A to Z Exams

If 1,ω,ω2 are the cube roots of unity, then (a+bω+cω2)/ (c+aω+bω2) is equal to:

If the inverse point of (2,-1) with respect to the circle x2+y2=9 is (p, q) then q=

The magnitude of the projection of the vector a = 4i - 3j + 2k on the line which makes equal angles with the coordinate axes is

If tan(α+θ)= ntan(α-θ), then (n+1)sin 2θ=

In the expansion of (2-3x)-1 the 3rd term is

In a ?ABC , orthocentre is H(2354,981), A(2,1), B (-10,6) then the distance between the orthocentres of ?HBC, ?HAC is

If one ticket is randomly selected from, tickets numbered from 1to 30 then the probabilitythat the numbered on the tickets i a multiple of 5 or 7 is

If A, B, C, D are the length of tangents to the curves 1.y=4x2 at (-1, 4) 2. Y=x3+1 at (1, 2) 3. Y=x3/2-x at (1, 1) 4. 2x2+3xy-2y2=8 at (2, 3) then the ascending order of A, B, C, D is

A bag contains 4 green, 6 black and 7 white balls. A ball is drawn at random .The probability that it is either black ball or a white ball is

The solution of (dy/dx)+y=1 is

If two circles(x-3) 2+(y-1)2=r2 and x2+y2-6x+4y+4=0 intersect in two distinct points then

Match the following Circle Radius I. x2+y2+4x-6y-12=0 a) 3 II. x2+y2-4x-2y-4=0 b) 5 III. x2+y2+6x+8y-96=0 c) 11

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

A gas holders contain 100 cubic ft of gas at a pressure of 5 lb per sq. inch. If the pressure is increasing at the rate of 0.05 lb per sq. inch per hour, then the rate of decrease of the volume assuming Boyle’s law pv=a constant is

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

If nεN, n is odd then n(n2-1) is divisible by

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

The maximum value of x3-3x in the interval [0,2] is:

The equation of the sphere through the points (1,0,0) (0,1,0) and (1,1,1) and having the smallest radius

The equation of the circle passing through the point (1, -2) and having its centre on the line 2x-y-14=0 and touching the line4x+3y-23=0 is

d/dx{sin-1(3x-4x3)}=

The derivative of (log x)xw.r.to x is

If the circle S=x2+y2-16=0 intersects another circle S’=0 of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to 3/4 then the centre of S’=0 is

Tan-1 3/2-Tan-11/5 =

If Two angles of a triangle are 300, 450 and the included side is √3+1, then the remaining sides are

The tangents at (at12, 2at1) and (at22, 2at2) on the parabola y2=4ax are at right angles then

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

The volume of the parallelepiped whose conterminal edges are 2i-3j+4k, i+2j-2k, 3i-j+k is

The area of the triangle formed by(a+3,a-2), (a-4,a+5) and  (a,a) is

d/dx{Tan-1√(1-cos x)/(1+cos x)}=

If Sinx Sinhy= cos θ and Cosx Coshy= Sinθ, then Cosh2y + Cos2x

The domain of Sinh-1 2x is

The vector equation of the plane passing through the point i+2j+5k, -5j+k, -3i+5j is

If a is the area bounded by y=x2,x-axis,x=0,x=2; b is the area bounded by y=x2+2,x-axis,x=1,x=2 and c is the area bounded by y=x3,x-axis,x=1,x=4 then the ascending order of a,b,c is

If the lines 2x+3y+1=0, 3x+2y-1=0 intersect the coordinate axes in four concyclic points then the equation of the circle passing through these four points is

If the circles x2+y2-4x+6y+8=0, x2+y2-10x-6y+14=0 touch each other , then the point of contact is

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

Focus of the parabola 4y2-20x-8y+39=0 is

The stability of hydrides increase from NH3 to BiH3 in group 15 of the periodic. The area of the region enclosed by the curves y = x, x = e, y =1/x and the

The distance between the origin and the normal to the curve y=e2x+x2 at x=0 is

Midpoints of the sides AB and AC of triangle ABC are (-3,5) and (-3,-3) respectively, then the length of BC=

If α,β,γ are the roots of x3-px2+qx-r=0 then α4+β4+γ4=

The point on the parabola y2 = 36x whose oridinate is three times its abscissa is

If (a1+ib1)(a2+ib2)……(an+ibn)=A+iB,then (a12+b12) (a22+b22)……. (an2+bn2) =

sin 120 sin 240 sin 480 sin840=

2 sin θ. tan θ(1-tan θ)+2 sin θ sec2 θ / (1+tan θ)2

The condition that the slope of a line represented by ax2+2hxy+by2=0 is thrice that of the other is

The equation to one asymptote of the hyperbola 14x2+38xy+20y2+x-7y-91=0 is 7x+5y-3=0, then the other asymptote is

If α,β,γ are the roots of x3+px2+qx+r=0 then β2+γ2/β γ+γ2+α2/γ α+α2+β2/α β=

Three students A,B,C are to take part in a swimming competition. The probabilities of A ‘s winning or the probability of B’s winning of B’s winning is 3 times the probability of C’s winning. The probability of the event of either B or C to win is

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

The length of the tangent from a point on the circle x2+y2+2gx+2fy+c=0 to the circle x2+y2+2gx+2fy+c’=0 is

The equation of the line passing through the point of intersection of  5x-2y=12,  4x-7y-15=0 and parallel to 5x-2y=7 is

The distance between the circumcentre and the orthocenter of the triangle formed by the points (2,1,5), (3,2,3), (4,0,4) is

cos3200+ cos31000 +cos3 1400=

At a selection, the probability of selection of A is 1/7 and that of B is 1/5.The probability that both of them would not be selected is

cot(A+150)- tan(A- 150)=

d/dx{x√a2+x2+a2Sinh-1(x/a)}=

C1+2.C2+3.C3+…….+n.Cn =

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 cos(x-y), cos x, cos(x+y) are three distinct numbers which are in harmonic progress and cos x≠cos y, then 1+ cos y=

The work done by the force F=2i-3j+2k in moving a particle from(3, 4, 5) to (1, 2, 3) is

The equation of  the straight line whose slope 2/3 and which divides the line segment joining (1, 2),(4,-3)  in the ratio 3:4 is 

If y=x+1/(x+1/x+....∞) then dy/dx=

If the circle x2 + y2 + 2x + 3y + 1 = 0 cuts another circle x2+y2 + 4x + 3y + 2 = 0 in A and B, then the equation of the circle with AB as a diameter is :

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

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

A lot consists of 12 good pencils, 6 with minor defects an d2 with major defects. A pencil is drawn at random. The probability that this pencil is not defective is

If x=a cos3 θ sin2 θ, y= a sin3θ cos2 θ and (x2+y2)p/(xy)q (p,q ε N) is independent of θ, then

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’ is differentiable function, f(1)=0, f1(1)=3/5 and y=f(e2x)ex then (dy/dx)x=0 =

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

If (-2, 6) is the image of the point (4, 2) with respect to the line L = 0, then L is equal to

If the plane 2ax-3ay+4az+6=0 passes through the midpoint of the line joining the centres of the spheres x2+y2+z2+6x-8y-2z=13 and x2+y2+z2-10x+4y-2z=8 then a=

The equation of the director circle of x2/12-y2/8=1 is

The extremities of a diagonal of a parallelogram are the points (3, -4) and(-6, 5). If the third vertex is (-2, 1) then the fourth vertex is

If A+B+C=00 then sin A+ sin B+ sin C=

The function tan-1(sin x) increases in

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

The locus of the point of intersection of two tangents drawn to the circle x2+y2=a2 which make a constant angle α to each other is

1+4+13+40+…n terms=

If the area of the triangle formed by the points (1,2), (2,3), (x,4) is 40sq.unit, then x is

If the algebraic sum of the perpendicular distances from the points(2,0),(0,2),(4,4) to a variable line is equal to zero. Then the line passes through the point

If the range of a random variable X is {0, 1, 2, 3, 4,........} with P(X = k) = (k+1)a / 3k for k ≥ 0 then a is equal to

The pairs of lines a2x2+2h(a+b)xy+b2y2=0, ax2+2hxy+by2=0 are

If tan (π/4 + θ)+ tan(π/4 -θ)= k sec 2θ, then the value of k is

cos(α+β+γ)+cos(α-β-γ)+cos(β-γ-α)+cos(γ-α-β) is equal to:

The angle between the circles x2 + y2 – 4x – 6y – 3=0 and x2 + y2 + 8x – 4y + 11=0 is:

If Tan-1 x+ Tan-1 y+ Tan-1 z=π, then x+y+z=

The number of normals to the hyperbola [(x2/a2)-(y2/b2)]=1 from an external point is

The ratio of the rth term and the (r + 1)th term in the expansion of (1 + x)n is:

The volume of the tetrahedrone formed by (1, 2, 3), (4, 3, 2), (5, 2, 7), (6, 4, 8) is

The circumcentre of the triangle with vertices at (4,6), (1,2) and (-3,5) is  

The equation of the sphere on the join of (3, 4, -1), (-2, -1, 0) as diameter is

(2+ω2+ω4)5

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

Tan [cos-1 4/5+tan-1 2/3] =

If x is real, then the minimum value of [(x2-x+1)/(x2+x+1)], is

If  (1-tan 20 cot220)/(tan 1520- cot 880)= k√3, then value of k is

The length of the normal from pole on the line rcos(θ-π/3)=5 is