A to Z Exams

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

mCr+ mCr-1nC1+mCr-2. nC2+………..+ nCr =

There are four balls of different colours and four boxes of colours same as those of the balls. The number of ways in which the balls, one each in a box could be placed such that a ball does not go to a box of its own colour is

tan (450+θ). tan (450-θ)=

A: If a, b, c are vectors such that [a b c]=4 then [axb bxc cxa]=64 R: [axb bxc cxa]=[a b c]2

The angle between the straight lines 3 x2-5xy+2 y2=0 is

the equation of the parabola whose axis is parallel to x –axis and passing through (- 2,1), (1,2), (-1,3) is

Observe the following statements :A : Integrating factor of (dy/dx) + y = x2 is exR :Integrating factor of (dy/dx) + P(x) y = Q(x) is e∫p(x)dx. Then the true statement among the following is

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

f(x) = |x| has

(sin 3θ/ sin θ)-(cos 3θ/ cos θ)=

The transformed equation of x4+2x3-12x2+2x-1=0,by eliminating third term is

If b2-4ac>0,then the graph of y= ax2+bx+c

The equation of the line whose x-intercept is 2/5 and which is parallel to 2x-3y+5=0 is

If two roots of 2x3-x2-22x-24=0 are in the ratio 3:4 then the roots are

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

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

3 red and 4 white balls of different sizes are arranged in a row at random. The probability that no two balls of the same colour are together is

The value of b so that x4-3x3+5 x2-33x+b is divisible by x2-5x+6 is

if the focus is (1,-1) and the directrix is the line x + 2y – 9 = 0, the vertex of the parabola is at

Tan [cos-1 4/5+tan-1 2/3] =

The slopes of the lines passing through A(2, 0) and making an angle of 450 with the tangent at A to the circle x2 + y2 +4x-6y-12=0 is

The eccentricity of the ellipse 25x2+9y2-150x-90y+225=0 is

The range of f(x)=10- |3-2x| is

The maximum value of 5 cos x+ 3 cos (x- 600)+7 is

If the product of two of 6x4-29x3+40x2-7x-12=0 is 2 then the roots are

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

A curve passes through the point (2, 0) and the slope of the tangent at any point is x2-2x for all values of x. The point of maximum or donation the curve is

There are 5 letters and 5 addressed envelopes. If the letters are put at random in the envelopes, the probability that at least one letter may be placed in wrongly addressed envelope is

If cosec θ-sin θ=m, sec θ-cos θ=n then (m2n)2/3+(mn2)2/3=

A tangent at a point on the circle x2+y2=a2 intersects a concentric circle S at P and Q. The tangents to S at P and Q meet on the circle x2+y2=b2. The equation to the circle S is

If 2 tan A+cot A=tan B, then cot A+2tan(A-B)=

A tangent to y2=7x is equally inclined with the coordinate axes.Then the area of the triangle formed by the tangent with the coordinate axes is

If (2, 1 )is limiting point of the coaxal system of which x2+y2-6x-4y-3=0 is a member, then the other limiting point is

The equation whose roots are multiplied by 3 of those 2x3-3x2+4x-5=0 is

Cos (sin-13/5+Sin-1 5/13)=

If the tangent at any point on the curve x4+y4=a4 cuts off intercepts  p and q on the coordinates axes then p-4/3+q-4/3=

If one of the root x4-5x3+10x2-20x+24=0 is purely imaginary then the roots are

The equation to the pair of lines joining the origin to the points of intersection of 2x+3y=1 and x2+y2=4 is

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

The stability of hydrides increase from NH3 to BiH3 in group 15 of the periodic. The area of the region enclosed by the curves y = x, x = e, y =1/x and the

The number of four digited even numbers that can be formed from the digits 0,1,2,5,7,8 is

The number of odd numbers between 1000 and 10000 can be formed with the digits 1,2,3,4,5,6,7,8,9 is

If f(x) = 10 cos x +(13+2x) sin x then f"(x) + f(x) is equal to

If tan θ + tan 2θ+ √3 tan θ tan 2θ=√3 then θ=

The solution set of sec θ=2cos θ is

If the circles x2+y2+2x-2y+4=0 cuts the circle x2+y2+4x-2fy+2=0 orthogonally, then f=

The equation of the sphere one of whose diameter has end points (1, 2, 4) and (3, 0, 2)

2.C0+22.C1/2+23.C3/3+……..+2n+1.Cn/n+1 =

If the roots of ax3+bx2+cx+d=0 are in A.P then the roots of dx3+cx2+bx+a=0 are in

A particle moves along the curve y = x2 + 2x. Then the point on the curve such that x and y co-ordinates of the particle change with the same rate is :

The chord of contact of tangents drawn from points on x2/a2+y2/b2=1 to the circle x2+ y2=c2 touches the ellipse

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

The centre of the circle (1+m2)(x2+y2)-2cx-2cmy=0 is

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

If log 2+(1/2)log a +(1/2) log b = log(a+b),then

If the roots of (a2+b2)x2-2b(a+c)x+(b2+c2)=0 are equal then a,b,c are in

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

A unit vector coplanar with i+j+2k and i+2j+k and perpendar to i+j+k is

In ΔABC, (r1 +r2) (r2 +r3) (r3+r1) =

(1-ω+ω2) (1-ω2+ω4) (1-ω4+ω8)... to 2n factors=

The equation of the line parallel to 2x+3y-5=0 and forming an area 4/3sq.unit with the coordinate axes is

The transformed equation of x3+6x2+12x-9=0 by eliminating second term is

(tan 230+ tan220)/(1- tan 230 .tan220)=

If the lines 2x+y+12=0, kx-3y-10=0 are conjugate w.r.t the circle x2+y2-4x+3y-1=0, then k=

If x2-xy+y2=1 and y’’(1)=

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

The roots of the equation a(b-c) x2+b(c-a)x +c(a-b) =0 are

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

If sin2 mx+cos2 ny=a2 then dy/dx=

The circle on the chord x cos α+ y sin α=p of the circle x2+y2=r2 as diameter is

(sin 4θ)/(sin θ)=

The points i+j+k, i+2j, 2i+2j+k, 2i+3j+2k are

A, B, C, D are four points with the position vectors a, b, c, d respectively such that (a-d). (b-c)=(b-d).(c-a)=0. The point D is the ….of ΔABC

Two equation sides of an isosceles triangle are 7x-y+3=0, x+y-3=0 and its third side passes through the point (1, -10). The equation of the third side is

The portion of a line intercepted between the coordinate axes is bisected by the point (2, -1) in the ratio 3:2. The equation of the line is

If tan θ+ tan 2θ+tan 3θ= 0 then θ=

Let ABC be a triangle. If P is point such that APdivides BC in the ratio 2:3, BP divides CA in the ratio 3:5 then the ratio in which CP divides AB is

The polar of the point(2t, t-4) w.r.t the circle x2+y2-4x-6y+1=0 passes through the point

3x-5x2+12 has maximum at x=

If 1,ω,ω2 are the cube roots of unity, then (a+bω+cω2)/ (c+aω+bω2) is equal to:

If the equation of the circle passing through the origin and the points of intersection of the two circles x2+y2-4x-6y-3=0, x2+y2+4x-2y-4=0 is x2+y2+2ax+2by+c=0  then the ascending order of a, b,c is

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

If tan θ= (cos 120+ sin 120)/ (cos 120- sin 120) then θ=

The number of real solutions of Tan1 x+Tan 1 (1/y) = Tan1 3 is

The equation of  the line having  intercepts a,b on the axes such that a+b =5, ab=6 is

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

sin 200.sin 400.sin 600 sin800=

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

tan 700-tan 200

E1: a + b + c = 0 if 1 is a root of ax2 + bx + c = 0E2: b2 - a2 = 2ac if sinθ, cosθ are the roots of ax2 + bx + c = 0Which of the following is true

The points (4, -2), (3, b) are conjugate w.r.t x2+y2=24 if b=

5 boys and 3 girls sit in a row at random. If a is the probability that all the girls sit together, b is the probability that all the boys sit together and c is the probability that all the boys and all the girls sit together then the ascending order a,b,c is

4(cos3 200 +cos34 00) =

The side of an equilateral triangle increases at the uniform rate 0.05 cm/sec. the rate of increase in the area of the triangle when the side is 20 cm is

If (cos 3α+i sin 3α)(cos 5β+i sin 5β)= cos θ+i sin θ then θ is

If A=i+2j+3k, B=3i+4j+7k and C= 2i+3j+5k are collinear, then the ratio in which B divides is

If α,β,γ are the roots of x3+qx+r=0 then the equation whose roots βγ+1/α,γα+1/β,αβ+1/γ is

Equation of the directrix of the parabola y2=5x – 4y – 9 is