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The straight line x + y = k touches the parabola y = x-x2, if k =

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

If p,q are the perpendiculars from the origin to the lines x sec α + y cosec α = a and xcosα-ysinα=acos2α, then 4p2+q2=

If A is an invertible matrix of order n, then the determinant of adj A is equal to :

The equation of the normal to the curve 2y=3-x2 at (1, 1) is

∫ (sin6x/cos8x) dx is equal to

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

Order and degree of (x2+2x)y22+(x2-2)y13-2(x+3)y=0 are

The extremities of a diameter of a circle have coordinates (-4, -3) and (2, -1). The length of the segment cut off by the circle on y-axis is

If 1,ω,ω2 are the cube roots of unity, then (a+bω+cω2)/ (c+aω+bω2) is equal to:

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

sin2 52 (1/2)0- sin2 22 (1/2)0=

(sin 4θ)/(sin θ)=

In an entrance test there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student know the answer to a question is 9/10.If he gets the correct answer to a question, then the probability that he was guessing is

The base radius of a cylindrical vessel full of oil is 30 cm. Oil is drawn at the rate of 27000 cubic cm per minute. The rate at which the level of oil is falling in the vessel is

If α,β,γ are the roots of x3-x2+33x+5=0 and A=s1,B=s2,C=s3 then the descending order of A,B,C is

If y=(x2-1)n, then (x2-1)yn+2+2xyn+1=

The sum of the distances of any point on the ellipse 3x2+4y2=24 from its foci is

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

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

The perpendicular distance of radical axis determined by the circles x2+y2+2x+4y-7=0 and x2+y2-6x+2y-5=0 from the origin is

d/dx{x1/x}=

The locus of the midpoints of chords of the circle x2+y2=25 which touch the circle (x-2)2+(y-5)2=289 is

If x cos α= y cos(2π/3+ α)= z cos(4π/3+ α),then xy+yz+zx=

If the circles described on the line joining the points (0, 1) and (α, β) as diameter cuts the axis of x in points whose abscissa are the roots of the equation x2-5x+3=0, then (α, β)=

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

The coefficients of x2 in the expansion of e2x+3 is

A three digit number n such that the last two digits of it are equal and differ from the first the number of such n is

2 sec2 θ- sec4 θ- 2 cosec2 θ+ cosec4θ=

A box is made from a piece of sheet of metal 12 inch square by cutting equal small squares from each corner and tuning up the edge. The dimensions of the box of largest volume which can be made in this way are

If A+B+C= 900 then cos 2A+cos2B+cos 2C-1/ (sin 2A sin 2B sin 2C)=

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

The chord of contact of tangents drawn from points on x2/a2+y2/b2=1 to the circle x2+ y2=c2 touches the ellipse

The equation of the circle passing through (2, 1) and touching the coordinate axes is

(12/3)+(12+22/5)+(12+22+32/7)+… n terms

The length of the direct common tangent of the circles x2+y2-4x-10y+28=0 and x2+y2+4x-6y+4=0 is

The equation of the line passing through the point of intersection of the lines 2x+3y-4=0, 3x-y+5=0 and the origin is

Let A be the centre of the circle x2+y2-2x-4y-20=0. Suppose that the tangent at the point B(1, 7) and D(4, -2) on the circle meet at the point C. The area of the quadrilateral ABCD is

The solution set of ,when x≠0 and x≠3 is

The portion of a line intercepted between the coordinate axes is bisected by the point (2, -1) in the ratio 3:2. The equation of the line is

In measuring the circumfence of a circle, there in an error of 0.05 cm. if with this error the circufence of the circle is measured of the circle is measured as c cm, then the percentage error in area is

The angle at which the circles x2+y2+8x-2y-9=0 and x2+y2-2x+8y-7=0 intersects is

The equation of the line passing through the point (5, -4), with slope -7/2 is

d/dx{(2x-3)/(3x+1)}=

The ends of the hypotenuse of a right angled triangle are (2,0,-3), (0,4,1) then the locus of the third vertex is

If x+y=1, then 2.nCrxr.yn-r =

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

If Q denotes the set of all rational numbers and f(p/q) = (p2 - q2)1/2 for any p/q belongs to R then observe the following statementsI.f(p/q) is real for each p/q belongs to QII..f(p/q) is complex number for each p/q belongs to QThen which of the following is correct

The centre of the incircle of the triangle formed by the line 3x+4y=24 with the axes is

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

The side of an equilateral triangle increases at the uniform rate 0.05 cm/sec. the rate of increase in the area of the triangle when the side is 20 cm is

The circumcentre of the triangle with vertices at A(5, 12),B(12, 5), c (2√(13 ) ,3√(13 )) is

Vertex of the parabola 2y2+3y+4x-2=0 is

The intercept made by the circle x2+y2-2hx sin θ-2ky sinθ=h2 cos2θ on the x-axis is

The equation whose roots are squares of the roots of x4+x3+2x2+x+1=0 is

If sinA + sinB = l, cosA - cosB = m, then the value of cos(A - B) =

The inverse point of (1, 2) with respect to the circle x2 + y2 - 4x - 6y +9 = 0 is

ABC is an isosceles triangle and B= 900. If B and the midpoint P of AC are represented by 3+2i and 1-i then the other vertices are

The angle between the tangents from a point on x2+y2+2x+4y-31=0 to the circle x2+y2+2x+4y-4=0 is

The radius of a sphere is 3 cm. if an error of 0.03 cm is made in measuring the radius of the sphere, then the error in surface area is

If Tan-1(x-1/x-2)+ Cot-1 (x+2/x+1)=π/4, then x=

The locus of the point of intersection of the tangents at the ends of a chord of a circle x2+y2=a2 which touches the circle x2+y2-2ax=0 is

The length of the normal from pole on the line rcos(θ-π/3)=5 is

d/dx{Tan-1(3a2x-x3/a3-3ax2)}=

If α and β are complex cube roots of unity, then α4+β4+α-1β-1=

The locus of a point which is at a distance of 5 unit from (2,1,-3) is

The length of the latus rectum of the parabola 4y2 + 12x – 20y + 67 = 0 is

The sum of the series log42-log82+log162-… is

For the parabola y2 +6y-2x+5 = 0(I) The vertex is (-2 , -3)(II) The directrix is y+3 = 0

In a business venture a man can make a profit of Rs.2000/- with probability of 0.4 or have a loss of Rs.1000/- with probability 0.6his expected profit is

In a class of 10 students, there are 3 girls A,B,C.The number of different ways that they can be arranged in a row such that no two of the three girls are consecutive is

The value of m for which one of the roots of x2-3x+2m=0 is double of one of the roots of x2-x+m=0 is

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

In ΔABC, if sin A: sin C = sin (A-B) :sin (B-C), then a2,b2,c2 are in

The transformed equation of x3+6x2+12x-9=0 by eliminating second term is

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

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

If x -y+ 1 = 0 meets the circle x2 + y2 + y - 1 = 0 at A and B, then the equation of the circle with AB as diameter is

The ascending order of A= Sin-1(sin 8π/7),B= Cos-1(cos 8π/7), ), C=Tan-1(tan 8π/7) is

If tan θ+ tan 2θ+tan 3θ= 0 then θ=

If A,B,C,D are angles of a cyclic quadrilateral,then cosA+cosB +cosC +cosD is equal to:

From an urn containing 3 white and 5 black balls , 4 balls are transfered in to an empty urn. From this urn a ball is drawn and found to be white. The probability that out of four balls transfered 3 are white and 1 is black is

The circles x2+y2-10x+16=0 and x2+y2=r2 intersect each other into distinct points if

If α, β, γ are the roots of x3+3x2+2x+3=0 then Σ(1/α2β2) =

The probabilities of problem being solved by two students are 1/2 and 1/3.Find the probability of the problem being solved.

If A(2, -1) and B(6, 5) are two points the ratio in which the foot of the perpendicular from (4, 1) to AB divides it is

α,β are the roots of the equation λ(x2-x)+x+5=0.If λ1 and λ2 are the two values of λ for which the roots α,β are connected by the relation α/β+β/α=4,then the value of λ1/λ2 + λ2/λ1 is

If (cos 3α + i sin 3α) (cos 5β+i sin 5β)=cos θ+i sin θ then θ is

Order of (dy/dx)3+(dy/dx)2+y4=0 is

If Tan-1 x+ Tan-1 y+ Tan-1 z=π, then x+y+z=

The equation of the circle cutting orthogonally circles x2+y2+2x+8=0, x2+y2-8x+8=0 and which touches the line x-y+4=0 is

The perpendicular form of the line 3x+4y-5=0 is

If one root of the equation ax2+bx+c=0 is equal to the nth power of the other then (acn)1/n+1+(anc)1/n+1+b=

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

The solution of (dy/dx)=ey-x is

2.C2+6.C3+12.C4+……….+n(n-1)Cn =

Tan (π/4+1/2cos-1a/b) +tan (π/4-1/2cos-1a/b) =

Equation of the latusrectum of the parabola x2+8x+12y+4=0

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

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