A to Z Exams

If f(x)= 2 x4+5 x3-7 x2-4x+3 then f(x-1)=

If A+B+C= 1800 then 4 cos(π-A/4)cos (π-B/4) cos(π-C/4)=

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

Two cards aredrawn from a pack. The probability that one of them is  a club and the  other is not a club is

The lines 2x+3y = 6,2x+3y = 8 cut the x-axis at A,B respectively.A line L=0 drawn,through the point(2,2) meets the x-axis at C in such a way that abscissa of A,B and C are in the arithmetic progression.Then the equation of L=0 is

The polars of the points (3, 4),(-5, 12) and (6, t) with respect to a circle are concurrent. Then t=

C0+C1/2+C3/3+ …………Cn/n+1+ =

The curve described parametrically by x=t2+t+1, y= t2-t+1 represents

If the vertex of the parabola y = x2 – 8x + c lies on x – axis, then the value of c is

If p=(2, 1, 3), q=(-2, 3, 1), r=(3, -2, 4) and j is the unit vector in the direction of y-axis then (2p+3q-4r). j=

The roots of x4-5x3+3x2+19x-30=0 are

The value of c for which the area bounded by the curve y=8x2-x5,the lines x=1,x=c and x-axis is 16/3 is

The points (-2,14), (-6, 8), (0, 4), (4,10) taken in order form

The maximum value of the area of the triangle with vertices (a, 0), (a cos θ, b sin θ), (a cos θ, -b sin θ) is

A person of height 180 cm starts from a lamp post of height 450 cm and walks at the constant rate of 4 km per hour. The rate at which his shadow increases is

If a= sin θ+ cos θ, b= sin3 θ+ cos3θ then

Equation x2+2ax-b2=0 has real roots α, β and equation x2+2px-q2=0 has real roots γ, δ. If circle C is drawn with the points (α, γ), (β, δ) as extremities of a diameter, then the equation of C is

(x+y+z)(x+yω+zω2)(x+yω2+zω)=

The equation of  the straight line whose slope 2/3 and which divides the line segment joining (1, 2),(4,-3)  in the ratio 3:4 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

I: The circum centre of the triangle with vertices (1, √3), (1, √2), (3, -√3) is (2, 0). II: The ortho-centre of the triangle formed by the lines 4x-7y+10=0, x+y=5, 7x+4y=15 is (1, 2)

A stone is projected vertically upwards with an initial velocity 112 ft/sec and moves such that s=112t-16t2 where s is the distance from the starting point and t is the time. The greatest height reached by the stone is

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 the distance the points(5,-1,7) and (c,5,1) is 9 then c=

The straight line passing through the point of intersection of the straight lines x-3y+1=0, 2x+5y-9=0 and have finite slope and at a distance of  2 unit from the origin has equation

The complex numbers sin x+ i cos 2x- i sin 2x are conjugate to each other for

In a ∆ ABC, the correct formulae among the following are: I. r=4Rsin(A/2)sin(B/2)sin(C/2) II. r1=(s-a)tan(A/2) III. r3=Δ/(s-c)

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

The conic represented by 2x2-12xy+23y2-4x-28y-48=0 is

An unbiased coin is tossed to get 2 points for turning up a head and one point forthe tail. If three unbiased coins are tossed simultaneously, then the probability ofgetting a total of odd number of points is:

If an error of 0.02 cm is made while measuring the radius 5 cm of a circle, then the relative error in the area is

sin(π/2+θ). Cos(π-θ) cot(3π/2+θ)- sin(π/2-θ). sin(3π/2-θ) cot(π/2+θ) =

The centroid of the triangle formed by the points (2,3,-1), (5,6,3),(2,-3,1) is

The locus of poles of tangets to the circle (x-p)2+y2=b2 w.r.t the circle x2+y2= a2 is

The radical axis of the circle x2+y2+4x-6y=12 and x2+y2+2x-2y-1=0 divides the line joining the centers of the circles in the ratio

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

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 point  [x1 )+t(x2-x1), y1+t(y2-y1)] divides the join of  (x1, y1) and (x2, y2) internally, then

If tan-13 + tan-1n= tan-18, then n is equal to

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

There are three events A,B and C one of which and only one can happen. The odds are 7 to 3 against A and 6 to 4 against B.The odds against C are

If the line lx+my+1=0 meets the circle x2+y2=a2 in P and Q and PQ subtends a right angle at the centre of the circle, then

The angle between the curves y2=4ax, ay= 2x2 is

The solution of (12x+5y-9)dx+(5x+2y-4)dy=0 is

If (tan 3A / tan A) =α then ( sin 3A/ sin A) =

If α,β,γ are the roots of x3+x2+x+1=0 then (α-β)2+(β-γ)2+(γ-α)2=

The point (-1, 0) lies on the circle x2+y2-4x+8y+k=0. The radius of the circle

The length of the latus rectum of the parabola x2 + 4x – 8y + 28 = 0 is

If the roots of x3-kx2+14x-8=0 are in G.P then k=

(cos 3θ - sin 3θ)/ (cos θ+ sin θ)=

If f(x) = 2x4+5x3-7 x2-4x+3 then f(x-1)=

An urn A contains 3 white and 5 black balls. Another urn B contains 6 white and 8 black balls. A ball is picked from A at random and then transferred to B. Then a ball is picked at random from B. The probability that it is a white ball is :

The centre of the circle r2 - 4r (cosθ + sin θ) - 4 = 0 in cartesian coordinates is :

sin5θ/sinθ is equal to

The number of numbers less than 2000 that can be formed using the digits 1,2,3,4 when repetition is allowed is

If A+B+C= 1800 then cos 2A- cos 2B+ cos 2C=

One extremity of a focal chord of y2=16x is A(1,4). Then the length of the focal chord at A is

A bag contains 3 red, 4 white and 5 black balls. One ball is drawn at random. If a,b,c are the probabilities of drawing a red a white, a black ball from the bag then the ascending order of a,b,c  is

32cos4 θ.sin2 θ=

A rectangular vessel is of 2mt long 0.5mt breadth and 1mt deep. If water flows in at the rate of 900 cubic cm per sec, than the rate of increase of water level when 25 cm deep is

The period of cos (5x/2) is

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

The locus of the midpoints of the chords of the circle x2+y2-2x+2y-2=0 parallel to the line y=x+5 is the line which passes through the point is

If xy=c2 then dy/dx=

The locus of the midpoint of the chord of the circle x2+y2-2x-2y-2=0, which makes an angle of 1200 at the centre is

If ax2+2hxy+by2=1 then (hx+by)3y2=

If (1,2),(3,4) are limiting points and x2+y2-x+ky=0 is one circle of a coaxal system then k=

If the lengths of the tangent from P(h,k) to the circles x2+y2-4x-5=0 and x2+y2+6x-2y+6=0 are equal then

If u=3(lx+my+nz)2-(x2+y2+z2) and l2+m2+n2=1 then uxx+uyy+uzz=

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

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

If [cos(θ1-θ2)/ cos(θ1+θ2)]+ [cos(θ3+θ4)/ cos(θ3-θ4)] =0, then tan θ3tan θ4=

cos2 (800+θ)+ sin2 (1000-θ)=

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

The angle between the normals at (1,3),(-3,1) to the circle x2+y2=10 is

The acute angle made by the line joining the points (1, -3, 2), and (3, -5, 1) with the coordinate axes are

If Tr+1 is the term independent of x in (3x-5/x3)8 then r=

The number of tangents that can be drawn from (6, 0) to the circle x2+y2-4x-6y-12=0 are

If the tangent  at the point  P (2,4) to the parabola y2= 4ax meets the parabola y2= 8x + 5 at Q and R, then the midpoint of QR is

The points (k,2-2k), (1-k,2k) and (-4-k,6-2k)are collinear. Then k =

The equation of the parabola whose axis is parallel to y –axis and passing through (4, 5) (-2, 11), (-4, 21) is

The cost of a cloth piece is Rs.35/-.If the length of the cloth piece is 4 metres more and each metre costs Rs.1/- less,the cost would remain unchanged.The length of the cloth piece is

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

If x2y-x3(dy/dx)=y4cosx then x3y is equal to

If two circles(x-3) 2+(y-1)2=r2 and x2+y2-6x+4y+4=0 intersect in two distinct points then

The equation of the lowest degree with rational coefficients having a root √2+√3+i is

If the orthocenter and the circumcentre of a triangle are (-3,5,1), (3,3,-1) then the circumcentre is

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

The locus of the point if the join of the points (-4,2,3), (2,-1,5) subtends a right angle at P is

P(-2, -1) and (0, -3) are the limiting points of a coaxal system of which C= x2+y2+5x+y+4=0 is a member. The circle S= x2+y2-4x-2y-15=0 is orthogonal to the circle C. The point where the polar P cuts the circle S is

If sin θ+ cos θ=a then sin4 θ+ cos 4 θ=

If α,β,γ are the roots of x3+ax2+bx+c=0 then π(α+β-2γ)=

The general term of (2a-3b)-1/2 is

If the line x + y + 2 = 0 touches the parabola y2 = kx, then k =

The positive integer which is just greater than (1+0.0001)10000 is

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

The equation of the parabola  with latusrectum joining the points (6,7) and (6,-1) is

If A+B+C = 7200 then tan A+ tan B+tan C=

The students while solving a quadratic equation in x,one copied the constant term incorrectly and got the roots 3 and 2.The other copied the constant term and coeffient of x2 as -6 and 1 respectively.The correct roots are: