A to Z Exams

The radical axis of the circles x2+y2-6x-4y-44=0 and x2+y2-14x-5y-24=0 is

The number of four digited numbers that can be formed from using the digits 2,4,5, 7,8 that are divisible by 4 is

The points (2a,4a), (2a,6a) and  ((2+√3)a,5a are the vertices of an

tan 750- tan 300- tan 750. tan 300=

C0-2. C1+3. C2………..+(-1)n(n+1).Cn =

Equation of the tangent to the curve  y=2x3+6x2-9 at the point where  the crosses the y-axis curve is

The subnormal to the curve y=ax at any point varies directly as

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

The curve represented by X= 2( cos t + sin t ), y=( cos t - sin t ) is

i) The coaxial system x2 + y2 + 2λx + 5=0 is a non intersecting system ii) The coaxial system x2 + y2 + 4λx – 3 =0 is an intersecting system Which o above statement is correct

sin2 θ+ sin2 (600+ θ)+ sin2 (600-θ)=

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

The equation of the tangent to the circle x2+y2-2x-4y+3=0 at (2, 3) is

The shortest distance between the straight line passing through the point A=(6, 2, 2) and parallel to the vector(1, -2, 2) and the straight line passing through A’=(-4, 0, 1) and parallel to the vector (3, -2, -2) is

The lines r=(6-6s)a+(4s-4)b+(4-8s)c  and r=(2t-1)a+(4t-2)b-(2t+3)c intersects at

Match the following Parabola Focus y2 –x – 2y + 2 = 0 (1,2) y2 – 8x – 4y – 4 = 0 (-2,5) x2 + 4x – 8y + 28 = 0 (1,-1) x2 – 2x – 8y – 23 = 0 (5/4,1)

The equation of the circle passing through (-7, 1) and having centre at (-4, -3) is

If one root of the equation 8x2-6x+k =0 is the square of the other, then k =

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

The points A (1, 2), B (3, -4) are two vertices of the rectangle ABCD. The point P (3, 8) lies on CD produced. Then C =

In measuring the circumfrence of a circle, there in an error of 0.05 cm. if with this error the cir cumfence of the circle is measured of the circle is measured as c cm, and then the error in area is

d/dx{log(x2/ex)}=

If (x1,y1) (x2,y2) are the extremities of a local chord of the parabola y2=16x then 4x1x2+y1y2=

A fruit basket contains 4 oranges, 5 apples, 6 mangoes. The number of ways a person make selection of fruits from among the fruits in the basket is

The equation of the tangent to the curve 2x2-xy+3y2=18 at (3, 1) is

(1/1+2ω)-(1/1+ω)+(1/2+ω)=

The ordinate of  the centroid of the triangle formed by conormal points on the parabola y2=4ax is

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

If y=sin(sin x)then y2+(tan x)y1+y(cos2x)=

The inverse of f(x)=10x-10-x/ 10x+10-x is

The equation of the circle passing through the intersection of the circles x2+y2=2ax and x2+y2=2by and having its centre on the x/a-y/b=2 is

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

A double decked bus can accommodate 100 passengers, 40 in the upper deck and 60 in the lower deck. In how many ways can a group of 100 passengers be accommodated if 15 refuse to sit in the lower deck and 20 refuse to sit in the upper deck?

If 9x2-24xy+ky2-12x+16y-12=0 represents a pair of parallel lines, then k=

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

The solution set of (5+4cosθ)(2cosθ+1) = 0 in the interval [0,2π],is

If the point of intersection of kx+4y+2=0, x-3y+5=0 lies on 2x+7y-3=0, then k=

The vector equation of the plane passing through the point (3, -2, 1) and perpendicular to the vector (4, 7, -4) is

d/dx{Sin-12x/1+x2}=

A bag A contains 2 white and 3 red balls and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. The probability that it was drawn from bag B is

The equation of  the transverse and conjugate axes of a hyperbola are respectively. X+2y-3=0, 2x-y+4=0 and their respective lengths are  √2 and 2/√3. The equation of the hyperbola is

Five digit numbers can be formed from the digits 1,2,3,4,5. If one number is selected at random, the probability that it is an even number is

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

The sum of numbers formed by talking all the digits 2,4,6,8 is

1.nC0+41.nC1+42.nC2+43.nC3+……..+4n.nCn =

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

The point equidistant from (24, 7),(7, 24) and (0, 25) is 

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

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

If A2 = A, B2 = B, AB = BA = O then (A+B)2 =

The values of the parameters a for which the quadratic equations (1-2a)x2-6ax-1=0 and ax2-x+1=0 have at least one root in common are

If x= a {cos θ + log tan (θ/2)} and y = a sin θ then dy/dx=

If the equation ax2+2hxy+by2+2gx+2fy+c=0 represents a pair of parallel lines, then f2/g2=

sin 850-sin 350- cos 650

If f(x) = 2x4+5x3-7 x2-4x+3 then f(x-1)=

The roots of √3x2 +10x-8√3=0

If z = log (tan x + tan y), then (sin 2x)∂z /∂x+(sin 2y) ∂z /∂y is equal to

If A+B+C= 1800 then cos2 A+ cos 2 B - cos2 C=

1.3+2.32+3.33+4.34+….+n.3n=

(13/1)+(13+23/1+3)+(13+23+33/1+3+5)+….. n terms

The point diametrically opposite to the point P(1, 0) on the circle x2+y2+2x+4y-3=0 is

Bag A contains 3 white and 2 black balls. Bag B contains 2 white and 4 black balls. One bag is selected at random and a ball is drawn from it. The probability that it is white is

The difference of focal distance of any point on the hyperbola [(x2/36)-(y2-9)]=1 is

The maximum value of sin2 x+ 2 sin x+3 is

If f(x,y)=x2Tan-1(y/x)-y2 Tan-1(x/y),x≠0,y≠0 then fxy=

sin 100 +sin 200 +sin  400 +sin 500 -sin 700 -sin 800=

The pole of the line 2x + 3y – 4 = 0 with respect to the parabola y2 = 4x is

The normal to the circle x2+y2+2x-10y+k=0 which is perpendicular to x-3y+2=0 is

The solution set of sec θ=2cos θ 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

A straight line through the point (2, 2) intersects the lines √3x-y=0 at the points A and B. the equation to the line AB so that the triangle OAB is equilateral is

x = cos θ, y = sin 5θ  ==>(1-x2) (d2y/dx2)  - x(dy/dx) =

If sinA + sinB = l, cosA - cosB = m, then the value of cos(A - B) =

The elevation of an object on a hill is observed from a certain point in the horizontal plane through its base, to be 300. After walking 120 metres towards it on level ground the elevation is found to be 600. Then the height of the object (in metres) is :

If Tan-1(x+1/x-1)+Tan-1(x-1/x)+ Tan-1(1/3), then x=

The value of k such that the straight line 3x+14y+7+k (5x+7y+6) =0 is perpendicular to x-axis is

The range of x2+4y2+9z2-6yz-3xz-2xy is

The equation of the axis of the parabola (y + 3)2 = 4(x – 2) is

If s and p are respectively the sum and the product of the slopes of the lines 3x2 - 2xy - 15y2 = 0, then s : p =

The odds against A solving a problem are 8 to 6 and the odds in favour of B solving the same problem are 14 to 10. Then the probability that the problem will be solved if both of them try the problem is

The angle between the lines x cos α + y sin α = p1 and x cos β +y sin β =p2 where α

The value of ‘a’ such that the sum of cubes of the roots of the equation x2 – ax + (2a – 3)=0 assumes the minimum value is

If sin A=sin B and cos A=cos B then A=

If the tangents at (3, -4) to the circle x2+y2-4x+2y-5=0 w.r.t the circle x2+y2+16x+2y+10=0 in A and B, then the midpoint of AB is

If f(x)=√(x+2√(2x-4))+ )=√(x-2√(2x-4)) then

The angle between the lines joining the origin to the points of intersection of 3x-y+1=0 and x2+2xy+y2+2x+2y-5=0 is

The equation of the line whose y-intercepts is -3/4 and which is parallel to 5x+3y-7=0 is

The points at which the tangent to the circle x2 + y2=13 is perpendicular to the line 2x + 3y +21=0 is:

The point A divides the join of P(-5,1) and Q=(3,5) in the ratio k:1. The value of k for which the area of ?ABC where B(1,5), C(7,-2) is 2 sq.units is

sin2 A cos2 B+ cos2 Asin2 B+sin2 Asin2 B+cos2 A cos2 B=

The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines x = 0 and y = 0 is  

If the angle between the pair of lines 2x2+λxy+3y2+8x+14y+8=0 is π/4, then the value of λ is

ABC is an isosceles triangle and B= 900. If B and the midpoint P of AC are represented by 3+2i and 1-i then the other vertices are

(sin 4θ)/(sin θ)=

The The limiting points of the coaxal system x2+y2+2µy+9=0 are

If the normal at ‘θ’ on the hyperbola x2/a2-y2/b2=1 meets the tansverse axis at G, the AG, AG’=

If sin 7θ+sin 4θ+ sin θ=0, 0≤θ≤ π/2 then θ=

If x4-5x3+9x2-7x+2=0 has a multiple root of order 3 then the roots are

If the locus of mid points of the chords of the parabola y2=4ax which passes through a fixed point (h, k) is also a parabola then its length of latusrectum is