JEE Maths - Tangent & Normal

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Question - 1

If the line joining the points (0, 3) and (5, -2) is a tangent to the curve y = \(\frac{C}{x +1}\), then find the value of c.

  • A 1.00
  • B 3.00
  • C 4.00
  • D 5.00

Question - 2

Find the number of points to the curve x2/3 + y2/3 =  a2/3 where the tangents are equally inclined to the axes

  • A 2.00
  • B 4.00
  • C 6.00
  • D 8.00

Question - 3

Find the length of the subtangent to the curve x2 + xy + y2 = 7 at (1, -3).

  • A 5.00
  • B 10.00
  • C 15.00
  • D 20.00

Question - 4

A particle moves along the curve y = x3/2 in the first quadrant in such a way that its distance from
the origin increases at the rate of 11 units per second. Then find the value of \(\frac{dx}{dy}\) at x = 3.

  • A 1.00
  • B 2.00
  • C 3.00
  • D 4.00

Question - 5

Let f(x) =x3 + ax +b with a \(\ne\) b and suppose the tangent lines to the graph of f at x = a & x =b
have the same gradient. Then find the value of f(1).

  • A 1.00
  • B 2.00
  • C 3.00
  • D 4.00

Question - 6

If the curves \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{4}\) = 1 and y3 = 16x intersect at right angle, then fi.nd value of a2.

  • A 1.33
  • B 1.23
  • C 1.43
  • D 1.53

Question - 7

Find the length of the sub-tangent to the curve \(\sqrt{x}+\sqrt{y}\) = 3 at the point (4, 1)

  • A 1.00
  • B 2.00
  • C 3.00
  • D 4.00

Question - 8

The tangent to the curve 2y2 = ax2 + x3 at (a, a) cuts of intercepts p and q on co-ordinate axes. If
p2 + q2 = 61, then find value of a.

  • A 10.00
  • B 20.00
  • C 30.00
  • D 40.00

Question - 9

Find the area of the triangle formed by the tangent to the curve sin y = x3 - x5 at the point (1, 0)
and the coordinate axes.

  • A 1.00
  • B 2.00
  • C 3.00
  • D 4.00

Question - 10

If tangent of acute angle between the curves y = |x2 - 1| and y = \(\sqrt{7-x^2}\) at their point of intersection is K\(\sqrt{3}\) then find k ?

  • A 1.25
  • B 1.50
  • C 1.75
  • D 1.95
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