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 value of x, where x > 0 and tan ( sec-1(1/x ) )= sin ( tan-1 2) 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

  

  

  

  

A value of n such that (√3 / 2    +   i / 2  )n  =  1 is

  

  

  

  

The locus of the Z in the argand plane for which |z+1|2+|z-1|2=4, is a

  

  

  

  

The condition for the coaxial system x2 + y2+ 2λx+ c = 0, where λ is a parameter and c is a constant, to have distinct limiting points, is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The Cartesian form of the polar equation θ = tan -1 2 is

  

  

  

  

If N denotes the set of all positive integers and if f:N->N is defined by f(n) = thesum of positive divisors of n then, f (2k, 3), where k is a positive integers is

  

  

  

  

If (1 + x)n = C0 + C1x + C2x2 + …. + CnXn, then C0 - C2 + C4 - C6 + … is equal to:

  

  

  

  

 If dx + dy =(x + y) ( dx- dy ) then log ( x  +  y ) is equal to

  

  

  

  

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

  

  

  

  

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

  

  

  

  

Coefficient of x10 in the expansion of (2 + 3x) e-x is :

  

  

  

  

From a point on the level ground, the angle of elevation of the top of a pole is 300 on moving 20 metres nearer, the angle of elevation is 450. Then the height of the pole (in metres), is:

  

  

  

  

If P1, P2, P3 are the perimeters of the three circles x2 + y2 + 8x - 6y = 0, 4x2 + 4y2 - 4x - 12y - 186 = 0 and x2 + y2 - 6x + 6y - 9 = 0 respectively, then :

  

  

  

  

If 1, ω, ω2 are the roots of unity, then (a + b)3+(aω + bω2)3+(aω2+bω)3 is equal to:

  

  

  

  

Area of the triangle formed by the lines 3x2 - 4 xy + y2 = 0, 2x - y = 6 is :

  

  

  

  

The coefficient of xk in the expansion of  (1-2x-x2) /e-x  is

  

  

  

  

If the direction ratio of two lines are given by l + m + n = 0, nm - 2ln + lm = 0, then theangle between the lines is :

  

  

  

  

A bag X contains 2 white and 3 black balls and another bag Y contains 4 white and 2 black balls.One bag is selected at random and a ball is drawn from it.Then the probability for the ball chosen be white,is

  

  

  

  

The pole of the straight line x+4y = 4 With respect to the ellipse x2 + 4y2 = 4 is

  

  

  

  

 A three digit number  n such that the last two  digits of it are equal and differ from the first the number of such n is

  

  

  

  

The number of circles that touch all the straight lines x + y = 4, x - y = -2 and y = 2 is:

  

  

  

  

The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines x = 0 and y = 0 is  

  

  

  

  

 If x -y+ 1 = 0 meets the circle x2 + y2 + y - 1 = 0 at A and B, then the equation of the circle with AB as diameter is

  

  

  

  

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

  

  

  

  

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 angle between the pair of lines 2x2+5xy+2y2+3x+3y+1=0,is:

  

  

  

  

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