A to Z Exams

In a throw with a pair of symmetrical dice the probability of obtaining a doublet is

The conjugate of (1+2i) (2-3i) is

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

In order to eliminate the first degree terms from the equation 2x2 + 4xy + 5y2 - 4x - 22y + 7 = 0, the pointto which origin is to be shifted, is

If α,β,γ are the roots of the equation 3x3+6x2-9x+2=0,then Σ(α/β) =

In ΔABC, R2 (sin 2A+sin 2B+sin 2C)=

sin (θ/2)sin (7θ/2)+sin(3θ/2). Sin(11θ/2)- sin 2θsin 5θ=

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

The number of common tangents that can be drawn to the circles x2+y2=1 and  x2+y2-2x-6y+6=0 is

(cos2 330-cos2570)/(sin 210- cos 210)=

The number of ways in which the following prizes be given to a class of 20 boys, first and second in Mathematics, first and second in Physics, first in Chemistry and first in English is

A person standing on the bank of a river observes that the angle of elevation of the angle of elevation of the top of a tree on the opposite bank of river is 600 and when he retires 40 meters away from the tree then the angle of elevation becomes 300, the breadth of river is

If cos  α+ cos β=0= sin α + sin β then cos(α - β)=

(1/1.3)+(1/3.5)+(1/5.7)+….n terms=

The harmonic mean of the roots of the equation (5+√2)x2-(4+√5)x+8+2√5)=0 is

The sum of all four digited that can be formed, using  the digits 0,2,4,7,8 without repetition 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

If 2x + y + a = 0 is a focal chord of the parbola y2 + 8x = 0

Two angles ofa triangle are Cot-1 2 and Cot-1 3.Then the third angle is

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

The sum of the series 1+3x+5x2+7x3+....+(2n-1)xn-1+....is:

The extremities of a diameter of a circle have coordinates (-4, -3) and (2, -1). The length of the segment cut off by the circle on y-axis is

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

The equation whose roots are multiplied by 3 of those of 2x2+3x-1=0 is

d/dx{Tan-1√(1-cos x)/(1+cos x)}=

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

The least distance of the line 8x-4y+73=0 from the circle 16x2+16y2+48x-8y-43=0 is

If u=(ax+by)2-(x2+y2) and a2+b2=1 then uxx+uyy=

The equation of the curve in polar coordinates is(1/r) =2sin2(θ/2).Then it represents

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

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

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

Consider the circle x2+y2-4x-2y+c=0 whose centre is A(2, 1). If the point P(10, 7) is such that the line segment PA meets the circle in Q with PQ=5, then c=

The locus of poles of  chords of the parabola  y2=4px which touch the hyperbola x2/a2-y2/b2=1is

If cos θ=cos 5π/4, then θ=

I: The modulus of √3+i/(1+i)(1+√3i) is 1/√2 II: The least positive value of n for which (1-i/1+i)n=1 is 2

If y= log sin x then y2=

If u=(x-y) (y-z) (z-x) then ux+uy+uz=

x2 +4ax+3 =0 and 2x2+3ax-9 =0 have a common root, then a =

If the line 3x-y =k is a hyperbola 3x2-y2=3, then k=

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

If α,β,γ are the roots of the equation x3+ax2+bx+c=0 then α-1+β-1+γ-1=

The vectors a+2b+3c, 2a+b-2c, 3a-7c are

Order and degree of (x2+2x)y22+(x2-2)y13-2(x+3)y=0 are

If α, β are the roots of x2+ ax+b=0 and γ, δ are the roots y2+cx+d=0 then the equation of the circle having the line joining (α, γ), (β, δ) as diameter is

There are three events A,B and C one of which and only one can happen. The odds are 7 to 3 against A and 6 to 4 against B.The odds against C are

If sin-1x+sin-1(1-x)=cos-1x, then x ε to

If a random variable X take values 0 and 1 with respective probabilities 2/3 and 1/3 then the expected value of X is:

Circum centre of the ?le formed by the points (2, -5), (2, 7), (4, 7) is

If V=πr2h then rVr+2hVh=

The chance of throwing an ace in the 1st only, of the two successive throws with an ordinary die is

Equation of the latusrectum of the parabola x2+8x+12y+4=0 is

The length of the line segment joining the points 2i-2j+3k, 5i+2j+3k is

If the orthocenter and the circumcentre of a triangle are (-3,5,2), (6,2,5) then its centroid is

The number of non-zero terms in the expansion of (1+3√2x)9+(1+3√2x)9is equal to:

If the orthocenter of the angle formed by the lines 2x+3y-1=0, x+2y-1=0, ax+by-1=0  is at the origin, then (a, b) is given by

If f(x)=[x], g(x)=x-[x]then which of the following functions is the zero functions

The length of the tangent from a point on the circle x2+y2+4x-6y-12=0 to the circle x2+y2+4x-6y+4=0 is

If 3y2-8xy-3x2-29x+3y-18 us resolvable into two linear factors then the factors are

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

If a and b are numbers between 0 and 1 such that the points z1= a+i, z2= 1+bi and z3= 0 from an equilateral triangle then a,b are

If the roots of 24x3-26x2+9x-1=0 are in H.P then the roots are

The normal at P cuts the axis of the parabola y2 = 4ax in G and S is the focus of the parabola.If Δ SPG is equilateral then each side is of length

(a+bω+cω2)/(c+aω+bω2)=

If the lines 3x+y+2=0, 2x-y+3=0, 2x+ay-6=0 are concurrent then a=

The area (in square units) bounded by the curves y2 = 4x and x2 = 4y in the plane is :

If O is the origin and if A(x1,y1), B(x2,y2) are two points then OA.OB.cos

The area bounded by the curves y=3x-x2 and y=x2-x 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=

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

The quadrilateral formed by the pairs of lines x2-7x+12=0, 4x2+12xy+9y2=0,8x+12y+3=0 is

If f(x)= (a-xn)1/n, where a>0 and n?N, then (fof)(x)=

If the area of an isosceles triangle is √2+1 and vertical angle is 450 then the base of the triangle is

(12/3)+(12+22/5)+(12+22+32/7)+… n terms

If α,β and γ are roots of x3+ax2+bx+c=0,then Σα2β=

sin2 3A/ sin2A)- (cos2 3A/ cos2A)=

If the tangents to the parabola y2=4ax at (x1,y1) and (x2,y2) meet on the axis 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 equations whose roots are exceed by 2 than those of x4+x3-10x2+4x+24=0 is

The value of k such that the lines 2x -3y + k = 0,3x - 4y - 13=0 and 8x - 11y -33 = 0are concurrent, is

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

10n+3.4n+2+k is divisible by 9 for all n?N. Then the least +ve integral value of k is

If the direction ratio of two lines are given by l + m + n = 0, nm - 2ln + lm = 0, then theangle between the lines is :

d/dx{(2x-3)/(3x+1)}=

The range of Sin-1 5x is

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

The equation to the sides of a triangle are x-3y=0, 4x+3y=5, 3x+y=0. The line 3x-4y=0 passes   through

If tan2 θ=3 cosec2 θ-1 then θ=

If θ is the angle of intersection of the curves y2=x3 and y=2x2-1 at (1, 1), then tanθ=

(tan 80o - tan 10o )  /  tan 70o  =

The points (2k, 3k), (1, 0), (0, 1) and (0, 0) lie on a circle for

The sum of the coefficients of even powers of x in the expansion of (1+x+x2)15 is

Radical centre of x2+y2-x+3y-3=0,x2+y2-2x+2y+2=0 and x2+y2+2x+3y-9=0

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

The pole of the straight line x+4y = 4 With respect to the ellipse x2 + 4y2 = 4 is

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 foot of the normal 3x+4y=7 to the hyperbola 4x2-3y2=1 is

Let Then which one of the following is true

If (3+i) is a root of the equation x2+ax+b=0 then a=

The polar equation of xcosα+ysinα=p is