Mathematical tools and vector questions with solutions

Showing 1–10 of 1122 questions

• MCQmediumMathematical tools and vectorIntegration

  Evaluate ∫₀¹ 2x/(1+x²) dx.

  Options

  • Option A

    0

  • Option B

    1

  • Option C

    log2 + C

  • Option D

    log2

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• IntegermediumMathematical tools and vectorGeometry & Mensuration

  A cube has volume 729 cm³. Find its edge length in cm.

  Your answer

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• MCQmediumMathematical tools and vectorCoordinate Geometry

  Which curve is represented by y² = 8x?

  Options

  • Option A

    Circle

  • Option B

    Ellipse

  • Option C

    Parabola

  • Option D

    Straight line

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• MCQmediumMathematical tools and vectorDifferentiation

  Differentiate y = x/log x.

  Options

  • Option A

    [log x-1]/(log x)²

  • Option B

    x/log x

  • Option C

    -([log x-1]/(log x)²)

  • Option D

    1

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• MCQdifficultMathematical tools and vectorVector

  Two vectors have magnitudes 5 and 10, and their resultant is perpendicular to the vector of magnitude 5. Which pair gives the angle between the vectors and the resultant magnitude?

  Options

  • Option A

    120°, 5√3

  • Option B

    60°, 5√3

  • Option C

    120°, 5

  • Option D

    90°, 5√5

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• MatchmediumMathematical tools and vectorIntegration

  Match List I with List II and choose the correct option.

  List 1

  1. ∫x³/√(1+x⁴)dx

  2. ∫4x³/(1+x⁴)³ᐟ²dx

  3. ∫4x³e⁽ˣ⁴⁾dx

  4. ∫4x³sin(x⁴)dx

  List 2

  1. -cos(x⁴)+C

  2. e⁽ˣ⁴⁾+C

  3. √(1+x⁴)/2+C

  4. -2/√(1+x⁴)+C

  Options

  • Option A

    P-3, Q-1, R-4, S-2

  • Option B

    P-3, Q-4, R-2, S-1

  • Option C

    P-1, Q-2, R-3, S-4

  • Option D

    P-2, Q-4, R-1, S-3

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• MCQdifficultMathematical tools and vectorQuadratic Equation

  A particle has velocity v(t)=t²-6t+k m/s. If its velocity never becomes zero for any real time, which condition must k satisfy?

  Options

  • Option A

    k<9

  • Option B

    k=9

  • Option C

    k>9

  • Option D

    k≥0

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• MCQmediumMathematical tools and vectorCoordinate Geometry

  Find the centre and radius of the circle x² + y² - 6x + 8y - 11 = 0.

  Options

  • Option A

    Centre (3, -4), radius 6

  • Option B

    Centre (-3, 4), radius 6

  • Option C

    Centre (3, 4), radius 4

  • Option D

    Centre (-3, -4), radius 6

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• A/RmediumMathematical tools and vectorVector

  Choose the correct option for the given Assertion and Reason.

  Assertion

  Two vectors of equal magnitude acting at 120° have a resultant equal in magnitude to either vector.

  Reason

  For two equal vectors of magnitude A separated by angle θ, R=2A cos(θ/2).

  Options

  • Option A

    Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

  • Option B

    Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion.

  • Option C

    Assertion is true, but Reason is false.

  • Option D

    Assertion is false, but Reason is true.

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• MCQeasyMathematical tools and vectorLogarithm Function

  For a > 0 and a ≠ 1, logₐ1 is:

  Options

  • Option A

    0

  • Option B

    1

  • Option C

    a

  • Option D

    -1

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