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 volume of the parallelepiped whose edges are represented by 2i-3j, i+j-k, 3i-k is

  

  

  

  

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

  

  

  

  

The area bounded by the curve y=x(x-1)2,y-axis and the line y=2 is

  

  

  

  

The co-efficient of x4 in the expansion of (1-3x)2/(1-2x) is equal to:

  

  

  

  

The inverse point of (1, 2) with respect to the circle x2+y2-4x-6y+9=0 is

  

  

  

  

If the roots of x4+5x3-30x2-40x+64=0 are in G.P then the roots are

  

  

  

  

C0-2. C1+3. C2………..+(-1)n(n+1).Cn =

  

  

  

  

If ax2+2hxy+by2=1 then (hx+by)3y2=

  

  

  

  

If the tangent at the point (at2, at3) on the curve ay2=x3 meets the curve again at Q, then Q=

  

  

  

  

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

  

  

  

  

The angle between the curves y2=4ax, ay= 2x2 is

  

  

  

  

The quadratic equations x2 – 6xa = 0 and x2 – cx + 6 = 0 and have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

  

  

  

  

If f : R → R is continuous such that f(x + y) = f(x) + f(y), ∀x∈R, y∈R, and f(1) = 2 then f(100) =

  

  

  

  

If α,β,γ are the roots of the equation x3+px2+qx+r=0,then Σ1/α β=

  

  

  

  

The points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle for

  

  

  

  

For the curve y2=(x+a)3, then square of the sub tangent is ….subnormal

  

  

  

  

The ordinate of  the centroid of the triangle formed by conormal points on the parabola y2=4ax 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 quadrilateral formed by the pairs of lines 6x2-5xy-6y2=0, 6x2-5xy-6y2+x+5y-1=0 is

  

  

  

  

The equation of the latus rectum  of the parbola x2 – 12x – 8y + 52 = 0 is

  

  

  

  

In a ∆ ABC, (a-b)2cos2(C/2)+(a+b)2sin2(C/2) is equal to

  

  

  

  

If Sn = 13 + 23 + .......... + n3  and Tn = 1+2+..................n then

  

  

  

  

the equation of the parabola whose vertex is at (0,0) and focus is the point of intersection of x+y  =2, 2x –y = 4 is

  

  

  

  

Arrange the magnitudes of following vectors in ascending order A) ixj+ jxk+kxi  B) If lal=2, lbl=3, (a, b)=450 then axb C) (2i-3j+2k)x(3i-j+4k)

  

  

  

  

The number of quadratic expressions with the coefficient drawn from the set (0, 1, 2, 3) is

  

  

  

  

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

  

  

  

  

If Cosec-1 x= 2Cot-1 7+ Cos-1(3/4) then the value of x is

  

  

  

  

If the lines x+ky+3=0 and 2x-5y+7=0 intersect the coordinate axis in concyclic points then k=

  

  

  

  

Consider the circle x2+y2-4x-2y+c=0 whose centre is A(2, 1). If the point P(10, 7) is such that the line segment PA meets the circle in Q with PQ=5, then c=

  

  

  

  

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

  

  

  

  

The diameter and altitude of a right circular cylinder are found at a certain instant to be 20 cm and 40 cm respectively. If the diameter is increasing at the rate of 2 cm/sec then the rate of the change in the altitude will keep the volume constant is

  

  

  

  

cos2 (800+θ)+ sin2 (1000-θ)=

  

  

  

  

The diameter x of a circle is found by measurements to be 5 cm with maximum error of 0.05 cm. the relevant error in the area is

  

  

  

  

The term independent of x in the expansion of (1+x+2x3)(3x2/2-1/3x/)9 is

  

  

  

  

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

  

  

  

  

Let Then which one of the following is true

  

  

  

  

If the asymptotes of the hyperbola 14x2+38xy+20y2+x-7y-91=0 are 7x+5y-3=0, ax+by+c=0 then the descending order of a, b, c is

  

  

  

  

If y=2ax and (dy/dx)=log256 at x=1,then a=

  

  

  

  

If tan(π/4 + θ)+tan(π/4- θ)=a then  tan3 (π/4+ θ)+ tan3 (π/4- θ)=

  

  

  

  

Angle between the tangents to the curve y=x2-5x+6 at the points (2, 0) and (3, 0) is

  

  

  

  

the equation of the parabola whose vertex is (3,-2) axis is parelle to x- axis and latus rectum 4 is

  

  

  

  

If sin θ=-7/25 and  is not in the first quadrant, then (7cot θ -24 tan θ) / (7cot θ+24 tan θ) =

  

  

  

  

(1-ω)(1-ω2) (1-ω4) (1-ω5)(1-ω7) )(1-ω8)=

  

  

  

  

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

  

  

  

  

Let C1=x2+y2-2x-4y=0, C2=x2+y2+2x+10y=0 and L=2x+7y+7=0 Then L is the

  

  

  

  

The equation of the circle passing through the points (1, 1), (2, -1), (3, 2) is

  

  

  

  

If x2+y2+z2≠0,x=cy+bz,y=az+cx,z=bx+ay then a2+b2+c2+2abc=

  

  

  

  

If it rains, a dealer in rain coats can earn Rs.500/- a day, If it is fair, he can lose Rs.40/- per day. If the probability of affair day is 0.6, his mean profit is

  

  

  

  

The function f(x) = tan x has

  

  

  

  

Counters numbered 1, 2, 3 are placed in a bag and one is drawn at random and replaced. The operation is being repeated three times. The probability of obtaining a total of 6 is

  

  

  

  

If y=(1+x2)Tan-1x then y2=

  

  

  

  

The derivative of √(Tan-1 x) w.r.to x is

  

  

  

  

If the points (0,0), (3,√3), (x,y) form an equilateral triangle, then (x,y)=

  

  

  

  

If the points (2,4), (k,6) are conjugate with respect to the parabola y2 = 4x then k =

  

  

  

  

The length of the tangent of the curves x=a cos 3θ, y= a sin3θ (a>0) is

  

  

  

  

If nεN then 10n+3.4n+2+5 is divisible by

  

  

  

  

The equation of the normal to the curve x2=4y at (2, 1) is

  

  

  

  

The coaxal system having limiting points (2,3), (-3, 2) is

  

  

  

  

The equation of tangent at θ on S ≡ x2 + y2 + 2gx+2fy+c =0

  

  

  

  

3 red and 4 white balls of different sizes are arranged in a row at random. The probability that no two balls of the same colour are together is

  

  

  

  

5 boys and 3 girls sit in a row at random. If a is the probability that all the girls sit together, b is the probability that all the boys sit together and c is the probability that all the boys and all the girls sit together then the ascending order a,b,c is

  

  

  

  

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

  

  

  

  

The tangent of the difference of the angles made by the lines 4x2-24xy+11y2=0 with x-axis is

  

  

  

  

The locus of the centre of the circle which touch lines 6x-8y+5=0 and 6x-8y+13=0 is 6x-8y+k=0 then k =

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If A+B+C= 1800 then cos2 A+ cos 2 B - cos2 C=

  

  

  

  

If √(x2+4ax+5)+√(x2+4bx+5)=2(a-b) then x=

  

  

  

  

Equation of the circle touching the y-axis at (0, √3) and cuts the x-axis in the points (- 1, 0) and (-3, 0) is

  

  

  

  

The equations whose roots are exceed by 1than those of x5+5x4+3x3+x2+x-1=0 is

  

  

  

  

The equation whose roots are smaller by 1 than those of 2x2-5x+6=0 is

  

  

  

  

The point on the curve y=x2+5, the tangent at which  is perpendicular to the line x+2y=2 is

  

  

  

  

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

  

  

  

  

The probability that the roots of equation x2+nx+1/2+n/2=0 are real ,where n ε N such that n ≤ 5, is

  

  

  

  

If the circle x2+y2+2a1x+b1y+c1=0 and 2x2+2y2+2ax+2by+c=0 intersect orthogonally,then

  

  

  

  

The equations of the tangents to the hyperbola 3x2-4y2=12 which are parallel to the line 2x+y+7 =0 are

  

  

  

  

The value of ‘α’ for which the equations x+y+z=1,x+2y+4z=α and x+4y+10z=α2have no solution, is

  

  

  

  

sin 210 cos 90-cos 840cos 60=

  

  

  

  

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

  

  

  

  

Through the point (2, 3) a straight line is drawn making positive intercept on the coordinate axes. The area of the triangle thus formed is least, when the ratio of the intercepts on the x and y axes is

  

  

  

  

If two of the roots of 2x3+7x2+2x-3=0 are differ by 2 then the roots are

  

  

  

  

(1+ cos π/10) (1+ cos 3π/10) (1+ cos 7π/10) (1+ cos 9π/10)=

  

  

  

  

If the equation ax2+2hxy+by2+2gx+2fy+c=0 represents a pair of parallel lines, then f2/g2=

  

  

  

  

cos 250 - cos650=

  

  

  

  

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

  

  

  

  

Two equal circles with their centers on X and Y-axis will posses the radical axis in the following form

  

  

  

  

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=

  

  

  

  

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

  

  

  

  

The angles between tangents to the parabola y2 = 4ax at the points where it intersects with the line x – y –a = 0 is

  

  

  

  

If coth x= sec θ, then cosech x=

  

  

  

  

The equation to the circle which is such that the lengths of the tangents to it from the points (1,0), (2,0) and (3,2)are 1,√7, √2, respectively is

  

  

  

  

If the quadratic equation ax2+bx+c=0 if a and c are of opposite signs and b is real,then roots of the equation are

  

  

  

  

The sum of the series log42-log82+log162-… is

  

  

  

  

The direction cosines of the line passing through P (2, 3, - 1) and the origin are

  

  

  

  

The distance between the line r=2i-2j+3k+λ(i-j+4k) and the plane r.(i+5j+k)=5 is

  

  

  

  

If cos θ+ sin θ=a, then sin 2θ=

  

  

  

  

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

  

  

  

  

If the equation λx2 – 5xy + 6y2 + x -3y=0, represents a pair of straight lines, then their point of intersection is

  

  

  

  

If α, β, γ are the roots of x3+px2+qx+r=0 then (β+γ-3α)(γ+α-3β)(α+β-3γ) =

  

  

  

  

(tan 230+ tan220)/(1- tan 230 .tan220)=

  

  

  

  

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