Eamcet - Maths - Geometry Test

Test Instructions :

1. The Test is 1hr duration.
2. The Test Paper consists of 30 questions. The maximum marks are 30.
3. All the questions are multiple choice question type with three options for each question.
4. Out of the three options given for each question, only one option is the correct answer.
5. Each question is allotted 1 mark for each correct response.
6. 0.25 will be deducted for incorrect response of each question.
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The equation of the circle which passes through the origin and cuts orthogonally each of the circles x2 + y2 -6x+ 8 = 0 and x2 + y2 - 2x - 2y = 7 is

  

  

  

  

sec h-1 (sin θ) is equal to

  

  

  

  

For all integers n ≥ 1, which of the following is divisible by 9

  

  

  

  

An unbiased coin is tossed to get 2 points for turning up a head and one point forthe tail. If three unbiased coins are tossed simultaneously, then the probability ofgetting a total of odd number of points is:

  

  

  

  

If ( x - 2 ) is a common factor of the expressions x2 + ax + b and x2 +cx+ d, then b-d/c-a is equal to :

  

  

  

  

Suppose E and F are two events of a random experiment. If the probability of occurrence of E is 1/5 and the probability of occurrence of F given E is 1/10, then the probability of non-occurrence of at least one of the events E and F is :

  

  

  

  

If nεN, and the period of [cosnx/sin(x/n)] is 4π, then n is equal to

  

  

  

  

sin -1(4/5) + 2 tan -1(1/3)  is equal to

  

  

  

  

Box A contains 2 black and 3 red balls, while Box B contains 3 black and 4 red balls. Out of these two boxes one is selected at random; and the probability of choosing Box A is double that of Box B. If a red ball is drawn from the selected box, then the probability that it has come from Box B, is

  

  

  

  

The point (3, -4) lies on both the circles x 2 + y2 - 2x + 8y + 13 = 0 and x2  + y2  - 4x + 6y + 11 = 0. Then the angle between the circles is

  

  

  

  

If 2x2-3xy+y2+x+2y-8 = 0, then dy/dx =

  

  

  

  

If the equations x2+ax+b=0 and x2+bx+a=0 (a≠b) have a common root, then a+b is equal to

  

  

  

  

Two consecutive sides of a parallelogram are 4x + 5y = 0 and 7x + 2y = 0. If the equation to one diagonal is 11x  + 7y = 9, then the equation of the other diagonal is:

  

  

  

  

If Q denotes the set of all rational numbers and f(p/q) = (p2 - q2)1/2 for any p/q belongs to R  then observe the following statementsI.f(p/q) is real for each p/q belongs to QII..f(p/q) is complex number for each p/q belongs to QThen which of the following is correct

  

  

  

  

Six faces of an unbiased die are numbered with 2, 3, 5, 7, 11 and 13. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is :

  

  

  

  

If three points A, B and C have position vectors (1, x, 3), (3, 4, 7) and (y, -2, -5) respectively and if they are collinear then (x, y) is equal to

  

  

  

  

If m and M respectively denote the minimum and maximum of f(x) = (x - 1)2+ 3 for x ε [ -3, 1], then the ordered pair (m, M) is equal to

  

  

  

  

If PM is the perpendicular from P (2, 3) onto the line x + y = 3, then the co-ordinates of M are

  

  

  

  

The roots of the equation x3 - 3x - 2 = 0 are

  

  

  

  

The solution of dy/dx = y2 / (xy - x2) is

  

  

  

  

A cylindrical vessel of radius 0.5mts. is filled with oil at the rate of 0.25 π.c mts./minute. The rate, at which the surface of oil is increasing is

  

  

  

  

If y = 3x is a tangent to a circle with centre (1,1), then the other tangent drawn through (0, 0) to the circle is

  

  

  

  

The area (in square unit) of the triangle formed by   the   points   with   polar   coordinates (1,0) , (2 , π/3)and (3, 2π/3)

  

  

  

  

The area (in square units) bounded by the curves y2 = 4x and x2 = 4y in the plane is :

  

  

  

  

One of the foci of hyperbola id origin and the corresponding directrix is 3x+4y+1=0.The eccentricity of the hyperbola is √5.The equation to the hyperbola is

  

  

  

  

A line l meets the circle x2 + y2 = 61 in A,B and P(-5,6) is such that PA = PB= 10.  Then the equation of l is :

  

  

  

  

If α1,α2,α3  respectively denotes the moduli of the complex number -i , (1+i) / 3  and -1+i  then their increasing order is

  

  

  

  

The image of the point (3,2,1) in the plane 2x - y + 3z= 7 is

  

  

  

  

A point equidistant from the lines 4x+3y=10=0,5x-12y+26=0 and 7x+24y-50=0 is:

  

  

  

  

The equation of the circle whose diameter is the common chord of the circlesx2 + y2 + 2x + 3y + 2 = 0 and x2 + y2 + 2x-4y-4 = 0 is

  

  

  

  

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