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

  

  

  

  

sin2200+ sin21000 +sin2 1400=

  

  

  

  

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

  

  

  

  

If n is even then C02-C12+C22-……….+(-1)n Cn2 =

  

  

  

  

If the orthocenter of the angle formed by the lines 2x+3y-1=0, x+2y-1=0, ax+by-1=0  is at the origin, then (a, b) is given by

  

  

  

  

A question paper contains 5 questions each having an alternative. The number of ways that a student can answer one or more questions is

  

  

  

  

Two angles ofa triangle are Cot-1 2 and Cot-1 3.Then the third angle is

  

  

  

  

(cos 3θ - sin 3θ)/ (cos θ+ sin θ)=

  

  

  

  

The length of the intercept made by the normal at (1,6) of the circle x2+y2-4x-6y+3=0 between the coordinate axes is

  

  

  

  

If α, β, γ are the angles made by a line with x, y, z axes in positive directions then the range of cos α cos β+ cos β cos γ+cos γ cos α is

  

  

  

  

If 3x-2y+4=0 and 2x+5y+k=0 are conjugate lines w.r to the ellipse 9x2+16y2=144 then the value of k is

  

  

  

  

The vertices of a hyperbola (2,0),(-2,0) and the foci are (3,0),(-3,0).The equation of the hyperbola is

  

  

  

  

For all values of λ, the polar of the point (2λ, λ-4) with respect to the circle x2+y2-4x-6y+1=0 passes through the fixed point

  

  

  

  

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

  

  

  

  

The term independent of x in (√(x/3)+√3/(2x2 ))10is:

  

  

  

  

(a-b).(b-c)x(c-a)=

  

  

  

  

The solution of (x2y3+x2)+(y2x3+y2)dy=0 is

  

  

  

  

If x

  

  

  

  

In ΔABC , cos(A+2B+3C/2)+cos(A-C/2) =

  

  

  

  

The equation of the circle passing through the points of intersection of the circlesx2+y2=5, x2+y2+12x+8y-33=0 and touching x-axis is

  

  

  

  

Equation of the latusrectum of the parabola x2+8x+12y+4=0 is

  

  

  

  

If the slope of one line of 8x2+2hxy+by2=0 is double the other, then h2=

  

  

  

  

A line which makes an acute  angle ? with the possitve direction f x-axis is drawn through the point P(3, 4) and cuts the curve =4x at Qand R . The lengths of the segments  PQ and PR  are numerical values of the roots of the equation

  

  

  

  

 If α is a non real root number of x6 = 1 then  (α5 + α3 +α +1 ) / (α2 +1) is equal to

  

  

  

  

The equation of the tangent to the  curve y2=4x+5 and which is parallel to0 y=2x+7 is

  

  

  

  

If the lines x2 + 2xy – 35y2 - 4x + 44y -12=0 and 5x +λy -8 = 0 are concurrent, then the value of λ is

  

  

  

  

d/dx{cos-1√(1+x)/2}=

  

  

  

  

If the area of the triangle formed by the points (t,2t), (-2,6), (3,1) is 5sq.unit, then t 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 a,b,c are distinct then (b-c)x+(c-a)y +(a-b)=0 and (b3-c3)x + (c3-a3)y+(a3-b3)=0 represent the same line when

  

  

  

  

3[sin4(3π/2-α)+ sin4(3π+α)]-2[sin6(π/2+α)+ sin6(5π-α)]=

  

  

  

  

The normal of the circle(x-2)2+(y-1)2=16 which bisects the chord cut off by the line x-2y-3=0 is

  

  

  

  

If α,β,γ are the roots of x3+2x2-5x+2=0 then the equation whose roots α-1/βγ,β-1/γα,γ–1/αβ is

  

  

  

  

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 roots of x3-6x2+7x+2=0, one root being 2+√5 are

  

  

  

  

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

  

  

  

  

If α,β,γ are the roots of x3+3px2+3qx+r=0 then the equation whose roots α-1/βγ,β-1/γα,γ–1/αβ is

  

  

  

  

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

  

  

  

  

The volume of the parallelepiped whose conterminal edges are 2i-3j+4k, i+2j-2k, 3i-j+k is

  

  

  

  

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

  

  

  

  

The locus of the middle point of chords of the ellipse x2/a2+y2/b2=1   which are at a constant distance d from the centre of the ellipse is

  

  

  

  

If y2=(x-a)(x-b) then d3/dx3[(d2y/dx2)-2/3]=

  

  

  

  

If an error of 0.02cm is made while   measuring the radius 10cm of a sphere, then the error in the volume is

  

  

  

  

The additive inverse of (1+2i)(3-4i) is

  

  

  

  

The angle between the lines x cos α + y sin α = p1 and x cos β +y sin β =p2 where α

  

  

  

  

d/dx{Sin-12x/1+x2}=

  

  

  

  

If cot θ+ cosec θ= √3 then θ=

  

  

  

  

The inverse point of (1, 2) w.r.t the circle x2+y2=25 is (5, k), then k=

  

  

  

  

If α,β are the roots of 6x2-6x+1=0 then 1/2(a+bα+cα2+dα3)+1/2(a+bβ+cβ2+dβ3)=

  

  

  

  

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

  

  

  

  

The point diametrically opposite to the point P(1, 0) on the circle x2+y2+2x+4y-3=0 is

  

  

  

  

A:The area of the triangle formed by the two rays whose combined equation is y=|x| and the line x+2y=2 is 3/4 R: The area of the triangle formed by the lines ax2+2hxy+by2=0,lx+my+n=0 is (n√h2-ab)/(|am2-2nlm+bl2|)

  

  

  

  

A family of curves has the differential equation (xy)dy/dx = 2y2 - x2. Then the family of curves 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 the roots of 2x3-3x2+kx+6=0 are in A.P then k=

  

  

  

  

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

  

  

  

  

The equation of the normal at the positive end of the latus rectum of the hyperbola x2-3y2=144 is

  

  

  

  

d/dx{Tanxn+Tannx+Tan-1(a+xn/1-axn)}=

  

  

  

  

Cos-1(63/65) + 2 Tan-1(1/5) =

  

  

  

  

If y= ax+b/(x-1)(x-4) has a maximum value at the point (2, -1) then

  

  

  

  

If in a binomial distribution n=20 and q=0.75,then its mean is

  

  

  

  

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

  

  

  

  

cos 200+cos 1000+cos 1400 =

  

  

  

  

The harmonic mean of the roots of the equation (5+√2)x2-(4+√5)x+8+2√5)=0 is

  

  

  

  

"The points (0,"  8/3   )," (1, 3), (82, 30) are"

  

  

  

  

A tower 51 m high has a mark at a height of 25m from the ground. If the two parts subtend equal angles to an eye at the height of 15 m from the ground, the distance of the tower from the observe 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 :

  

  

  

  

The equations of the tangents to the hyperbola 9x2-16y2 =144 at the ends of latus recta are

  

  

  

  

If θ= Sin-1 x+ Cos-1 x+ Tan-1 x, 0≤x≤1, then the smallest interval in which θ lies is given by

  

  

  

  

If two angles of ∆ ABC are 45o and 60o, then the ratio of the smallest and the greatest sides are

  

  

  

  

If cot θ=-3/4 and θ is not in the second quadrant then 5 sin θ+10 cos θ+9 sec θ-16 cosecθ- 4cot θ=

  

  

  

  

If (2i+4j+2k)x(2i-xj+5k)=16i-6j+2xk then the value of x is

  

  

  

  

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

  

  

  

  

In a ?ABC , orthocentre is H(2354,981), A(2,1), B (-10,6) then the distance between the orthocentres of ?HBC, ?HAC is

  

  

  

  

cos(n+1)α cos(n-1)α+ sin(n+1)α.sin(n+1)α

  

  

  

  

The transformed equation of x3-(5/2)x2-(7/18)x+(1/108)=0 by removing fractional coefficients is

  

  

  

  

The sum of the distances of any point on the ellipse 3x2+4y2=24 from its foci is

  

  

  

  

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

  

  

  

  

tan 200+ tan 400+√3 tan 200. tan 400=

  

  

  

  

The points on the ellipse x2/25+y2/9=1 whose angles differ by a right angle are

  

  

  

  

Let a, b, c be the distinct non-negative numbers. If the vectors ai+aj+ck, i+k and ci+cj+bk lie in a plane then c is

  

  

  

  

The sides of triangle are 3x+2y-6=0, 2x-3y+6=0, x+2y+2=0. P(0, b) is a point on y-axis. If P lies on the triangle or inside the triangle then the range of b is

  

  

  

  

A man is known to speak the truth 2 out of 3 times. He throws a die and reports that it is a six. The probability that it is actually a five is

  

  

  

  

If α,β are acute angles, sin α=4/5, tan β=5/12 then the descending order of A=sin(α+β) ,B= cos(α+β), C= tan(α+β) is

  

  

  

  

x+(x2/3!)+(x3/5!)+....∞=

  

  

  

  

The period of cos (5x/2) is

  

  

  

  

Statement I: The points 4i+5i+k, -j-k, 3i+9j+ 4k and -4i+4j+4k are coplanar Statement II  : The given points from  the  vertices of a parallelogram. Which of the following is true? a)  Both statements  are  true and statement II is correct explanation of statement I b)  Both  statements  are true  and statement II is not correct explanation of statement I cv) Statement I is true and statement II is false d)  Statement I is false and  Statement II is true

  

  

  

  

In a ∆ABC ,  ∑(b+c) tan a/2 tan(b-c)/2  is equal to

  

  

  

  

C2+C4+C6+……….. =

  

  

  

  

If a random variable X take values 0 and 1 with respective probabilities 2/3 and 1/3 then the expected value of X is:

  

  

  

  

The equation of the circle cutting orthogonally circles x2+y2-4x+3y-1=0 and passing through the points (-2, 5), (0, 0) is

  

  

  

  

If α,β,γ are the roots of 4x3-6x2+7x+3=0 then αβ+βγ+αγ=

  

  

  

  

The shortest distance between the straight line passing through the point A=(6, 2, 2) and parallel to the vector(1, -2, 2) and the straight line passing through A’=(-4, 0, 1) and parallel to the vector (3, -2, -2) is

  

  

  

  

If x= a(2 cos θ+cos 2θ), y= a(2 sin θ+sin 2θ)then dy/dx=

  

  

  

  

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

  

  

  

  

If f(x) =2x2+3x-5, x=3, δx=0.02, then  δf=

  

  

  

  

The solution of x2dy-y2dx=0 is

  

  

  

  

If the sum of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 6,then k=

  

  

  

  

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

  

  

  

  

The value of ‘a’ such that the sum of cubes of the roots of the equation x2 – ax + (2a – 3)=0 assumes the minimum value is

  

  

  

  

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