Engineering Mathematics MCQ

Test your knowledge with important Engineering Mathematics MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Engineering Mathematics MCQs at Bissoy

• Find the laplace transform of input x(t) if the system given by d3⁄dt3 y(t) – 2 d2⁄dt2 y(t) –d⁄dt y(t) + 2y(t) = x(t), is stable.
  ক

  s + 1

  খ

  s – 1

  গ

  s + 2

  ঘ

  s – 2
• Any system is said to be stable if and only if ____________
  ক

  It poles lies at the left of imaginary axis

  খ

  It zeros lies at the left of imaginary axis

  গ

  It poles lies at the right of imaginary axis

  ঘ

  It zeros lies at the right of imaginary axis
• Find the transfer function of a system given by equation d2⁄dt2 y(t-
  ক

  + x(t) + 5 d⁄dt y(t) = x(t-]. ] (e-as-s)/(1+e-as s2)

  খ

  (e-as-5s)/(e-as s2)

  গ

  (e-as-s)/(2+e-as s2)

  ঘ

  (e-as-5s)/(1+e-as s2)
• Zeros of any transfer function is define as the roots of equation of numerator of transfer function.
  ক

  True

  খ

  False
• Poles of any transfer function is define as the roots of equation of denominator of transfer function.
  ক

  True

  খ

  False
• Transfer function may be defined as ____________
  ক

  Ratio of out to input

  খ

  Ratio of laplace transform of output to input

  গ

  Ratio of laplace transform of output to input with zero initial conditions

  ঘ

  None of the mentioned
• Distance travelled by any object is _____________
  ক

  Double integral of its acceleration

  খ

  Double integral of its velocity

  গ

  Double integral of its Force

  ঘ

  Double integral of its Momentum
• Find the ∫∫x3 y3 sin⁡(x)sin⁡(y) dxdy. ]) b) (-x3 Cos(x) – 3x2 Sin(x) – 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3]) c) (-x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3y2 Sin(y) + 6yCos(y) – 6Sin(y)) d) (–x3 Cos(x) + 6xCos(x) – 6Sin(x))(-y3 Cos(y))
  ক

  (x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(y3 Cos(y) + 3]) ) c) (-x3 Cos(x) + 3x2 Sin(x) + 6xCos(x)-6Sin(x))(-y3 Cos(y) + 3y2 Sin(y) + 6yCos(y) – 6Sin(y)) d) (–x3 Cos(x) + 6xCos(x) – 6Sin(x))(-y3 Cos(y)) View Answer]

  খ

  y2 Sin(y) – 2[-yCos(y) + Sin(y)

  গ

  y2 Sin(y) – 2[-yCos(y) + Sin(y)

  ঘ

  y2 Sin(y) – 2[-yCos(y) + Sin(y)
• Find the value of ∫∫xyex + y dxdy.
  ক

  yey (xex-ex)

  খ

  (yey-ey)(xex-ex)

  গ

  (yey-ey)xex

  ঘ

  (yey-ey)(xex+ex)
• Temperature of a rod is increased by moving x distance from origin and is given by equation T(x) = x2 + 2x, where x is the distance and T(x) is change of temperature w.r.t distance. If, at x = 0, temperature is 40 C, find temperature at x=10.
  ক

  473 C

  খ

  472 C

  গ

  474 C

  ঘ

  475 C
• Find the area of a function f(x) = x2 + xCos(x) from x = 0 to a, where, a>0.
  ক

  a2⁄2 + aSin(] + Cos(] – 1 + Cos(] c) a3⁄3 + aSin(] + Cos(] – 1 d) a3⁄3 + Cos(] + Sin(] – 1 View Answer]

  খ

  a3⁄3 + aSin(a) + Cos(a)

  গ

  a3⁄3 + aSin(a) + Cos(a) – 1

  ঘ

  a3⁄3 + Cos(a) + Sin(a) – 1
• Find the value of ∫x3 Sin(x)dx.
  ক

  x3 Cos(x) + 3x2 Sin(x) + 6xCos(x) – 6Sin(x)

  খ

  – x3 Cos(x) + 3x2 Sin(x) – 6Sin(x)

  গ

  – x3 Cos(x) – 3x2 Sin(x) + 6xCos(x) – 6Sin(x)

  ঘ

  – x3 Cos(x) + 3x2 Sin(x) + 6xCos(x) – 6Sin(x)
• Integration of (Sin(x) + Cos(x))ex is?
  ক

  ex Cos(x)

  খ

  ex Sin(x)

  গ

  ex Tan(x)

  ঘ

  ex (Sin(x) + Cos(x))
• Find the value of ∫tan-1⁡(x)dx.
  ক

  sec-1 (x) – 1⁄2 ln⁡(1 + x2)

  খ

  xtan-1 (x) – 1⁄2 ln⁡(1 + x2)

  গ

  xsec-1 (x) – 1⁄2 ln⁡(1 + x2)

  ঘ

  tan-1 (x) – 1⁄2 ln⁡(1 + x2)
• Find the value of ∫ cot3(x) cosec4 (x). \) b) –\(\) c) –\(\) d) –\(\)
  ক

  –\(\)

  খ

  \frac{cot^4⁡(x)}{4}+\frac{cosec^6⁡(x)}{6}

  গ

  \frac{cot^4⁡(x)}{4}+\frac{cosec^6⁡(x)}{6}

  ঘ

  \frac{cot^4⁡(x)}{4}+\frac{cosec^6⁡(x)}{6}
• Integration of function y = f(x) from limit x1 < x < x2 , y1 < y < y2, gives ___________
  ক

  Area of f(x) within x1 < x < x2

  খ

  Volume of f(x) within x1 < x < x2

  গ

  Slope of f(x) within x1 < x < x2

  ঘ

  Maximum value of f(x) within x1 < x < x2
• If differentiation of any function is infinite at any point and constant at other points then it means ___________
  ক

  Function is parallel to x-axis at that point

  খ

  Function is parallel to y-axis at that point

  গ

  Function is constant

  ঘ

  Function is discontinuous at that point
• If differentiation of any function is zero at any point and constant at other points then it means?
  ক

  Function is parallel to x-axis at that point

  খ

  Function is parallel to y-axis at that point

  গ

  Function is constant

  ঘ

  Function is discontinuous at that point
• Integration of (Sin(x) – Cos(x))ex is ___________
  ক

  -ex Cos(x)

  খ

  ex Cos(x)

  গ

  -ex Sin(x)

  ঘ

  ex Sin(x)
• Integration of (Sin(x) + Cos(x))ex is______________
  ক

  ex Cos(x)

  খ

  ex Sin(x)

  গ

  ex Tan(x)

  ঘ

  ex (Sin(x)+Cos(x))
• Integration of function is same as the ___________
  ক

  Joining many small entities to create a large entity

  খ

  Indefinitely small difference of a function

  গ

  Multiplication of two function with very small change in value

  ঘ

  Point where function neither have maximum value nor minimum value
• The span of a Astroid is increased along both the x and y axes equally. Then the maximum value of: z = x + y along the Astroid is?
  ক

  Increases

  খ

  Decreases

  গ

  Invariant

  ঘ

  The scaling of Astroid is irrelevant
• Consider the points closest to the origin on the planes x + y + z = a.
  ক

  The closest point travels farther as a is increased

  খ

  The closest point travels nearer as a is increased

  গ

  The closest point is independent of a as a is not there in the expression of the gradient.

  ঘ

  Varies as a2, away from the origin.
• Find the points on the plane x + y + z = 9 which are closest to origin.
  ক

  (3,3,3)

  খ

  (2,1,3)

  গ

  (2,2,2)

  ঘ

  (3,4,1)
• Maximum value of a 3-d plane is to be found over a circular region. Which of the following happens if we increase the radius of the circular region.
  ক

  Maximum value is invariant

  খ

  Maximum value decreases

  গ

  Maximum value increases and minimum value goes lesser

  ঘ

  minimum value goes higher
• Which one of these is the right formula for the Lagrange multiplier with more than one constraint?
  ক

  ∇f = (μ)2 * ∇g1 + ∇g2

  খ

  Cannot be applied to more than one constraint function.

  গ

  ∇f = μ * ∇g1 + λ * ∇g2

  ঘ

  ∇f = μ * ∇g1 + ∇g2
• Maximize the function x + y – z = 1 with respect to the constraint xy=36.
  ক

  0

  খ

  -8

  গ

  8

  ঘ

  No Maxima exists
• In a simple one-constraint Lagrange multiplier setup, the constraint has to be always one dimension lesser than the objective function.
  ক

  True

  খ

  False
• The drawback of Lagrange’s Method of Maxima and minima is?
  ক

  Maxima or Minima is not fixed

  খ

  Nature of stationary point is can not be known

  গ

  Accuracy is not good

  ঘ

  Nature of stationary point is known but can not give maxima or minima
• Find the maximum value of Sin(A)Sin(B)Sin(C) if A, B, C are the angles of triangle.
  ক

  3√3⁄8

  খ

  3√4⁄8

  গ

  –3√3⁄8

  ঘ

  π⁄8