A to Z Exams

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

Equation of the circle passing through (0,0),(a,b) and (b,a) is

A student has to answer 10 out of 13 questions in an examination choosing at least 5 questions from the first 6 questions. The number of choice available to the student is

The distance between the foci of the hyperbola x2- 3y2- 4x - 6y - 11 = 0 is

A bag contain 12 two rupee coins, 7one rupee coins and 4 half rupee coins. If 3 coins are selectedat random, then the probability that each coin is of different value is

If f(x)=cos2x+cos2(600+x) + cos2(600-x) and g(3/2)=5 then gof(x)=

The multiplicative inverse of (4+3i) is

If (1, 2) is the mid point of chords 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=

If tan (cot x) = cot (tan x), then sin 2x=

If sum of the roots of the equation 2x9-11x7+6x4+8=0 is ‘a’ then ‘a’=

The locus of the poles w.r.t the ellipse x2/a2+y2/b2=1 of tangents to its auxiliary circle is

If the sum of two of the roots of x4-2x3-3x2+10x-10=0 is zero then the roots are

The number of terms in the expansion of (a+b+c+d)5 is

The points (-a, -b), (0, 0), (a, b), (" a^2 ",ab) are

Let f(x+y)= f(x)f(y) for all x,y ε R. If f is differentiable at x=0, then

If tan β= n tan α / 1+(1-n)tan2 α, then tan(α - β)=

The multiple roots of x4-2x3+11x2-12x+36=0 are

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

If A+B+C= 1800 then sin2 A/2+ sin 2 B/2 - sin2 C/2=

If sinh 9- k sinh k=(k+1)sinh3 k,then k=

49n+16n+k is divisible by 64 for n?N. Then the numerically least –ve integer value of k is

The distance between the limiting points of the coaxial system x2 + y2 – 4x – 2y – 4 + 2λ(3x + 4y + 10)=0

C0-2. C1+3. C2………..+(-1)n(n+1).Cn =

A unit vector perpendicular to the plane of a=2i-6j-3k, b=4i+3j-k is

It is given that there are 52 Fridays in a leap year. The probability that it will have 53 Saturdays is

The lines 2x+y-1=0, ax+3y-3=0, 3x+2y-2=0 are concurrent

(cosh x+ sinh x)n=

cos π/11 cos 2π/11 cos 3π/11 cos 4π/11 cos 5π/11=

If the first three terms of (1+ax)n are 1,6x,6x2 then (a,n)=

(cos A+ cos 3A+cos 5A+cos 7A)/ (sin A+sin 3A+sin 5A+sin 7A)=

An equilateral triangle is inscribed in the circle x2+y2=a2 . The length of the side of the triangle is

The locus of a point P such that the distances from P to the points (2,3,5) ,( 1,2,-1)  are in the ratio 5:2 is

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

A bag containing 12 two rupee coins, 7 one rupee coins and 4 half rupee coins.If 3 coinsare selected at random, then the probability that the sum of 3 coins is maximum is

If x=sin-1t, y= √(1-t2) then d2y/dx2=

If a tangent to the circle x2 + y2 + 4x - 4y+4=0 makes a equal intercepts on the coordinate axes then the equation of that tangent is

The area (in square unit) of the region enclosed by the curves y=x2 and y=x3 is

d/dx{Tan-1(x-√x/1+x3/2}=

The area of the triangle formed by the lines 3x+4y+5=0, (3x+4y)2-3(y-4x)2=0 is

7/5(1+1/?102 +1.3/1.2.1/104 +1.3.5/1.2.3.1/106 +...........∞)

The lines represented by the equation 3x2-5xy+2y2=0 are

In ΔABC,   tan (A/2)tan (B/2)+ tan (B/2)tan (C/2)+ tan (C/2) tan (A/2)=

If a tangent drawn from the point (4, 0) to the circle x2+y2=8 touches it at a point in the first quadrant, then the coordinates of another point B on the circle such that AB=4 are

If tan2 θ=3 cosec2 θ-1 then θ=

The equations whose roots are opposite in sign and equal in magnitude of the roots of x7+3x5+x3-x2+7x+2=0 is

The solution of (x2y3+x2)+(y2x3+y2)dy=0 is

The point on the curve x2=2y which is closest to the point (0, 5) is

If y=(1+x2)Tan-1x then y2=

If two consecutive terms in the expansion of (x+a)n are equal where n is a positive integer then (n+1)a/x+a is

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

If the length of a chord of the circle x2 + y2=a2is 2K then the locus of the midpoint of that chord is a circle of radius

If the acute angle between the lines 2x+3y-5=0, 5x+ky-6=0 is  then the value of k is

The equation of the tangent to the parabola y2 = 12x at (3, -6) is

The angles between tangents to the parabola y2 = 4ax at the points where it intersects with the line x – y –a = 0 is

The maximum value of a2-abx-b2x2 is

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

If ax+by+c=0 is the equation of the common radical axis of the coaxial system (3x2+3y2-2x-2y-1)+λ(x2+y2-x-2y-3)=0 then ab+bc+ca=

If x= a cos θ (1+cos θ), y=sin θ(1+cos θ) then (dy/dx)θ=π/2

The number of positive divisors of 253673 is

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

The point of intersection of straight lines represented by 6x2 + xy - 40y2 – 35x - 83y + 11 = 0 is:

The equation of the common chord of the two circles (x-a)2+(y-b)2=c2, (x-b)2+(y-a)2=c2 is

Tan (tan-1 1/2+ tan-11/3) =

The value of k so that 3x4+4x3+2 x2+10x+k is divisible by x+2 is

If x= 2 cos t- cos 2t, y= 2 sin t- sin 2t then dy/dx=

cosec2 θ. cot2 θ- sec2 θ. tan2 θ-( cot2 θ- tan2 θ)( sec2 θ. cosec2θ-1)=

If f(x)=3x-7/5x-3 then (fof)(x)=

Let a, b, c be the distinct non-negative numbers. If the vectors ai+aj+ck, i+k and ci+cj+bk lie in a plane then c is

If f(x)=√(x+2√(2x-4))+ )=√(x-2√(2x-4)) then

The lines x+2y-3=0, x+2y+7=0, 2x-y-4=0 from three sides of two squares.

The solution of x2dy-y2dx=0 is

lf the centroid of the triangle formed by (p, q),(q,1),(1,p) is  the origin, then p3+q3+1=

If x+iy= cis α cis β then the value of x2+y2 is

The solution of y dx-x dy+log x dx=0 is

From 101 to 1000 natural numbers a number is taken at random. The probability that the number is divisible by 17 is:

If there is an error of 0.05 cm, while measuring the side of equilateral triangles as 5 cm, then the percentage error in area is

If the foot of the perpendicular from (0,0,0) to a plane is (1,2,3), then the equation of the plane is

If the lines 4x+3y-1=0,x-y+5=0 and kx+5y-3=0 are concurrent,then k is equal to

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

The angle between the pair of straight lines  formed by joining the points of intersection of  x2 + y2 = 4 and y = 3x + c to the origin is a right angle. Then c2 is equal to

sin A+sin 5A+sin 9A)/(cos A+ cos 5A+ cos 9A)=

If the length of the tangent from (h, k) to the circle x2+y2=16 is twice the length of the tangent from the same point to the circle x2+y2+2x+2y=0, then

A man 6 feet height walks at a uniform of 20 above the floor. An object falls freely under gravity, starting from rest at the same height as the lamp, put at a horizontal distance of 5 ft from it. The speed of the shadow of the object on the floor when it has fallen through 15 ft is

If A+B+C =900 then cos2 A+cos2B+ cos2 C=

If y√1+x2=log(x+√1+x2) then  (1+x2)y1+xy=

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=

α and β are the roots of the equation x2+px+p3=0,(p≠0).If the points (α,β) lies on the curve x=y2,then the roots of the given equation are

A: The angle between the tangents drawn from origin to the circle x2+y2-14x+2y+25=0 is π/2 R: If θ is the angle between the pair of tangents drawn from (x1, y1) to the circle S=0 of radius r then tanθ/2=r/√S11

Sum of n brackets of (1)+(1/3+1/32)+(1/33+1/34+1/35)+…. Is

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

The value of sin[(1/2)cot-1(3/4)] is equal to

If the area of the triangle formed by the points (t,2t), (-2,6), (3,1) is 5sq.unit, then t is

sin 1200 cos 1500-cos 2400 sin 3300 is equal to :

If α,β,γ,δ are the roots of x4+px3+qx2+rx+s=0 then Σα2βγ

If p1,p2,p3 are the product of perpendiculars from (0,0) to xy+x+y+1=0, x2-y2+2x+1=0, 2x2+3xy-2y2+3x+y+1=0 respectively then ascending order of p1,p2,p3 is

If cos x+ cos y=4/5, cos x- cos y=2/7, then 14 tan(x-y/2)+ 5 cot (x+y/2)=

If the line 2x+3y+1=0 and 3x-y-4=0 lie along diameters of a circle of circumference 10π, then the equation of the circle is

 If dx + dy =(x + y) ( dx- dy ) then log ( x  +  y ) is equal to

(x+y+z)(x+yω+zω2)(x+yω2+zω)=

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