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MHT-CET Mathematical Methods — practice questions — page 2

Explore 48 free Mathematical Methods questions in MHT-CET Physics. Open each question or exercise to read its content, reference answers and available explanation.

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Mathematical Methods questions and exercises with answers

Showing questions 31–48 of 48.

A definite integral of f(x) gives which geometric quantity?Read the answer and worked solution →The derivative dy/dx of a curve geometrically represents which quantity?Read the answer and worked solution →Differentiate x^3 sin x with respect to x.Read the answer and worked solution →A vector R makes angle θ with the x-axis. Its x-component is?Read the answer and worked solution →If Ax i + Ay j = Bx i + By j, which must hold?Read the answer and worked solution →Vectors OA and OB start at O. Along which line does their resultant lie?Read the answer and worked solution →Two parallel vectors of magnitude 3 and 4 add to a resultant of?Read the answer and worked solution →Multiplying a scalar by a vector always gives what kind of quantity?Read the answer and worked solution →Find the scalar product (2i + 3j) · (4i - j).Read the answer and worked solution →Determine a × b for a = 2i + 3j and b = i + 2j.Read the answer and worked solution →What is the scalar product of two perpendicular unit vectors?Read the answer and worked solution →The magnitude of the vector product of two unit vectors at 60 degrees is?Read the answer and worked solution →For what value of a are 5i + 2j and ai - 6j perpendicular?Read the answer and worked solution →Forces of 10 N along +x and 15 N along -x act on a body. Resultant?Read the answer and worked solution →Find the unit vector along 3i + 4j.Read the answer and worked solution →Two 10 N forces act in opposite directions along one line. Resultant?Read the answer and worked solution →Evaluate the definite integral of 3x^2 dx from x = 0 to x = 2.Read the answer and worked solution →If x = t^4, what is dx/dt?Read the answer and worked solution →

Worked practice questions

A definite integral of f(x) gives which geometric quantity?

  1. Length of the curve
  2. Area under the curve
  3. Curvature at a point
  4. Rate of change of f
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Correct answer: B. Area under the curve

Summing thin strips of height f(x) gives the area between the curve and the axis.

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The derivative dy/dx of a curve geometrically represents which quantity?

  1. Total area enclosed
  2. Length of the curve
  3. Slope of the tangent
  4. Intercept on the y-axis
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Correct answer: C. Slope of the tangent

As the second point approaches the first, the chord slope becomes the tangent slope.

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Differentiate x^3 sin x with respect to x.

  1. 3x^2 cos x + x^3 sin x
  2. x^3 cos x - 3x^2 sin x
  3. x^3 cos x + 3x^2 sin x
  4. 3x^2 sin x - x^3 cos x
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Correct answer: C. x^3 cos x + 3x^2 sin x

The product rule gives x^3 times cos x plus sin x times 3x^2.

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