Eamcet - Maths 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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If α and β are the roots of the equation ax2 + bx + c = 0 and, if px2 + qx + r = 0 has roots (1-α)/ α  and (1-β) / β, then r is equal to

  

  

  

  

The first three terms in the expansion of (1+x+x2)10 are

  

  

  

  

The length of the tangent from the point (-1, 1) to the circle x2+y2-4x+k=0 is equal to 2 then k=

  

  

  

  

If AB=2a+b and AD=a-2b where |a|=1, |b|=1 and (a, b)=600 are the adjacent sides of a parallelogram, then the length of the diagonal BD is

  

  

  

  

The locus of the centre of the circles which touché both the circles x2+y2=a2 and x2+y2=4ax externally has the equation

  

  

  

  

The equation of the line passing through the point (2, -3), and parallel to 3x-4y+7=0 is

  

  

  

  

The asymptotes of a hyperbola are parallel to 2x + 3y = O and 3x+2y=0.  Its centre is at (1,  2) and it  passes through the point (5, 3).  Its equation is

  

  

  

  

The polar of the point(t-1, 2t) w.r.t the circle x2+y2-4x-6y+4=0 passes through the point of intersection of the lines

  

  

  

  

The harmonic mean of the roots of the equation (5+√2)x2-(4+√5)x+8+2√5)=0 is

  

  

  

  

d/dx{Tan-1(x-√x/1+x3/2}=

  

  

  

  

d/dx{cos[2 sin-1(cos x)]}=

  

  

  

  

The period of sin(x+4x+9x+...+n2x) is

  

  

  

  

The area bounded by the curve y=x(x-1)2,y-axis and the line y=2 is

  

  

  

  

If x is real, the maximum value of 3x2+9x+17/3x2-9x+17 is

  

  

  

  

The point on the parabola y = x2 + 7x + 2 closest to the line y = 3x – 3 is

  

  

  

  

If f(x)= x(√x-√(x+1)) then

  

  

  

  

The point collinear with (1,-2,-3) and (2,0, 0) among the following is

  

  

  

  

The modules of (3+2i)(2-i)/ (1+i) is

  

  

  

  

If the points whose position vectors are 2i+j+k, 6i-j+2k and 14i-5j+pk are  collinear, then the value of p is

  

  

  

  

P and Q are two points on the line x-y+1=0. If OP=OQ=6 then length of median of Δ OPQ through O is

  

  

  

  

The number of non-zero terms in the expansion of (1+3√2x)9+(1+3√2x)9is equal to:

  

  

  

  

The domain of Cos-1(2x-3)+√9-4x2 is

  

  

  

  

If α, β are the roots of ax2-bx+c=0 then α3β3 +α2β3 + α3β2=

  

  

  

  

If |a+b|2=|a|2+|b|2 then the angle between a and b is

  

  

  

  

If b2-4ac>0,then the graph of y= ax2+bx+c

  

  

  

  

If x2+y2+z2≠0,x=cy+bz,y=az+cx,z=bx+ay then a2+b2+c2+2abc=

  

  

  

  

If the pair of straight lines xy - x - y + l = 0 and the line ax + 2y - 3a = 0 are concurrent, then a is equal to

  

  

  

  

The line y =2x + k is a normal to the parabola y2= 4x,then=

  

  

  

  

A gas holders contain 100 cubic ft of gas at a pressure of 5 lb per sq. inch. If the pressure is increasing at the rate of 0.05 lb per sq. inch per hour, then the rate of decrease of the volume assuming Boyle’s law pv=a constant is

  

  

  

  

Consider the circle x2+y2-4x-2y+c=0 whose centre is A(2, 1). If the point P(10, 7) is such that the line segment PA meets the circle in Q with PQ=5, then c=

  

  

  

  

The value of a for which the equation (1-a2)x2+2ax-1=0 has roots belonging to(0,1) is

  

  

  

  

The equation of the circle passing through the intersection of the circles x2+y2=2ax and x2+y2=2by and having its centre on the x/a-y/b=2 is

  

  

  

  

If y= xsin x+(sin x)x then dy/dx=

  

  

  

  

If x is real,then the maximum value of the expression 5+4x-4x2 is

  

  

  

  

The two circles x2+y2+2ax+2by+c=0 and x2+y2+2bx+2ay+c=0 have three real common tangents, then

  

  

  

  

The locus of the point  of intersection of tangents to the parabola y2 = 4(x + 1) and y2 = 8(x+2) which are perpendicular to each other is

  

  

  

  

For all values of a and b(a + 2b)x + (a- b)y + (a + 5b) = 0 passes through the point:

  

  

  

  

If 2x2+mxy+3y2-5y-2 can be resolvable into two linear factors then m=

  

  

  

  

The condition that the pair of tangents drawn from the origin to the circle x2+y2+2gx+2fy+c=0 may be at right angles is

  

  

  

  

The solution of (dy/dx)+y=1 is

  

  

  

  

sin (θ/2)sin (7θ/2)+sin(3θ/2). Sin(11θ/2)- sin 2θsin 5θ=

  

  

  

  

If one ticket is randomly selected from, tickets numbered from 1to 30 then the probabilitythat the numbered on the tickets i a multiple of 5 or 7 is

  

  

  

  

If P is appoint on the line passing through A(3i+j-k) and parallel to 2i-j+2k such that AP=15 then position vector of P is

  

  

  

  

A number consists of two digits whose product is 30.If the digits are interchanged the resulting numbers will exceed the previously by 9.The number is

  

  

  

  

If the roots of a(b-c)x2+b(c-a)x+c(a-b)=0 are equal,then a,b,c are in

  

  

  

  

If A+B+C=1800 then sin2A- sin2 B- sin2 C=

  

  

  

  

The number of common tangents to the circles x2+y2+2x+8y-23=0, x2+y2-4x-10y+19=0 is

  

  

  

  

If the circles (x+a) 2+(y+b) 2=a2,(x+α) 2+(y+β) 2=β2 cut orthogonally then α2+b2=

  

  

  

  

The lines 2x+y-1=0, ax+3y-3=0, 3x+2y-2=0 are concurrent

  

  

  

  

If the product of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 2,then k=

  

  

  

  

If two roots of x4-16x3+86x2-176x+105=0 are 1,7 then the roots are

  

  

  

  

If the area of the triangle formed by the pair of lines 8x2-6xy+y2=0 and the line 2x + 3y = a is 7 then

  

  

  

  

A rod of 10 feet long moves with its ends A and B always on the axes of x and y respectively. If A is 8ft from the origin and is moving away at the rate of 2ft per second. At what rate the area formed by AB and the axes changing …?

  

  

  

  

For the circle x2+y2-6x-6y+5=0 the lines 3x+y-2=0, x+7y-11=0 are

  

  

  

  

The equation of the axis of the parabola 3x2 – 9x + 5y -2 = 0 is

  

  

  

  

The area of the triangle formed by the polar of (1,2) with respect to the circle 2x2+2y2-3x=0 and the coordinate axes (in square units) is

  

  

  

  

The equation of the auxiliary circle of x2/16-y2/25=1 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 centre of the circumscribing the quadrilateral whose sides are 3x+y=22, x-3y=14 and 3x+ y=62 is

  

  

  

  

S1, S2,....., S10 are the speakers in a conference. If S1 addresses only after S2, then the number of ways the speakers address is :

  

  

  

  

If -3,1,8 are the roots of px3+qx2+rx+s=0 then the roots of p(x-3)3+q(x-3)2+r(x-3)+s=0 are

  

  

  

  

The odds against an event is 5 to 2 and the odds in favour of another disjoint event are 3 to 5. Then the probability that one at least of the event will happen is

  

  

  

  

If 6 Sec2 θ-5 Sec θ+1=0 then θ=

  

  

  

  

The equation of the straight line passing through the intersection of x+2y-19=0, x-2y-3=0 and at a distance of 5 unit from (-2, 4) is

  

  

  

  

If α,β,γ are the roots of the equation x3-7x+7=0,then the value of α-4+β-4+γ-4 is

  

  

  

  

The portion of the tangent drawn at any point on x2/3+y2/3=a2/3 (a>0), except the points on the coordinate axes, included between the coordinate axes is

  

  

  

  

The value of ‘α’ for which the equations x+y+z=1,x+2y+4z=α and x+4y+10z=α2have no solution, is

  

  

  

  

If f(x,y)=xy+(1/x)+(1/y) then fxx?fyy-fxy2 at (1,1) is

  

  

  

  

The length of the side of the square formed by the lines 2x2+3xy-2y2=0, 2x2+3xy-2y2+3x-5y+1=0 is

  

  

  

  

If ax2+2hxy+by2=1 then (hx+by)3y2=

  

  

  

  

If the range of a random variable X is {0, 1, 2, 3, 4,........} with P(X = k) = (k+1)a / 3k for k ≥ 0 then a is equal to

  

  

  

  

The function f(x) =√25-4x2 is decreasing in

  

  

  

  

The solution of 3excos2ydx+(1-ex)cot y dy=0 is

  

  

  

  

If α,β,γ are the roots of x3 - 2x2 + 3x - 4 = 0, then the value of α2β2 + β2γ2+ γ2 α2 is

  

  

  

  

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

  

  

  

  

The domain of 1/√[x]2-[x]-6 is

  

  

  

  

Sum of n brackets of (1)+(1/3+1/32)+(1/33+1/34+1/35)+…. Is

  

  

  

  

(1/1.3)+(1/2.5)+(1/3.7)+(1/4.9)+……..=

  

  

  

  

cos 240 cos 480 cos 960 cos 1680 =

  

  

  

  

Number of spheres drawn through the points(0,0,0),(1,0,0),(0,1,0),(1,1,0) are

  

  

  

  

If one root of x2+px+1=0 is square that of the order,then p=

  

  

  

  

If sin α+ sin β= a, cos α+ cos β = b then sin(α+β)=

  

  

  

  

If x,a,b,c are real and (x-a+b)2+(x-b+c)2=0 then a,b,c are in

  

  

  

  

If two of the roots of 2x3-3x2-3x+2=0 are differ by 3 then the roots are

  

  

  

  

The locus of the poles of chords of  the ellipse x2/a2+y2/b2=1 which touch The locus of the poles w.r.t the ellipse x2/α2+y2/β2=1 is

  

  

  

  

The parametric equation of the circle x2+y2+x+√3y=0 is

  

  

  

  

A box contains 10 mangoes out of which 4 are rotten. Two mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is

  

  

  

  

If the circle x2+y2+6x+8y+a = 0 bisects the circumference of the circle x2+y2+2x-6y-b=0,then a+b is equal to

  

  

  

  

cos4 π/8+ cos4 3π/8+ cos4 5π/8+ cos4 7π/8=

  

  

  

  

If (1, a), (b, 2) are conjugate points with respect to the circle x2 + y2 = 25, then4a + 2b is equal to :

  

  

  

  

The equation of the normal to the curve y=3x2+4x-6 at (1, 1) is

  

  

  

  

d/dx{Tan-1(x/1-√1-x2)}=

  

  

  

  

4(cos3 100 +sin32 00) =

  

  

  

  

In ΔABC , if a=7, b=7√3 and right angled at C, then c=

  

  

  

  

If the sum of the squares of the roots of the equation x2-(sin α-2)x-(1+sin α)=0 is least,then α=

  

  

  

  

For the circle x2+y2-6x+8y-1=0, the points (2, 3) (-2, -1) are

  

  

  

  

If y = e-12x Cos (5x+2) then yx =

  

  

  

  

The locus of midpoint of the chord of the ellipse x2/a2+y2/b2=1 which pass through the fixed point  (h, k) is

  

  

  

  

The stability of hydrides increase from NH3 to BiH3 in group 15 of the periodic. The area of the region enclosed by the curves y = x, x = e, y =1/x and the

  

  

  

  

The amplitude of 1+cos θ+ i sin θ is

  

  

  

  

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