# NCERT Class 12-Mathematics: Chapter – 6 Application of Derivatives Part 6 (For CBSE, ICSE, IAS, NET, NRA 2023)

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## Objective Type Questions

### Choose the Correct Answer from the Given Four Options in Each of the Following Examples 19 to 23

Question 19:

The abscissa of the point on the curve , the normal at which passes through origin is:

(A)

(B)

(C)

(D)

Let be the point on the given curve at which the normal passes through the origin. Then we have . Again the equation of the normal at passing through the origin gives .

Since satisfies the equation, therefore, Correct answer is (A) .

Question 20:

The two curves and

(A) Touch each other

(B) Cut at right angle

(C) Cut at an angle

(D) Cut at an angle

From first equation of the curve, we have

say and second equation of the curve gives

Since . Therefore, correct answer is (B) .

Question 21:

The tangent to the curve given by makes with axis an angle:

(A)

(B)

(C)

(D)

Therefore, and hence the correct answer is (D) .

Question 22:

The equation of the normal to the curve at is:

(A)

(B)

(C)

(D)

Therefore, slope of normal . Hence the equation of normal is

Therefore, correct answer is (C) .

Question 23:

The point on the curve , where the tangent makes an angle of with axis is

(A)

(B)

(C)

(D)

### Fill in the Blanks in Each of the Following Examples 24 to 29

Question 24:

The values of a for which touches the axis of are________.