Eamcet - Maths Test

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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 vector equation of the plane passing through A and perpendicular to AB where 3i+j+2k, i-2j-4k are the position vectors of A, B respectively

  

  

  

  

If y=2ax and (dy/dx)=log256 at x=1,then a=

  

  

  

  

The condition for f(x)= x3+px2+qx+r(x R) to have no extreme value, is

  

  

  

  

The value of (λ > 0) so that the line 3x – 4y =λ may touch the circle x2 + y2 -4x -8y -5=0 is

  

  

  

  

A circle passes through the point (3,4) and cuts the circle x2+y2 = a2 orthogonally; the locus of its centre is a straight line. If the distance of this straight line from the origin is 25, then a2 =

  

  

  

  

The acute angle between the lines x2-2xycotθ+ y2=0 is

  

  

  

  

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

  

  

  

  

The term independent of x in (x+1/x)6 is

  

  

  

  

The equation of the line whose y-intercepts is -3/4 and which is parallel to 5x+3y-7=0 is

  

  

  

  

The eccentricity of the ellipse 5x2+9y2=1 is

  

  

  

  

If A= (-2, 5), B = (3, 1) and P,Q are the points of trisection of  ¯AB, then mid point of ¯PQ is

  

  

  

  

If y = sin (logex) then x2 (d2y/dx2) + x (dy/dx) =

  

  

  

  

In the expression of (x4- (1/x3))15 coefficient of x32 is equal to :

  

  

  

  

The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle x2+y2=9 is

  

  

  

  

If x+iy= cis α cis β then the value of x2+y2 is

  

  

  

  

If the roots of a2x2+2bx+c2=0 are imaginary,then the roots of b(x2+1)+2acx=0 are

  

  

  

  

If  a circle passes through the point (a, b) and cuts the circle x2+y2=4 orthogonally, then the locus of its centre is

  

  

  

  

If 2x-3y=5 and 3x-4y=7 are the equation of two diameters of a circle whose area is 154sq units, then the equation of the circle is

  

  

  

  

If f(x)=x-k/x has a maximum value at x=-2. Then k=

  

  

  

  

d/dx{Tan-1(x/1-√1-x2)}=

  

  

  

  

If ay= sin(x+y) then y2+(1+y1)3 y=

  

  

  

  

If f(x)=x2sin(1/x) for x≠0, f(0)=0 then

  

  

  

  

The abscissa of points whose ordinate is 4 and which are at a distance of 5 units from (5, 0) is

  

  

  

  

5 digit numbers can be formed from the digits 0, 2,2,4,5. One number is selected at random.the probability that it is divisible by 5 is

  

  

  

  

The radical axis of the circle x2+y2+4x-6y=12 and x2+y2+2x-2y-1=0 divides the line joining the centers of the circles in the ratio

  

  

  

  

 If θ is the angle between the lines y=2x+3, y=x+1 then the value of tan θ =

  

  

  

  

The inverse point of (2, -3) with respect to the circle x2+y2+6x-4y-12=0 is

  

  

  

  

The scalar product of the vector i+j+k with the unit vector parallel to sum of the vectors 2i+ 4j-5k and λi+2j+ 3k is equal to 1. Then the value of the constant λ is

  

  

  

  

If x= a {cos θ + log tan (θ/2)} and y = a sin θ then dy/dx=

  

  

  

  

If 5x-12y+10=0 and 12y-5x+16=0 are two tangents to a circle,then the radius of the circle is

  

  

  

  

The condition that the circles x2+y2+2ax+2by+c=0, x2+y2+2bx+2ay+c=0 to touch each other is

  

  

  

  

If fg=ch, the lines represented by hxy+gx+fy+c=0 fprm a quadrilateral with coordinate axes which is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If a chord of length 2√2 subtends a right angle at the centre of the circle then its radius is

  

  

  

  

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

  

  

  

  

The inverse of f(x)=10x-10-x/ 10x+10-x is

  

  

  

  

The chord through (1,-2) cuts the curve 3x2-y2-2x+4y=0 in p and Q. Then PQ subtends at the origin an angle of

  

  

  

  

The lines 2x+3y = 6,2x+3y = 8 cut the x-axis at A,B respectively.A line L=0 drawn,through the point(2,2) meets the x-axis at C in such a way that abscissa of A,B and C are in the arithmetic progression.Then the equation of L=0 is

  

  

  

  

If u=(y+sin x)3+(y-sin x)2,then uxx=

  

  

  

  

If the lines 4x+3y-1=0,x-y+5=0 and kx+5y-3=0 are concurrent,then k is equal to

  

  

  

  

If z2 = (x1/2 + y1/2)/(x1/3 + y1/3), then x(∂z/∂x) + y(∂z/∂y) is :

  

  

  

  

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

  

  

  

  

If α,β,γ are the roots of x3+3px+q=0 then the equation whose roots are α+1/β+γ–α,β+1/γ+α–β and γ+1/α+β–γ is

  

  

  

  

Match the following. Equation Roots I.x3-3x2-16x+48 =0 a)6,4,-1 II.x3-7x2+14x-8=0 b)1,1/3,1/5 III.15x3-23x2-9x-1=0 c)1,2,4 IV. x3-9x2+14x+24=0 d)4,-4,3

  

  

  

  

If 2,-3,5 are the roots of ax3+bx2+cx+d=0 then the roots of a(x-1)3+b(x-1)2+c(x-1)+d=0 are

  

  

  

  

If tan (cot x) = cot (tan x), then sin 2x=

  

  

  

  

The locus of middle points of chords of the hyperbola 2x2-3y2=5 which passes through the point (1,-2) is

  

  

  

  

xn-1 is divisible by x-k. Then the least +ve integral value of K is

  

  

  

  

If P = (0, 1, 2), Q = (4, -2, 1), 0 = (0, 0, 0), then LPOQ is equal to:

  

  

  

  

The equation of the tangent to the parabola y2 = 12x at (3, -6) is

  

  

  

  

The conjugate line of 3x+4y-45=0 with respect to x2+y2-6x-8y+5=0 which is perpendicular to x+y=0 is

  

  

  

  

The condition f(x) = x3 + px2 + qx + r (xЄR) to have no extreme value, is

  

  

  

  

If f={(a, 1), (b, -2), (c, 3)}, g={(a, -2), (b, 0), (c, 1)} then f2+g2=

  

  

  

  

100 tickets are numbered as 00,01, 02,...,09,10,11,...99. When a ticket is drawn at random from them and if B is the event of getting 0 as the product of the numbers on the ticket, then P(B)=

  

  

  

  

If f(x)=√(1-√(1-x2)), then

  

  

  

  

The number of points where the circle x2+y2-4x-4y=1 cuts the sides of the rectangle x=2 , x=5 , y=-1 and y=5 is

  

  

  

  

On a symmetrical die the numbers 1,-1,2,-2,3 and 0 are marked on its 6 faces. If such a die is thrown 3 times, the probability that the sum of points on them is 6 is

  

  

  

  

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

  

  

  

  

The volume of the tetrahedrone formed by (1, 2, 3), (4, 3, 2), (5, 2, 7), (6, 4, 8) is

  

  

  

  

If the probability that A and B will die with in a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is

  

  

  

  

How many different combination of 5 can be formed 6 men and 4 women on which exact 3 men and 2 women serve

  

  

  

  

A particle is moving along a straight line according to the law s=16+48+t-t3. Then distance travelled by the particle before coming to rest at an instant is

  

  

  

  

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

  

  

  

  

(1)+(2+3)+(4+5+6)+….n brackets=

  

  

  

  

The maximum value of sin2(π/3+x)+ sin2(π/3-x) is

  

  

  

  

32cos4 θ.sin2 θ=

  

  

  

  

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

  

  

  

  

If the straight line a(x+y-1)+b(2x-3y+1)=0 for different values of a and b are parallel to y- axis then the realization ship between  a& b is

  

  

  

  

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

  

  

  

  

If the pair of lines 3x2+hxy+5y2=0 bisects the angles between the coordinate axes then h=

  

  

  

  

The centroid of the tetrahedron formed by the points(3,2,5), (-3,8,-5), (-3,2,1),(-1,4,-3) is

  

  

  

  

d/dx{Tan-1√(1-cos x)/(1+cos x)}=

  

  

  

  

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

  

  

  

  

Orthocentre of the ?le whose vertices are (2,-5), (2, 5), (4, 5) is

  

  

  

  

If nPr =30240 and nCr=252then the ordered pair (n, r) is equal to

  

  

  

  

The functions y=x4-6x2+8x+15 has minimum at x=A, y=x(x-1)(x-2) has maximum at x=B, y=2x3-3x2-12x+5 has minimum at x=C. The ascending order of A, B, C is

  

  

  

  

If α,β are the roots of ax2+bx+c=0 then (α/β – β/α)2=

  

  

  

  

If α,β are the roots of ax2+bx+c=0 and γ,δ are the roots of lx2+mx+n=0,then the equation whose roots are αγ+βδ and αδ+βγ is

  

  

  

  

The point of contact of 5x+6y+1=0 to the hyperbola 2x2-3y2 =2 is

  

  

  

  

All the values of x satisfying sin 2x+ sin 4x= 2 sin 3x are

  

  

  

  

sin 700+cos 400/(cos 150-cos 750)=

  

  

  

  

The domain of sin-1(2x-7) 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

  

  

  

  

If the point of intersection  of kx+4y+2=0, x-3y+5=0 lies on 2x+7y-3=0 then k=

  

  

  

  

The distance between the parallel lines given by (x + 7y)2+4√2(x+7y)-42=0 is

  

  

  

  

How many circles can be drawn each touching all the three lines x+y=1, x+1=y, 7x-y=6

  

  

  

  

If sin θ=-7/25 and  is not in the first quadrant, then (7cot θ -24 tan θ) / (7cot θ+24 tan θ) =

  

  

  

  

(1+ω-ω2) (1-ω+ω2)=

  

  

  

  

If the chord of contact of the point (1, -2) with respect to the ellipse 4x2+5y2=20 is ax+by+c=0 then the ascending order  of a, b, c is

  

  

  

  

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

  

  

  

  

Equation x2+2ax-b2=0 has real roots α, β and equation x2+2px-q2=0 has real roots γ, δ. If circle C is drawn with the points (α, γ), (β, δ) as extremities of a diameter, then the equation of C is

  

  

  

  

The sum of the series log42-log82+log162-… is

  

  

  

  

If (-2, 6) is the image of the point (4, 2) with respect to the line L = 0, then L is equal to

  

  

  

  

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 normal at (1,1) on 2x2+2y2-2x-5y+k=0 is x+2y-3=0 then k=

  

  

  

  

The quadrilateral formed by the pairs of lines x2-7x+12=0, 4x2+12xy+9y2=0,8x+12y+3=0 is

  

  

  

  

If [(3x+4)/(x2-3x+2)]=[A/(x-2)]+[B/(x-1)] then (A,B)=

  

  

  

  

If a chord of the circle x2+y2=8 makes equal intercepts of length a on the coordinate axes, then |a|

  

  

  

  

The number of ways a pack of 52 cards can be divided amongst four players in 4 sets, three of them having 17 cards each and the fourth one just 1 card is

  

  

  

  

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