which of the following describes the equation?

    1. A point (0, 2)
    2. A point (2, 0)
    3. A line parallel to x-axis
    4. A line parallel to y-axis

50. If \( f(x) = (sec \; x + x^4)^5 \), then the derivative of \( f(x) \) is ________.

    1. \( 5(sec \; x + x^4)^4 \; (sec(x) \; tan(x) + 4x^3) \).
    2. \( 5(sec \; x + x^4)^4 \; (sec(x) \; tan(x) - 4x^3) \).
    3. \( 5(sec \; x + x^4)^4 \).
    4. None of the given

51. There is one-to-one correspondence between the points on co-ordinate line and ________.

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

Select a course code for Objective Questions:

ACC311 ACC501 BIF101 BIF401 BIF501 BIO101 BIO201 BIO202 BIO203 BIO204 BIO301 BIO302 BIO303 BIO401 BIO503 BNK603 BT101 BT201 BT301 BT302 BT401 BT402 BT403 BT404 BT405 BT406 BT501 BT504 BT505 BT604 CHE201 CHE301 CS001 CS101 CS201 CS202 CS204 CS301 CS302 CS304 CS311 CS401 CS402 CS403 CS408 CS501 CS502 CS504 CS506 CS508 CS601 CS602 CS604 CS605 CS607 CS609 CS610 CS614 CS707 CS710 ECO401 ECO402 ECO403 ECO404 EDU302 EDU401 EDU402 EDU501 EDU601 ENG101 ENG201 ENG301 ENG501 FIN611 FIN624 FIN625 ISL201 IT430 MCM101 MCM301 MGMT623 MGT101 MGT211 MGT301 MGT401 MGT402 MGT501 MGT502 MGT503 MGT510 MGT601 MGT603 MKT501 MKT610 MKT630 MTH101 MTH202 MTH302 MTH501 MTH601 MTH634 PAK301 PHY101 PHY301 PSY101 PSY403 PSY502 PSY512 SOC101 SOC301 SOC401 STA301 STA630 STA641 ZOO102 ZOO401 ZOO501 ZOO502 ZOO503 ZOO504 ZOO505 ZOO506 ZOO510 ZOO630

Select a course code for Subjective Questions:

ACC311 CS001 CS101 CS201 CS301 CS607 CS701 CS702 CS703 CS704 CS707 CS708 CS710 CS711 CS718 CS721 CS724 ECO401 ECO403 ENG101 ENG301 MGT703 MTH501 STA301