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 equation of the line passing through the point (-2, 1) and having intercepts whose product is 1 is

  

  

  

  

The circumradius of the triangle formed by the points (2,-1,1) , (1,-3,-5), (3,-4,-4) is

  

  

  

  

If(1.5)n=(0.15)b=100, then 1/a-1/b is equal to:

  

  

  

  

Equation of the parabola having focus (3,-2) and vertex (3,1) is

  

  

  

  

The equations whose roots are exceed by 1 than those of x3-5x2+6x-3=0 is

  

  

  

  

If 3x2+4xy+2y2+x-8=0 and dy/dx at (1,1),(1,2),(2,-1),(-1,3) are respectively A,B,C,D then the descending order of A,B,C,D is

  

  

  

  

The roots of ax2+3bx+c=0 are given by if 3b=a + c

  

  

  

  

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

  

  

  

  

The number of rational roots of (2x+3)(2x+5)(x-1)(x-2)=30 is

  

  

  

  

Observe the following statements : A : Three vectors are coplanar if one of them is expressible as a linear combination ofthe other two. R : Any three coplanar vectors are linearly dependent.Then which of the following is true

  

  

  

  

If the equation of the circle passing through the origin and the points of intersection of the two circles x2+y2-4x-6y-3=0;x2+y2+4x-2y-4=0 is x2+y2+2ax+2by+c=0 then ascending order of a,b,c

  

  

  

  

(1)+(2+3)+(4+5+6)+….n brackets=

  

  

  

  

Let f(x)=-2sinx, if x≤-π/2; f(x)=a sinx+b,if –π/2

  

  

  

  

A rectangle ABCD is inscribed in a circle with a diameter lying along the line 3y=x+10. If A=(-6, 7), B=(4, 7) then the area of the rectangle is

  

  

  

  

The length of the intercept on the y-axis cut by the pair of lines 2x2+4xy-6y2+3x+y+1=0 is

  

  

  

  

If α, β are the roots of ax2+bx+c=0 then α3+ β3 =

  

  

  

  

The derivative of Sin-12x/1+x2 w.r.to Tan-12x/1-x2is

  

  

  

  

The length of the common chord of the circles x2+y2+2hx=0, x2+y2-2ky=0 is

  

  

  

  

The radical centre of the circle x2+y2=1, x2+y2-2x=1, x2+y2-2y=1 is

  

  

  

  

The angle at which the circles x2+y2+8x-2y-9=0 and x2+y2-2x+8y-7=0 intersects is

  

  

  

  

In ∆ ABC, with usual notation, observe the two statements given below I. rr1r2r3 = ∆2II.r1r2 + r2r3+r3r1 = s2Which of the following is correct

  

  

  

  

The arrangement of the following straight lines in ascending order of their slopes A) 2y=√3x    B) y=2     C) y=x               D) y=-x

  

  

  

  

If a is any vector then (axi)2+(axj)2+(axk)2=

  

  

  

  

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 :

  

  

  

  

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

  

  

  

  

If  |z-1/z+a|=1 where Re(a)≠0 then the locus of z=x+iy is

  

  

  

  

The area (in sq unit ) of the region bounded by the curves 2x = y2-1 and x = 0 is

  

  

  

  

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

  

  

  

  

. I: The equation to the pair of lines passing through the point (2,-1) and parallel to the pair of lines 3x2-5xy+2y2-17x+14y+24=0. II: The equation to the pair of lines passing through (1,-1) and perpendicular to the pair of lines x2-xy-2y2=0 is 2x2-xy-y2-5x-y+2=0.

  

  

  

  

The angle between the circles x2+y2-4x-6y-3=0 and x2+y2+8x-4y+11=0 is

  

  

  

  

(i): If 12Cr+1=12C3r-5, then r=3 or 4 (ii): 9C3+9C5=10Cr, then r=4 or 6

  

  

  

  

The solution set of (5+4cosθ)(2cosθ+1) = 0 in the interval [0,2π],is

  

  

  

  

If the circle x2 + y2 + 2x + 3y + 1 = 0 cuts another circle x2+y2 + 4x + 3y + 2 = 0 in A and B, then the equation of the circle with AB as a diameter is :

  

  

  

  

The range of f(x)=10- |3-2x| is

  

  

  

  

The angle between the lines joining the origion to the points of intersection of the line y=3x+2 with the curve x2+2xy+3y2+4x+8y=11 is

  

  

  

  

The derivative of Sin-1 cos x w.r.to x is

  

  

  

  

If (2, 1),(-1, -2),(3, 3) are the midpoints of the sides BC,CA,AB of Δ ABC, then the equation of AB is

  

  

  

  

If ak is the coefficient of xk in the expansion of  (1+x+x2)n for k = 0,1,2,..........2n then a1 + 2a2 +.....+2na2n  =

  

  

  

  

The range of 5 Co-1(3x) is

  

  

  

  

49n+16n+k is divisible by 64 for n?N. Then the numerically least –ve integer value of k is

  

  

  

  

If θ is the angle between the curves y=sin x, y =cosx at x=π/4 then tan θ=

  

  

  

  

The length of the tangent from a point on the circle x2+y2+4x-6y-12=0 to the circle x2+y2+4x-6y+4=0 is

  

  

  

  

The number of non zero terms in the expansion of (x+a)100 + (x-a)100 is

  

  

  

  

The polar equation of xcosα+ysinα=p is

  

  

  

  

The point of concurrence of the lines (3k+1) x-(2k+3)y+(9-k)=0 is

  

  

  

  

Equation of the circle touching the y-axis at (0, √3) and cuts the x-axis in the points (- 1, 0) and (-3, 0) is

  

  

  

  

If y = sin-1 x-sin-1√1- x2 then d2y/dx2=

  

  

  

  

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

  

  

  

  

One extremity of a focal chord of y2=16x is A(1,4). Then the length of the focal chord at A is

  

  

  

  

The equation of the circle whose radius is 5 and which touches the circle x2+y2-2x-4y-20=0 at the point (5, 5) is

  

  

  

  

A five digit number is formed by using the digits 0, 1,2,3,4 and 5 without repetetion.The probability that the number is divisible by 6 is

  

  

  

  

The locus of a point P such that PA+PB=4 where A=(2,3,4) ,B=(-2,3,4) is

  

  

  

  

The locus of the middle points of the chords of the circle x2+y2=8 which are at a distance of √2 units from the centre of circle is

  

  

  

  

If cos α=3/5, cos β=5/13, then cos2(α - β/2)=

  

  

  

  

If α,β,γ are the roots of x3-px2+qx-r=0 then α4+β4+γ4=

  

  

  

  

The line among the following which touches the parabola y2=4ax, is

  

  

  

  

If X follows a binomial distribution with parameters n = 6 and p. If 4P(X = 4) = P(X = 2), then p is equal to

  

  

  

  

If k=(1+sin A)(1+sinB)(1+sin C)=(1-sinA)(1-sin B)(1-sin C) then k=

  

  

  

  

Observe the following statements A: f'(x) = 2x3 - 9x2  + 12x - 3 is increasing outside the interval (1, 2)R: f'(x) < 0 for x belongs to (1,2).Then which of the following is true

  

  

  

  

A plane π makes intercepts 3 and 4 respectively on z-axis.If π is parallel to y-axis,then its equation is

  

  

  

  

I: If tan A + tan B = P and Cot A + Cot B = q then cot (A + B) = (q-p) / pq II : If 2 tan A + cot A = tan B then cot A +2 tan (A –B) = 0

  

  

  

  

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 :

  

  

  

  

A, B, C are three routes from the house to the office. On any day, the route selected by the officer is independent of the climate. On a rainy day, the probabilities of reaching the office late, through these routes are 1/25, 1/10, 1/4respectively. If a rainy day the officer is late to the office then the probability that the route to be B 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

  

  

  

  

The equation of the circle whose diameter is the common chord of the circlesx2 + y2 + 2x + 3y + 2 = 0 and x2 + y2 + 2x-4y-4 = 0 is

  

  

  

  

if the points (0, 0), (2, 0), (0, 4),(1, k) are concyclic then k2-4k=

  

  

  

  

If three six faced dice are thrown together, then the probability that the sum of the numbers appearing on the dice is k(3≤k≤8)is

  

  

  

  

If the roots of x3-9x2+23x-15=0 are in A.P then the common difference in A.P. is

  

  

  

  

The condition that a root of ax2+bx+c=0 may be the reciprocal of a root of a1x2+b1x+c1=0 is

  

  

  

  

Find the equation of the parabola, whose axis parallel to the y-axis and which passes through the points (0,4),(1,9) and (4,5) is

  

  

  

  

Six faces of an unbiased die are numbered with 2, 3, 5, 7, 11 and 13. If two such dice are thrown, then the probability that the sum on the uppermost faces of the dice is an odd number is :

  

  

  

  

The equation whose roots are multiplied by 3 of those of 2x2+3x-1=0 is

  

  

  

  

The eccentricity of the conic 36x2+ 144 y2- 36x - 96y - 119 = 0 is:

  

  

  

  

A curve passes through the point (2, 0) and the slope of the tangent at any point is x2-2x for all values of x. The point of maximum or donation the curve is

  

  

  

  

The period of the function tan(3x+5) is:

  

  

  

  

A: The equation of the common chord of the two circles x2+y2+2x+3y+1=0, x2+y2+4x+3y+2=0 is 2x+1=0 R: If two circles intersect at two points then their common chord is the radical axis

  

  

  

  

In ΔABC, 1+4 sin(π-A/4)sin(π-B/4)sin(π-C/4)=

  

  

  

  

(1+ tan 320)(1+ tan130)/ (1+tan 230)(1+ tan220)=

  

  

  

  

A person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score X is observed, then the range of x is :

  

  

  

  

Five digit numbers can be formed from the digits 1,2,3,4,5. If one number is selected at random, the probability that it is an even number is

  

  

  

  

The point (3, 2) undergoes the following three transformations in the order given i) Reflection about the line y = x ii) Translation by the distance 1 unit in the positive direction of x – axis iii) Rotation by an angle π/4 about the origin in the anticlockwise direction. Then the final position of the point is

  

  

  

  

The harmonic conjugate of (-9,27) with respect to the points (1,7) and (6,-3) is 

  

  

  

  

The line joining the points (2,3,4) and (4,10,7) intersects the line joining(2,-1,5) and (4, -30,17). Then the coordinates of the point of intersection are

  

  

  

  

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

  

  

  

  

The approximate percentage reduction in the volume of a cube of ice, if each side of the ice cube to reduced by 0.7% due to melting to:

  

  

  

  

The length of the subtangent at (2, 2) to the curve x5 = 2y4 is

  

  

  

  

If a=2i-3j-k, b=i+4j-2k then (a+b)x(a-b)=

  

  

  

  

The eccentricity o the ellipse 9x2+16y2=576 is

  

  

  

  

If A=(2,3), B=(-2,-5),C=(-4,6) and if P is a point on BC such that AP bisects the angle A, then P=

  

  

  

  

The number of real solutions of Tan1 x+Tan 1 (1/y) = Tan1 3 is

  

  

  

  

The triangle formed by 2x+3y-7=0 and 3(2x+3y)2-(3x-2y)2=0 is

  

  

  

  

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

  

  

  

  

If (a+ib)2= x+iy then x2+y2=

  

  

  

  

The midpoint of the chord formed by the polar of (-9, 12) w.r.t x2+y2=100 is

  

  

  

  

The locus of the middle points of portions of the tangents to the circle x2+y2=a2 terminated by the axes is

  

  

  

  

If z = log (tan x + tan y), then (sin 2x)∂z /∂x+(sin 2y) ∂z /∂y is equal to

  

  

  

  

The equation to the normal to the parabola y2 = 4x at (1,2) is

  

  

  

  

If, in aΔABC, r3=r1+r2+r , then ‹A+‹B is equal to

  

  

  

  

If 1,-1,2 are the roots of x3+Ax2+Bx+C=0 then the ascending order of A,B,C is

  

  

  

  

A person has 3 shares in a lottery containing 2 prizes and 5 blanks. The chance of getting prize is

  

  

  

  

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