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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The length of the intercept made by the normal at (1,6) of the circle x2+y2-4x-6y+3=0 between the coordinate axes is

  

  

  

  

The The limiting points of the coaxal system x2+y2+2µy+9=0 are

  

  

  

  

The curve y=a2+bx has minimum at (2, -1) on it. Then (a, b)=

  

  

  

  

If (1,2), (4, 3) are the limiting points of a coaxal system , then the equation of the circle in its conjugate system having minimum area is

  

  

  

  

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

  

  

  

  

In ΔABC, R2 (sin 2A+sin 2B+sin 2C)=

  

  

  

  

The length of the chord intercepted bt the parabola y = x2 + 3x  on the line x + y = 5 is

  

  

  

  

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

  

  

  

  

C2+C4+C6+……….. =

  

  

  

  

The number of ways that all the letters of the word SWORD can be arranged such that no letter is in its original position is

  

  

  

  

If ay4=(x+b)5then 5yy2=1

  

  

  

  

The equation whose roots are 2√3-5 and -2√3-5 is

  

  

  

  

One focus of an ellipse is (1,0) and (0,0). If the length of major axis is 6 its e=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If the length of the tangent from (h, k) to the circle x2+y2=16 is twice the length of the tangent from the same point to the circle x2+y2+2x+2y=0, then

  

  

  

  

The odds against A solving a problem are 3 to 2 and the odds in favour of B solving the same problem ae5 to 4.Thenthe probability that the problem will be solved if both of them try the problem is

  

  

  

  

If y = xn-1 log x then xy1-(n-1)y =

  

  

  

  

If a,b,c are three non-collinear points then r=(1-p-q)a+pb+qc represents

  

  

  

  

x2-y2+5x+8y-4=0 represents

  

  

  

  

The coefficient of x6 in (1+x+x2+x3+x4+x5)6 is

  

  

  

  

If (cos 3α + i sin 3α) (cos 5β+i sin 5β)=cos θ+i sin θ then θ is

  

  

  

  

If the roots of px3+qx2+rx+s=0 are in A.P,then the roots of 8px3+4qx2+2rx+s=0 are in

  

  

  

  

If the polar of (2, -1) with respect to the ellipse 3x2+4y2=12 is  ax+by+c=0 then the ascending order  of a, b, c is

  

  

  

  

If the circles x2+y2+2x+c=0 and x2+y2+2y+c=0 touch each other then c=

  

  

  

  

An observer finds that the angular elevation of a tower is θ. On advancing ‘a’ metres towards the tower, the elevation is 450 and on advancing b metres the elevation is 900-θ. The height of the tower is

  

  

  

  

In the Argand plane, the points represented by the complex number s 2-6i, 4-7i, 3-5i and 1-4i form

  

  

  

  

If cos 2θ+cos 8θ= cos 5θ then θ=

  

  

  

  

If a=i+j-2k , b=-i+2j+k, c=i-2j+2k then a unit vector parallel to a+b+c=

  

  

  

  

The value of k if (1,2), (k,-1) are conjugate points with respect to the ellipse 2x2+3y2=6 is

  

  

  

  

If the area of the triangle formed by the points (t,2t), (-2,6), (3,1) is 5sq.unit, then t is

  

  

  

  

d/dx{√(1+cos x)/sin x}=

  

  

  

  

{n (n+1) (2n+1) : n Є Z }  is subset of

  

  

  

  

I: In a ΔABC, if 4s(s-a) (s-b) (s-c) =a2b2 then it is right angled triangle II: In a ΔABC, if sin A+ sin B +sin C maximum then triangle is equilateral

  

  

  

  

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

  

  

  

  

The equation of the circle cutting orthogonally the circles x2+y2-8x-2y+16=0, x2+y2-4x-4y-1=0 and passing through the point (1, 1) is

  

  

  

  

In a class 40% of students read History, 25% Civics and 15% both History and Civics. If a student is selected at random from that class, the probability that he reads history, if it is known that he reads Civics is

  

  

  

  

The roots of the equation a(b-c)x2+b(c-a)x+c(a-b)=0 are

  

  

  

  

The point of contact of  2x – y + 2 = 0 to the parabolay2 = 16x is

  

  

  

  

If log 2+(1/2)log a +(1/2) log b = log(a+b),then

  

  

  

  

If A=sin2θ + cos4θ, then for all values of θ, where

  

  

  

  

The value of Cot [Cot-1 7+ Cot-1 8+ Cot-1 (18)] is

  

  

  

  

If u=3(lx+my+nz)2-(x2+y2+z2) and l2+m2+n2=1 then uxx+uyy+uzz=

  

  

  

  

If 9P5+5.9P4=10Pr then r=

  

  

  

  

The equation of the normal at a point hose eccentric angle is 3π/2+θ to the ellipse x2/9+y2/4=1 is

  

  

  

  

The fourth vertex of the parallelogram whose consecutive vertices are (2,4,-1), (3,6,-1),(4,5,1) is

  

  

  

  

The equation of the line passing through the point P (1, 2) such that P bisects the part intercepted between the axes is

  

  

  

  

The length of the intercept made by the sphere x2+y2+z2-4x+6y+8z+4=0 on z axis is

  

  

  

  

The perpendicular distance of radical axis determined by the circles x2 + y2 + 2x + 4y – 7 =0 and x2 + y2 – 6x + 2y – 5 =0 from the origin is:

  

  

  

  

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

  

  

  

  

If tan A,tan B are the roots of x2-px+q=0,the value of sin2(A+B) is

  

  

  

  

A plane passes through (2, 3, -1) and is perpendicular to the line having direction ratios ( 3, -4, 7). The perpendicular distance from the origin to this plane is

  

  

  

  

d/dx{Tan-1(a+bcos x/b+a cos x)}=

  

  

  

  

The derivative of (x2+1)5(2x+3)3 w.r.t is

  

  

  

  

If x-y=Sin-1 x-Sin-1 y then dy/dx=

  

  

  

  

I .thev locusv of the midpoints of chords of the parabola y2 = 4ax which substends a right angle at the vertex is y2 = 2a (x – 4a) II. the locus of midpoint of chords of the parabola y2 = 4ax which touch the circle X2 + y2 = a2 is (y2- 2ax)2 = a2 (y2 + 4a2)  

  

  

  

  

The radius of the sphere x2+y2+z2-2x+4y-6z+7=0 is

  

  

  

  

If y= x2+1/(x2+1/x2+....∞), then dy/dx=

  

  

  

  

If f(x)= (a-xn)1/n, where a>0 and n?N, then (fof)(x)=

  

  

  

  

Tangents are drawn  from  the Point (-2, -1) to the hyperbola 2x2-3y2=6. Their equations are

  

  

  

  

The condition that the pairs of lines ax2+2pxy-ay2=0, bx2-2qxy-by2=0 are such that each pair bisects the angle between the other pair is

  

  

  

  

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

  

  

  

  

The ratio in which yz-plane divides the line segment joining (3,4,5) ,(2,-3,1) is

  

  

  

  

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

  

  

  

  

The coefficient of x2 in1+x2/(1-x)3 is

  

  

  

  

If a, b, c are the sides of a triangle then the range of ab+bc+ca/a2+b2+c2 is

  

  

  

  

The 1st  and  2nd points of trisection of the join of (-2, 11), (-5, 2) are

  

  

  

  

d/dx{Tan-1(acos x-bsin x/b cos x+a sin x)}=

  

  

  

  

If a hyperbola has one focus at the origin and its eccentricity is √2. One of the directries is x+y+1=0. Then the equations to its asymptotes are

  

  

  

  

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

  

  

  

  

If A+B+C= 1800 then cos A+cos B+ cos C=

  

  

  

  

If y= x log|x+√(1+x2)|-√(1+x2) then dy/dx=

  

  

  

  

Sin (4 arc Tan-11/3) =

  

  

  

  

The condition that the line x cos α + y sin α =p to be a tangent to the hyperbola x2/a2 -y2/b2 =1 is

  

  

  

  

1+[(1/2).(3/5)]+[(1.3/2.4)(3/5)2]+[(1.3.5/2.4.6)(3/5)3]+-------∞=

  

  

  

  

sin2200+ sin21000 +sin2 1400=

  

  

  

  

cos2 360+ cos2 720=

  

  

  

  

If b + c = 3a, then cot B/2 cot C/2  is equal to :

  

  

  

  

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 quadrilateral formed by the lines x-y+2=0, x+y=0, x-y-4=0, x+y-12=0 is

  

  

  

  

The condition that the slope of a line represented by ax2+2hxy+by2=0 is thrice that of the other is

  

  

  

  

The derivative of cot-1(cosec x-cot x) w.r.to x is

  

  

  

  

The area bounded by the curve xy=4,x-axis and the ordinates x=2,x=5 is

  

  

  

  

The centres of similitude of the circles x2+y2-2x-6y+9=0, x2+y2=1 is

  

  

  

  

The equation of the sphere which passes through the four points (0,0,0), (1,0,0), (0,1,0) and (0,0,1) is

  

  

  

  

The equation of the line passing through the point of intersection of the lines x+y-5=0, 2x-y+4=0 and having intercepts numerically equal is

  

  

  

  

If tan(A+B)=m,tan(A-B)= n,then tan 2A=

  

  

  

  

A bag contains four balls. Two balls are drawn and found them to be white. The probability that all the balls are white is

  

  

  

  

If nεN then 3.52n+1+23n+1 is divisible by

  

  

  

  

18 guests have to be seated half on each side of a long table. 4 particular guests desire to sit on one particular side and 3 others on the other side. Determine the number of ways in which the sitting arrangements cn be made

  

  

  

  

The circumcentre of the triangle formed by 3x+4y-20=0 with the pair of lines 2x2-3xy-2y2=0 is

  

  

  

  

The area of the triangle whose vertices are (a,θ),(2a,θ+π/3) and (3a,θ+2π/3) is (in sq.unit)

  

  

  

  

cot(A+150)- tan(A- 150)=

  

  

  

  

If cosec θ-sin θ=m, sec θ-cos θ=n then (m2n)2/3+(mn2)2/3=

  

  

  

  

If ax= by= cz = dw then the value of x[(1/y)+(1/z)+(1/w)]is

  

  

  

  

The tower of a bridge ,hung in the form of a parabola,have their tops 30meters above the rod way are 200 meters apart .If the cable is 5 meters above the road way at the center of bridge ,then the length of the vertical supporting cable 30 meters from the centre 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

  

  

  

  

If x= -5+4i then x4+9x3+35x2-x+4=

  

  

  

  

If f(x)=log (x-5)(2-x), g(x)=log (x-5), h(x)= log (2-x) then

  

  

  

  

If x2-xy+y2=1 and y’’(1)=

  

  

  

  

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