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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An aeroplane flying with uniform speed horizontally one kilometer above the ground is observed at an elevation of 600. After 10 seconds if the elevation is observed to be 300, then the speed of the plane (in km/hr) is:

  

  

  

  

If the points (3,2,-4) ,(5,4,k), (9,8,-10) are collinear then k=

  

  

  

  

If (2, 1),(-1, -2),(3, 3) are the midpoints of the sides BC,CA,AB of Δ ABC, then the equation of AB is

  

  

  

  

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

  

  

  

  

If (x+1)/(2x-1)(3x+1)=A/(2x-1)+B/(3x+1), then 16A+9B is equal to :

  

  

  

  

The locus of the centre of a circle which cuts the circles 2x2+2y2-x-7=0 and 4x2+4y2-3x-y=0 orthogonally is a straight line whose slope is

  

  

  

  

If 2Sin2 θ=3 Cos θ, then the valueof θ in [0,2π] are

  

  

  

  

The stationary point of f(x)=2x3-9x2+12x-3 is

  

  

  

  

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 nεN, and the period of [cosnx/sin(x/n)] is 4π, then n is equal to

  

  

  

  

The derivative of Sin-12x/1+x2 w.r.to Tan-12x/1-x2is

  

  

  

  

The arrangement of the following straight lines in ascending order of their slopes A) 2y=√3x    B) y=2     C) y=x               D) y=-x

  

  

  

  

For the circle2x2+2y2-5x-4y-3=0, the point (4, 2)

  

  

  

  

If there is a possible error of 0.02 cm in the measurement of the diameter of a spare then the possible percentage error in its volume when the radius 10 cm is

  

  

  

  

If the probability that A and B will die with in a year are p and q respectively, then the probability that only one of them will be alive at the end of the year is

  

  

  

  

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

  

  

  

  

If P(x)is a polynomial of 3rd degree and P’’(1)=0, P’’’(1)=6 then P’’(0)=

  

  

  

  

Observe the following statements : A : Three vectors are coplanar if one of them is expressible as a linear combination ofthe other two. R : Any three coplanar vectors are linearly dependent.Then which of the following is true

  

  

  

  

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

  

  

  

  

The line among the following which touches the parabola y2=4ax, is

  

  

  

  

Two opposite vertices of a square are (1,-2) and (-5,6) then the other two vertices are

  

  

  

  

If f : R→R is an even function having derivatives of all orders, then an odd function among the following is:

  

  

  

  

cos 60 sin 240cos 720 is equal to

  

  

  

  

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

  

  

  

  

The length of the transverse axis of the hyperbola 4x2-9y2+8x+40=0 is

  

  

  

  

The parametric equation of the circle x2+y2+x+√3y=0 is

  

  

  

  

Find the equation of the parabola, whose axis parallel to the y-axis and which passes through the points (0,4),(1,9) and (4,5) is

  

  

  

  

The equation of the circle cutting orthogonally circles x2+y2+2x+8=0, x2+y2-8x+8=0 and which touches the line x-y+4=0 is

  

  

  

  

If y = 3x is a tangent to a circle with centre (1,1), then the other tangent drawn through (0, 0) to the circle is

  

  

  

  

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

  

  

  

  

The circumference of a circle is measured as 56 cm with an error 0,02 cm. The percentage error in its area is

  

  

  

  

 A three digit number  n such that the last two  digits of it are equal and differ from the first the number of such n is

  

  

  

  

One hundred cards are numbered from 1 to 100. The probability that a randomly chosen card has a digit 5 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

  

  

  

  

I: The circum centre of the triangle with vertices (1, √3), (1, √2), (3, -√3) is (2, 0). II: The ortho-centre of the triangle formed by the lines 4x-7y+10=0, x+y=5, 7x+4y=15 is (1, 2)

  

  

  

  

The angle subtended by the double double ordinate of length 16 of the parabola y2=8x at its vertex is

  

  

  

  

The term in the independent of x in the expansion of (3+2x)44, is

  

  

  

  

The area between the curves y2=8x and x2=8y is

  

  

  

  

If A+B+C = 3600 then tan A/2+ tan B/2+ tan C/2=

  

  

  

  

The length of the sub tangent   of the curve y2=x3/2a-x at (a, a) is

  

  

  

  

Coeff. of x3 in log(1 + x + x2)

  

  

  

  

The function f(x) = x/√1-x2 and g(x)=x/√1+x2, find fog(x).

  

  

  

  

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 f(x)=[x], g(x)=x-[x]then which of the following functions is the zero functions

  

  

  

  

The vectors (1, 2, 3), (4, 5, 6), (6, 7, 8) are

  

  

  

  

The circumradius of the triangle formed by the points (2,-1,1) , (1,-3,-5), (3,-4,-4) is

  

  

  

  

In ΔABC, if r1 =3, r2= 10, r3= 15, then c=

  

  

  

  

The point on the curve x2+y2-2x-3=0 at which the tangent is parallel to x-axis is

  

  

  

  

The radical centre of the circle x2+y2=1, x2+y2-2x=1, x2+y2-2y=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

  

  

  

  

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

  

  

  

  

If tan A,tan B are the roots of x2-px+q=0,the value of sin2(A+B) is

  

  

  

  

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is

  

  

  

  

The area (in sq.units) of the circle which touches the lines 4x+3y=15 and 4x+3y=5  is

  

  

  

  

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

  

  

  

  

If A+B+C=1800 then sin2A- sin2 B- sin2 C=

  

  

  

  

If the equations x2+ax+b=0 and x2+bx+a=0 (a≠b) have a common root, then a+b is equal to

  

  

  

  

The area (in square units) of the triangle formed by the lines x = 0,y = 0 and 3x + 4y = 12, is

  

  

  

  

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

  

  

  

  

The centre of the sphere (r-3i+3j+5k).(r+i-j+3k)=0 is

  

  

  

  

The transformed equation of x3-4x2+1/4x-1/9=0,by eliminating fractional coefficients is

  

  

  

  

The locus of the midpoints of chords of the circle x2+y2=25 which touch the circle (x-2)2+(y-5)2=289 is

  

  

  

  

The equation whose roots are multiplied by 3 of those of 2x2+3x-1=0 is

  

  

  

  

If (dy/dx)=[y+xtan(y/x)]/x then sin(y/x) is equal to

  

  

  

  

If ( x - 2 ) is a common factor of the expressions x2 + ax + b and x2 +cx+ d, then b-d/c-a is equal to :

  

  

  

  

For the circle x2+y2-6x+8y-1=0, the points (2, 3) (-2, -1) are

  

  

  

  

The number having two digits such that it is 4 times the sum and three times the product of its two digits are

  

  

  

  

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

  

  

  

  

∫ex(1+cot x+cot2x) dx is equal to:

  

  

  

  

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

  

  

  

  

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

  

  

  

  

Assertion(A):x2+x+1 is greater than zero for all real x. Reason(R):when b2-4ac

  

  

  

  

The values of x for which 2x3-3x2-36x+10 has extreme values are

  

  

  

  

Pole of the line 2x+3y+4=0 w.r.to the ellipse x2/2+y2/4=1 is

  

  

  

  

The number of ways in which 5 red balls and 4 black balls of different sizes can be arranged in a row so that two balls of the same colour come together is

  

  

  

  

The triangle formed by 2x+3y-7=0 and 3(2x+3y)2-(3x-2y)2=0 is

  

  

  

  

If Cos (A-B) =  3/5 and tan A tan B  = 2 then which one of the following is true

  

  

  

  

If (cos 3α+i sin 3α)(cos 5β+i sin 5β)= cos θ+i sin θ then θ is

  

  

  

  

Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the midpoints of the chords of the circle C that subtend an angle of 2π/3 at its centre is

  

  

  

  

If 2 Sinh-1 (a/√(1-a2))= log(1+x/1-x), then x=

  

  

  

  

Integrating factor of (x+2y3)dy / dx = y2 is :

  

  

  

  

If ∫sin-1[2x/(1+x2)]dx=f(x)-log(1+x2)+c then f(x) is equal to

  

  

  

  

If a=2i+2j+k, a.b=14, axb=3i-j-8k then b=

  

  

  

  

A particle moves along the curve y = x2 + 2x. Then the point on the curve such that x and y co-ordinates of the particle change with the same rate 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 equation to the circle touching the y-axis at the origin and passing through(b, c) is

  

  

  

  

The stationary points of 2x3-9x2-24x+16 are

  

  

  

  

The number of four digited numbers which are not divisible by 5 that can be formed from by using the digits 0,2,4,5 is

  

  

  

  

The circle x2+y2=4x+8y+5=0 intersects the line 3x-4y=m at two distinct points if

  

  

  

  

If n positive integers are taken at random and multiplied together , the probability that the last digit of the product is 2,4,6 or 8 is

  

  

  

  

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

  

  

  

  

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 equations to its asymptotes are

  

  

  

  

If a = i^ - j^ -k^ and b = + λ i^ - 3 j^ + k^ and the orthogonal   projection   of   b   on   a   is (4/3) (i^ - j^ -k^), then λ  is equal to

  

  

  

  

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

  

  

  

  

The point on the parabola y = x2 + 7x + 2 closest to the line y = 3x – 3 is

  

  

  

  

A plane π makes intercepts 3 and 4 respectively on z-axis.If π is parallel to y-axis,then its equation is

  

  

  

  

If k=(1+sin A)(1+sinB)(1+sin C)=(1-sinA)(1-sin B)(1-sin C) then k=

  

  

  

  

Statement I : If f:A→B, g:B→C are such that gof is an injection, then f is an injection. Statement II : If f:A→B, g:B→C are such that gof is an injection, then g is an injection. The correct statement is

  

  

  

  

If a,b,c are three non-collinear points then r=(1-p-q)a+pb+qc represents

  

  

  

  

The function y=f(x) satisfying the condition f(x+1/x)=x3+1/x3 is

  

  

  

  

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