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 lines 2x-3y=5 and 3x-4y=7 are two diameters of a circle of area 154 sq unit. Then the equation of this circle is

  

  

  

  

Equation of the circle passing through (0,0),(a,b) and (b,a) is

  

  

  

  

A student has to answer 10 out of 13 questions in an examination choosing at least 5 questions from the first 6 questions. The number of choice available to the student is

  

  

  

  

The distance between the foci of the hyperbola x2- 3y2- 4x - 6y - 11 = 0 is

  

  

  

  

A bag contain 12 two rupee coins, 7one rupee coins and 4 half rupee coins. If 3 coins are selectedat random, then the probability that each coin is of different value is

  

  

  

  

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

  

  

  

  

The multiplicative inverse of (4+3i) is

  

  

  

  

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=

  

  

  

  

If tan (cot x) = cot (tan x), then sin 2x=

  

  

  

  

If sum of the roots of the equation 2x9-11x7+6x4+8=0 is ‘a’ then ‘a’=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

The number of terms in the expansion of (a+b+c+d)5 is

  

  

  

  

The points (-a, -b), (0, 0), (a, b), (" a^2 ",ab) are

  

  

  

  

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

  

  

  

  

If tan β= n tan α / 1+(1-n)tan2 α, then tan(α - β)=

  

  

  

  

The multiple roots of x4-2x3+11x2-12x+36=0 are

  

  

  

  

(cosh x/1- tanh x)+(sinh x/ 1- coth x)=

  

  

  

  

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

  

  

  

  

If sinh 9- k sinh k=(k+1)sinh3 k,then k=

  

  

  

  

49n+16n+k is divisible by 64 for n?N. Then the numerically least –ve integer value of k is

  

  

  

  

The distance between the limiting points of the coaxial system x2 + y2 – 4x – 2y – 4 + 2λ(3x + 4y + 10)=0

  

  

  

  

C0-2. C1+3. C2………..+(-1)n(n+1).Cn =

  

  

  

  

A unit vector perpendicular to the plane of a=2i-6j-3k, b=4i+3j-k is

  

  

  

  

It is given that there are 52 Fridays in a leap year. The probability that it will have 53 Saturdays is

  

  

  

  

The lines 2x+y-1=0, ax+3y-3=0, 3x+2y-2=0 are concurrent

  

  

  

  

(cosh x+ sinh x)n=

  

  

  

  

cos π/11 cos 2π/11 cos 3π/11 cos 4π/11 cos 5π/11=

  

  

  

  

If the first three terms of (1+ax)n are 1,6x,6x2 then (a,n)=

  

  

  

  

(cos A+ cos 3A+cos 5A+cos 7A)/ (sin A+sin 3A+sin 5A+sin 7A)=

  

  

  

  

An equilateral triangle is inscribed in the circle x2+y2=a2 . The length of the side of the triangle is

  

  

  

  

The locus of a point P such that the distances from P to the points (2,3,5) ,( 1,2,-1)  are in the ratio 5:2 is

  

  

  

  

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 bag containing 12 two rupee coins, 7 one rupee coins and 4 half rupee coins.If 3 coinsare selected at random, then the probability that the sum of 3 coins is maximum is

  

  

  

  

If x=sin-1t, y= √(1-t2) then d2y/dx2=

  

  

  

  

If a tangent to the circle x2 + y2 + 4x - 4y+4=0 makes a equal intercepts on the coordinate axes then the equation of that tangent is

  

  

  

  

The area (in square unit) of the region enclosed by the curves y=x2 and y=x3 is

  

  

  

  

d/dx{Tan-1(x-√x/1+x3/2}=

  

  

  

  

The area of the triangle formed by the lines 3x+4y+5=0, (3x+4y)2-3(y-4x)2=0 is

  

  

  

  

7/5(1+1/?102 +1.3/1.2.1/104 +1.3.5/1.2.3.1/106 +...........∞)

  

  

  

  

The lines represented by the equation 3x2-5xy+2y2=0 are

  

  

  

  

In ΔABC,   tan (A/2)tan (B/2)+ tan (B/2)tan (C/2)+ tan (C/2) tan (A/2)=

  

  

  

  

If a tangent drawn from the point (4, 0) to the circle x2+y2=8 touches it at a point in the first quadrant, then the coordinates of another point B on the circle such that AB=4 are

  

  

  

  

If tan2 θ=3 cosec2 θ-1 then θ=

  

  

  

  

The equations whose roots are opposite in sign and equal in magnitude of the roots of x7+3x5+x3-x2+7x+2=0 is

  

  

  

  

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

  

  

  

  

The point on the curve x2=2y which is closest to the point (0, 5) is

  

  

  

  

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

  

  

  

  

If two consecutive terms in the expansion of (x+a)n are equal where n is a positive integer then (n+1)a/x+a is

  

  

  

  

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

  

  

  

  

If the length of a chord of the circle x2 + y2=a2is 2K then the locus of the midpoint of that chord is a circle of radius

  

  

  

  

If the acute angle between the lines 2x+3y-5=0, 5x+ky-6=0 is  then the value of k is

  

  

  

  

The equation of the tangent to the parabola y2 = 12x at (3, -6) is

  

  

  

  

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

  

  

  

  

The maximum value of a2-abx-b2x2 is

  

  

  

  

The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle x2+y2=9 is

  

  

  

  

If ax+by+c=0 is the equation of the common radical axis of the coaxial system (3x2+3y2-2x-2y-1)+λ(x2+y2-x-2y-3)=0 then ab+bc+ca=

  

  

  

  

If x= a cos θ (1+cos θ), y=sin θ(1+cos θ) then (dy/dx)θ=π/2

  

  

  

  

The number of positive divisors of 253673 is

  

  

  

  

The modulus and principal argument of complex number (1+2i)/(1-2i) are respectively:

  

  

  

  

The point of intersection of straight lines represented by 6x2 + xy - 40y2 – 35x - 83y + 11 = 0 is:

  

  

  

  

The equation of the common chord of the two circles (x-a)2+(y-b)2=c2, (x-b)2+(y-a)2=c2 is

  

  

  

  

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

  

  

  

  

The value of k so that 3x4+4x3+2 x2+10x+k is divisible by x+2 is

  

  

  

  

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

  

  

  

  

cosec2 θ. cot2 θ- sec2 θ. tan2 θ-( cot2 θ- tan2 θ)( sec2 θ. cosec2θ-1)=

  

  

  

  

If f(x)=3x-7/5x-3 then (fof)(x)=

  

  

  

  

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

  

  

  

  

If f(x)=√(x+2√(2x-4))+ )=√(x-2√(2x-4)) then

  

  

  

  

The lines x+2y-3=0, x+2y+7=0, 2x-y-4=0 from three sides of two squares.

  

  

  

  

The solution of x2dy-y2dx=0 is

  

  

  

  

lf the centroid of the triangle formed by (p, q),(q,1),(1,p) is  the origin, then p3+q3+1=

  

  

  

  

If x+iy= cis α cis β then the value of x2+y2 is

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If there is an error of 0.05 cm, while measuring the side of equilateral triangles as 5 cm, then the percentage error in area is

  

  

  

  

If the foot of the perpendicular from (0,0,0) to a plane is (1,2,3), then the equation of the plane is

  

  

  

  

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

  

  

  

  

If (3+i) is a root of the equation x2 + ax+ b=0 then a =

  

  

  

  

The angle between the pair of straight lines  formed by joining the points of intersection of  x2 + y2 = 4 and y = 3x + c to the origin is a right angle. Then c2 is equal to

  

  

  

  

sin A+sin 5A+sin 9A)/(cos A+ cos 5A+ cos 9A)=

  

  

  

  

If the length of the tangent from (h, k) to the circle x2+y2=16 is twice the length of the tangent from the same point to the circle x2+y2+2x+2y=0, then

  

  

  

  

A man 6 feet height walks at a uniform of 20 above the floor. An object falls freely under gravity, starting from rest at the same height as the lamp, put at a horizontal distance of 5 ft from it. The speed of the shadow of the object on the floor when it has fallen through 15 ft is

  

  

  

  

If A+B+C =900 then cos2 A+cos2B+ cos2 C=

  

  

  

  

If y√1+x2=log(x+√1+x2) then  (1+x2)y1+xy=

  

  

  

  

If tan θ=-4/3 and θ is not in the fourth quadrant , then the value of 5 sin θ+10cos θ+ 9 secθ+16 cosec θ – 4 cot θ=

  

  

  

  

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

  

  

  

  

A: The angle between the tangents drawn from origin to the circle x2+y2-14x+2y+25=0 is π/2 R: If θ is the angle between the pair of tangents drawn from (x1, y1) to the circle S=0 of radius r then tanθ/2=r/√S11

  

  

  

  

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

  

  

  

  

Tangents are drawn  from  the Point (-2, -1) to the hyperbola 2x2-3y2=6. Their equations are

  

  

  

  

The value of sin[(1/2)cot-1(3/4)] is equal to

  

  

  

  

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

  

  

  

  

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

  

  

  

  

If α,β,γ,δ are the roots of x4+px3+qx2+rx+s=0 then Σα2βγ

  

  

  

  

If p1,p2,p3 are the product of perpendiculars from (0,0) to xy+x+y+1=0, x2-y2+2x+1=0, 2x2+3xy-2y2+3x+y+1=0 respectively then ascending order of p1,p2,p3 is

  

  

  

  

If cos x+ cos y=4/5, cos x- cos y=2/7, then 14 tan(x-y/2)+ 5 cot (x+y/2)=

  

  

  

  

If the line 2x+3y+1=0 and 3x-y-4=0 lie along diameters of a circle of circumference 10π, then the equation of the circle is

  

  

  

  

 If dx + dy =(x + y) ( dx- dy ) then log ( x  +  y ) is equal to

  

  

  

  

(x+y+z)(x+yω+zω2)(x+yω2+zω)=

  

  

  

  

Four tickets marked 00,01,11 respectively are placed in a bag. A ticket is drawn at random 5 times being replaced each time. The probability that the sum of the numbers on the tickets is 22 is

  

  

  

  

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