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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   Time Left : 00 : 30    : 00

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

  

  

  

  

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?

  

  

  

  

cos2 π/5+ sin2 4π/5=

  

  

  

  

(cos 2α /cos4α- sin4 α)- (cos4 α+ sin4 α/ 2- sin22α)=

  

  

  

  

If (1,2), (4, 3) are the limiting points of a coaxal system , then the equation of the circle in its conjugate system having minimum area is

  

  

  

  

The quadrilateral formed by the pairs of lines 2x2+5xy+2y2=0, 2x2+5xy+2y2=0, 2x2+5xy+2y2-15x-15y+25=0 is

  

  

  

  

If sin x-3 sin 2x+sin 3x=cos x-3cos 2x+cos 3x then x=

  

  

  

  

A unit vector in the xy-plane that makes an angle of 450 with the vector i+j and an angle of 600 with the vector 3i-4j is

  

  

  

  

If (1,2),(3,4) are limiting points and x2+y2-x+ky=0 is one circle of a coaxal system then k=

  

  

  

  

If the of the circle passing through the points (3,4),(3,2),(1,4) is x2+y2+2ax+2by+c=0, then the ascending order of a, b, c is

  

  

  

  

For all values of a and b(a + 2b)x + (a- b)y + (a + 5b) = 0 passes through the point:

  

  

  

  

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

  

  

  

  

If (1, 2) is the mid point of chords of the circle (x -2)2 +(y -4)2=10 and the equation of the chord is ax + by + c=0(a > 0) then a – b + c=

  

  

  

  

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

  

  

  

  

A: The polar of (2, 3) with respect to the circle x2+y2-4x-6y+5=0 is 2x+3y=0 R: The polar of (x1, y1) with respect to the circle S=0 is S1=0

  

  

  

  

A boat is to be manned by 9 crew with 4 on the stroke side, 4 on the row side and one to steer. There are 11 crew of which 2 can stroke only, 1 can row only while 3 can steer only. In how many ways the crew can be arranged for the boat?

  

  

  

  

The locus of the centre of circle which touches the line x cos α+y sin α=p and circle (x-a)2+(y-b)2=c2 is

  

  

  

  

The external centre of similitude of the two circles x2+y2-2x-6y+9=0, x2+y2=4 is

  

  

  

  

The equation of the circle whose radius is 5 and which touches the circle x2+y2-2x-4y-20=0 at the point (5, 5) is

  

  

  

  

Let f(x+y)= f(x)f(y) for all x,y ε R. If f is differentiable at x=0, then

  

  

  

  

The locus of the point of intersection of two tangents to the parabola y2 = 4ax which intercept a constant length d on the directrix is

  

  

  

  

Which term of (2x-3y)12 when x=1, y=5/2 numerically greatest?

  

  

  

  

Two tangents are drawn from the point (-2, -1) to the parabola y2 = 4x. If α is the angle between those tangents then tan α =

  

  

  

  

If θ is the angle between the curves xy=2, x2 +4y=0 then tan θ=

  

  

  

  

The equation of the tangent to the curve y=x3+3x2-5 and which is perpendicular  to y=2x-6y+1=0  is

  

  

  

  

If y = xn-1 log x then xy1-(n-1)y =

  

  

  

  

If the orthocenter and the circumcentre of a triangle are (-3,5,1), (3,3,-1) then the circumcentre is

  

  

  

  

A line passing through (1,0) intersects the curve 2x2+5y2-7x=0 in A and B. Then AB subtends at the origin an angle

  

  

  

  

The point of intersection of the diagonals of the quadrilateral with vertices (1, 2), (3, 4), (2, 1), (-1, -2) is

  

  

  

  

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

  

  

  

  

The extreme values of  4 cos(x2) cos(π/3  + x2 ) cos(π/3 - x2) over IR are

  

  

  

  

In ΔABC,   cot A/2+ cot B/2+ cot C/2=

  

  

  

  

If the equation 2x2+7xy+3y2-x+7y-6=0 represents a pair of lines then the pair of lines parallel to them and passing through the point (2,-1) is

  

  

  

  

Tangents OA and OB are drawn to the circle x2+y2+gx+fy+c=0 from O(0,0). The equation of the circum circle of the ?OAB is

  

  

  

  

I: The equation of the circle concentric with x2+y2-2x+8y-23=0 and passing through (2, 3) is x2+y2-2x+8y-33=0 II: : The equation of the circle passing through  the points (1, 1), (2, -1), (3, 2) is x2+y2-5x-y+4=0

  

  

  

  

The odds against A solving a problem are 3 to 2 and the odds in favour of B solving the same problem ae5 to 4.Thenthe probability that the problem will be solved if both of them try the problem is

  

  

  

  

If x,a,b,c are real and (x-a+b)2+(x-b+c)2=0 then a,b,c are in

  

  

  

  

The number of common tangents to the two circles x2+y2-8x+2y=0 and  x2+y2-2x-16y+25=0 is

  

  

  

  

If α,β,γ are the roots of the equation x3+ax2+bx+c=0 then α-1+β-1+γ-1=

  

  

  

  

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

  

  

  

  

If  f(x)=1og(cos x),  then  domain f.=

  

  

  

  

If α,β,γ are the roots of x3-px2+qx-r=0 then α4+β4+γ4=

  

  

  

  

P and Q are points on the line joining A(-2,5), B(3,-1) such that AP=PQ=QB. Then the mid point of PQ is

  

  

  

  

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

  

  

  

  

If α, β, γ are the roots of x3-3x+7=0 then α β γ=

  

  

  

  

The unit vector orthogonal to a=2i+2j+k, b=3i+4j-12k and forming a right handed system with a and b is

  

  

  

  

The point (3, -4) lies on both the circles x2+y2-2x+8y+13=0 and x2+y2-4x+6+11=0. Then the angle between the circles is

  

  

  

  

(1+ω)(1+ω2) )(1+ω3)(1+ω4)(1+ω5) (1+ω6)...(1+ω3n)=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The equation to the pair of asymptotes of the hyperbola 2x2-y2=1 is

  

  

  

  

If the roots of (3m+1)x2+2(m+1)x+m=0 are equal then m=

  

  

  

  

If the vectors i - 2xj - 3yk and i + 3xj + 2yk are orthogonal to each other, then the locus of the point (x, y) is

  

  

  

  

1- cos A+ cos B- cos (A+B)/1+cos A- cos B- cos(A+B)=

  

  

  

  

If the sum of two of the roots of x4-2x3-3x2+10x-10=0 is zero then the roots are

  

  

  

  

If α, β, γ are the roots of x3+3x2+2x+3=0 then Σ(1/α2β2) =

  

  

  

  

If α, β are the roots of ax2+bx+c=0 then α3+ β3 =

  

  

  

  

If α+β+γ=1,α2+β2+γ2=2 and α3+β3+γ3=3,then α5+β5+γ5=

  

  

  

  

If (1, a), (b, 2) are conjugate points with respect to the circle x2+y2=25, then 4a+2b=

  

  

  

  

The value if b such that x4-3x3+5x2-33x+b is divisible by x2-5x+6 is

  

  

  

  

If one roots of the equation 5x2+13x+k=0 is the reciprocal of the other then

  

  

  

  

sin 6θ(2cos2θ-1)=

  

  

  

  

If B,A, A+B are acute angles, sin(A+B)=12/13, sin B=5/13 then sin A=

  

  

  

  

The equation of the chord of the ellipse 2x2+3y2=6 having (1, -1) as its midpoint is

  

  

  

  

For x є IR, 3cos(4x-5) + 4 lies in the interval :

  

  

  

  

If xr occurs in the expansion (x+1/x2)2n, then its coefficient is:

  

  

  

  

The locus of the poles of chords of the parabola y2 = 4ax, which subtend a right angle at the vertex is

  

  

  

  

If α,β,γ are the roots of x3-px2+qx-r=0 then α2+β2+γ2=

  

  

  

  

P(-1, -3) is a centre of similitude for the two circles x2+y2=1 and x2+y2-2x-6y+6=0. The length of the common tangent through P to the circle is

  

  

  

  

A boats crew consists of 16 men, 6 of whom can only row on one side and 4 only on the other. The number of ways in which the crew can be arranged 8 on each side is

  

  

  

  

If 3p2=5p+2 and 3q2=5q+2 where p≠q,then the equation whose roots are 3p-2q and 3q-2p is

  

  

  

  

If the coefficient of rth term and (r + l)th term in the expansion of (1 + x)20 are in the ratio 1 : 2, then r is equal to:

  

  

  

  

If cos(x-y)=3.cos(x+y), then cot x.cot y=

  

  

  

  

Each side of a square is of length 4. The centre of the square is (3, 7) and one of its diagonals is parallel to y=x. then the coordinates of its vertices are

  

  

  

  

cos2(450- α)+ cos2(150+ α)- cos2(150- α)=

  

  

  

  

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

  

  

  

  

If Tan-1 (sec x + tan x)=π/4+kx then k=

  

  

  

  

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

  

  

  

  

The angle between the tangents from the origin to the circle (x-7)2+(y+1)2 = 25 is

  

  

  

  

The number of 3 letter words formed that containing atleast one vowel from the letters a,b,c,d,e,f is

  

  

  

  

The value of √3cot 200- 4cos 200 is

  

  

  

  

One focus of an ellipse is (1,0) and (0,0). If the length of major axis is 6 its e=

  

  

  

  

The circle orthogonal to the  three circles x2+y2+aix+biy+c=0, i=1, 2, 3 is

  

  

  

  

If m and M respectively denote the minimum and maximum of f(x) = (x - 1)2+ 3 for x ε [ -3, 1], then the ordered pair (m, M) is equal to

  

  

  

  

If the lines 3x-4y-7 =0and 2x-3y-5=0 are two diameters of a circle of area 49π sq unit. Then the equation of this circle is

  

  

  

  

If 6 Sec2 θ-5 Sec θ+1=0 then θ=

  

  

  

  

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

  

  

  

  

If a, b, c are the sides of a triangle then the range of ab+bc+ca/a2+b2+c2 is

  

  

  

  

The pole of a straight line with respect to the circle x2+y2=a2 lies on the circle x2+y2=9a2. If the straight line touches the circle x2+y2=r2, then

  

  

  

  

The height of a hill is 3300 mt. From a point P on the ground the angle of elevation of the top of elevation of the top of the hill is 600. A balloon is moving with constant speed vertically upwards from P. After 5 minutes of its movement, a person sitting in it observes the angle of elevation of the top of the hill is 300. What is speed of the balloon?

  

  

  

  

The point equidistant from (24, 7),(7, 24) and (0, 25) 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 the circles x2+y2+2x-2y+4=0 cuts the circle x2+y2+4x-2fy+2=0 orthogonally, then f=

  

  

  

  

The latusrectum of a hyperbola is 9/2 and eccentricity is 5/4.Its standard equation in standard form is

  

  

  

  

If the points whose position vectors are -2i+3j+5k, i+2j+3k, λi-k are collinear, then λ=

  

  

  

  

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 area of the region bounded by the curve y=(x2+2)2+2x between the ordinates x=0,x=2 is

  

  

  

  

Let P be a point on the circle x2+y2=9, Q a point on the line 7x+y+3=0, and  the perpendicular bisector of PQ be the line x-y+1=0. Then the coordinates of P are

  

  

  

  

If a hyperbola has one focus at the origin and its eccentricity is 2. One of the directries is x+y+1=0. Then the centre of the hyperbola is

  

  

  

  

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