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Two straight lines are perpendicular to each other. One of them touches the parabola y2 = 4a (x + a) and the other touches y2 = 4b (x + b). the locus of the point of intersectionof the two lines is

tan θ+ 2 tan 2θ+4 tan 4θ+ 8 tan 8θ+16 tan 16θ+32 cot 32θ=

The point on the curve y=x2+5, the tangent at which is perpendicular to the line x+2y=2 is

If the equations x2-x-p=0 and x2+2px-12=0 have a common root,then that root is

The maximum value of a2-abx-b2x2 is

The polar of the point(t-1, 2t) w.r.t the circle x2+y2-4x-6y+4=0 passes through the point of intersection of the lines

If 2-cos3 θ=3 sin θ cos θ then θ=

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:

If the circles x2+y2+2ax+4ay-3a2=0 and x2+y2-8ax-6ay+7a2=0 touch each other externally, the point of contact is

If the roots of a2x2+2bx+c2=0 are imaginary,then the roots of b(x2+1)+2acx=0 are

If Sin6θ + Cos6θ + Kcos2θ=1 then k=

If xy=c2 then dy/dx=

The number of four digited numbers which are not divisible by 5 that can be formed from by using the digits 0,2,4,5 is

If x4 then the value of x2-7x+12 is

The circle described on the line joining the points (0, 1), (a, b) as diameter cuts the x-axis in points whose abscissa are roots of the equation

The equation of the normal at a point hose eccentric angle is 3π/2+θ to the ellipse x2/9+y2/4=1 is

If a,b,c ≠ 0 and belong to the set { 0,1,2,3,................9 then log10[(a+10b+102c)/(10-4a+10-3b+10-2c)] is equal to

cos 250 - cos650=

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

The locus of a point which is equidistant from the points(-2,2,3), (3,4,5) is

If f(x)=log (x-5)(2-x), g(x)=log (x-5), h(x)= log (2-x) then

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

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

The equation of the common chord of the two circles x2+y2+2x+3y+1=0, x2+y2+4x+3y+2=0 is

The coefficient of xr (0

Orthocentre of thele whose vertices are (2,-1/2), (1/2,-1/2), (2,(√3-1)/2) is

The normal at P cuts the axis of the parabola y2 = 4ax in G and S is the focus of the parabola.If Δ SPG is equilateral then each side is of length

The quadratic equation x2 + ax + bc = 0, x2 + bx + ca = 0 have a common root, then the quadratic equations whose roots are the remaining roots in the given equations is (where, a ≠ b)

If fg=ch, the lines represented by hxy+gx+fy+c=0 fprm a quadrilateral with coordinate axes which is

If y = sin-1 x-sin-1√1- x2 then d2y/dx2=

The circles x2+y2+4x-2y+4=0 and x2+y2-2x-4y-20=0

The polar equation of xcosα+ysinα=p is

If the sum of odd terms and the sum of even terms in the expansion of (x+a)n are p and q respectively then p2+q2=

From a point on the level ground, the angle of elevation of the top of a pole is 300 on moving 20 metres nearer, the angle of elevation is 450. Then the height of the pole (in metres), is:

The centre of the circle whose centre is on the straight line 5x – 2y +1=0 and cuts the x-axis at two points whose abscissa are -5 and 3 is

If (1,2) is a limiting point of a coaxial system of circles containing the circle x2+y2+x-5y+9=0,then the equation of radical axis is

If the straight line ax+by+c=0 and x cos α+ y sin α=c, enclose an angle π/4 between them and meet the stright line x sin α – y cos α =0 in the same point , then

A coin and six faced die, both unbiased, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die, is

A man observes a tower AB of height h from a point P on the ground. He moves a distance ‘d’ towards the foot of the tower and finds that the angle of elevation is doubled. He further moves a distance 3d/4 in the same direction and the angle of elevation is three times that at P. Then 36h2=

(1-i)(1+2i)(1-3i)=

100 tickets are numbered as 00,01, 02,...,09,10,11,...99. When a ticket is drawn at random from them and if B is the event of getting 0 as the product of the numbers on the ticket, then P(B)=

L and L’are ends of the latus rectum of the parabola x2 = 6y. the equation of OL and OL’ where O is the origin is

The angle between a pair-of tangents drawn from a point P to the circle x2+y2+4x-6y+9sin2α+13cos2 α=0 is 2α.The equation of the locus of the point P is

Axes are coordinate axes and area of maximum rectangle inscribe in the ellipse is 16 and e= √15/4 then equation of ellipse

(2 cos θ-1) (2 cos 2θ-1) (2 cos 4θ-1) (2 cos 8θ-1)=

If θ is the angle between the curves xy=2, x2 +4y=0 then tan θ=

In a class there are 60 boys and 20 girls. In it, half of the boys and half of the girls know cricket. The probability of a person selected from the class is either a boy or a person who knows ticket is

The number of ways in which 5 boys and 4 girls can sit in a row so that all the girls come together and 2 particular girls never be together is

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

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 :

The locus of the point of intersection of two perpendicular tangents to the circle x2+y2=a2, x2+y2=b2 is

d/dx{Tan-1√(x2/a2-x2)}=

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

If cot θ - tan θ= sec θ, then θ =

The equation of the circle passing through the points of intersection of the circlesx2+y2=5, x2+y2+12x+8y-33=0 and touching x-axis is

The equation of the normal to the curve 3y2=4x+1 at (1, 2) is

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

If the roots of (c2-ab)x2-2(a2-bc)x+(b2-ac)=0 are equal,then

The derivative of Sin-1(3x-4x3) w.r.to Tan-1x/√ (1-x2) is

The length of latus rectum of parabola y2+8x-2y+17 = 0 is:

Let the base of the triangle lie along the line x=a and be of the length a. The area of the triangle id a2 if the vertex lies on

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

The value of k if (1,2), (k,-1) are conjugate points with respect to the ellipse 2x2+3y2=6 is

If x= acos3θ, y= asin3θ then d2y/dx2 at θ=π/4 is

If 3y2-8xy-3x2-29x+3y-18 us resolvable into two linear factors then the factors are

4 sin 5θ cos 3θ sin 2θ=

If a straight line L is perpendicular to the line 4x-2y=1 and forms a triangle of a area 4 square units with the coordinate axes is

The region represented by |z+a|+|z-a|

If n is a positive integer, then the coefficient of xn in the expansion of (1 + x)n/(1-x) is

The direction cosines of the line passing through P (2, 3, - 1) and the origin are

A, B, C are three routes from the house to the office. On any day, the route selected by the officer is independent of the climate. On a rainy day, the probabilities of reaching the office late, through these routes are 1/25, 1/10, 1/4respectively. If a rainy day the officer is late to the office then the probability that the route to be B is

An experiment yields 3 mutually exclusive and exhaustive events A, B and C. If P(A)=2P(B)=3P(C) then P(A) =

x2n-1+y2n-1 is divisible by x+y if n 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 u=3(lx+my+nz)2-(x2+y2+z2) and l2+m2+n2=1 then uxx+uyy+uzz=

The angle of elevation of the summit of a mountain at a point A is 450. After walking 200 mt from A towards the mountain along a road included at 150, it is observed that the angle of elevation of the summit is 600. The height of the mountain is

if the points (0, 0), (2, 0), (0, 4),(1, k) are concyclic then k2-4k=

The equation whose roots are multiplied by 3 of those 2x3-3x2+4x-5=0 is

The probability of drawing two red balls in succession from a bag containing 3 red balls and 4 black balls when the ball that is drawn first is replaced is

The angle subtended at the focus by the normal chord of a parabola y2= 4ax at a point whose ordinate equal to abscisa is

If the roots of the equation ax2+bx+c=0 be the square roots of the roots of the equation lx2+mx+n=0,then

The lines 2x+3y=6, 2x+3y=8 cut the X-axis at A , B respectively. A line 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 arithmetic progration. Then the equation of the line l is

The slope of the radical axis of the circles (x+2) 2+(y+3)2=25 and (x+1) 2+(y-1) 2=25 is

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

The number of four digited numbers that can be formed from using the digits 2,4,5, 7,8 that are divisible by 4 is

For real values of x the expression x2-x+1/x2+x+1 takes values in interval

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

If 2x2+mxy+3y2-5y-2 can be resolvable into two linear factors then m=

The point diametrically opposite to the point P(1, 0) on the circle x2+y2+2x+4y-3=0 is

The inclination of the line passing through the points (-2,3),(-1,4) is

The area of the figure bounded by the curves y2=2x+1 and x-y-1=0 is

The value of k if (1, 2) (k, -1) are conjugate points with respect to the ellipse 2x2+3y2=6 is

The longest distance from (-3, 2) to the circles x2+y2-2x+2y+1=0 is

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

The coefficient of x7 in (1+2x+3x2+4x3+……..∞)-3 is

The solution of is (dy/dx)=(y/x)+sin(y/x) is

Two angles ofa triangle are Cot-1 2 and Cot-1 3.Then the third angle is

The angle between the circles x2+y2-4x-6y-3=0 and x2+y2+8x-4y+11=0 is

If (3 + 4i) is a root of x2+px+q=0, then (p, q) is:

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