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 the pairs of lines x2-2pxy-y2=0 and x2-4xy-y2=0 be such that each pair bisects the angle between the other pair, then p=

  

  

  

  

If the lines x+ky+3=0 and 2x-5y+7=0 intersects the coordinates axes in concyclic points then k =

  

  

  

  

. I: The equation to the pair of lines passing through the point (2,-1) and parallel to the pair of lines 3x2-5xy+2y2-17x+14y+24=0. II: The equation to the pair of lines passing through (1,-1) and perpendicular to the pair of lines x2-xy-2y2=0 is 2x2-xy-y2-5x-y+2=0.

  

  

  

  

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 the roots of 24x3-26x2+9x-1=0 are in H.P then the roots are

  

  

  

  

The portion of a line intercepted between the coordinate axes is bisected by the point (2, -1) in the ratio 3:2. The equation of the line is

  

  

  

  

A cylindrical vessel of radius 0.5mts. is filled with oil at the rate of 0.25 π.c mts./minute. The rate, at which the surface of oil is increasing is

  

  

  

  

If the tangent to the circle x2+y2=5 at (1, -2) also touches the circle x2+y2-8x+6y+20=0, then the point of contact is

  

  

  

  

A curve passes through the point (2, 0) and the slope of the tangent at any point is x2-2x for all values of x. The point of maximum or donation the curve is

  

  

  

  

The function f(x)=a sin x+1/3x has maximum value at x =π/3. The value of a is

  

  

  

  

The probabilities of problem being solved by two students are 1/2 and 1/3.Find the probability of the problem being solved.

  

  

  

  

(sin θ+ cosec θ)2+(cos θ+ sec θ)2 =

  

  

  

  

The radii of two circles are 2 units and 3 units.If the radical axis of the circles cuts one of the common tangents of the circles in P then ratio in which P divides the common tangent is

  

  

  

  

If f(x) is a polynomial of degree n with rational coefficients and 1+2i, 2-√3 and 5 are three roots of       f(x) = 0, then the least value of n is :

  

  

  

  

If the roots of (c2-ab)x2-2(a2-bc)x+(b2-ac)=0 are equal,then

  

  

  

  

The distances travelled by a particle in time t is given by s=t3-2t2-3t+5. The velocity of the partial when t=2 sec. is

  

  

  

  

An aircraft gun can take a maximum of three shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second and third shot are 0.5,0.4,0.3 respectively. The probability that the gun hits the place is

  

  

  

  

The length of the direct common tangent of the circles x2+y2-4x-10y+28=0 and x2+y2+4x-6y+4=0 is

  

  

  

  

If 1,α1,α2,....,αn-1 are the roots of xn-1=0 then(1-α1)(1-α2)...(1-αn-1)=

  

  

  

  

If Tan A+ Tan B=p and Cot A+ cot B= q then cot (A+B)=

  

  

  

  

If α,β,γ,δ are the roots of x4-x3-7x2+x+6=0 then α4+β4+γ4+δ4=

  

  

  

  

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

  

  

  

  

Four numbers are chosen at random from {1, 2, 3, .... 40}. The probability that they are not consecutive, is 

  

  

  

  

If u=x2+y2+z2,x=et,y=et sin t,z=et cos t then du/dt=

  

  

  

  

The approximate change in y, when y=x2+2x, x=3, δx=0.01 is

  

  

  

  

If α+β=-2 and α3+β3=-56 then the quadratic equation whose roots α,β is

  

  

  

  

If x= sin t cos 2t, y= cos t sin 2t then (dy/dx)t=π/4

  

  

  

  

The line y = m(x + a)+a/m touch the parabola y2= 4a(x+ a) form

  

  

  

  

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

  

  

  

  

(1.02)6 + (0.98)6 =

  

  

  

  

The number of common tangents to the two circles x2+y2-x=0, x2+y2+x=0 is

  

  

  

  

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

  

  

  

  

The image of the point (4, -13) with respect to the line 5x + y + 6 = 0 is

  

  

  

  

If the product of the roots of x3+kx2-3x+4=0 may be -1 then k=

  

  

  

  

The shortest distance from (-2, 14) to the circles x2+y2-6x-4y-12=0 is

  

  

  

  

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

  

  

  

  

A:The area of the triangle formed by the two rays whose combined equation is y=|x| and the line x+2y=2 is 3/4 R: The area of the triangle formed by the lines ax2+2hxy+by2=0,lx+my+n=0 is (n√h2-ab)/(|am2-2nlm+bl2|)

  

  

  

  

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

  

  

  

  

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

  

  

  

  

A box contains 10 mangoes out of which 4 are rotten. Two mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is

  

  

  

  

The equation of the circle cutting orthogonally circles x2+y2-4x+3y-1=0 and passing through the points (-2, 5), (0, 0) is

  

  

  

  

The parabola with directrix x + 2y -1 =0 and focus (1,00) is

  

  

  

  

If one root of 24x3-14x2-63x+45=0 is the double the other then the roots are

  

  

  

  

The locus of the    point z = x + iy  satisfying | (z-2i) / (z+2i) |  =  1 is

  

  

  

  

If 1,2,3,4 are the roots of the equation x4+ax3+bx2+cx+d=0 then a+2b+c=

  

  

  

  

If a= sin θ+ cos θ, b= sin3 θ+ cos3θ then

  

  

  

  

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

  

  

  

  

If A+B+C= 2S, then cos2 S+ cos2 (S-A)+ cos2 (S-B)+ cos2 (S-C)=

  

  

  

  

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

  

  

  

  

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

  

  

  

  

3 integers are chosen at random without replacement from the first 20 integers. The probability that the product is odd is

  

  

  

  

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

  

  

  

  

If the middle term of (1+x)2n is 1.3.5...(2n-1)k/n! then k=

  

  

  

  

If the line x + y + 2 = 0 touches the parabola y2 = kx, then k =

  

  

  

  

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

  

  

  

  

If (a+ib)2= x+iy then x2+y2=

  

  

  

  

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

  

  

  

  

The roots of x4-12x3+34x2-12x+1=0 are

  

  

  

  

15 buses fly between Hyderabad and tirupathi. The number of ways can a man go to Tirupathi from Hyderabad by a bus and return by a different bus is

  

  

  

  

From an urn containing 3 white and 5 black balls , 4 balls are transfered in to an empty urn. From this urn a ball is drawn and found to be white. The probability that out of four balls transfered 3 are white and 1 is black is

  

  

  

  

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

  

  

  

  

The domain of log10 (x3-x) is

  

  

  

  

The two circles x2+y2=a2, x2+y2=c2(c>0) touch each other if

  

  

  

  

The equation of the normal to the curve 3y2=4x+1 at (1, 2) is

  

  

  

  

If α,β,γ are the roots of the equation x3+px2+qx+r = 0 then the coefficient of x in the cubic equation whose roots are α(β+γ), β(γ+α) and γ(α+β) is

  

  

  

  

tan θ+ 2 tan 2θ+4 tan 4θ+ 8 tan 8θ+16 tan 16θ+32 cot 32θ=

  

  

  

  

sin4 π/8+ sin4 3π/8+ sin4 5π/8+ sin4 7π/8=

  

  

  

  

If  O(0,0), A(3,4), B(4,3) are the vertices of a triangle then the length of the altitude from O is

  

  

  

  

If the lines x2+(2+h)xy-4y2=0 are equally inclined to the coordinate axes then h=

  

  

  

  

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

  

  

  

  

d/dx{(√(a2+x2)+ √(a2-x2))/ (√(a2+x2)- √(a2-x2))}

  

  

  

  

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

  

  

  

  

If the rate of change of the side of a square is 0.05 cm/sec, then the rate of change in the area of the square when the side is 10 cm is

  

  

  

  

If A,B are acute angles, tan A=5/12, cos B=3/5, then cos (A+B)=

  

  

  

  

128 sin8 θ=

  

  

  

  

If the 2nd term in the expansion (13√a+a/√a-1) is 14a5/2, then the value of nC3/nC2 is

  

  

  

  

If cos θ= cos α- cos β/ (1-cos α cos β) then tan2(θ/2)tan2(β/2)=

  

  

  

  

If the 5th term is 24 times the 3rd term in the expansion of (1+x)11 then x=

  

  

  

  

Let AB be the chord 4x-3y +5 = 0 with respect to the circle x2+y2-2x+4y-20=0. If C= (7, 1), then the area of the triangle ABC is

  

  

  

  

Equation of the tangent to the circle x2+y2=3, which is include at 600 with the x-axis is

  

  

  

  

Sin-1(sin 2π/3) =

  

  

  

  

The sum of the fifth powers of the roots of the equation x4-3x3+5x2-12x+4=0 is

  

  

  

  

The condition that the two spheres a(x2 + y2 + z2)=k2 may cut orthogonally (k ≠0)

  

  

  

  

If α,β,γ are the roots of the equation 3x3+6x2-9x+2=0,then Σ(α/β) =

  

  

  

  

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

  

  

  

  

2 cosh 3 cosh 5=

  

  

  

  

If x2y-x3(dy/dx)=y4cosx then x3y is equal to

  

  

  

  

The radius of the circle passing through the point (6, 2) and two of whose diameters are x+y=6 and x+2y=4 is

  

  

  

  

The displacement of a body of mass 100kg in a rectilinear motion is given by the formula s=2t2+3t+1. The K.E of the body 5 sec after the start is

  

  

  

  

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

  

  

  

  

If 1,-1,2 are the roots of x3+Ax2+Bx+C=0 then the ascending order of A,B,C is

  

  

  

  

If Cot-1 4/3+Cot-1 5/3= Tan-1 k, then k=

  

  

  

  

Minimum value of cos x+ sin x is obtained at

  

  

  

  

If A, B, C are the maximum heights reached when three stones projected vertically upwards moves according to the law s= 60t-5t3, s=6t-1/2t2, s=10t-7t3 respectively then the ascending order of A,B,C is

  

  

  

  

If y= ax2+b/x then x2y2=

  

  

  

  

If 2x+ky-10=0, 5x+2y-7=0 are parallel, then the value of k =

  

  

  

  

If √2 and 3i are the two roots of a biquadratic equation with rational coefficients,then its equation is

  

  

  

  

The quadrilateral formed by the lines x-y+2=0, x+y=0, x-y-4=0, x+y-12=0 is

  

  

  

  

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