A to Z Exams

If α, β are the roots of ax2-bx+c=0 then α3β3 +α2β3 + α3β2=

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

If the circle x2+y2+6x+8y+a = 0 bisects the circumference of the circle x2+y2+2x-6y-b=0,then a+b is equal to

If sin θ=-7/25 and  is not in the first quadrant, then (7cot θ -24 tan θ) / (7cot θ+24 tan θ) =

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

If (1 + x)n = C0 + C1x + C2x2 + …. + CnXn, then C0 - C2 + C4 - C6 + … is equal to:

A stone is thrown vertically up and height s reached in time t is given by the formula s=2t2+3t+1. The stone reaches the maximum height in time t =

The value of λ such that (x, y, z)≠(0, 0, 0) and (i+j+3k)x+(3i-3j+k)y+(-4i+5j)z=λ(xi+yj+zk) are

P,Q,R are the midpoints of AB,BC,CA of ?ABC and the area of ?ABC is 20. The area of ?POQ is

If α, β, γ are the roots of x3+2x2+3x+4=0 then Σα2β2 =

Cos23π/5 + Cos24π/5 is equal to

If the quadratic equations ax2+2cx+b=0 and ax2+2bx+c=0, (b ≠ c) have a common root then a+4b+4c =

The lines x-y—2=0, x+y-4=0 and x+3y=6 meet in the common point

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

The tangent of the acute angle between the pair of lines 2x2+5xy+2y2=0 is

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 lines 2x+y=1, x+2y=1, 2x+y=3, x+2y=3 form

If log27 (log3 x) = 1/3, then the value of x is :

If 2 numbers are randomly selected from 20 consecutive natural numbers, then the probability that the sum of the two numbers is an even number is

Find the equation of the parabola, whose axis parallel to the y-axis and which passes through the points (0,4),(1,9) and (4,5) is

The coefficient of xr in (1+x)2/(1-2x)3 is

The equation of the bisector of the obtuse angle between the lines x-y+2=0,7x+y+1=0 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 cot θ=-3/4 and θ is not in the second quadrant then 5 sin θ+10 cos θ+9 sec θ-16 cosecθ- 4cot θ=

If area bounded by the curves y2=4ax and y=mx is a2/3,then the value of m is

If the points (0, 0), (2, 0), (0, 4), (1, k) are concyclic then k2-4k =

The equation of the circle belonging to the coaxal system of which (1, 2)(4, 3) are the limiting points and passing through the origin is

The equation of the circle with centre (-1, 1) and touching the circle x2+y2-4x+6y-3=0 externally is

If ax2+6xy+9y2+4x+12y+3=0, x2-bxy+y2+2y+2=0, 3x2+11xy+10y2+7x+13y+c=0 represents pairs of straight lines then the ascending order of a,b,c is

The lines 2x-3y=5 and 3x-4y=7 are two diameters of a circle of area 154 sq unit. Then the equation of this circle is

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

An experiment yields 3 mutually exclusive and exhaustive events A, B and C. If P(A)=2P(B)=3P(C) then P(A) =

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=

In ΔABC, if sin A: sin C = sin (A-B) :sin (B-C), then a2,b2,c2 are in

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

A is one of 6 horses entered for a race and is to be ridden by one of two jockeysP and Q. It is 2 to 1 that P rides A, in which case all the horses are likely to win. If Q rides A, his chance is tribled. The probability of A’s winning is

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

The equation of the hyperbola with its axes as coordinate axes, whose transverse axis 8 and eccentricity 3/2 is

A, B, Care 3 news papers published from a city.20%of the population read A,16% read B,14% read C, 8% both A and C, 4% B and C,and2% read all the three. The percentage of then population who read at least one paper is

cos2(π/4+x)- sin2(π/4-x) =

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

Radius of the director circle of the hyperbola (x2/81) - (y2/36) = 1 is

If tan(π/4+θ)+tan(π/4- θ)=3, then tan2 (π/4+θ)+ tan2 (π/4-θ)=

If (1,2) is the midpoint of a chord of the circle (x-2)2+(y-4)2=10 and the equation of the chord is ax+by+c=0(a>0) then a-b+c=

The point (3, -4) lies on both the circles x2+y2-2x+8y+13=0 and x2+y2-4x+6+11=0. Then the angle between the circles is

A coin and six faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die, is

The equation ax2+8xy+2y2+2gx+13y+c=0 represents a pair of parallel straight lines then ascending order a,g,c is

The parabola x2=py passes through (12,16).Then the focal length of the point is

If (2i+4j+2k)x(2i-xj+5k)=16i-6j+2xk then the value of x is

If  f(x)=αx+β and f={(1, 1), (2,3), (3,5), (4, 7)} then the values of α, β are

If α,β,γ are the roots of x3+3x+2=0 then the equation whose roots are (β–γ)2,(γ–α)2,(α–β)2 is

The centroid of the tetrahedron formed by the points(3,2,5), (-3,8,-5), (-3,2,1),(-1,4,-3) is

In a business venture a man can make a profit of Rs.2000/- with probability of 0.4 or have a loss of Rs.1000/- with probability 0.6his expected profit is

The number of common tangents to the two circles x2+y2=4, x2+y2-8x+12=0 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 f(x)=x3-x, g(x)=sin 2x, then

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

If (a+bx)ey/x=x,then x3y2=

The equation to the circle touching the y-axis at the origin and passing through(b, c) is

Sin (2Tan-13/4) =

tan 700-tan 200

The angle at which the circles x2+y2+8x-2y-9=0 and x2+y2-2x+8y-7=0 intersects is

On the interval [0, 1] the function x25(1-x)75 takes its maximum value at the point

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

If the roots of x2+bx+c=0 are two consecutive integers then b2-4c=

If the line hx+ky=1/a touches the circle x2+y2=a2 then the locus of (h,k) is a circle of radius

The radius of the sphere (r-2i+3j-k).(r+3i-j+2k)=0 is

sin 700+cos 400/(cos 150-cos 750)=

The students while solving a quadratic equation in x,one copied the constant term incorrectly and got the roots 3 and 2.The other copied the constant term and coeffient of x2 as -6 and 1 respectively.The correct roots are:

In measuring the circumfence of a circle, there in an error of 0.05 cm. if with this error the circufence of the circle is measured of the circle is measured as c cm, then the percentage error in area is

 If x -y+ 1 = 0 meets the circle x2 + y2 + y - 1 = 0 at A and B, then the equation of the circle with AB as diameter is

The equation of the circle belonging to the coaxal system of which (2, -3)(0, -4) are the limiting points and passing through the point (2, -1) is

The locus of the midpoint of chords of the parabola y2 = 4ax parallel to the line y = mx + c is

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

The period of sec(2x+5) is

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

In a triangle, the orthocentre and the circumcentre are (-4, 0), (8, 6 ) respectively; the centroid is

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

The equation of the tangent to the parabola y2 = 8x and which is parallel to the line x – y + 3 = 0

If there is a possible error of 0.01 cm in the measurement of side of a cube, the possible error in its surface area when the side is 10 cm is

The centre of the circle passing through the points (0, 0), (1, 0) and touching the circle x2+y2=9 is

The letters of word VICTORY are permuted in all possible ways and the words thus formed are arranged as in a dictionary.The rank of the word VICTORY is

Statement I: The points 4i+5i+k, -j-k, 3i+9j+ 4k and -4i+4j+4k are coplanar Statement II  : The given points from  the  vertices of a parallelogram. Which of the following is true? a)  Both statements  are  true and statement II is correct explanation of statement I b)  Both  statements  are true  and statement II is not correct explanation of statement I cv) Statement I is true and statement II is false d)  Statement I is false and  Statement II is true

(sin 3A+ sin A) sin A+ (cos 3A- cos A) cos A=

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

The triangle formed by the pair of lines 3x2+48xy+23y2=0 and the line 3x-2y+4=0 is

The pressure p and the volume v of gas are connected by the relation pv=300. If the volume is increasing at the rate of 0.6 cubic cm per minute then the rate of change in pressure of the gas when the volume is 30 cubic cm is

The vertex and focus of a parabola are (0,0) and (0,4) then its directrix is

If 2x-y+3=0, 4x+ky+3=0 are conjugate with respect to the ellipse 5x2+6y2-15=0 then k=

If cos α=3/5, cos β=5/13, then cos2(α - β/2)=

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

If au+b=a2x+y then uxuy=

If the polar of P with respect to the circle x2+y2=a2 touches the parabola y2=4ax, then the locus of P is

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

Sand is being poured on the ground from the orifice of an elevated pipe and forms a pile which has always the shape of a right circular cone whose height is equal to the radius of the base. If the sand is falling at the rate of 1000 cubic cm per sec, the rate at which the height of the pile is rising when the height is 40 cm is

sin A+ sin B = √3( cos B - cos A)  then sin 3A + sin 3B is equal to

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

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

Tangents are drawn  from  the Point (-2, -1) to the hyperbola 2x2-3y2=6. Their equations are