A to Z Exams

If sin-1 (3/5)+sin-1(5/13)= sin-1 x, then x=

If α, β, γ are the roots of x3-3x+7=0 then α β γ=

The coefficient of x6 in (1+x+x2+x3+x4+x5)6 is

13+23+ 33+….+1003=k2, then k=

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

How many circles can be drawn each touching all the three lines x+y=1, x+1=y, 7x-y=6

sin 3θ/2 cot θ/2 cosθ=

x-axis divides the line segment joining (2,-3), (5,7) in the ratio

The 7th term of loge(5/4) is

The ratio of the rth term and the (r + 1)th term in the expansion of (1 + x)n is:

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

The length of the latus rectum of the hyperbola 9x2-16y2+72x-32y-16=0 is

If the asymptotes of the hyperbola 14x2+38xy+20y2+x-7y-91=0 are 7x+5y-3=0, ax+by+c=0 then the descending order of a, b, c is

f(x)=(sin-1x)2+(cos-1x)2 is stationary at

The value of Cot [Cot-1 7+ Cot-1 8+ Cot-1 (18)] is

Equation of one of the tangents passing through (2,8) to the hyperbola 5x2- y2 = 5 is

If (cos 3A+sin 3A)/ (cos A-sin A)=1-k sin 2A, the value of k is

Coefficient of x4 in (1+x+x2+x3)11 is

Focus of the parabola 4y2-20x-8y+39=0 is

If tan(α+θ)= ntan(α-θ), then (n+1)sin 2θ=

sin 6θ(2cos2θ-1)=

If a hyperbola has one focus at the origin and its eccentricity is √2. One of the directries is x+y+1=0. Then the equations to its asymptotes are

If the tangents at the point (1,-3) and (-3,1) of a circle are perpendicular then the radius of the circle is

Coeff. of x3 in log(1 + x + x2)

The value of tan 150+ tan 300+ tan 150 tan 300 is

If OA, OB are two equal chords of the circle x2+y2-2x+4y=0 perpendicular to each other and passing through the origin, then the equations of OA and OB are

2 Tan-1 1/3+Tan-1 1/7=

The equation of the tangent to the curve y=x3+3x2-5 and which is perpendicular  to y=2x-6y+1=0  is

The derivative of √(Tan-1 x) w.r.to x is

The approximate change in y, when y=x2+2x, x=3, δx=0.01 is

The probability that India wins a cricket match against England is given to be 1/3.If India and England play, 3matches, what is the probability that India will loose all three matches is

The area of the triangle formed by the tangents from (1, 3) to the circle x2+y2-4x+6y+1=0 and its chord of contact is

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

From a lot of 10 items containing 3 defectives, a sample of 4 items is drawn at random without replacement. The expected number of defective items is:

If the length of the tangent from (1, 1) to the circle 2x2 + 2y2 – 4x – 6y+k=0 is 5 units then k-1 =√

The inverse point of (1, 2) w.r.t the circle x2+y2=25 is (5, k), then k=

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?

The locus of the point which moves such that the sum of the squares of its distance from (0, a) is 2r2, is

If f(x)=x3/x2-1,then f111(0)=

If the roots of x2-2(5+2k)x+3(7+10k)=0 are equal then k=

In a class 40% of students read History, 25% Civics and 15% both History and Civics. If a student is selected at random from that class, the probability that he reads history, if it is known that he reads Civics is

If the tangent at P on the circle x2+y2=a2 cuts two parallel tangents of the circle at A and B then PA. PB=

If α is a non real root of the equation x6-1=0 then (α2+α3+α4+α5)/(α+1) is

cot2θ(sec θ-1/ (1+sin θ))+ sec2 θ (sin θ-1/ (1+sec θ))=

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

xn-1 is divisible by x-k. Then the least +ve integral value of K is

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)

If α, β are the roots of ax2+bx+c=0 then the value of (α /β –β /α)2

If P = (0, 1, 2), Q = (4, -2, 1), 0 = (0, 0, 0), then LPOQ is equal to:

If tan2 θ=3 cosec2 θ-1 then θ=

The vector equation of the plane passing through the point (3, -2, 1) and perpendicular to the vector (4, 7, -4) is

If the sum of the squares of the sides of triangle is 16 then the sum of the squares of the medians is

If V=πr2h then rVr+2hVh=

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 :

If the expression x2 –(5m-2)x+(4 m2 +10m +25)=0 can be expressed as a perfect square, then m =

If the diagonals of a parallelogram are given by 3i+j-2k and i-3j+4k, then the lengths of its sides are

From the point A(0,3) on the circle x2+4x+(y-3)2=0, a chord, AB is drawn and extended to a point P, such that AP = 2AB. The locus of P is

If the parabola y2=-4ax passes through (-3,2) then the length of its latusrectum is

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

If au+b=a2x+y then uxuy=

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

If α,β,γ are the roots of x3+x2+2x+3=0 then the equation whose roots β+γ,γ+α,α+β is

If α,β are the roots of x2-p(x+1)+c=0 then (1+α)(1+β)=

In how many ways can a collection of 30 books be divided into two groups of 10 and 20 so that the first group always contains a particular book?

The vectors (1, -1, 1), (0, 1, 1), (0, 0, 2) are

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 α, β, γ are the roots of x3+2x2+3x+4=0 then Σα2β2 =

1+4+13+40+…n terms=

If three complex numbers are in A.P. then they lie on

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

The circumcircle of a triangle is given by x2+y2-4x+6y-3=0. The radius of the nine point circle of the triangle is

If A=cos θ+ 2√2 sin θ, then for all real values of θ

The radius of the circle r2-2√2r(cos θ + sin θ)-5=0 is

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

Water flows into a conical  vessel is at the rate of 5 cubic cm per sec. if the semi vertical angle of the vessel is 300, then the rate of increase of water level when the water level in the vessel is 6 cm is

If (1,2) is the midpoint of a chord 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=

C1+2.C2+3.C3+…….+n.Cn =

The equation of the medians of the triangle with vertices (0, -1),(-2, 0),(-1, -3) are

The area of the quadrilateral formed by the tangents from the point (4,5) to the circle x2+y2-4x-2y-11=0 with a pair of radii joining the points of contact of these tangents is

The inverse point of (2,-3) with respect to the circle x2+y2+6x-4y-12=0

If 2x-3y=5 and 3x-4y=7 are the equation of two diameters of a circle whose area is 154sq units, then the equation of the circle is

The circle passing through the points (1, t), (t, 1) and (t, t) for all values of t passes through the point

If y = sin (logex) then x2 (d2y/dx2) + x (dy/dx) =

If n is a positive integer, then value of (3n+2)nC0+(3n-1) nC1+(3n-4) nC2+……..+ 2(nCn) is

The angle between the lines represented by y2sin2θ-xysin2θ+x2(cos2θ-1)=0 is

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

A and B throw a pair of dice. A wins if he throw 6 before B throws 7 and B wins if he throws 7 before A throws 6. If A begins, his chance of winning is

The point of concurrence of the lines (3k+1) x-(2k+3)y+(9-k)=0 is

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

Equation to the circle whose one of the diameters is the common chord of (x-a)2+y2=a2,x2+(y-b)2=b2 is

The greatest negative integer satisfying x2+4x-774 is

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

If 2x+ky-10=0, 5x+2y-7=0 are parallel, then the value of k =

The value of k such that the straight line (2x+3y+5)+k(x-7y+6)=0 is parallel to x- axis is

The parametric equation of the circle x2+y2+x+√3y=0 is

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

If the tangent at (1,-2) to the circle x2+y2=5 touches the circle x2+y2-8x+6y+20=0 at p.Then Py =

The  harmonic conjugate of (7,5) w.r.t. (4,2), (9,7) is

cos 60 cos 420 cos 600 cos780=

From a well shuffled pack of 52 playing cards two cards are drawn at random, one after another without replacement. The probability that 1st one is a king and second one is queen is