TG EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)
TG EAMCET Mathematics - MCQs (Serial No. 201 to 210)
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201. The angle between two intersecting circles is given by:
- A) \( \cos \theta = \frac{r_1 r_2}{d^2} \)
- B) \( \cos \theta = \frac{r_1^2 + r_2^2 - d^2}{2r_1 r_2} \)
- C) \( \sin \theta = \frac{r_1 + r_2}{d} \)
- D) \( \tan \theta = \frac{r_1}{r_2} \)
Answer: B) \( \cos \theta = \frac{r_1^2 + r_2^2 - d^2}{2r_1 r_2} \)
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202. The condition for orthogonality of two circles is:
- A) \( r_1^2 + r_2^2 = d^2 \)
- B) \( r_1^2 - r_2^2 = d^2 \)
- C) \( r_1^2 + r_2^2 = 2d^2 \)
- D) \( r_1^2 - r_2^2 = 2d^2 \)
Answer: A) \( r_1^2 + r_2^2 = d^2 \)
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203. The radical axis of two circles is:
- A) The line joining the points of intersection of the circles
- B) Perpendicular to the line joining the centers of the circles
- C) The line equidistant from the two centers
- D) The line joining the centers of the circles
Answer: B) Perpendicular to the line joining the centers of the circles
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204. The common chord of two intersecting circles:
- A) Lies on the radical axis of the circles
- B) Passes through the centers of the circles
- C) Is perpendicular to the line joining the centers
- D) Is parallel to the radical axis
Answer: A) Lies on the radical axis of the circles
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205. The radical center of three circles is:
- A) The point of intersection of their radical axes
- B) The point where the three centers coincide
- C) The point equidistant from the three centers
- D) The point of tangency of the common tangents
Answer: A) The point of intersection of their radical axes
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206. The equation of a parabola in standard form is:
- A) \( y^2 = 4ax \)
- B) \( x^2 = 4ay \)
- C) \( x^2 = 4a(y - k) \)
- D) \( y^2 = 4a(x - h) \)
Answer: A) \( y^2 = 4ax \)
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207. The parametric equations of a parabola \( y^2 = 4ax \) are:
- A) \( x = at^2, y = 2at \)
- B) \( x = 2at^2, y = at \)
- C) \( x = 2at, y = at^2 \)
- D) \( x = at^2, y = at \)
Answer: A) \( x = at^2, y = 2at \)
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208. The equation of the tangent to a parabola \( y^2 = 4ax \) at the point \( (x_1, y_1) \) is:
- A) \( y y_1 = 2a(x + x_1) \)
- B) \( y y_1 = 2a(x - x_1) \)
- C) \( x x_1 = 2a(y + y_1) \)
- D) \( x x_1 = 2a(y - y_1) \)
Answer: B) \( y y_1 = 2a(x - x_1) \)
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209. The equation of the normal to the parabola \( y^2 = 4ax \) at the point \( (x_1, y_1) \) is:
- A) \( y - y_1 = \frac{a}{y_1}(x - x_1) \)
- B) \( y - y_1 = -\frac{a}{y_1}(x - x_1) \)
- C) \( y + y_1 = \frac{a}{x_1}(x - x_1) \)
- D) \( y + y_1 = -\frac{a}{x_1}(x - x_1) \)
Answer: A) \( y - y_1 = \frac{a}{y_1}(x - x_1) \)
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210. The equation of the ellipse in standard form is:
- A) \( x^2 + y^2 = r^2 \)
- B) \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)
- C) \( x^2 + y^2 = 1 \)
- D) \( \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1 \)
Answer: B) \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \)
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