### Eamcet Test

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In ΔABC , if A=750, B=450, C=√3, then b=

{n (n+1) (2n+1) : n Є Z }  is subset of

If α,β,γ are the roots of the equation x3+px2+qx+r=0,then Σ(α-β)2=

(1)+(2+3)+(4+5+6)+….n brackets=

The points (0,-1), (-2,3), (6,7), (8,3) form

2 cosh 3 cosh 5=

A problem in EAMCET examination is given to three students A, B and C, whose chances of solving it are 1/2, 1/3, 1/4 respectively. The probability that the problem will be solved is

The vertices of a triangle are (2, 4), (4, -2), (-3, -6).Then the origin lies

The midpoint of the line segment joining (2,3,-1), (4,5,3) is

A thin magnetic iron rod of lenght 30cm is suspended in a uniform magnetic filed.Its time period of oscillation is \$s.It is broken into three equal parts.The time period in seconds of oscialltion of one part when suspended in the same magnetic filed is:

The function f(x)= x3-9x2+15x+25 is decreasing in

If the circles x2+y2=4 and x2+y2-6x-8y+K=0 touch internally then K=

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

A wire carrying a current of 4A is in the form of a circle it is necessary to have a magnetic field of induction πx10-5T at the center.The radius of the circle must be

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

The tangents at (3, 4), (4, -3) to the circle x2+y2=25 are

The pole of the straight line x+4y = 4 With respect to the ellipse x2 + 4y2 = 4 is

If tangent to the x2+y2=c2 makes intercepts a and b on the coordinate axes then

4(cos3 100 +sin32 00) =

If A= cos2 3π/5+ cos2 4π/5, b= cos2 π/8+ sin2 3π/8, C= cosec 100- √3 sec 100 then

If the angle of minimum deviation produced by equilateral prism is 300.The refractive index of the prism is

Which of the following biomolecules acts as specific catalysts in biological reaction

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

C1+2.C2+ 3.C3+…….+n.Cn=

The condition f(x) = x3 + px2 + qx + r (xЄR) to have no extreme value, is

If f(x)=1/2[3x+3-x], g(x)=1/2[3x-3-x], then f(x) g(y)+f(y)g(x)=

The sum and product of the slops of the tangents to the hyperbola 2x2-3y2=6 drawn from the point (-1,1) are

The molar conductance of HCl,NaCl and CH3COONa are 426,126 and 91Ω-1cm2mol-1 Respectively. The molar conductance for CH3COOH is

The points of trisection of the line segment joining (2,-3,5), (3,1,-2) are

If α and β are the roots of the equation ax2 + bx + c = 0 and, if px2 + qx + r = 0 has roots (1-α)/ α  and (1-β) / β, then r is equal to

The circumcentre of the triangle with vertices at A(5, 12),B(12, 5), c (2√(13 ) ,3√(13 )) is

5th term of (2x2+3/x)5 is 10. Then x=

One atom of 3919K contains:

A wooden block is dropped from the top of a cliff 100m high.Simultaneously a bullet of mass 10g is fired from the foor of the cliff upwards with a velocity of 100 m/s.The bullet and wooden block will meet each other after a time:

In ΔABC, 1+4 sin(π-A/4)sin(π-B/4)sin(π-C/4)=

If C0, C1, C2,...... are binomial coefficients , then C1+C2+C3+C4+....+Cr+....+Cn is equal to :

sec h-1 (sin θ) is equal to

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

A machine gun fires 360 bullets per minute. Each bullet moves with a velocity of 600ms-1, If the power of the gun is 5.4kw, the mass of each bullet is,

if f(x)=a2x-a-2x/a2x+a-2x, then f(x) is

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

The centres of the three circles x2+y2-10x+9=0, x2+y2-6x+2y+1=0, x2+y2-9x-4y+2=0 lie on the line

If α,β,γ are the roots of x3-px2+qx-r=0,then Σα2(β+γ)=

If A,B,C are the remainders of x3-3x2-x+5,3x4-x3+2x2-2x-4,2x5-3x4+5x3-7x2+3x-4 when divided by x+1,x+2,x-2 respectively then the ascending order of A,B,C is

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

The sub-tangent, ordinate and sub-normal to the parabola y2 = 4ax at a point ( diffferent from the origin ) are in

If the lines y=4-3x; ay=x+10; 2y+bx+9=0 from three sides of the rectangle in order and the fourth side passes through (1, -2) then other sides are

The line x cosα+y sinα=p touches the circle x2+y2-2axcosα-2aysinα=0, then p=

If z1=1+2i,z2=2+3i,z3=3+4i,then z1,z2 and z3 represents the vertices of

Tan-1(cot x) - Tan-1(cot 2x)=

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

If n is a positive integer, then the coefficient of xn in the expansion of (1 + 2x)n/(1-x) is:

The odds against A solving a problem are 3 to 2 and the odds in favour of B solving the same problem ae5 to 4.Thenthe probability that the problem will be solved if both of them try the problem is

The weight in grams of a non-volatile solute (M.wt:60) to be dissolved in 90 g of water to produce a relative lowering of vapour pressure of 0.02 is

If the equation of the circle which cuts orthogonally the circle x2+y2-4x+2y-7=0 and having centre at (2, 3) is x2+y2+2ax+2by+c=0 then the ascending order of a, b, c is

Calculate the emf of the cell   Cu (s) | Cu2+ (aq) || Ag+ (aq) | Ag (s)  GivenEoCu2+/Cu  = +0.34V ,  EoAg+/Ag  =0.80 V

If α is a non real root of the equation x6-1=0 then (α2+α3+α4+α5)/(α+1) is

The area of the triangle whose sides are given by 2i-7j+k and 4j-3k is

Which of the following is not correct

. 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 x = sint; y = sin pt then (1-x2) (d2y/dx2) -x(dy/dx) +p2y =

At the foot of a mountain the angle of elevation of a summit is found to be 450. After ascending 1 km towards the mountain up, a slope of inclination 300, the angle of elevation is found to be 600. The height of the mountain is

If A=(1, 1, 1), B=(1, 2, 3), C=(2, -1, 1) be two vertices of ΔABC, then the length of internal bisector of the angle A is

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

The perpendicular distance of radical axis determined by the circles x2 + y2 + 2x + 4y – 7 =0 and x2 + y2 – 6x + 2y – 5 =0 from the origin is:

The lines ax2+2hxy+by2+2gx+2fy+c=0 intersect x-axis at A and B, y-axis at c and d, then the combined equation to AB and CD is

If x2-3x+2 is a factor of x4-px2+q=0,then(p,q)=

When ethyl alcohol reacts with bromine in the presence of alkali the compound formed

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

Sin-1 (16/65) +2 Tan-1 (1/5) =

The circumfence of a circle measured as 14cm with   an error of 0.01 cm. the approximate percentage error in the area of the circle is

8sin4θ=

In the reaction AlCl3+Cl-→AlCl4-, AlCl3 is

Origin is the centre of a circle passing through the vertices of an equilateral triangle whose median is of length 3a, then the equation of the circle is

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

If α,β,γ are the roots of x3+2x2-5x+2=0 then the equation whose roots α-1/βγ,β-1/γα,γ–1/αβ is

The solution of (x2+x)(dy/dx)=1+2x is

In ΔABC , if c2= a2+b2, 2s= a+b+c, then 4s (s-a) (s-b) (s-c) =

The ratio of radii of first orbits of H, He+ and Li+2 i

The difference in ΔH and ΔE for the combustion of methane at 270C would be

Two identical stringed instruments have a frequency of 100Hz.The tension in one of them is increased by 4%.If they are now sounded together the number of beats per second is

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

If α,β,γ are the roots of the equation x3+qx+c=0 the equation whose roots are -α-1,-β-1,-γ-1 is

The locus of the point of intersection of the perpendicular tangents to the parabola x2 = 4ay is

The area of the quadrilateral formed by the tangents from the point (4,5) to the circle x2+y2-4x-2y-11=0 with a pair of radii joining the points of contact of these tangents is

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

For all integers n ≥ 1, which of the following is divisible by 9

If α,β are the roots of ax2+bx+c=0 then 1/α3+1/β3=

If Sinh-1 √3= log(sec θ+tan θ), then θ=

If A is an invertible matrix of order n, then the determinant of adj A is equal to :

1+cos 2x+cos 4x+cos 6x- 4 cosxcos 2xcos 3x=

The set of all values of a for which the function f(x)=(a2-3a+2)(cos2x/4-sin2x/4)+(a-1)x+sin 1 does not possess critical points is

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

In a compensated pendulum two rods of  different metals are used with their lengths in ratio of 2 : 3. The coefficients of linear expansions for metals in the ratio is :

If the line lx+my = 1 is a normal to the hyperbola (x2 /a2 ) - (y2 / b2)  =1 then (a2/l2)  - (b2/m2) is equal to

List -I List-II (A) Flespar (I) [Ag3SbS3] (B) Asbestos (II) Al2O3 . H2O (C) Pyrargyrite (III) MgSO4 . H2O (D) Diaspore (IV) KAlSi3O3 (V) CaMg3(SiO3)4

If x4-6x3+3x2+26x-24 is divided by x-4 then the quotient is

A= cos 200- sin 200, B= cos 1000+ sin 1000, C= cos 5π/6+ sin 2π/3 then the ascending order is

If the lengths of the tangent from P(h,k) to the circles x2+y2-4x-5=0 and x2+y2+6x-2y+6=0 are equal then

If |x|

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