VU Midterm Past Papers
200 solved midterm past paper MCQs for MTH101 (Calculus & Analytical Geometry) at Virtual University, each with the correct answer marked. Use them to learn the VU question style and test your recall. An independent study tool — not affiliated with VU.
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Q1. The value of I d= N
Q2. The region bounded by the curves y = sqrt(x), y=1 and x=4
Q3. Find the area of the region between the x-axis, the f(z) = 2^z - 2^z - 22, 1<z<2
Q4. If we change the letter for the variable of integration but don't change the limits, then the values of the definite integral are
Q5. First fundamental theorem of calculus tells us how to evaluate the ...... in a quick way.
Q6. The volume of a cylinder is the area of a cross section of the cylinder multiplied by the ______ of the cylinder.
Q7. EVERY continuous function on an interval has an anti-derivative ...
Q8. For the adjacent intervals, [a,c] and [c,b] where c is any number, ∫_a^b f(x) dx =
Q9. The integral of f(x)=sin(2x) from x=0 to x=pi is
Q10. The value of ∫ y^2 dy =
Q11. The value of ∫ f(x) dx =
Q12. The conclusion of the 2nd fundamental theorem of calculus can be expressed in words as: the derivative of an integral of a function is that.
Q13. If the upper and lower limits for the definite integral are the same, then ∫_a^a f(x) dx =
Q14. F(x) (antiderivative of f) was determined to be 4x+C where C denotes the
Q15. The value of ∫_0^1 dt =
Q16. The volume of solid obtained when the region under the curve y = x^2 over the interval [1,3] is revolved about the x-axis is
Q17. In integration of f(x) = x(x^2+1)^5 from x=0 to x=2 by substitution method, we take u = x^2+1 then du = ...
Q18. If the solid is revolved around the y-axis and generates a solid with a circular cross section of radius g(y) at y. Then the area of this cross section is
Q19. The volume of solid obtained when the region under the curve x=y over the interval [1,4] is revolved about the y-axis is
Q20. If the function and limits of definite integral are the same and variable of integration are changed, i.e ∫_a^b f(x) dx = ∫_a^b f(t) dt. Then the answer would be
Q21. If ∫_0^2 (x^2+1) dx = 14/3, then the solution of ∫_2^0 (x^2+1) dx =
Q22. If sinx=t then dt=....
Q23. The integral of f(x)=cos(2x) from x=0 to x=pi is
Q24. Which of the following is the definite integral of f(x)=x^2 from x=1 to x=2
Q25. If f is continuous at every point of [a,b] and F is anti-derivative of f on [a,b], then
Q26. ∫_a^b f(x) dx =
Q27. ...... can be used to find the area under the curve and volume of the solids.
Q28. The integral of f(x)=sin(x+1) from x=0 to x=1 is
Q29. The area of the ellipse x^2/a^2 + y^2/b^2 = 1
Q30. The bounded region between the parabola y=4x^2 and the line y=6x-2
Q31. Evaluate d/dx ∫_1^x t^2 dt
Q32. Cannot evaluate definite integrals by substitution method
Q33. The volume V of a cylinder with base area A and height h is calculated by
Q34. 30° = ________
Q35. Let a function f be defined on an interval, and let x1 and x2 denote two distinct points in that interval. If f(x1) = f(x2) for all points x1 and x2 then which of the following statement is correct?
Q36. Tan(x) is continuous everywhere except at points
Q37. lim (x→∞) (2 - x) =
Q38. Suppose that f and g are differentiable functions of x then d/dx [f g] =
Q39. The solution set of the inequality |x+4| ≥ 2 is
Q40. A line is called a tangent line to the circle if it meets the circle at precisely _________.
Q41. Let a function f be defined on an interval, and let x1 and x2 denote points in that interval. If f(x1) < f(x2) whenever x1 < x2 then which of the following statement is correct?
Q42. If f(x) = 3x^8 + 2x + 1 then f'(x) = __________
Q43. π is a .............number
Q44. The set {x : a ≤ x ≤ b} can be written in the form of interval
Q45. The graph y = x^2 is symmetric about ---------axis
Q46. lim (x→-7) (x^2 - 49)/(x + 7)
Q47. Chain rule is a rule for differentiating ___________ of functions.
Q48. The lim (x→a) f(x) = ........ where f(x) = k (k is a constant)
Q49. For any number ε > 0 if we can find an open interval (x0, x1) on the x-axis containing the point 'a' such that L - ε < f(x) < L + ε for each x in (x0, x1) except the possible x = a then we say lim (x→a) f(x) = ---------
Q50. If 2x - y = -3 then dy/dx =
Q51. The graph of the equation y = x^2 - 4x + 5 will represent
Q52. The equation of line of the form y - y1 = m(x - x1) is known as
Q53. The base of the natural logarithm is
Q54. If a function satisfies the conditions: f(c) is defined, lim_{x→c+} f(x) exists, and lim_{x→c+} f(x) = f(c), then the function is said to be
Q55. If f''(x) < 0 on an open interval (a,b) then f is --------------- on (a,b)
Q56. If y = 1/(1-x) then dy/dx =
Q57. If x^2 + y^2 = 9 then dy/dx =
Q58. Let y = (2x^3 + 7)^7. Which of the following is correct?
Q59. If x > 0 then d/dx [ln x] = ___________
Q60. log_b (ac) = ----------
Q61. log_b (1/c) = ________
Q62. log_b (1/t) = ________
Q63. If we have x^2 + y^2 = 1 then dy/dx = __________
Q64. log_b (a^r) = ________
Q65. What are critical points of the function f(x) =*-1?
Q66. Let A be the area of a rectangle under a continuous function f(x) over a closed interval (o, b]. If this area is divided in to 'n' sub-rectangles, then width of each approximated sub-intervals is____
Q67. Increase in number of rectangles under any continuous function gives_________approximation to area.
Q68. If Newton's Method succeeded to get the approximate solution of an equation, then which of the following is NOT true about it.
Q69. If the closed interval f-10,x] is divided into 20' equally spaced subintervals each of which having the width equals to 1' unit then the value of* is_______
Q70. If fx)=x^4, then which of the following is Not true about it.
Q71. Let y f() be a discontinuous function on a finite closed interval, then which ofthe following is true about it
Q72. Integral of 52 is NOTE: X'n means '* to the power’s
Q73. If f(x)=x^3 is defined on the interval! [1, 3], then which of the following is true about it.
Q74. If fx)= Sec^(2) x+x^3, then which of the fallowing is NOT true about it.
Q75. Integration of 5 with respect to x is_______
Q76. 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____
Q77. Newton's method uses the______________to approximate the root.
Q78. The polynomial function f(x)=6x*2-30x+36 has the critical point over the reel line is____
Q79. If fx)=x*5+6, then which of the following is Not true about it.
Q80. If x =1+2 +3+4...+20, then x=_____________
Q81. In sigma notation 12+14+16+18+20 can be written as___________
Q82. If f(x ) 2x+7 is defined on the interval (2,4). then which of the following is true about it.
Q83. The indefinite integral of 5sinxis_____
Q84. Which of the following will be left end points if the interval (-2,2] is divided into 4 equal subintervals
Q85. If x= (1^2)(2^2)+(3^2)+(4^2)*... +(30^2), then x=______
Q86. If ‘n' goes from 1 to 4 and the summation of 'na' =Maxima of (ex) in the interval[-e,0]. then the value of 'a' is______________
Q87. Subdivide the interval [o, b] into 4 equal subintervals then the width of each subinterval is________
Q88. Subdivide the interval 3, 5] into n equal parts, and then the width gf each subinterval is_________
Q89. If f(x)= x^ 5+x, then which of the following is true about it__________
Q90. Newton's Method fails to find the approximate solution of an equation it_____
Q91. If 'n' goes from 1 to 3 and the summation of 'na'= 6, then the value of 'a' is________
Q92. 1+2+3________+1000 equals_____
Q93. If f(x) = I x l -2 is defined on the interval [-2, 2]. then which of the following is true about it.
Q94. Which of the following is the absolute minima of the function f(x)=x in the interval [-1,1]?
Q95. If f(x)= Cos(x) + Sin(x)+x, then which of the following is NOT true about it.
Q96. Maximum of the function f(x)=2x+7 occurs at
Q97. What are critical points of the function f(x) =x^2-1? NOTE:x^n means ‘x’ to the power 'n’
Q98. If Sin(3x^2)/6+C is the anti–derivative of a function f(x), then f(x)=__________.
Q99. Which of the following is the integral of Sin(3x+5) with respect to x?
Q100. If ‘n’ goes from 1 to 3 and the summation of ‘na’ = 6a, then the value of ‘a’ is----------
Q101. If ‘n’ goes from 1 to any large ODD number then the summation of ‘(-1)^n’ =---------
Q102. 1+2+3.........+t equals
Q103. If definite integral of f(x)=Sinx over [a,0] is equal to ‘-2’ then the value ‘a’ is---------
Q104. If the definite integral of f(x)=3 over [1,x] is greater than ‘12’ then-----
Q105. If [-8,8] is subdivided into ‘16’ equally spaced subintervals, then the RIGHT endpoint of 13th sub-interval will be--------.
Q106. Which of the following is the integral of sin(2x)?
Q107. Sum of cubes of n-terms of a series whose nth term is ‘n’ =---
Q108. |x^2-9| =..........
Q109. Usually the number that signifies the idea of f(x) being as close to limit L as want to be must be a/an...............
Q110. 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
Q111. 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).
Q112. 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---------
Q113. |x-3|<1 implies.....
Q114. 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)=............
Q115. Integral of (1-2x) from [0,1] is...........
Q116. If f(x)=Cos(x)+x, then which of the following is NOT true about it.
Q117. Integral of 5^2 is NOTE: x^n means ‘x’ to the power ‘n’
Q118. In the indefinite integral of x(y^2) w.r.t ‘y’, the term..... serves to identify the independent variable in the function.
Q119. If f(x)=Sin(5x), then which of the following is NOT true about it.
Q120. If g is differentiable at a point x and f is differentiable at a point g(x), then the ------ is differentiable at point x .
Showing the first 120 of 200 MCQs.