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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E1: a + b + c = 0 if 1 is a root of ax2 + bx + c = 0E2: b2 - a2 = 2ac if sinθ, cosθ are the roots of ax2 + bx + c = 0Which of the following is true

  

  

  

  

The angle of elevation of an object from a point P on the level ground is α. Moving d metres on the ground towards the object, the angle of elevation is found to be β. Then the height (in metres) of the object is

  

  

  

  

The inverse point of (1, 2) with respect to the circle x2 + y2 - 4x - 6y +9 = 0 is

  

  

  

  

Suppose    A, B    are    two    points    on 2x-y + 3=0  and  P(l, 2)  is such  that PA = PB. Then the mid-point of AB is :

  

  

  

  

The radius of a circle plate is increasing at the rate of  0.01 cm/s when the radius is at 12 cm . then the rate at which the area increases 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 Cos (A-B) =  3/5 and tan A tan B  = 2 then which one of the following is true

  

  

  

  

If x > 0, x y = ex - y , then dy/dx is equal to :

  

  

  

  

The function f : c → c defined by  f(x) = (ax+b) / (cx+d) for x ε c where bd ≠ 0 reduces to a constant function, if

  

  

  

  

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

  

  

  

  

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

  

  

  

  

2 tan h -1 1/2  is equal to

  

  

  

  

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

  

  

  

  

If the lines x2 + 2xy – 35y2 - 4x + 44y -12=0 and 5x +λy -8 = 0 are concurrent, then the value of λ is

  

  

  

  

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 one root of the quadratic equation ax2+bx+c=0 is 3-4i, then a+b+c is :

  

  

  

  

The angle between the line joining the points (1, - 2), (3, 2) and the line x + 2y - 7 = 0 is

  

  

  

  

The condition f(x) = x3 + px2 + qx + r (xЄR) to have no extreme value, is

  

  

  

  

If θ lies in the first quadrant and 5 tan θ = 4 then (5 sin θ  -  3 cos θ) / (sin θ + 2 cos θ) is equal to

  

  

  

  

If a polygon of n sides has 275 diagonals, then n is equal to

  

  

  

  

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

  

  

  

  

If a, b c are in AP,    b- a, c - b and a are in GP, then a: b: c is

  

  

  

  

Observe the statements given below : Assertion (A) : f (x) = xe-x has the maximum at x = 1Reason (R) :  f’(1)= 0 and f” (1) < 0 Which of the following is correct

  

  

  

  

If cosh-1 x = loge (2+√3), then x is equal to

  

  

  

  

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

  

  

  

  

The centre of the circle r2 - 4r (cosθ + sin θ) - 4 = 0 in cartesian coordinates is :

  

  

  

  

If f(x) = 10 cos x +(13+2x) sin x then f"(x) + f(x) is equal to

  

  

  

  

The number of circles that touch all the three lines x + y-l = 0, x-y-l=0 and y + 1 = 0 is :

  

  

  

  

The four distinct points (0, 0), (2, 0), (0, - 2) and (k, - 2) are concylic, if k is equal to

  

  

  

  

If ΔABC is right angled at A, then r2 + r3 is equal to

  

  

  

  

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