A to Z Exams

If α,β are the roots of ax2+bx+c=0;α+h,β+h are the roots of px2+qx+r=0;and D1,D2 the respective discriminants of these equations,then D1:D2=

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

1 /3 – 1! + 1 / 4.2! + 1 / 5.3! +………. =

If (1+x+x2)n =Σr=02n rxr then a0+a2+a4+……….+a2n=

cot(A+150)- tan(A- 150)=

The latusrectum of a hyperbola is 9/2 and eccentricity is 5/4.Its standard equation in standard form is

A bag contains 6 white and 4 black balls. Two balls are drawn at random. The probability that they are of the same colour, is

In the expansion of (2-3x)-1 the 3rd term is

If the slope of one line of 8x2+2hxy+by2=0 is double the other, then h2=

If the line lx+my=1 is a normal to the ellipse x2/a2+y2/b2=1 then a2/l2-b2/m2=1

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

If f(x)=√(1-√(1-x2)), then

A gas holders contain 100 cubic ft of gas at a pressure of 5 lb per sq. inch. If the pressure is increasing at the rate of 0.05 lb per sq. inch per hour, then the rate of decrease of the volume assuming Boyle’s law pv=a constant is

If the circles (x+a)2+(y+b)2=a2, (x+α)2+(y+β)2=β2 cut orthogonally then α2+b2

If two angles of ∆ ABC are 45o and 60o, then the ratio of the smallest and the greatest sides are

A line through the origin meets the circle x2+y2=a2 at P and the hyperbola x2-y2=a2 at Q. The locus the point of  intersection of the tangent at P to the circle and with the tangent t Q to the hyperbola is

If two lines represented by ax3+bx2y+cxy2+dy3=0 are mutually perpendicular, then the slope of third line is

The slope of the radical axis of the circles x2+y2+3x+4y-5=0 and x2+y2-5x+5y-6=0 is

If y= a cos mx+b sin m=mx, then d2y/dx2=

The polar equation cos θ + 7 sin θ = 1/r represents a :

The number of quadratic expressions with the coefficient drawn from the set (0, 1, 2, 3) is

If A lies in the third quadrant and 3 tanA – 4 = 0, then 5 sin2A + 3 sinA + 4 cosA is equal to

nC0+nC1+nC2+………+nCn =

The angle between the lines 4x-y+9=0, 25x+15y+27=0 is

The length of tangent from (0,0) to the circle 2(x2+y2)+x–y+5=0,is:

If 5 biscuits are distributed among 6 children, the probability that a particular child gets 4 sweets is

The number of common tangents to the two circles x2+y2-8x+2y=0 and  x2+y2-2x-16y+25=0 is

A car starts from rest and attains the speed of 10km/hr,20km/hr respectively at the end of the first and second minutes.If the car moves on a straight road,the distance travelled in 2 miuntes is:

If x=-5+4i then x4+9x3+35x2-x+4=

The set of values of x for which the inequalities   x2-3x-10<0  and  10x-x2-16>0 hold simultaneously is

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

The length of the intercept made by the sphere x2+y2+z2-4x+6y+8z+4=0 on z axis is

4(cos3 200 +cos34 00) =

The equation of the auxiliary circle of x2/16-y2/25=1 is

The circle x2+y2=4x+8y+5=0 intersects the line 3x-4y=m at two distinct points if

d/dx{Tan-1x/√1-x2+Sec-11/√1-x2}=

The equation of the sphere with centre at (-1, 2, 3) and which passes through (1, -1, 2) is:

The lines r=(6-6s)a+(4s-4)b+(4-8s)c  and r=(2t-1)a+(4t-2)b-(2t+3)c intersects at

A: The polar of (2, 3) with respect to the circle x2+y2-4x-6y+5=0 is 2x+3y=0 R: The polar of (x1, y1) with respect to the circle S=0 is S1=0

In the argand plane the area in square units of the triangle formed by the points1 + i, 1 –i, 2i is

The odds against an event is 5 to 2 and the odds in favour of another disjoint event are 3 to 5. Then the probability that one at least of the event will happen is

The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines x = 0 and y = 0 is  

If cot θ - tan θ= sec θ, then θ =

The circle orthogonal to the  three circles x2+y2+aix+biy+c=0, i=1, 2, 3 is

If A=(1,1) ,B=(4,5) and C=(6,13) then cos A=

The radius of the circle which touches y-axis at (0, 0) and passes through the point (b, c) is:

The equation of the hyperbola with its axes as coordinate axes, whose transverse axis 8 and eccentricity 3/2 is

In ΔABC, R2 (sin 2A+sin 2B+sin 2C)=

If a=i+4j, b=2i-3j and c=5i+9j then c=

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

The equation of the normal to the curve (x/a)2/3+(y/b)2/3=1 at (a cos3θ, b sin3θ ) is

There are 3 routes from Tenali to Vijaywada and 4 routes from Vijaywada to Hyderabad,in how many different ways a person can travel from Tenali to Hyderabad via Vijaywada?

If ax= by= cz = dw then the value of x[(1/y)+(1/z)+(1/w)]is

The derivative of (ax+b)cx+d w.r.to x is

The line y = m(x + a)+a/m touch the parabola y2= 4a(x+ a) form

A cylindrical gas container is closed at the top and open at the bottom. If the iron plate of the top is 5/4 times as thick as the plate forming the cylindrical sides, the ratio of the radius to the height of the cylinder using minimum material for the same capacity is

The value of a such that x3+3ax2+3a2x+b is increasing on R-{-a} are

Equation of the parabola having focus (3,-2) and vertex (3,1) is

Let α,β be the roots of x2-x+p=0 and γ,δ be the roots of x2-4x+q=0.If α,β,γ,δ are in G.P then the integral values of p and q respectively,are

The length of the sub tangent of the curve 2x2+3xy-2y2=8 at (2, 3) is

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

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

If y= acos (log x)+b sin (log x) then x2y2+xy1+y=

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

If x = sint; y = sin pt then (1-x2) (d2y/dx2) -x(dy/dx) +p2y =

The equation of the tangents to a circle x2+y2-4x-6y-12=0 and parallel to 4x-3y=1 are

If the circles x2+y2=4 and x2+y2-6x-8y+K=0 touch internally then K=

If the tangents to the parabola y2=4ax at (x1,y1) and (x2,y2) meet on the axis then

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 θ= Sin-1 x+ Cos-1 x+ Tan-1 x, 0≤x≤1, then the smallest interval in which θ lies is given by

The equation of the tangents from the origin to x2+y2-6x-2y+8=0 are

If α and β are two points on the hyperbola x2/a2-y2/b2=1 and the chord joining these two points passes through the focus (ae, 0) then e cos α-β/2=

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

If f=x2yz+y2zx+z2xy then fxyz=

If  cos θ - 4 sin θ = 1 then  sin θ + 4 cos θ   is equal to

The approximate percentage reduction in the volume of a cube of ice, if each side of the ice cube to reduced by 0.7% due to melting to:

The equation of the tangents to a circle x2+y2-4x-6y-12=0 and parallel to 4x-3y=1 are

If z= (λ+3)+i√(5-λ2), then the locus of z is a circle with centre at

The values of the parameters a for which the quadratic equations (1-2a)x2-6ax-1=0 and ax2-x+1=0 have at least one root in common are

If one root of the quadratic equation ax2+bx+c=0 is 3-4i, then a+b+c is :

The sum of the length of the sub tangents and subnormal at θ=π/3 on the cycloid x=a(θ-sinθ), y=a(1-cosθ) is

The locus of middle points of chords of the hyperbola 2x2-3y2=5 which passes through the point (1,-2) is

The angle between the lines whose direction cosines satisfy the equations l + m+ n =0, l2 + m2 – n2 = 0 is

The locus of middle point of the chord of the ellipse x2/a2+y2/b2=1 touching the ellipse The locus of midpoint of the chord of the ellipse x2/α2+y2/β2=1

The equation of the line dividing the line segment joining the points (5, 3), (3, -3) in the ratio 5:3 externally and perpendicular to   2x+3y-5=0.  Is

If a, b and c are mutually perpendicular unit vectors, then [a b c]2=

If y= xsin x+(sin x)x then dy/dx=

If the normal at (1,2) on the parabola again at the point (l2,2t), then the value of t is

Tangent at any point of the curve (x/a)2/3+(y/b)2/3=1 makes intercepts x1and y1 on the axes. Then

If the product of two of the roots of x4-5x3+5x2+5x-6=0 is 3 then the roots are

The equations of the tangents drawn from the origin x2+y2+2gx+2fy+f2=0 is

If the roots of 2x3-3x2+kx+6=0 are in A.P then k=

128 sin8 θ=

The perpendicular distance of the straight line 7x+24y=15 from the point of intersection of the lines 3x+2y+4=0, 2x+5y-1=0

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 3x  /(x-a) (x-b)  =  2/(x-a)  +  1/(x-b)  then a:b =

The equation of the normal to the curve x2=4y at (2, 1) is

If r2=(x-a)2+(y-b)2 then rxx+ryy=

The angle between the tangents drawn from (0,0) to the circle x2+y2+4x-6y+4=0 is

If 5,-7,2 are the roots of lx3+mx2+nx+p=0 then the roots of lx3-mx2+nx-p=0 are