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A variable plane meets the coordinate ax...

A variable plane meets the coordinate axes at P, Q, R points. If the plane passes through a fixed point (a, b, c), prove that the centre of the shpere passing the origin and P, Q, R will lie on the surface `a/x+b/y+c/z=2`

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MODERN PUBLICATION-TEST PAPER 2-PROBLEM
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  2. Show that hat(i) xx (vec(a) xx hat(i)) + hat(j) xx (vec(a) xx hat(j)) ...

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  3. A variable plane meets the coordinate axes at P, Q, R points. If the p...

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  4. Write whether the following statements are true or false. The equati...

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  5. Show that the operation * given by x*y=x+y+ -xy is a binary oeration o...

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  6. Solve the following : [[x+1,omega,omega^2],[omega,x+omega^2,1],[omega^...

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  7. If f'(x)=sqrt(2x^2-1) and y=f(x^2) then what is dy/dx at x = 1 ?

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  8. Find the extreme points of the function y= x+1/x.

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  9. What is the differential equation whose solution is y = c (sin x + cos...

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  10. For what value of lambda, the vectors lambda hat(i) + 3hat(j) + lambda...

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  11. Let A and B be sets. Show that f : A xx B rarr B xx A such that f (...

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  12. Maximise Z=50x(1)+60x(2) Subject to 2x(1)+3x(2)le6,x(1),x(2)ge0.

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  13. Let ~ be defined by (m,n)~(p,q) if mq=np where m, n, p,qinZ-{0}. Show ...

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  14. If A=[[2,1],[-1,3]], B=[[2,3],[1,1]] "and" C=[[1,0,2],[-2,3,0]],verify...

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  15. Prove that all the diagonal elements of a skew symmetric matrix are ze...

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  16. If x,y,z are positive and are the pth, qth and rth terms of a G.P. the...

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  17. Answer the following: What is the value of [[o,-h,-g],[h,o,-f],[g,f,...

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  18. Show that no two normals to a parabola are parallel.

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  19. Find the intervals where the following functions are (a) increasing an...

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  20. Find int (cos x /sin^(2) x + sin x ) dx

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