### Eamcet - Maths - Geometry Test

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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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