Tangents and Normals, Class 12 Mathematics NCERT Solutions

1. There will be total 10 MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying

1. Find slope of normal to the curve y=5x²-10x + 7 at x=1

 not defined

 -1

 1

 zero

Question 1 of 10

2. The equation of the tangent line to the curve y = which is parallel to the line 4x -2y + 3 = 0 is

  80x +40y – 193 = 0

  4x – 2y – 3 = 0

 80x – 40y + 103 = 0

 80x – 40y – 193 = 0

Question 2 of 10

3. Find the equation of tangent to which has slope 2.

 2x – y = 1

 No tangent

  y – 2x = 0

 y – 2x = 3

Question 3 of 10

4. If y = – sin2x. Find the values of x at which the tangents drawn to the graph of this function is parallel to the x- axis.

 A

 B

 C

 D

Question 4 of 10

5. The normal at any point q to the curve x = a (cos q + q sin q), y = a (sin q – q cos q)
is at distance from the origin that is equal to… .

  a

 2a

 4a

 3a

Question 5 of 10

6. The equation of the normal to the curve x² = 4y which passes through the point (1, 2) is.

 x + y – 3 = 0

 4x – y = 2

 4x – 2y = 0

 4x – 3y + 2= 0

Question 6 of 10

7. The curve y = ax³ + bx² + cx + 5 touches the x-axis at P(-2, 0) and cuts the y-axis at the point Q where its gradient is 3. the equation of the curve is… .

 A

 B

 C

 D

Question 7 of 10

8. The condition that the curves ax² + by² = 1 …..(i)
and a’x² + b’y² = 1 …(ii) Should intersect orthogonally is…… .

 A

 B

 C

 D

Question 8 of 10

9. The equation of tangent to the curve y = x³ + 2x + 6 which is perpendicular to the line x + 14y + 4 = 0 is :

 14x- y + 18 = 0

 14x -y + 1= 0

 14x- y + 22 = 0

 14x – y + 5 = 0

Question 9 of 10

10. The equations of the tangents drawn to the curve y² – 2x³ – 4y + 8 = 0 from the point (1, 2) is… .

 A

 B

 C

 D

Question 10 of 10

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