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TG EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

APEAPCET Mathematics MCQs

APEAPCET Mathematics MCQs (191-200)

191. The equation of a pair of straight lines passing through the origin is given by:

A) \( ax^2 + by^2 + 2hxy = 0 \)
B) \( ax^2 + by^2 - 2hxy = 0 \)
C) \( ax^2 + by^2 + hxy = 0 \)
D) \( ax^2 + by^2 - hxy = 0 \)

Answer: B) \( ax^2 + by^2 - 2hxy = 0 \)

192. The condition for two lines to be perpendicular is:

A) \( h^2 = ab \)
B) \( h = 0 \)
C) \( h^2 = -ab \)
D) \( h = ab \)

Answer: C) \( h^2 = -ab \)

193. The angle between the pair of lines \( ax^2 + by^2 - 2hxy = 0 \) is given by:

A) \( \tan \theta = \frac{2\sqrt{h^2 - ab}}{a + b} \)
B) \( \tan \theta = \frac{\sqrt{h^2 - ab}}{a + b} \)
C) \( \tan \theta = \frac{2\sqrt{a^2 + b^2}}{h} \)
D) \( \tan \theta = \frac{h}{a + b} \)

Answer: A) \( \tan \theta = \frac{2\sqrt{h^2 - ab}}{a + b} \)

194. The equation of a circle with a given line segment as the diameter is:

A) \( x^2 + y^2 = r^2 \)
B) \( (x - h)^2 + (y - k)^2 = r^2 \)
C) \( (x - x_1)(x - x_2) + (y - y_1)(y - y_2) = 0 \)
D) \( (x - x_1)(x - x_2) + (y - y_1)(y - y_2) = r^2 \)

Answer: D) \( (x - x_1)(x - x_2) + (y - y_1)(y - y_2) = r^2 \)

195. The parametric equations of a circle \( x^2 + y^2 = r^2 \) are:

A) \( x = r \cos \theta, y = r \sin \theta \)
B) \( x = r \sin \theta, y = r \cos \theta \)
C) \( x = \cos \theta, y = \sin \theta \)
D) \( x = r \cos \theta, y = r \cos \theta \)

Answer: A) \( x = r \cos \theta, y = r \sin \theta \)

196. The length of the tangent from a point \( P(x_1, y_1) \) to a circle \( x^2 + y^2 = r^2 \) is:

A) \( \sqrt{x_1^2 + y_1^2 - r^2} \)
B) \( \sqrt{x_1^2 + y_1^2 + r^2} \)
C) \( \sqrt{r^2 - x_1^2 - y_1^2} \)
D) \( \sqrt{x_1^2 + y_1^2} \)

Answer: A) \( \sqrt{x_1^2 + y_1^2 - r^2} \)

197. The equation of the tangent to a circle \( x^2 + y^2 = r^2 \) at the point \( P(x_1, y_1) \) is:

A) \( xx_1 + yy_1 = r^2 \)
B) \( xx_1 + yy_1 = 0 \)
C) \( x^2 + y^2 = r^2 \)
D) \( x_1^2 + y_1^2 = r^2 \)

Answer: A) \( xx_1 + yy_1 = r^2 \)

198. The equation of the normal to the circle \( x^2 + y^2 = r^2 \) at the point \( P(x_1, y_1) \) is:

A) \( x_1 x + y_1 y = r^2 \)
B) \( x x_1 + y y_1 = r^2 \)
C) \( x_1^2 + y_1^2 = r^2 \)
D) \( x^2 + y^2 = r^2 \)

Answer: B) \( x x_1 + y y_1 = r^2 \)

199. The equation of the pair of tangents drawn from an external point \( P(x_1, y_1) \) to a circle \( x^2 + y^2 = r^2 \) is:

A) \( x_1x + y_1y = r^2 \)
B) \( x_1x + y_1y = 0 \)
C) \( x_1^2 + y_1^2 - r^2 = 0 \)
D) \( x_1^2 + y_1^2 = r^2 \)

Answer: A) \( x_1x + y_1y = r^2 \)

200. The relative position of two circles with equations \( x^2 + y^2 = r_1^2 \) and \( (x - h)^2 + (y - k)^2 = r_2^2 \) is determined by:

A) \( \sqrt{h^2 + k^2} = r_1 + r_2 \) for external tangency
B) \( \sqrt{h^2 + k^2} = r_1 - r_2 \) for internal tangency
C) Both A and B
D) \( \sqrt{h^2 + k^2} > r_1 + r_2 \)

Answer: C) Both A and B

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TG EAMCET (EAPCET) Mathematic Multiple Choice Questions (MCQs)

APEAPCET Mathematics MCQs (191-200)

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