Limit(x tends to infinity)   ((2^1/x + 27^1/x +81/x)/3)^x

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Integrate the following

cos²dx / (cos²x+4sin²x)

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If two tangents to the parabola y²=4ax makes angle A& B with the X axis and tan²A +tan²B=c.Find the locus of the point of intersection of the tangents.

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If two tangents to the parabola y²=4ax makes angle A & B with the X axis and tan²A +tan²B=c.Find the locus of the point of intersection of the tangents.

Please show how 2 solve....rates assured

w is a root other than 1 of the equationof w⁷=1.Prove that

1)the other roots are w²,w³,w⁴,w⁵,w⁶ if

   A=w+ w⁶

   B=w²+w⁵

   C+w³+w⁴

2)the equation with the root only A,B and C

is z³+z²-2z-1=0

Hence or otherwise findthe values of

i)cos 2(pi)/7   +  cos 4(pi)/7  +  cos 6(pi)/7

ii)(cos 2(pi)/7)(cos 4(pi)/7)(cos 6(pi)/7)

Prove that

1 + (1/2²) + (1/3²) +........+ (1/n²) < 7/4

 

Plz show how to solve.....

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Let l,m,n be three consecutive natural numbers(l>m>n).If the angle A of the triangle ABC be given by

sin A=[(a²+b²+c²)(l²+m²+n²)]  /  (al + bm + cn)²

and the perimeter of the triangle is 12 units,then the area of the triangle ABC is

(Here a=side opp to angle A.......same goes for b and c)

        b)6    c)15/2   d)none

If u guys can do it and show how u did it....rates assured....

 

If sin(A+B)sin(A-B)=sin C(2sinB+sinC),0<A,B,C<pi, then the family of lines sin Ax+sin By+sin C=0 passes through

a)(-1,1)  b)(1,1) c)(1,-1) d)(-1,-1)

If u guys can do it and show how u did it....rates assured....

In triangle ABC , AB=AC,extend AB and AC upto E and F such that BE x CF=AB^2.Prove that EF always passes through a fixed point......And please show how to solve

The expression

[acos(P+Q)+bsin(P+R)] / [a'sin(P+Q)+b'cos(P+R)]

is independent of P.

Prove that aa'-bb'=(a'b-ab')sin(Q-R)

Please show how to solve...

A Body of mass m is subjected to motion along the periphery of a polygon of 2n sides.What is the impulse experienced by it at each vertex of the polygon?

Please Show How To Solve....

Will Arihant's subjective books in physics by D.C.Pandey suffice iit preparation.....

Try solving these questions and show me how to do them.....Thank you

1) A charge q is spread uniformly inthe form of a line charge density h=Q/3a on the sides of an equilateral triangle of perimeter 3a.Calculate the potential at the centroid C of the triangle.

2) Two concentric rings placed in agravity free region in yz-plane one of radius R carries a charge +Q and second of radius 4R and charge -8Q distributed uniformly over it.Find the minimum velocity with which a point charge of mass m and charge -q should be projected from a point at a distance 3R from the centre of rings on its axis so that it will reach the centre of the rings.

3) Two point charge q and -q are seperated by a distance 2l.Find the flux of electric field strength vector across the circle of radius R placed with its centre coinciding with the midpoint of the line joining the two charges in the perpendicular plane.

4) A point charge q is placed at the origin.Calculate the electric flux through the open hemispherical surface:     (x-a)²+y²+z²=a², x>=a 

Can someone please do the problem no. 25,26,27, fron fluid mechanics of h.c.verma(vol-1).....and please show  how to solve.....rates assured