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 foot of the perpendicular from the point (3, 4) on the line 3x-4y+5=0 is:

  

  

  

  

If the length of the tangets from two points A, B to a circles are 6, 7 respectively. If A, B are conjugate points then AB=

  

  

  

  

The number of solutions of the system of equations 2x+y-z =7,x-3y+2z =1,x+4y-3z =5 is

  

  

  

  

If x2+4y2-8x+12=0 is satisfied by real values of x and y then y must lies between

  

  

  

  

The quadrilateral formed by the lines x+8y+37=0, 7x-6y+11=0, x+8y-87=0, 7x-6y-51=0 is

  

  

  

  

The equation of the tangent to the parabola y2 = 8x and which is parallel to the line x – y + 3 = 0

  

  

  

  

The 7th term of loge(5/4) is

  

  

  

  

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

  

  

  

  

7 Coupons are numbered 1 to 7. Four are drawn one by one with replacement. The probability that the least number appearing on any selected coupon is greater then or equal to 5 is

  

  

  

  

If 10 balls are to be distributed among 4 boxes, that the probability for the first box always to contain 4 ball is

  

  

  

  

If the roots of 24x3-26x2+9x-1=0 are in H.P then the roots are

  

  

  

  

Length of the tangent of the circle x2+y2=4 drawn from the image of origin with respect to 3x+4y+25=0 is

  

  

  

  

The equation of the circle having centre on the line x+y=1 and touching the lines 3x-4y+2=0, 4x+3y+7= 0 is

  

  

  

  

The distance of (1, -2) from the common chord of x2+y2-5x+4y-2=0 and x2+y2-2x+8y+3=0 is

  

  

  

  

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

  

  

  

  

The curve represented by X= 2( cos t + sin t ), y=( cos t - sin t ) is

  

  

  

  

Order and degree of (d2y/dx2)3+(dy/dx)=ex are

  

  

  

  

If n=3m then the coefficient of xn in the expansion of log(1+x+x2) is

  

  

  

  

The lines x-y—2=0, x+y-4=0 and x+3y=6 meet in the common point

  

  

  

  

The circumcentre of the triangle formed by the points(1,2,3), (3,-1,5), (4,0,-3) is

  

  

  

  

The lines (a+b) x+(a-b)y=2ab, (a-b)x+(a+b)y=2ab,x+y=0 form an isosceles triangle whose vertical angle is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The angle between the lines 4x-y+9=0, 25x+15y+27=0 is

  

  

  

  

The equation of the straight line perpendicular  to the straight line 3x+2y=0 and passing through the point of intersection of the lines x+3y-1=0 and x-2y+4=0 is

  

  

  

  

The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the x-axis in points whose abscissa are roots of the equation

  

  

  

  

The line 4x + 6y + 9=0, touches the parabola y2=4x at the point

  

  

  

  

The angle between the lines joining the origin to the points of intersection of 3x-y+1=0 and x2+2xy+y2+2x+2y-5=0 is

  

  

  

  

The ratio in which (5,4,-6) divides the line segment joining (3,2,-4),(9,8,-10) is

  

  

  

  

The values of the parameters a for which the quadratic equations (1-2a)x2-6ax-1=0 and ax2-x+1=0 have at least one root in common are

  

  

  

  

The equation of the circle which cuts orthogonally the  three circles x2+y2+2x+17y+4=0, x2+y2+7x+6y+11=0 , x2+y2-x+22y+3=0 is

  

  

  

  

The number of numbers greater than 1000 but not greater than 4000 that can be formed with the digits 0,1,2,3,4 repetition of digits being allowed is

  

  

  

  

The perpendicular distance from the point 3i-2j+k to the line joining the points i-3j+5k, 2i+j-4k is

  

  

  

  

There are 3 routes from Tenali to Vijaywada and 4 routes from Vijaywada to Hyderabad,in how many different ways a person can travel from Tenali to Hyderabad via Vijaywada?

  

  

  

  

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 equation of the sphere through the points (1,0,0) (0,1,0) and (1,1,1) and having the smallest radius

  

  

  

  

The least interval value of x such that (x-5)/(x2+5x-14)>0 is

  

  

  

  

The domain of √[x-1/2-x] is

  

  

  

  

The last terms in the expantions of sin 8θ, sin 9θ respectively are

  

  

  

  

The transformed equation of x3+6x2+12x-19=0 by eliminating second term is

  

  

  

  

A: The orthocentre of the triangle having vertices as (2,3), (2,5), (4,3) is (2,3) R: Orthocentre of a right angled triangle is midpoint of a hypotenuse

  

  

  

  

If one root of px2-14x+8=0 is 6 times the other,then p=

  

  

  

  

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

  

  

  

  

A person of height 180 cm starts from a lamp post of height 450 cm and walks at the constant rate of 4 km per hour. The rate at which his shadow increases is

  

  

  

  

If the acute angle between the lines 2x+3y-5=0, 5x+ky-6=0 is  then the value of k is

  

  

  

  

The positive integer which is just greater than (1+0.0001)10000 is

  

  

  

  

A tangent to the circle x2+y2=a2 intersects the coordinate axes at A and B. The locus of the point of intersection of the lines passing through A, B and parallel to the coordinate axes is

  

  

  

  

L and L’are ends of the latus rectum of the parabola x2 = 6y. the equation of OL and OL’ where O is the origin is

  

  

  

  

The relation between the vectors a+3b+4c, a-2b+3c, a+5b-2c, 6a+14b+4c 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

  

  

  

  

If p,q are the perpendiculars from the origin to the lines x sec α + y cosec α = a  and  xcosα-ysinα=acos2α, then 4p2+q2=

  

  

  

  

d/dx{Tan-1√(1+x2)+√(1-x2)/(√(1+x2)-√(1-x2))}=

  

  

  

  

If x+iy= 1/1+ cos θ+ i sin θ, then 4x2=

  

  

  

  

If u=(x-y) (y-z) (z-x) then ux+uy+uz=

  

  

  

  

The volume of a metal hollow sphere is constant. If the outer radius is increasing at the rate of ¼ cm per sec. the rate at which the inner radius is increasing when the radii are 8 cm and 4 cm respectively is

  

  

  

  

If cos-1 x= cot-1(4/3)+Tan-1(1/7), then x=

  

  

  

  

If α,β are the roots of 3x2+5x-7=0,then the value of (1/3α+5)2+(1/3β+5)2 is

  

  

  

  

If cos 5θ=a cos θ+bcos3 θ+c cos5 θ+d, then

  

  

  

  

The radical axis of the circles x2+y2-6x-4y-44=0 and x2+y2-14x-5y-24=0 is

  

  

  

  

The equations whose roots are exceed by 2 than those of x4+x3-10x2+4x+24=0 is

  

  

  

  

(tan hx/ Sechx-1)+ (sinh x/ sech x+1)

  

  

  

  

The pole of the line y=x+2 e with respect to the ellipse x2+4y2-2x-6y-10=0 is

  

  

  

  

The sum and product of the slops of the tangents to the hyperbola 2x2-3y2=6 drawn from the point (-1,1) are

  

  

  

  

The condition that the two spheres a(x2 + y2 + z2)=k2 may cut orthogonally (k ≠0)

  

  

  

  

If the diagonals of a parallelogram are given by 3i+j-2k and i-3j+4k, then the lengths of its sides are

  

  

  

  

3 faces of a fair die are yellow, two faces red and one blue. The die is tossed 3 times. The probability that the colours yellow, red and blue appear in the second and third tosses respectively is

  

  

  

  

Pole of the line 2x+3y+4=0 w.r.to the ellipse x2/2+y2/4=1 is

  

  

  

  

The focus of a parabola is (2,3) and the foot of the perpendicular from the focus to the directrix is (4,5). The equation to the parabola is

  

  

  

  

tan 2A- sec Asin A=

  

  

  

  

Sin-1(3/5)+Sin-1(8/17)=

  

  

  

  

Tangents to x2/a2+y2/b2=1 make an angles θ1, θ2 with traverse axis. The equation of the locus of their intersection when cot (θ1+θ2)=k is

  

  

  

  

The area of the triangle formed by the line x/4+y/6=1 with the coordinate axes is

  

  

  

  

The intersection of the sphere x2+y2+z2+7x – 2y –z =13 and x2+y2+z2-3x+3y+4z=8 is the same as the intersection of one of the sphere and the plane

  

  

  

  

The product of the slopes of the tangents to the ellipse 2x2+3y2=6 draw from the point (1, 2) is

  

  

  

  

The equation of the line perpendicular to the line x=3 and passing through (-4, 2) is

  

  

  

  

A, B, C, D are four points with the position vectors a, b, c, d respectively such that (a-d). (b-c)=(b-d).(c-a)=0. The point D is the ….of ΔABC

  

  

  

  

The equation of the circle belonging to the coaxal system of which (1, 2)(4, 3) are the limiting points and passing through the origin is

  

  

  

  

If the lines y=4-3x; ay=x+10; 2y+bx+9=0 from three sides of the rectangle in order and the fourth side passes through (1, -2) then other sides are

  

  

  

  

The ordinate PN of P(a cos θ, b sin θ) on the ellipse x2/a2+y2/b2=1 meets the auxiliary circle at Q,. The locus of the point of intersection of normal at P and Q is

  

  

  

  

The points (-1, 3), (-2, 4 ), (2, -5) are the mid points of the sides o f a triangle, then the vertex opposite to (-1, 3) is 

  

  

  

  

The coefficient of x7 in (1+2x+3x2+4x3+……..∞)-3 is

  

  

  

  

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

  

  

  

  

Two cards aredrawn from a pack. The probability that one of them is  a club and the  other is not a club is

  

  

  

  

The radius of one circle is twice the radius of another circle whose centres are (2,0),(1,2) respectively cutting orthogonally.Then the radius of the first circle is

  

  

  

  

The cost of a cloth piece is Rs.35/-.If the length of the cloth piece is 4 metres more and each metre costs Rs.1/- less,the cost would remain unchanged.The length of the cloth piece is

  

  

  

  

(cos θ- cos 3θ)( sin 8θ+ sin 2θ)/(sin 5θ-sin θ)(cos 4θ- cos 6θ)=

  

  

  

  

If x2+px+q=0 and x2+qx+p=0 have a common root,then their other roots are the roots of

  

  

  

  

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

  

  

  

  

The equation of the hyperbola whose eccentricity 2 and foci are the foci of the ellipse x2/25 +y2/9 =1 is

  

  

  

  

x2+y2=t+(1/t),x4+y4=t2+(1/t2)⇒x3y(dy/dx)=

  

  

  

  

If tan A=18/17, tan B= 1/35 then tan(A-B)=

  

  

  

  

In how many ways 4 sovereigns be given away, when there are 5 applicants and any applicant may have either 0,1,2,3or4 sovereigns?

  

  

  

  

If 7x4+kx-9=0 and S3=-8 then k=

  

  

  

  

If cos θ+ sin θ=a, then sin 2θ=

  

  

  

  

A bag consists a white and b black balls. Two players A and B alternatively draw a ball from the bag, replacing the ball each time after the draw till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B, then a:b=

  

  

  

  

O is the origin and Ax(xk,yk) where k=1.2 are two points.If the circles are described on OA1 and OA2 as diameters,then the length of their common chord is equal to

  

  

  

  

If s=cot θ+cos θ,y= cot θ- cos θ, then (x2-y2)2=

  

  

  

  

Assertion(A):x2+x+1 is greater than zero for all real x. Reason(R):when b2-4ac

  

  

  

  

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

  

  

  

  

If tan θ+sin θ=m ,tan θ- sin θ=n then (m2-n2)2

  

  

  

  

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