# 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)

**Answer**:

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

**Answer**:

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)

**Answer**:

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

**Question 22**:

The equation of the normal to the curve at is:

(A)

(B)

(C)

(D)

**Answer**:

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)

**Answer**:

Therefore, correct answer is B.

### 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________.

**Answer**:

Therefore,

Hence, the values of are .

**Question 25**:

If then its maximum value is ________.

**Answer**:

For to be maximum, should be minimum i.e.. Hence maximum value of .