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,β,γ are the roots of x3+ax+b=0 then (α+β)-1+(β+γ)-1+(γ+α)-1=

  

  

  

  

The centre of similitude of the two circles x2+y2+4x+2y-4=0 and x2+y2-4x-2y+4=0 is

  

  

  

  

If a tangent to the circle x2 + y2 + 4x - 4y+4=0 makes a equal intercepts on the coordinate axes then the equation of that tangent is

  

  

  

  

The position vector of the centroid of the triangle formed by the points 2a+3b, 5a+4b, 2a-b is

  

  

  

  

The point on the line 3x+4y=5 which is equidistance from (1, 2) and (3, 4) is

  

  

  

  

The angle between the tangents from a point on x2+y2+2x+4y-31=0 to the circle x2+y2+2x+4y-4=0 is

  

  

  

  

If 6 Sec2 θ-5 Sec θ+1=0 then θ=

  

  

  

  

Bag A contains 2 red, 3 black balls. Bag B contains 3 red, 2 black balls. One ball is drawn from the bag A and placed in B. One ball is drawn from bag B and placed in A. The probability that the composition of balls in the bags unaltered is

  

  

  

  

The ascending order of the moduli of the complex numbers z1=1+i,z2=1+2i,z3=1-i/√2,z4=3+4i is

  

  

  

  

If x2+ky2+x-y is resolvable into two linear factors then k=

  

  

  

  

sin-1(2cos2 x-1)cos-1(1-2sin2 x)

  

  

  

  

If α, β are different values of θ satisfying the equations 5 cos θ+12 sin θ=11 then the value of sin (α+β)=

  

  

  

  

The value of √3cot 200- 4cos 200 is

  

  

  

  

The 4th term of (1-2x)-1 when x=1/3 is

  

  

  

  

A cylindrical vessel of radius 0.5mts. is filled with oil at the rate of 0.25 π.c mts./minute. The rate, at which the surface of oil is increasing is

  

  

  

  

1+cos 2x+cos 4x+cos 6x- 4 cosxcos 2xcos 3x=

  

  

  

  

A particle moves along the curve y = x2 + 2x. Then the point on the curve such that x and y co-ordinates of the particle change with the same rate is :

  

  

  

  

If θ is the parameter, then the family of lines (2 cos θ +3 sin θ)x +(3 cos θ -5 sin θ)y-(5cos θ -2sin θ)=0 pass through the fixed point

  

  

  

  

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

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If cos x+ cos y=4/5, cos x- cos y=2/7, then 14 tan(x-y/2)+ 5 cot (x+y/2)=

  

  

  

  

The equation of the line passing through (-10, 4) and making an angel tan-12 with the line 2y=x-10 are

  

  

  

  

The circumfernce of a circle is measured as 56 cm with error 0.02 cm. the percentage error in its area is

  

  

  

  

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 α and β are different values of x satisfying a cos x+b sin x=c then tan (α+β/2) =

  

  

  

  

d/dx{Tan-1√(1-cos x)/(1+cos x)}=

  

  

  

  

The general term of (2a-3b)-1/2 is

  

  

  

  

The equation of the circle which bisects the circumference of the circle x2+y2=1,  x2+y2+2x=3, x2+y2+2y=3 is

  

  

  

  

(1+sec 200)( 1+sec 400) (1+sec 800)=

  

  

  

  

If the circles x2+y2+2ax+c=0 and x2+y2+2bx+c=0 touch eachother then 1/c=

  

  

  

  

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

  

  

  

  

If x4+2x3-4x2-4x+4=0 then 2s1-s2+s3-s4=

  

  

  

  

The coefficients of three consecutive terms in the expansion of (1+x)n are in the ratio 1:7:42, then n=

  

  

  

  

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

  

  

  

  

The radius of a sphere is 3 cm. if an error of 0.03 cm is made in measuring the radius of the sphere, then the error in surface area is

  

  

  

  

The locus of the point of intersection of two tangents drawn to the circle x2+y2=a2 which make a constant angle α to each other is

  

  

  

  

A: If there are 8 points in a plane no three of which are on the same straight line except 4 points are collinear then the number of straight lines formed by joining them is 23 R: If there are n points in a plane no three of which are on the same straight lie except p points are collinear then the number of straight lines formed by joining them is nC2 – pC2 +1

  

  

  

  

If the tangent at θ=π/4 to the curve x=a cos3θ, y= a sin3θ meets the x and y axis in A and B, then the length of AB is

  

  

  

  

If one root of the equation ix2-2(1+i)x+(2-i)=0 is 2-I,then the other root is

  

  

  

  

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

  

  

  

  

The area of the triangle with vertices at (-4,-1), (1,2), (4,-3) is

  

  

  

  

If a is the area bounded by x=4-y2 with y-axis,b is the area bounded by x=6+5y-y2 with y axis and c is the area bounded by 2x=y2-1 with y-axis then the ascending order of a,b,c is

  

  

  

  

A problem in EAMCET examination is given to three students A, B and C, whose chances of solving it are 1/2, 1/3, 1/4 respectively. The probability that the problem will be solved is

  

  

  

  

The shortest distance between the line y-x=1 and the curve x=y2 is

  

  

  

  

If the expression x2 –(5m-2)x+(4 m2 +10m +25)=0 can be expressed as a perfect square, then m =

  

  

  

  

Tan-1 5/6+ 1/2 Tan-1 11/60 =

  

  

  

  

If the length of a chord of the circle x2 + y2=a2is 2K then the locus of the midpoint of that chord is a circle of radius

  

  

  

  

cos 60 cos 420 cos 600 cos780=

  

  

  

  

The number of tangents that can be drawn from (6, 0) to the circle x2+y2-4x-6y-12=0 are

  

  

  

  

If f(x,y)=x2Tan-1(y/x)-y2 Tan-1(x/y),x≠0,y≠0 then fxy=

  

  

  

  

The area of the triangle formed by the lines 2x+y-4=0, 3x+2y-5=0, x+y+1=0 is

  

  

  

  

A stone is dropped into a quiet pond and waves move in circles outward from the place where it strikes, at a speed of 30 cm per second. At the instant when the radius of the wave ring is 50 mt, the rate increase in the circumference of the wave ring is

  

  

  

  

x2-6x+8=0, y2-5y+6=0 are the four sides of a

  

  

  

  

If nPr=5040 then (n,r)=

  

  

  

  

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

  

  

  

  

If a line makes an intercept PQ between the pair of lines x2-4xy+2y2=0 and if (-1,1) is the midpoint of PQ then the equation of PQ is

  

  

  

  

The area bounded by the circles x2+y2=1 and x2+y2=2, and the pair of lines 2x2-3xy-2y2=0(y>0)is

  

  

  

  

If 2 Sinh-1 (a/√(1-a2))= log(1+x/1-x), then x=

  

  

  

  

If |x|

  

  

  

  

sin 3π/5+sin 4π/5+ sin 6π/5+sin 7π/5=

  

  

  

  

If tan (πcos x) = cot (π sinx) then cos(x-π/4) =

  

  

  

  

A, B,C are aiming to shot a balloon. A will succeed 4 times out of 5 attempts. The chance of B to shoot the balloon is 3out of 4 and that of C is 2out of 3. If the three aim the balloon simultaneously, then the probability that at least two of them hit the balloon is

  

  

  

  

If AB= 3p-q and AD=p+3q are the adjacent sides of a parallelogram ABCD where |p|=2=|q| and (p, q)=π/3, then the length of the diagonal AC is

  

  

  

  

The value of C for which P(X=k)=CK2 can be the probability mass function of a random variable x that takes values 0,1,2,3,4 is

  

  

  

  

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 the ascending order of a, b,c is

  

  

  

  

If y= log sin x then y2=

  

  

  

  

The locus of the middle point of chords of the ellipse x2/a2+y2/b2=1   whose pole lies on the auxiliary circle is

  

  

  

  

The vectors a+2b+3c, 2a+b-2c, 3a-7c are

  

  

  

  

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

  

  

  

  

The period of cos x cos(π/3+x) sin(π/3-x)is

  

  

  

  

sin2 3A/ sin2A)- (cos2 3A/ cos2A)=

  

  

  

  

If (a1+ib1)( (a2+ib2)…. (an+ibn)= A+iB, then (a12 +b12)( a22 +b22 )….(an2 +bn2)=

  

  

  

  

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

  

  

  

  

If three complex numbers are in A.P. then they lie on

  

  

  

  

In a triangle, the orthocentre and the circumcentre are (-4, 0), (8, 6 ) respectively; the centroid is

  

  

  

  

The lines joining the origin to the points of intersection of the line x-y=2 with the curve 5x2+12xy-8y2+8x-4y+12=0 are equally inclined to

  

  

  

  

If sinA + sinB = l, cosA - cosB = m, then the value of cos(A - B) =

  

  

  

  

If the points 3i-2j-k, 2i+3j-4k, i+j+2k, 4i+5j+λk are coplanar then λ=

  

  

  

  

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

  

  

  

  

A= sin 780- sin 180+ cos 1320, B= cos 120+ cos 840+ cos 1320+ cos 1560 and C= (sin 750+sin 150)/ (sin 750+cos 150) then by arranging in the ascending order

  

  

  

  

If a is the area bounded by y=x2,x-axis,x=0,x=2; b is the area bounded by y=x2+2,x-axis,x=1,x=2 and c is the area bounded by y=x3,x-axis,x=1,x=4 then the ascending order of a,b,c is

  

  

  

  

If A=(1, 1, 1), B=(1, 2, 3), C=(2, -1, 1) be two vertices of ΔABC, then the length of internal bisector of the angle A is

  

  

  

  

cos2 (800+θ)+ sin2 (1000-θ)=

  

  

  

  

If α and β are two points on the hyperbola x2/a2-y2/b2=1 and the chord joining these two points passes through the focus (ae, 0) then e cos α-β/2=

  

  

  

  

The solution of x log x (dy/dx)+y=2 log x is

  

  

  

  

If two circles(x-3) 2+(y-1)2=r2 and x2+y2-6x+4y+4=0 intersect in two distinct points then

  

  

  

  

If b=4i+3j and c be two vectors perpendicular to each other in xy-plane. The vector in the same plane having components 1, 2 along b and c respectively is

  

  

  

  

cos(π/4+A) cos(π/4-B)+ sin(π/4+A) sin(π/4-B)=

  

  

  

  

At a given instant the legs of a right angled triangle are 8 inch and 6 inch respectively. The first leg decreases1inch per minute and second increases at 2 inch per minute. The rate of increasing of the area after 2 minute is

  

  

  

  

The coefficient of xk in the expansion of  (1-2x-x2) /e-x  is

  

  

  

  

The length of the normal of the curve 2x2+3xy-2y2=8 at (2, 3) is

  

  

  

  

100 tickets are numbered as 00, 01, 02,...,09, 10, 11,...99. When a ticket is drawn at random from them and if A is the event of getting 9 as the sum of the numbers on the ticket, then P(A)=

  

  

  

  

The equation whose roots are 2+√3,2-√3,1+2i,1-2i is

  

  

  

  

The domain of √(x-1)(x-2)(x-3) is

  

  

  

  

If (x1,y1), (x2,y2),(x3,y3)are the vertices of an equilateral triangle such that(x1-2)2+( y1-3)2=( x2-2)2+( y2 -3)2=(x3-2)2+(y3 -3)2thenx1+ x2+x3=

  

  

  

  

x2+y2+kx+(1-k)y+5=0 represents a circle with radius less than or equal to 5.Then number of integral values of ‘k’ are

  

  

  

  

Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the midpoints of the chords of the circle C that subtend an angle of 2π/3 at its centre 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

  

  

  

  

Tan (tan-1 1/2+ tan-11/3) =

  

  

  

  

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