A to Z Exams

A man is known to speak the truth 2 out of 3 times. He throws a die and reports that it is a six. The probability that it is actually a five is

If the product of the roots of the equation 5x2-4x+2+k(4x2-2x-1)=0 is 2,then k=

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

If n is even then C02-C12+C22-……….+(-1)n Cn2 =

Observe the statements given below : Assertion (A) : f (x) = xe-x has the maximum at x = 1Reason (R) :  f’(1)= 0 and f” (1) < 0 Which of the following is correct

The vectors i-2j+3k, 2i-3j+4k, i-3j+5k are

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

If y=aex+be-x+c,where a,b,c are parameters,then x2y11+xy1 is equal to:

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

The quotient we get when we divide x4-8x3+25 x2-46x+40 with -6x+8 is

If one root of x2+px+1=0 is square that of the order,then p=

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

If 5cosx + 12cosy=13 then the max value of 5sinx + 12siny is

If α,β,γ are the roots of the equation x3+px2+qx+r = 0 then the coefficient of x in the cubic equation whose roots are α(β+γ), β(γ+α) and γ(α+β) is

The centre of the circle passing through the points (a, b), (a, -b), (a+b, a-b) is

The system of circles orthogonal to x2+y2+2x+4y+7=0 is a member, then the equation of the orthogonal system is

A and B throw with 3 dice. If A throws a sum of 16 points, the probability of B throwing a higher sum is

sin 2α+ sin2β+sin 2γ- sin 2(α+β+γ)=

If pr=2(q+s) then among the equations x2+px+q=0 and x2+rx+s=0 have

If the plane 2ax-3ay+4az+6=0 passes through the midpoint of the line joining the centres of the spheres x2+y2+z2+6x-8y-2z=13 and x2+y2+z2-10x+4y-2z=8 then a=

The area of the triangle formed by the polar of (1,2) with respect to the circle 2x2+2y2-3x=0 and the coordinate axes (in square units) is

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

For the curve y2=(x+a)3, then square of the sub tangent is ….subnormal

If au+b=a2x+y then uxuy=

If a sinx=b cosx= 2ctanx/1-tan2 x then (a2-b2)2/a2+b2=

The derivative of Sin-1 cos x w.r.to x is

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

The extreme value of x2-5x+6 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

The length of the tangent from the point (-1, 1) to the circle x2+y2-4x+k=0 is equal to 2 then k=

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

4 sin(4200- α)cos(600+α)=

In measuring the vertical angle  of the sector of acircle of radius  30cms, an error of  10 is made. The error in the area of the sector is

d/dx{x√a2+x2+a2Sinh-1(x/a)}=

The area of the triangle formed by the tangent and normal at (2,4) on the circle x2+y2=20 and X-axis (in sq.units) is

If x= acos3θ, y= asin3θ then d2y/dx2 at θ=π/4 is

If the circle x2 + y2 + 2x + 3y + 1 = 0 cuts another circle x2+y2 + 4x + 3y + 2 = 0 in A and B, then the equation of the circle with AB as a diameter is :

One ticket is selected at random from 100 tickets numbered 00,01,02,...99. Suppose A and B are the sum and product of the digits found on the ticket. Then P(A=7 | B=0) is given by

Cos-1(63/65) + 2 Tan-1(1/5) =

If f(x)=x3-2x2+7x+5 then f(x-2)=

If ax2+2bx+c=0 and px2+2qx+r=0 have one and only one root in common and a,b,c being rational,then

The condition that the three different   lines ax+by+c=0, bx+cy+a=0, cx+ay+b=0 to be concurrent is

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

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

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

The equation to the parabola having focus (-1,-1) and directrix 2x -3y +6 = 0 is

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

The equation of the circle passing through the points of intersection of the circles x2+y2+2x+3y+1=0,  x2+y2+4x+3y+2=0 and through the point (-1, 2)is

The points(3,2,-4),(5,4,-6),(9,8,10) are

I: If tan A + tan B = P and Cot A + Cot B = q then cot (A + B) = (q-p) / pq II : If 2 tan A + cot A = tan B then cot A +2 tan (A –B) = 0

The locus of the middle points of the chords of the circle x2+y2=8 which are at a distance of √2 units from the centre of circle is

If the circles x2+y2+2x+c=0 and x2+y2+2y+c=0 touch each other then c=

The equation of the circle touching the line 3x-4y-15=0 and belonging to the coaxal system having limiting points (2, 0), (-2, 0) is

4 cos 6θ cos 4θ cos 2θ=

The coordinate of the point on the parabola y2 = 2x whose focal distance is 5/2 are

The product of the slopes of the tangents to the ellipse 2x2+3y2=6 draw from the point (1, 2) is

The ratio in which ys-plane divides the line segment joining (-3, 4, - 2) and (2,1, 3)  is

The area of the triangle formed by the positive x-axis and the tangent and the normal at (1, √3) to the circle x2+y2=4 is

The equation of the line passing through the point (-2, 1) and having intercepts whose product is 1 is

If sin x-3 sin 2x+sin 3x=cos x-3cos 2x+cos 3x then x=

Larger of 199100+200100and 201100 is

If x2+y2+z2≠0,x=cy+bz,y=az+cx,z=bx+ay then a2+b2+c2+2abc=

The approximate value of e2 is

If (2, 1),(-1, -2),(3, 3) are the midpoints of the sides BC,CA,AB of Δ ABC, then the equation of AB is

2.12+3.22+4.32+….+(n+1)n2=

The tangents at (3, 4), (4, -3) to the circle x2+y2=25 are

(cosh x/1- tanh x)+(sinh x/ 1- coth x)=

If the circles x2+y2+2ax+4ay-3a2=0 and x2+y2-8ax-6ay+7a2=0 touch each other externally, the point of contact is

The function f(x)=√9-x2 is increasing in

The number of arrangements of arranging 6 players to throw the cricket ball so that the oldest player may not throw first is

A(3x1, 3y1), B(3x2,3y2),C(3x3,3y3) are vertices of a triangle with orthocenter H at (x1+x2+x3,y1+y2+y3) then the

If m1, m2 are slopes of the tangents to the hyperbola x2/25-y2/16=1 which pass through the point (6, 2) then

If the slope of the tangent to the curve xy+ax=by at (1, 1) is 2, then (a, b)

The minimum value of x3-9x2+24x-12 is

The length of the side of the square formed by the lines 2x2+3xy-2y2=0, 2x2+3xy-2y2+3x-5y+1=0 is

If A+B+C=1800 then sin A+sin B+sin C=

The point on the parabola y = x2 + 7x + 2 closest to the line y = 3x – 3 is

If |a+b|2=|a|2+|b|2 then the angle between a and b is

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

Four persons entered the lift cabin on the ground floor f a 7 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first. The probability of all 4 persons leaving at different floors is

If both the roots of the equation x2-6ax+2-2a+9a2=0 exceed 3,then

If g is the inverse of f and f1(x)=1/(1+xn),then g1(x) equals,

The point on the parabola y2 = 36x whose oridinate is three times its abscissa is

The derivative of Sin-1(3x-4x3) w.r.to Tan-1x/√ (1-x2) is

If a = i^ - j^ -k^ and b = + λ i^ - 3 j^ + k^ and the orthogonal   projection   of   b   on   a   is (4/3) (i^ - j^ -k^), then λ  is equal to

If X is a passion Poisson variate such that P(X = 1) = P( X = 2 ), then P( X = 4 ) is equal to

If Sin-1 x+ Sin-1 y+ Sin-1 z=π then x2+y2+z2+2xyz=

The circumference of a circle is measured as 56 cm with an error 0,02 cm. The percentage error in its area is

In the first box there are tickets marked with numbers 1,2,3,4. In the second box there are tickets marked with numbers 2, 4, 6,7,8,9. If a box is chosen and at a ticket is drawn from it at random, the probability for the number of the ticket to be 2 or 4 is

If α+β=-2 and α3+β3=-56 then the quadratic equation whose roots α,β is

If y2=(x-a)(x-b) then d3/dx3[(d2y/dx2)-2/3]=

Arrange the magnitudes of following vectors in ascending order A) ixj+ jxk+kxi  B) If lal=2, lbl=3, (a, b)=450 then axb C) (2i-3j+2k)x(3i-j+4k)

The condition that the slope of a line represented by ax2+2hxy+by2=0 is thrice that of the other is

∑((12+22+32+….+n2)/1+2+3+….+n)=

If x2+y2-2x+3y+k=0 and  x2+y2+8x-6y-7=0 cut each orthogonally, the value of k must be

Let A and B be any two points on each of the circles x2+y2-8x-8y+28=0 and x2+y2-2x-3=0 respectively. If d is the distance between A and B then the set of all possible values of d is

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

If y=4x-5 is a tangent to the curve y2=px3+q at (2, 3), then

If p and q are the coefficients of xn in (1+x)2n-1 and (1+x)2n respectively then 2p=

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