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 to the circles whose radius is 3 and which touches internally the circle x2+y2-4x+6y-12=0 at he point (-1, 1) is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If  f(x)=αx+β and f={(1, 1), (2,3), (3,5), (4, 7)} then the values of α, β are

  

  

  

  

In a throw with a pair of symmetrical dice the probability of obtaining a doublet is

  

  

  

  

The sum of the series 1+3x+5x2+7x3+....+(2n-1)xn-1+....is:

  

  

  

  

The equation to the locus of the midpoint of the chords of the circle x2+y2=r2 having a constant length 2l is

  

  

  

  

For a binominal variate X, if n = 4 and P(X = 4) = 6 P(X = 2), then the value of p is:

  

  

  

  

The angle between the line joining the points (1, -2), (3, 2) and the line x+2y-7=0 is

  

  

  

  

The angle between the lines joining the origin to the points of intersection of y-3x+2=0, 7x2-4xy+8y2+2x-4y-8=0 is

  

  

  

  

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

  

  

  

  

If Tan A+ Tan B=p and Cot A+ cot B= q then cot (A+B)=

  

  

  

  

The sum of divisors of 253453 is

  

  

  

  

The number of circles which touch all the 3 lines x+y=1,x-y=1 and 2x+3y+4=0 is

  

  

  

  

If α,β,γ are the roots of the equation x3+px2+qx+r=0,then Σ(α-β)2=

  

  

  

  

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 20Pr : 20Pr-1 = 15 : 1 then r =

  

  

  

  

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

  

  

  

  

If cos-1(3/5) - sin-1(4/5) = cos-1(x), then x

  

  

  

  

The number of ways in which an examiner can assign 30 marks to 8 questions giving not less than 2 marks to any question is

  

  

  

  

The parabola with directrix x + 2y - 1 = 0 and focus (1, 0) is

  

  

  

  

(cos θ+ sin θ)2+(cos θ- sin θ)2 =

  

  

  

  

The equation to the pair of lines passing through the origin and perpendicular to 3x2-5xy+2y2=0 is

  

  

  

  

If z= x+iy such that cos z= 2, then z=

  

  

  

  

If 23+43+63+….+(2n)3=kn2(n+1)2, then k=

  

  

  

  

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

  

  

  

  

If a,b,c are the number of 4 digited numbers that can be formed using the digits 2,4,5,7,8 that are divisible by 3,4,5 respectively then the ascending order of a,b,c is

  

  

  

  

If the length of the tangent from (2, 3) to circle x2+y2+6x+2ky-6=0 is equal to 7. Then k=

  

  

  

  

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 :

  

  

  

  

In ΔABC,tan A+tan B+tan C =

  

  

  

  

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

  

  

  

  

The solution of y dx-x dy+log x dx=0 is

  

  

  

  

A straight line which makes equal intercepts on positive  X and Y axes and which is at a distance 1 unit from the origin intersects the straight line  y =2x+3+√2 at (x0, y0). Then 2x0+y0=

  

  

  

  

If A+B+C= 1800 then sin2 A/2+ sin 2 B/2 - sin2 C/2=

  

  

  

  

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 equation of the tangents drawn from (3,2)  to the parabola x2 = 4y are

  

  

  

  

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

  

  

  

  

sin 1200 cos 1500-cos 2400 sin 3300 is equal to :

  

  

  

  

d/dx{Tan-1(x-√x/1+x3/2}=

  

  

  

  

Axes are coordinate axes and area of maximum rectangle inscribe in the ellipse is 16 and e= √15/4 then equation of ellipse

  

  

  

  

tan 200+ tan 400+√3 tan 200. tan 400=

  

  

  

  

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

  

  

  

  

If the tangents to the circle x2 + y2 = a2 at (p, q) and (r, s) are parallel then

  

  

  

  

If α,β,γ are the roots of 2x3+3x2-6x+3=0,then the value of 1/α4+1/β4+1/γ4=

  

  

  

  

the equation of the parabola whose axis is parallel to y –axis and passing through  is (-3,1), (1,1) is

  

  

  

  

In the Argand plane, the points represented by the complex numbers 2-i,-4+3i and -3-2i form

  

  

  

  

If three points A, B, C have position vectors (1, x, 3) and (y, -2, -5) respectively and if they are collinear, then (x, y)=

  

  

  

  

A man throws a die until he gets a number bigger than 3. The probability that he gets a 5 in the last throw is

  

  

  

  

If f : R → R is defined by f(x) = [2x] - 2[x] for x ε R, where [x] is the greatest integer not exceeding x, then the range of f is :

  

  

  

  

If u=(ax+by)2-(x2+y2) and a2+b2=1 then uxx+uyy=

  

  

  

  

If the line 3x - 2y + 6 = 0 meets X-axis and Y-axis respectively at A and B, then theequation of the circle with radius AB and centre at A is :

  

  

  

  

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

  

  

  

  

The transformed equation of x4+2x3-12x2+2x-1=0,by eliminating third term is

  

  

  

  

The locus of middle point of the chord of the ellipse x2/a2+y2/b2=1 touching the ellipse The locus of midpoint of the chord of the ellipse x2/α2+y2/β2=1

  

  

  

  

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

  

  

  

  

15 buses fly between Hyderabad and tirupathi. The number of ways can a man go to Tirupathi from Hyderabad by a bus and return by a different bus is

  

  

  

  

When a circular oil drop expands on water, its area increases at the uniform rate of 40sq. cm per minute. The rate of increase in the radius when the radius 5 cm is

  

  

  

  

The quadrilateral formed by the pairs of lines xy+x+y+1=0, xy+3x+3y+9=0 is

  

  

  

  

If u+iv= 2+i/z+3, where z=x+iy, then the values of u, v are

  

  

  

  

The locus of the poles w.r.t the ellipse x2/a2+y2/b2=1 of tangents to its auxiliary circle is

  

  

  

  

The quadratic equation for which the sum of the roots is 12 and the sum of the cubes of the roots is 468 is

  

  

  

  

A point is moving on y = 4-2x2. The x-co-ordinate of the point is decreasing at the rate of 5 units per second. Then the rate at which y co-ordinate of the point is changing when the point isat (1, 2) is :

  

  

  

  

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

  

  

  

  

(1-ω+ω2) (1-ω2+ω4) (1-ω4+ω8)... to 2n factors=

  

  

  

  

Equation of the circle passing through A(1, 2), B(5, 2) so that the angle substended by AB at points on the circle is π/4 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)=

  

  

  

  

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

  

  

  

  

d/dx{x2+3x+6/(x+3)(x-5)}=

  

  

  

  

sin 4200. cos 3900 – cos(-3300). Sin(-3000)=

  

  

  

  

If f: R-{5/2}→R-{-1} defined by f(x)=2x+3/5-2x then f-1(x)=

  

  

  

  

A coin and six faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die, is

  

  

  

  

tan 2030+tan 220+tan 2030 tan 220 =

  

  

  

  

If the origin is the centroid of the tetrahedron for which (2,-1,3), (-1,3,1), (3,4,-2) are three vertices then the fourth vertex is

  

  

  

  

In how many ways can a collection of 30 books be divided into two groups of 10 and 20 so that the first group always contains a particular book?

  

  

  

  

If x= 2 cos t- cos 2t, y= 2 sin t- sin 2t then dy/dx=

  

  

  

  

If (1 + cos θ + i sin θ)(1 + cos 2θ + i sin 2θ)=x+iy then y=

  

  

  

  

The coefficient of x5 in the expression of (1+x)21+(1+x)22+……+(1+x)30 is

  

  

  

  

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

  

  

  

  

The value of cos θ+3√2 sin( θ+π/4)+6 lies between

  

  

  

  

If α, β, γ are the roots of x3+2x2+3x+4=0 then Σα2β2 =

  

  

  

  

The value of k such that the lines 2x-3y+k=0, 3x-4y-18=0 and 8x-11y-33=0 are concurrent, is

  

  

  

  

α and β are the roots of the equation x2+px+p3=0,(p≠0).If the points (α,β) lies on the curve x=y2,then the roots of the given equation are

  

  

  

  

If A=(1,1) ,B=(4,5) and C=(6,13) then cos A=

  

  

  

  

The equation of the tangent to the curve x2+2y=8 and which is perpendicular to x-2y+1=0 is

  

  

  

  

sec2 720- sec 360=

  

  

  

  

If α,β are the roots of ax2+bx+c=0;α+h,β+h are the roots of px2+qx+r=0;and D1,D2 the respective discriminants of these equations,then D1:D2=

  

  

  

  

If n positive integers are taken at random and multiplied together , the probability that the last digit of the product is 2,4,6 or 8 is

  

  

  

  

If (2, -2),(-1, 2),(3, 5) are the vertices of a triangle then the equation of the side not passing through (2, -2) is

  

  

  

  

A stone is projected vertically upwards with an initial velocity 112 ft/sec and moves such that s=112t-16t2 where s is the distance from the starting point and t is the time. The greatest height reached by the stone is

  

  

  

  

The equation of the tangents to a circle x2+y2-4x-6y-12=0 and parallel to 4x-3y=1 are

  

  

  

  

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

  

  

  

  

The period of cot(5x+3)+sin(3x+4)/ sec(3-4x)-cos(4-6x) is

  

  

  

  

If 4l2-5m2+6l+1=0, then the line lx+my+1=0 touches the circle

  

  

  

  

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

  

  

  

  

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

  

  

  

  

(a+b)xc+(b+c)xa+(c+a)xb=

  

  

  

  

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

  

  

  

  

If A,B,C are the minimum value of x2-8x+17,2x2+4x-5,3x2-7x+1 then the ascending order of A,B,C is

  

  

  

  

The equation of the circle passing through the points of intersection of the circle x2+y2-2x+4y-20=0, the line 4x-3y-10=0 and the point (3, 1) is

  

  

  

  

The centre of the circle (1+m2)(x2+y2)-2cx-2cmy=0 is

  

  

  

  

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