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Tangents and Normals Maths - Tangents and Normals

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 134 questions in this chapter.

Question types

Tangents and Normals question types

134 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

134
Questions
4
Question groups
5
Question types
Sample Questions

Tangents and Normals questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The point on the curve y2 = x where tangent makes 45° angle with x-axis is:
  1. $\Big(\frac{1}{2},\frac{1}{4}\Big)$
  2. $\Big(\frac{1}{4},\frac{1}{2}\Big)$
  3. $(4, 2)$
  4. $(1, 1)$
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Q 2M.C.Q (1 Marks)1 Mark
The point on the curve y2 = x where tangent makes 45° angle with x-axis is:

  1. $\Big(\frac{1}{2},\frac{1}{4}\Big)$

  2. $\Big(\frac{1}{4},\frac{1}{2}\Big)$

  3. $(4,2)$

  4. $(1,1)$

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Q 4M.C.Q (1 Marks)1 Mark
At what point the slope of the tangent to the curve x2 + y2 - 2x - 3 = 0 is zero:
  1. (3, 0), (-1, 0)
  2. (3, 0), (1, 2)
  3. (-1, 0), (1, 2)
  4. (1, 2), (1, -2)
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Q 62 Marks2 Marks
Write the value of $\Big(\frac{\text{dy}}{\text{dx}}\Big),$ if the normal to the curve y = f(x) at (x, y) is parallel to y-axis. 
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Q 72 Marks2 Marks
If the tangent to a curve at a point (x, y) is equally inclined to the co-ordinates axes then write the value of $\frac{\text{dy}}{\text{dx}}.$
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Q 92 Marks2 Marks
Write the slop of the normal to the curve $\text{y}=\frac{1}{\text{x}}$ at the point $\Big(3,\frac{1}{3}\Big).$
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Q 102 Marks2 Marks
 If the tangent line at a point (x, y) on the curve y = f(x) is parallel to y-axis, find the value of $\frac{\text{dy}}{\text{dx}}.$
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Q 113 Marks3 Marks
Find the slope of the normal at the point 't' on the curve $\text{x}=\frac{1}{\text{t}},\text{y}=\text{t}.$
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Q 123 Marks3 Marks
Find the point on the curve y = x2 where the slope of the tangent is equal to the x-coordinate of the point.
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Q 133 Marks3 Marks
Write the coordinates of the point at which the tangent to the curve y = 2x2 - x + 1 is parallel to the line y = 3x + 9.
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Q 174 Marks4 Marks
Find the points on the curve x2 + y2 = 13, the tangent at each one of which is parallel to the line 2x + 3y = 7.
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Q 184 Marks4 Marks
If the tangent to the curve y = x3 + ax + b at (1, − 6) is parallel to the line x − y + 5 = 0, find a and b.
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