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 |x|

  

  

  

  

The polar of the point(t-1, 2t) w.r.t the circle x2+y2-4x-6y+4=0 passes through the point of intersection of the lines

  

  

  

  

The area under the curve y=x2-3x+2 with boundaries as x-axis and the ordinates at x=0,x=3 is

  

  

  

  

If y=x2+2x+1/x2+2x+7, then inverse function x is defined only when

  

  

  

  

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

  

  

  

  

If ax= by= cz = dw then the value of x[(1/y)+(1/z)+(1/w)]is

  

  

  

  

The transformed equation x4 + 4x3 + 2x2 – 4x – 2=0 by eliminating 2nd term is

  

  

  

  

If P(-1,4), Q(11,-8) divides AB harmonically in the ratio 3:2 then A,B in order are

  

  

  

  

The function f(x) = tan x has

  

  

  

  

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

  

  

  

  

The lines acosθ+2asinθ+(1/r)=0, bcosθ+3bsinθ+(1/r)=0 and ccosθ+4csinθ+(1/r)=0 are concurrent then a,b,c are in

  

  

  

  

The minimum value of sin6 x+ cos6 x is

  

  

  

  

If f(x)=cos2x+cos2(600+x) + cos2(600-x) and g(3/2)=5 then gof(x)=

  

  

  

  

If sin-1 (3/5)+sin-1(5/13)= sin-1 x, then x=

  

  

  

  

The difference of the slopes of the lines 3x2-8xy-3y2=0 is

  

  

  

  

The pressure p and the volume v of gas are connected by the relation pv=300. If the volume is increasing at the rate of 0.6 cubic cm per minute then the rate of change in pressure of the gas when the volume is 30 cubic cm is

  

  

  

  

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

  

  

  

  

The slope of the radical axis of the circles (x+2) 2+(y+3)2=25 and (x+1) 2+(y-1) 2=25 is

  

  

  

  

The coefficient of x10 in 1-2x+3x2/1-x is

  

  

  

  

the equation of the parabola whose axis is parallel to x –axis and passing through (- 2,1), (1,2), (-1,3) 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

  

  

  

  

The circle passing through the points (1, t), (t, 1) and (t, t) for all values of t passes through the point

  

  

  

  

In the expansion of (1-2x+3x2)/(1-x)2coefficient of x20 is

  

  

  

  

The domain of Cos-1 (2/2+sinx) in [0,2π] is

  

  

  

  

If V=πr2h then rVr+2hVh=

  

  

  

  

The perimeter of a triangle is 16 cm, one of the sides is of length 6 cm. If the area of the triangle is 12 sq cm. Then the triangle is

  

  

  

  

If the sum of two of the roots of 4x3+16x2-9x-36=0 is zero then the roots are

  

  

  

  

Orthocentre of thele whose vertices are (2,-1/2), (1/2,-1/2), (2,(√3-1)/2) is

  

  

  

  

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

  

  

  

  

The domain of √1-3x+Cos-1 3x-1/2 is

  

  

  

  

The equation of the chord of the circle x2+y2-4x+6y-3=0 having (1, -2) as its midpoint is

  

  

  

  

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 volume of a metal hollow sphere is constant. If the outer radius is increasing at the rate of ¼ cm per sec. the rate at which the inner radius is increasing when the radii are 8 cm and 4 cm respectively is

  

  

  

  

Sum of n brackets of (1)+(1/3+1/32)+(1/33+1/34+1/35)+…. Is

  

  

  

  

If the range of the random variable X is from a to b, a < b F(X < a)=

  

  

  

  

sin 2θ / (1+ cos 2θ) =

  

  

  

  

AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C.The projection of BC on the axis of the parabola 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 (2, -2),(-1, 2),(3, 5) are the vertices of a triangle then the equation of the side not passing through (2, -2) is

  

  

  

  

From 101 to 1000 natural numbers a number is taken at random. The probability that the number is divisible by 17 is:

  

  

  

  

If the tangent at P on the circle x2+y2=a2 cuts two parallel tangents of the circle at A and B then PA. PB=

  

  

  

  

tan 150+tan 750 =

  

  

  

  

If the product of two of the roots of x4-5x3+5x2+5x-6=0 is 3 then the roots are

  

  

  

  

The angles of a triangle are in the ratio 3: 5:10. Then the ratio of the smallest side to the greatest side is:

  

  

  

  

The roots of √3x2 +10x-8√3=0

  

  

  

  

The value of sin θ / ( sin2(π/8+ θ/2)- sin2(π/8-θ/2)) =

  

  

  

  

The derivative of axlog x+(x2-1) sin x w.r.t x is

  

  

  

  

C0+C1/2+C2/22+C3/23+.....Cn/2n

  

  

  

  

1.4.7+4.7.10+7.10.13+…. n terms

  

  

  

  

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

  

  

  

  

If a=2i+3j+6k, b=3i-6j+2k, c=6i+2j-3k then axb=

  

  

  

  

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

  

  

  

  

Bag A contains 3 white and 2 black balls. Bag B contains 2 white and 4 black balls. One bag is selected at random and a ball is drawn from it. The probability that it is white is

  

  

  

  

If the point  [x1 )+t(x2-x1), y1+t(y2-y1)] divides the join of  (x1, y1) and (x2, y2) internally, then

  

  

  

  

If a straight line L is perpendicular to the line 4x - 2y = 1 and forms & triangle of area 4 square units with the coordinate axes, then an equation of the line L is :

  

  

  

  

If y = e-12x Cos (5x+2) then yx =

  

  

  

  

5 different engineering, 4 different mathematics and 2 different chemistry books are placed in a shelf at random. The probability that the books of each kind are all together is

  

  

  

  

The derivative of cot-1(cosec x-cot x) w.r.to x is

  

  

  

  

If A(2, -l)and B(6, 5) are two points the ratio in which the foot of the perpendicular from (4, 1 ) to AB divides it, is

  

  

  

  

The fourth vertex of the square whose consecutive vertices are (4,5,1), (2,4,-1), (3,6,-3) is

  

  

  

  

sin A+ sin B = √3( cos B - cos A)  then sin 3A + sin 3B is equal to

  

  

  

  

The equation of the line dividing the line segment joining two pairs of points (0, 0),(-4, 7) and (2, 3), (4, -5) in the ratio 1:2 and 5:3 respectively  is

  

  

  

  

In a triangle ABC, if cot A = (x3+x2+x)1/2, cot B= (x+x-1+1)1/2 and cot C= (x-3+x-2+x-1) -1/2 then the triangle is

  

  

  

  

sin2 α+ cos2 (α + β)+ 2 sin α sin β. cos(α + β) =

  

  

  

  

If α1,α2,α3  respectively denotes the moduli of the complex number -i , (1+i) / 3  and -1+i  then their increasing order is

  

  

  

  

If  cos θ - 4 sin θ = 1 then  sin θ + 4 cos θ   is equal to

  

  

  

  

The angle between the curves xy=4 and x2-y2=15 at the point (-4, -1) is

  

  

  

  

The roots of x3+x2-2x-2=0 are

  

  

  

  

If 5,-7,2 are the roots of lx3+mx2+nx+p=0 then the roots of lx3-mx2+nx-p=0 are

  

  

  

  

The solution of y2 dx+(3xy-1)dy=0 is

  

  

  

  

A bag contains four balls. Two balls are drawn and found them to be white. The probability that all the balls are white is

  

  

  

  

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

  

  

  

  

cot2θ(sec θ-1/ (1+sin θ))+ sec2 θ (sin θ-1/ (1+sec θ))=

  

  

  

  

∑((12+22+32+….+n2)/1+2+3+….+n)=

  

  

  

  

The equation of the circle cutting orthogonally the circles x2+y2-8x-2y+16=0, x2+y2-4x-4y-1=0 and passing through the point (1, 1) is

  

  

  

  

8sin4θ=

  

  

  

  

The equation of the sphere one of whose diameter has end points (1, 2, 4) and (3, 0, 2)

  

  

  

  

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

  

  

  

  

C0-2. C1+3. C2………..+(-1)n(n+1).Cn =

  

  

  

  

If 5x2+λy2=20 represents a rectangular hyperbola, then λ is equal to

  

  

  

  

If y=(ax+b/cx+d) then 2y1y3=

  

  

  

  

The equation of  the line having  intercepts a,b on the axes such that a+b =5, ab=6 is

  

  

  

  

If cosec θ-sin θ=m, sec θ-cos θ=n then (m2n)2/3+(mn2)2/3=

  

  

  

  

The lines 2x + 3y = 6, 2x + 3y = 8 cut the x-axis at A and B respectively, drawn through the point (2, 2) meets the x-axis as C in such a way that abscissae of A, B and C are in arithmetic progression. Then the equation of the line L is:

  

  

  

  

Let α,β be the roots of x2-x+p=0 and γ,δ be the roots of x2-4x+q=0.If α,β,γ,δ are in G.P then the integral values of p and q respectively,are

  

  

  

  

If normal at (1,1) on 2x2+2y2-2x-5y+k=0 is x+2y-3=0 then k=

  

  

  

  

The locus of the point of intersection of the tangents at the ends of a chord of a circle x2+y2=a2 which touches the circle x2+y2-2ax=0 is

  

  

  

  

If an error of 0.02 cm is made while measuring the radius 5 cm of a circle, then the relative error in the area is

  

  

  

  

The condition that the circles x2+y2+2ax+2by+c=0, x2+y2+2bx+2ay+c=0 to touch each other is

  

  

  

  

A student is allowed to select atmost n books from a collection of (2n+1) books. If the total number of ways in which he can select books is 63, then n=

  

  

  

  

The vector a=αi+2j+βk lies in the plane of the vectors b=i+j and c=j+k and bisects the angle between b and c. Then which one of the following gives possible values α and β

  

  

  

  

x2n-1+y2n-1 is divisible by x+y if n is

  

  

  

  

Let f(x)=1/|x| for |x| ≤1, f(x)=ax2+b for |x|>1. If f is differentiable at any point, then

  

  

  

  

If y=x+1/(x+1/x+....∞) then dy/dx=

  

  

  

  

A: The equation of the common chord of the two circles x2+y2+2x+3y+1=0, x2+y2+4x+3y+2=0 is 2x+1=0 R: If two circles intersect at two points then their common chord is the radical axis

  

  

  

  

The orthocentre of the triangle formed by(-1,-3), (-1,4), (5,-3) is

  

  

  

  

If the normal at ‘θ’ on the hyperbola x2/a2-y2/b2=1 meets the tansverse axis at G, the AG, AG’=

  

  

  

  

The circles x2+y2+4x-2y+4=0 and x2+y2-2x-4y-20=0 

  

  

  

  

The equation of the tangents from the origin to x2+y2-6x-2y+8=0 are

  

  

  

  

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

  

  

  

  

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