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If `"sin"^(-1)x + "sin"^(-1)y +"sin"^(-1)z = pi "prove that" x^4+y^4+z^4 +4x^2y^2z^2=2(x^2y^2+y^2z^2+z^2x^2)`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Find the distance of the point (2,3,4) from the plane 3x+2y+2z+5=0 mea...

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  2. Prove by vector method that in a parallelogram, the line joining a ve...

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  3. If "sin"^(-1)x + "sin"^(-1)y +"sin"^(-1)z = pi "prove that" x^4+y^4+z^...

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  4. Maximize Z=6x1+10x2subject to x1+2x2gt10,2x1+2x2gt12,3x1+x2gt8,x1,x2gt...

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  5. Show the f:R-{-1)rightarrowR-{1} given by f(x)=frac[x][x-1] is inverti...

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  6. Prove that the following. |[(v+w)^2,u^2,u^2],[v^2,(w+u)^2,v^2],[w^2,w...

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  7. Show that P(m,1)+P (n,1)=P(M+n,1)for all positive integers m, n.

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  8. Prove that the curves x = y^(2) and xy = k cut at right angles, if 8k^...

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  9. Show that the semivertical angle of a cone of given slant height is ta...

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  10. A ladder 5m long is leaning against a wall. The bottom of ladder is pu...

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  11. Find the area of the smaller region bounded by the ellipse frac[x^2][a...

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  12. Find the co-ordinates of the foot of the perpendicular from the point ...

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  13. If with reference to the eight handed system of mutually perpendicular...

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  14. Prove that the lines (x+4)/3=(y+6)/5=(z-1)/(-2) and 3x-2y+z+5=0=2x+3y...

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  15. What is int5^x.e^(3x) ?

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  16. If abs(X)=m and absY= n, then what is the total number of functions fr...

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  17. If the tangent to the curve y=x^2+3x at P has slope 5, then what are t...

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  18. Fill in the blank choosing correct answer from the brackets cot^(-1)[(...

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  19. What is the symmetric form of the equation of z-axis ?

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  20. If A is a non singular square matrix of order n, then what is abs(adj ...

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