A to Z Exams

Vertex of the parabola 2y2+3y+4x-2=0 is

If ak is the coefficient of xk in the expansion of  (1+x+x2)n for k = 0,1,2,..........2n then a1 + 2a2 +.....+2na2n  =

Consider the circles x2+(y-1)2=9,(x-1)2+y2=25 .They are such that :

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

If |x|

One side of a rectangle lies along the line 4x+7y+5=0.Two of its vertices are (-3, 1), and (1, 1).Then the equation of the other sides are

The length of the subtangent at (2, 2) to the curve x5 = 2y4 is

If x2+xy+y2=a2, then y2=

The modulus of (3-4i)(4+5i) is

Counters numbered 1, 2, 3 are placed in a bag and one is drawn at random and replaced. The operation is being repeated three times. The probability of obtaining a total of 6 is

If there is an error of 0.02 cm in the measurement of the side 10 cm of a cube, then error in the surface area is

If cos x+ cos2x=1, then sin12x+ 3sin10x+ 3sin8x+ sin6x=

If α,β,γ are the roots of x3+px2+qx+r=0 then form an equation whose roots are α(β+ γ),β(γ+α ),γ(α+β) is

If a=cos 2π/7+i sin 2π/7,α=a+a2+a4 and β=a3+a5+a6 then α,β are the roots of the equation

The modules of √3+i/(1+i)(1+√3i) is

If α,β,γ are the roots of 2x3+3x2-6x+3=0,then the value of 1/α4+1/β4+1/γ4=

If a=(1, 1, 1), c=(0, 1, -1) are given vectors then a vector b sastisfying the equations axb=c and a.b=3 is

Reduce the equation of the line 8x+6y-15=0

cos2 720- sin2 540=

The equation of the normal at a point hose eccentric angle is 3π/2+θ to the ellipse x2/9+y2/4=1 is

If α,β and γ are roots of x3+ax2+bx+c=0 then(α2+1)(β2+1)(γ2+1)

If the vector –i+j-k bisects the angle between the vector c and the vector 3i+4j, then the unit vector in the direction of c is

1+(1+2)/2!+(1+2+22)/3!+(1+2+22+23)/4!+ ....... =

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

cos θ+ cos (2400 + θ)- sin (2400- θ)=

The equation of the circle whose center lies on the X- axis and which passes through the points (0, 1) (1, 1) is

Equation of the parabola whose axis is horizontal and passing through points (-2,1),(1,2),(-1,3) is

If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve x2/3+y2/3=a2/3, then 4p2+q2 =

The sum of the first n terms of the series 12+2.22+32+2.42+52+2.62+…. Is n(n+1)2/2 when n is even. When n is odd the sum is

If log2(sin x)- log2(cos x)- log2(1-tan x)- log2(1+tan  x)= -1 then tan 2x=

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

The point on the line 3x+4y = 5 which is equidistant from (1,2) and (3,4) is

The equation of the straight line perpendicular to the straight line 3* + 2y = 0 and passing through the point of intersection of the lines x + 3y - 1 = 0 and x - 2y + 4 = 0 is

In ΔABC , if a=7, b=7√3 and right angled at C, then c=

sin4 θ+2 sin2 θ(1- 1/cosec2θ)+ cos4θ=

The point on the curve y=x2+5, the tangent at which  is perpendicular to the line x+2y=2 is

There are 12 boys to be seated on 2 benches, 6 on each bench. Two of them desire to sit on one bench and two others on the other. The number of ways in which the boys can be seated on the two benches is

If n ≥ 2, then 3.C0 – 5.C1 + 7.C2 – ……+(-1)n(2n +3).Cn=

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?

tan (1/2 cos-1(0)) =

If α, β, γ are the roots of x3+3x2+2x+3=0 then Σ(1/α2β2) =

The first three terms in the expansion of (1+x+x2)10 are

The length of the direct common tangent of the circles x2+y2-4x-10y+28=0 and x2+y2+4x-6y+4=0 is

The harmonic conjugate of (-9,27) with respect to the points (1,7) and (6,-3) is 

The solution set of ,when x≠0 and x≠3 is

If the centroid of the triangle formed by (a,1,3), (-2,b,-5) and (4,7,c) is the origin then(a,b,c)=

The equation of lines passing through the intersection of  lines x-2y+5=0 and 3x+2y+7=0 and perpendicular to x-y=0 is

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 angle between the tangents from a point on x2+y2+2x+4y-31=0 to the circle x2+y2+2x+4y-4=0 is

If the lines x2 + 2xy – 35y2 - 4x + 44y -12=0 and 5x +λy -8 = 0 are concurrent, then the value of λ is

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

The radius of the circular disc increases at a uniform rate of 0.025 cm per sec. the rate at which the area of the disc increases, when the radius is 15 cm is

If the line x+y+1=0 touches the circle x2+y2-3x+7y+14=0, then the point of contact is

The locus of the midpoint of the chords of the parabola y2= 6x which touch the circle x2 + y2 + 4x – 12 = 0 is

d/dx{Tan-1 1/√x2-1}=

The locus of the point whose shortest distance from the circle x2-2x+6y-6=0 is equal to its distance from the line x-3=0 is

If y= {(3x-5)2/3(x2+1)3/2/(2x+3)5/2(3x2-1)1/3}then dy/dx=

The area of the triangle formed by the pair of straight lines (ax + by)2 - 3(bx - ay)2 = 0 and ax + by + c = 10, is

The equation of the circle which cuts orthogonally the  three circles x2+y2+4x+2y+1=0, 2x2+2y2+8x+6y-3=0 , x2+y2+6x-2y-3=0 is

If cos-1 x= cot-1(4/3)+Tan-1(1/7), then x=

The modulus and principal argument of complex number (1+2i)/(1-2i) are respectively:

If the distance of two points P and Q on the parabola y2 = 4ax are 4 and 9 respectively,then 9  respectively,then the distance of the point of intersection of the tangents at P and Q fro the focus is

On a symmetrical die the numbers 1,-1,2,-2,3 and 0 are marked on its 6 faces. If such a die is thrown 3 times, the probability that the sum of points on them is 6 is

The equation of the line passing through the point (2, -3), and parallel to 3x-4y+7=0 is

The parametric equations of circle x2+y2+8x-6y=0 are

In the expression of (x4- (1/x3))15 coefficient of x32 is equal to :

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

The equation of the circle passing through the point of intersection of the circles x2+y2-3x-6y+8=0, x2+y2-2x-4y+4=0 and touching the line x+2v=5 is

If a,b, c are the probabilities of getting the sums 6,7,10 when 2 dice are thrown  when the descending order of a,b,c is

If the center of the circle 2x2+pxy+qy2+2gx+2fy+3=0 is (1,-3) then the radius of the circle is

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

If (9,12) is one end of a focal chord of the parabola y2=16x then the slope of the chord is

The equation to the locus of point of intersection of the line y-mx=√(4m2+3), my+x = √(4+3m2) is

If α,β are the roots of 8x2-3x+27=0 then the value of (α2/β)1/3+(β2/α)1/3 is

If 1,-2,3 are the roots of ax3+bx2+cx+d=0 then the roots of ax3+3bx2+9cx+27d=0 are

The derivative of Sin-12x/1+x2 w.r.to Tan-12x/1-x2is

The locus of the point of intersection of two tangents to the parabola y2 = 4ax which make complementary angles wit the axis of the parabola 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

The equation of the tangents from the origin to x2+y2-6x-2y+8=0 are

The condition that a root of ax2+bx+c=0 may be the reciprocal of a root of a1x2+b1x+c1=0 is

If the length of the tangent from (2, 3) to circle x2+y2+6x+2ky-6=0 is equal to 7. Then k=

The curve described parametrically by x=t2+t+1, y= t2-t+1 represents

The derivative of √(tan x+√tan x) w.r.t x is

If P1, P2, P3 are the perimeters of the three circles x2 + y2 + 8x - 6y = 0, 4x2 + 4y2 - 4x - 12y - 186 = 0 and x2 + y2 - 6x + 6y - 9 = 0 respectively, then :

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

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

Mr. A gave his telephone number to Mr. B remembers that the first two digits were 40 and the remaining four digits were two 3’s, one 6 and one 8. He is not certain about the order of the digits. Mr. B dials 403638. The probability that he will get A’s house is

In an entrance test there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student know the answer to a question is 9/10.If he gets the correct answer to a question, then the probability that he was guessing is

The solution of 2xy(dy/dx)=1+y2 is

If 2,-3,5 are the roots of ax3+bx2+cx+d=0 then the roots of a(x-1)3+b(x-1)2+c(x-1)+d=0 are

The scalar product of the vector i+j+k with the unit vector parallel to sum of the vectors 2i+ 4j-5k and λi+2j+ 3k is equal to 1. Then the value of the constant λ is

The difference of two positive numbers is 10. If the square of the greater exceeds twice the square of the smaller by maximum value then they are

In the argand plane the area in square units of the triangle formed by the points1 + i, 1 –i, 2i is

Domain of log(x-2)/√3-x is

A line l meets the circle x2 + y2 = 61 in A,B and P(-5,6) is such that PA = PB= 10.  Then the equation of l is :

x2+y2-4x-6y+9=0 and (x+3)2+(y+2)2=25 are two circles. The line x=2 is a

If xy+2x-3y-k is resolvable into two linear factors then k=

If the position vectors of three consecutive vertices of a parallelogram are i+j+k, 3i+5k and 7i+9j+11k, then fourth vertex is

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

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