A to Z Exams

The locus of the middle point of chords of the ellipse x2/a2+y2/b2=1   whose pole lies on the auxiliary circle is

The angle between the two line having slopes 3/2 and -2/3

Orthocentre of thele whose vertices are (2,-1/2), (1/2,-1/2), (2,(√3-1)/2) is

If X is a poisson variate with P(X = 0) = 0.8, then the variance of X is :

(√2+1)6+(√2-1)6=

If f : R → R is defined by f(x) = [2x] - 2[x] for x ε R, where [x] is the greatest integer not exceeding x, then the range of f is :

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

There are 25 railway stations between Nellore and Hyderabad.The number of different kinds of single second class tickets to be printed so as to enable a passenger to travel from the station to another is

The roots of x5-5x4+9x3-9x2+5x-1=0 are

If ax2+bx+c=0 and bx2+cx+a=0 have a common root and a≠0 then a3+b3+c3/abc=

The co-efficient of x4 in the expansion of (1-3x)2/(1-2x) is equal to:

The equation of the circle passing through the points of intersection of the circle x2+y2-2x+4y-20=0, the line 4x-3y-10=0 and the point (3, 1) is

The two curves y=x-3, y=e3(1-x) at (1, 1)

The equation of the tangent to the curve y2=4ax at (at2, 2at) is

The equation of the line joining the points represented by 2-3i and -3+4i in the Argand plane is

If 2x-3y=5 and 3x-4y=7 are the equation of two diameters of a circle whose area is 154sq units, then the equation of the circle is

The locus of the point of intersection of perpendicular tangents to the circle x2 + y2 = 16 is a circle whose diameter is

The ratio in which ys-plane divides the line segment joining (-3, 4, - 2) and (2,1, 3)  is

A=(cosθ, sinθ) and B==(sinθ, -cosθ) are two points. The locus of the centroid of ΔOAB where O is the origin is

C1+2.C2+ 3.C3+…….+n.Cn=

If the number of common tangents of the circles x2+y2+8x+6y+21=0, x2+y2+2y-15=0 are 2,then the point of their intersection is

The equation of the circle passing through the points of intersection of the circlesx2+y2=5, x2+y2+12x+8y-33=0 and touching x-axis is

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

tan 100. tan 200. tan 300. tan 400. tan 500. tan 600. tan 700. tan 800 =

I: In a ΔABC, if 4s(s-a) (s-b) (s-c) =a2b2 then it is right angled triangle II: In a ΔABC, if sin A+ sin B +sin C maximum then triangle is equilateral

Let A and B be two fixed points, If a perpendicular p is drawn from A to the polar of B with respect to the circle x2+y2=a2 and perpendicular q is drawn from B to the polar of A then

If [(x2+x+1)/(x2+2x+1)]=A+[B/(x+1)]+[C/(x+1)2] then A-B=

A(3x1, 3y1), B(3x2,3y2),C(3x3,3y3) are vertices of a triangle with orthocenter H at (x1+x2+x3,y1+y2+y3) then the

y = Aex + Be2x + Ce3x satisfies the differential equation :

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

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

If f: R→R,, g: R→R, are defined by f(x)=4x-1, g(x)=x3+2, then gof(a+1/4)=

The equation of one tangent to the circle with Centre(2,-1) from the origin is 3x + y = 0, then the equation of the other tangent through the origin is

√3 cosec 200- sec 200 =

If Q is the radical centre of the three circles x2+y2=a2, (x-g)2+y2=a2and x2+(y-f)2=a2,then Qx+Qy=

If 4 sin(600+ θ) sin(600-θ)-1= kcos 2θ, the value of k is

The locus of the centre of the circles which touch the lines 6x – 8y + 5=0 and 6x – 8y + 13=0 is 6x – 8y+k=0 then k is

The number of positive divisors of 253673 is

The locus of the midpoint of the chord of the circle x2+y2=25 which subtends a right angle at (2,-3) is

If x ≥ y and y > 1, then the value of the expression logx (x/y) + logy (y/x) can never be

The unit vector orthogonal to a=2i+2j+k, b=3i+4j-12k and forming a right handed system with a and b is

cos A+sin(2700+A)-sin(2700-A)+cos(1800-A)=

The point of the curve y=x4-4x3+4x2+1 at which the tangent is parallel to x-axis is

The locus of the midpoints of the chords of the circle x2+y2-2x+2y-2=0 parallel to the line y=x+5 is the line which passes through the point is

The pole of the line y=x+2 e with respect to the ellipse x2+4y2-2x-6y-10=0 is

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

For any integer n ≥ 1, the number of positive divisors of n is denoted by d(n). Then for   a prime P, d(d(d(P7}}) =

If the parabola y2=-4ax passes through (-3,2) then the length of its latusrectum is

2+3+5+6+8+9+…..2n terms=

f(x)= x-1/x is

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

For all values of a and b(a + 2b)x + (a- b)y + (a + 5b) = 0 passes through the point:

I: If the vectors a=(1, x, -2), b=(x, 3, -4) are mutually perpendicular,then x=2 II: If a=i+2j+3k, b=-i+2j+k, c=3i+j and a+tb is perpendicular to c then t=5

cos θ+ cos (2400 + θ)- sin (2400- θ)=

If 3-√2 is a root of x4-8x3+21x2-26x+14=0 then the roots are

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

The length of the latus rectum of the hyperbola 9x2-16y2+72x-32y-16=0 is

Angle between the tangents to the curve y=x2-5x+6 at the points (2, 0) and (3, 0) is

If the equation x2+2(k+1)x+9k-5=0 has only negative roots,then

The angle between the pair of lines 2x2+5xy+2y2+3x+3y+1=0,is:

. 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.

The angle between the curves y2=8, x2=4y-12 at (2, 4) is

If y=(x+√x2-1)m then (x2-1)y2+xy1=

B and C are two points on the circle x2+y2=a2. From a point A(b, c) on that circle AB=AC=d. The equation to Bc is

The solution of (dy/dx)=ey-x is

The minimum value of 2x2+x-1 is

The area of the plane region bounded by the curve x + 2y2 = 0 and 3y2 = 1 is equal to

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

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

If an error of 0.01 cm is made while measuring the radius 10cm of a circle, then the relative error in the area is

The length of the chord of the circle x2+y2+4x-7y+12=0 along the y-axis is

The centre of the circle x2+y2-4x-2y-4=0 is

If x2+y2=a2 then dy/dx=

The intercepts of  line joining the points (4,-7),(1, -5) are

d/dx{Tan-1(3a2x-x3/a3-3ax2)}=

If α, β, γ are the roots of x3+px2+qx+r=0 then (β+γ-3α)(γ+α-3β)(α+β-3γ) =

 I: The equation of the line parallel to 2x+3y-5=0 and passing through the point (3, -4) is 2x+3y-13=0 II: The equation of the line perpendicular to 2x+3y-5=0 and passing through the point (3, -4) is 3x-2y- 17=0

A tower 51 m high has a mark at a height of 25m from the ground. If the two parts subtend equal angles to an eye at the height of 15 m from the ground, the distance of the tower from the observe is

The angle between the lines whose direction cosines satisfy the equations l + m+ n =0, l2 + m2 – n2 = 0 is

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 :

∑((12+22+32+….+n2)/1+2+3+….+n)=

The equation of the circle passing the origin having its centre on the line x+y=4 and cutting the circle x2+y2-4x+2y+4=0  orthogonally is

A bag contains n white and n black balls. Pairs of balls are drawn at random without replacement successively , until the bag is empty , if the number of ways in which each pair consists of one white and one black ball is 14,400 then n=

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

Observe the following statements A: f'(x) = 2x3 - 9x2  + 12x - 3 is increasing outside the interval (1, 2)R: f'(x) < 0 for x belongs to (1,2).Then which of the following is true

The tangents are drawn to the ellipse x2/a2+y2/b2=1 at point where it is intersected by the line lx+my+n=0. The point of intersection of tangents at these points is

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=

A line segment of length 10 cm is divided into two parts and a rectangle is formed with these as adjacent sides, then the dimensions of the rectangle in order that its area is maximum is

The distance of the point (1,2) from the common chord of the circles x2+y2-2x-6y-6=0 and x2+y2+6x-16=0 is

If  |z-1/z+a|=1 where Re(a)≠0 then the locus of z=x+iy is

If the normals from any point to the parabola x2 = 4y cuts the line  y = 2 in points whose abscissa are in A.P, then the slopes of the tangents at the 3 conormal points are in

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

The centre of the circumscribing the quadrilateral whose sides are 3x+y=22, x-3y=14 and 3x+ y=62 is

The number of common tangents to the circles x2+y2+2x+8y-23=0, x2+y2-4x-10y+19=0 is

(1+sec 200)( 1+sec 400) (1+sec 800)=

The sum of the slopes of the lines represented by 6x2-5xy+y2=0 is

In a ΔABC, cos[(B+2C+3A)/2]+cos[(A-B)/2] is equal to

In a class there are 60 boys and 20 girls. In it, half of the boys and half of the girls know cricket. The probability of a person selected from the class is either a boy or a person who knows ticket is

If u=3(lx+my+nz)2-(x2+y2+z2) and l2+m2+n2=1 then uxx+uyy+uzz=

3√1003 -3√997