Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Application of Derivatives

Name: Zigya - For The Curious Learner
Rating: 4.4 (740 reviews)

Short Answer Type

51.

Find the points on the curve y = x³ at which the slope of the tangent is equal to the y-coordinate of the point.

75 Views

52. Find the slope of the tangent to the curve x = at², y = 2at at t = 1.

The curve is x = at², y = 2at
$therefore space space space space dx over dt space equals space 2 at comma space space dy over dt space equals space 2 straight a comma space space space space space space space space space space space space space space space therefore space space space space dy over dx space equals fraction numerator begin display style dy over dt end style over denominator begin display style dx over dt end style end fraction space equals fraction numerator 2 straight a over denominator 2 at end fraction space equals 1 over straight t therefore space space space space value space of space dy over dx at space straight t space equals 1 space is space equals space 1 over 1 space equals space 1 Hence space the space slope space of space the space tangent space of space the space curve space at space straight t space equals space 1 space is space 1.$

88 Views

53.

Find the slope of the tangent to the curve y = x³ – x at x = 2.

85 Views

54.

Find the slope of the tangent to the curve y = 3x⁴ – 4x at (i) x = 1 (ii) x = 4.

91 Views

55.

Find the slope of the tangent to the curve $straight y space equals fraction numerator straight x minus 1 over denominator straight x minus 2 end fraction comma space space space straight x not equal to space 2 space space at space straight x space equals space 10$ .

94 Views

56. For the curve y = 3x² + 4 x , find the slope of the tangent to the curve at the point whose x-coordrnate is – 2.

84 Views

57. Find the slope of the tangent to the curve y = x³ – x + 1 at the point whose x-coordmate is 2.

93 Views

58.

Find the slope of the tangent to the curve y = x³ – 3x + 2 at the point whose. x-coordinate is 3.

87 Views

59.

Find the slope of the normal to the curve $straight x equals space straight a space cos cubed straight theta comma space space space straight y space equals space straight a space sin cubed straight theta space space space at space straight theta space equals space straight pi over 4$ .

99 Views

60.

Find the slope of the normal to the curve $straight x space equals space 1 minus straight a space sin space straight theta comma space space space straight y space equals space space straight b space cos squared straight theta space space at space straight theta space equals space straight pi over 2.$

79 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

52. Find the slope of the tangent to the curve x = at2, y = 2at at t = 1.

52. Find the slope of the tangent to the curve x = at², y = 2at at t = 1.