SATHEE: Circle 1 Question 23

Circle 1 Question 23

23. The straight line $2 x - 3 y = 1$ divide the circular region $x^{2} + y^{2} \leq 6$ into two parts. If $S = 2, \frac{3}{4}, \frac{5}{2}, \frac{3}{4}, \frac{1}{4}, - \frac{1}{4}, \frac{1}{8}, \frac{1}{4}$ , then the number of point (s) in $S$ lying inside the smaller part is … .

Paragraph Based Questions

Let $S$ be the circle in the $X Y$ -plane defined by the equation

$x^{2} + y^{2} = 4$

(2018 Adv.)

(There are two questions based on above Paragraph, the question given below is one of them)

Show Answer

Answer:

Correct Answer: 23. (2)

Solution:

$x^{2} + y^{2} \leq 6$ and $2 x - 3 y = 1$ is shown as

For the point to lie in the shade part, origin and the point lie on opposite side of straight line $L$ .

$∴$ For any point in shaded part $L > 0$ and for any point inside the circle $S < 0$ .

Now, for $2, \frac{3}{4} L : 2 x - 3 y - 1$

$L : 4 - \frac{9}{4} - 1 = \frac{3}{4} > 0$

and $S : x^{2} + y^{2} - 6, S : 4 + \frac{9}{16} - 6 < 0$

$\Rightarrow 2, \frac{3}{4}$ lies in shaded part.

For $\frac{5}{2}, \frac{3}{4}, L : 5 - 9 - 1 < 0$

[neglect]

For $\frac{1}{4}, - \frac{1}{4}, L : \frac{1}{2} + \frac{3}{4} - 1 > 0$ $∴ \frac{1}{4}, - \frac{1}{4}$ lies in the shaded part.

For $\frac{1}{8}, \frac{1}{4}, L : \frac{1}{4} - \frac{3}{4} - 1 < 0$

[neglect]

$\Rightarrow$ Only 2 points lie in the shaded part.

Circle 1 Question 23

23. The straight line $2 x - 3 y = 1$ divide the circular region $x^{2} + y^{2} \leq 6$ into two parts. If $S = 2, \frac{3}{4}, \frac{5}{2}, \frac{3}{4}, \frac{1}{4}, - \frac{1}{4}, \frac{1}{8}, \frac{1}{4}$ , then the number of point (s) in $S$ lying inside the smaller part is … .

Paragraph Based Questions

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

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Syllabus

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Sample Mock Test

Mentorship

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Circle 1 Question 23

23. The straight line 2x−3y=1 divide the circular region x2+y2≤6 into two parts. If S=2,34,52,34,14,−14,18,14, then the number of point (s) in S lying inside the smaller part is … .

Paragraph Based Questions

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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23. The straight line $2 x - 3 y = 1$ divide the circular region $x^{2} + y^{2} \leq 6$ into two parts. If $S = 2, \frac{3}{4}, \frac{5}{2}, \frac{3}{4}, \frac{1}{4}, - \frac{1}{4}, \frac{1}{8}, \frac{1}{4}$ , then the number of point (s) in $S$ lying inside the smaller part is … .