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RD Sharma Solution CLass 12 Mathematics Chapter 16 Tangents and Normals 

 

Chapter 16 – Tangents and Normals Exercise Ex. 16.1

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 19
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 24
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 24
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 25
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 25
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 26
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 27
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 27
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 28
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 29
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 29
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 30
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 30
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Chapter 16 – Tangents and Normals Exercise Ex. 16.2

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 9
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 16
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 17
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 18
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 19

Find the equations of
the tangent and the normal to the given curves at the indicated points:

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And NormalsRd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 20
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 21
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 22
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 23
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 24
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 24
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 25
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 25
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 26

Find the equations of the tangent
and the normal to the following curves at the indicated points:

X = 3 cosθ
– cos3θ , y = 3 sinθ
– sin3θ

Solution 26

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 27
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 27
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 28
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 28

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 29
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 29
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 30
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 30
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 31
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 31
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 32
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 32
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 33
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 33

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 34
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 34

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 35
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 35
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 36
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 36
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 37
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 37

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 38
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 38
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 39
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 39
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 40

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 41

Find the equation of the tangents to
the curve
3x2 – y2 = 8, which passes through the point (4/3, 0).

Solution 41

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And NormalsRd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Chapter 16 – Tangents and Normals Exercise Ex. 16.3

Question 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 1
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 2
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 3
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 4
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 5
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 6
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 7
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 8
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 9

Find the angle of intersection of
the following curves:

Y = 4 – x2 and y = x2

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 10
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 11
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 12
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 13
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 14
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Solution 15
Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals
Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 18

Prove that the curves xy =
4 and x2 + y2 = 8 touch each other.

Solution 18

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 19

Prove that the curves y2 = 4x and x2
+ y2 – 6x + 1 = 0 touch each other at the point (1, 2)

Solution 19

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 20

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 21

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 22

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 23

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Chapter 16 – Tangents and Normals Exercise Ex. 16VSAQ

Question 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 1

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 2

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 3

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 4

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 5

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 6

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 7

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 8

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 9

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 10

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 11

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 12

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 13

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 14

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 15

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 16

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 17

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Chapter 16 – Tangents and Normals Exercise MCQ

Question 1

The equation to the normal to the curve y = sin x at (0,0) is

  1. x = 0
  2. y = 0
  3. x + y = 0
  4. x – y = 0
Solution 1

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 2

The equation of the normal to the curve y = x + sin x cos x at x = π/2 is

  1. x = 2
  2. x = π
  3. x + π = 0
  4. 2x = π
Solution 2

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 3

The equation of the normal to the curve y = x (2-x) at the point (2,0) is

  1. x – 2y = 2
  2. x – 2y + 2 = 0
  3. 2x + y = 4
  4. 2x + y – 4 = 0
Solution 3

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 4

The point on the curve y2 = x where tangent makes 45° angles with x-axis is

  1. (1/2,1/4)
  2. (1/4,1/2)
  3. (4,2)
  4. (1,1)
Solution 4

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 5

If the tangent to the curve x = at2, y=2at is perpendicular to x-axis , then its point of contact is

  1. (a, a)
  2. (0, a)
  3. (0, 0)
  4. (a, 0)
Solution 5

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 6

The point on the curve y = x2 – 3x + 2 where tangent is perpendicular to y = x is

  1. (0,2)
  2. (1,0)
  3. (-1,6)
  4. (2,-2)
Solution 6

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 7

The point on the curve y2 = x where tangent makes 45° angle with x-axis is

  1. (1/2,1/4)
  2. (1/4,1/2)
  3. (4,2)
  4. (1,1)
Solution 7

Correct option:(b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 8

The point on the curve y = 12x – x2 where the slope of the tangent is zero will be

  1. (0,0)
  2. (2,16)
  3. (3,9)
  4. (6,36)
Solution 8

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 9

The angle between the curves y2 = x and x2 = y at (1,1) is

 Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Solution 9

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 10

The equation of the normal to the curve 3x2 – y2 = 8 which is parallel to x + 3y = 8 is

  1. x – 3y = 8
  2. x – 3y + 8 = 0
  3. x + 3y ± 8 = 0
  4. x + 3y = 0
Solution 10

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 11

The equation of tangent at those points where the curve y = x2 – 3x + 2 meets x-axis are

  1. x – y + 2 = 0 = x – y – 1
  2. x + y – 1 = 0 = x – y – 2
  3. x – y – 1 = 0 = x – y
  4. x – y = 0 = x + y
Solution 11

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 12

The slope of tangent to the curve x = t2 + 3t – 8, y = 2t2 – 2t – 5 at point (2,-1) is

  1. 22 /7
  2. 6/7
  3. -6
  4. 7/6
Solution 12

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 13

The what points 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)
Solution 13

Correct option: (d)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 14

The angle of intersection of the curves xy = a2 and x2 – y2 = 2a2 is

  1. 45°
  2. 90°
  3. 30°
Solution 14

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 15

If the curve ay + x2 = 7 and x3 = y cut orthogonally at (1,1), then a is equal to

  1. 1
  2. -6
  3. 6
  4. 0
Solution 15

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 16

If the line y = x touches the curve y = x2 + bx + c at a point (1,1) then

  1. b = 1, c = 2
  2. b =-1, c = 1
  3. b = 2, c = 1
  4. b = -2, c = 1
Solution 16

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 17

The slope of the tangent to the curve x = 3t2 + 1, y = t3-1 at x = 1 is

  1. 1/2
  2. 0
  3. -2
Solution 17

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 18

The curves y = aex and y = be-x cut orthogonally, if

  1. a = b
  2. a = -b
  3. ab = 1
  4. ab =2
Solution 18

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 19

The equation of the normal to the curve x = a cos3θ, y = a sin3θ at the point θ = π/4 is

  1. x = 0
  2. y = 0
  3. x = y
  4. x + y = a
Solution 19

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 20

If the curves y = 2 ex and y = ae-x intersect orthogonally, then a =

  1. 1/2
  2. -1/2
  3. 2
  4. 2e2
Solution 20

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 21

The point on the curve y = 6x – x2 at which the tangent to the curve is inclined at π/4 to the line x + y = 0

  1. (-3,-27)
  2. (3,9)
  3. 7/2, 35/4
  4. (0,0)
Solution 21

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 22

The angle of intersection of the parabolas y2 = 4 ax and x2 = 4ay at the origin is

  1. π/6
  2. π/3
  3. π/2
  4. π/6
Solution 22

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 23

The angle of intersection of the curve y = 2 sin2 x and y = cos 2 x at x Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

  1. π/4
  2. π /2
  3. π /3
  4. π /6
Solution 23

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 24

Any tangent to the curve y = 2x7 + 3x + 5

  1. is parallel to x-axis
  2. is parallel to y -axis
  3. makes an acute angle with x- axis
  4. makes an obtuse angle with x -axis
Solution 24

Correct option: (c)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 25

The point on the curve 9y2 = x3, where the normal to the curve makes equal intercepts with the axis is

  1. (4, ±8/3)
  2. (-4, 8/3)
  3. (-4,-8/3)
  4. (8/3,4)
Solution 25

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 26

The slope of the tangent to the curve x = t2 + 3t – 8, y = 2t2 – 2t – 5 at the point (2,-1) is

  1. 22/7
  2. 6/7
  3. 7/6
  4. -6/7
Solution 26

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 27

The line y = mx + 1 is a tangent to the curve y2 = 4x, if the value of m is

  1. 1
  2. 2
  3. 3
  4. 1/2
Solution 27

Correct option: (a)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 28

The normal at the point (1,1) on the curve 2y + x2 = 3 is

  1. x + y = 0
  2. x – y = 0
  3. x + y +1 = 0
  4. x – y = 1
Solution 28

Correct option: (b)

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

Question 29

The normal to the curve x2 = 4y passing through (1,2) is

  1. x + y = 3
  2. x – y = 3
  3. x + y = 1
  4. x – y = 1
Solution 29

Rd-sharma Solutions Cbse Class 12-science Mathematics Chapter - Tangents And Normals

 

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