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Show that the semivertical angle of a co...

Show that the semivertical angle of a cone of given slant height is `tan^1 sqrt2` when its volume is maximum.

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
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  2. Prove that the curves x = y^(2) and xy = k cut at right angles, if 8k^...

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

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

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

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

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

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  8. 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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  9. What is int5^x.e^(3x) ?

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

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

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

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

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

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  15. Answer any three questions if hat(a), hat(b) and hat(c ) are unit ve...

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  16. If A is a symmetric matrix, then A- A is both symmetric and skew symme...

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  17. If f(x)={(x,0lexle1),(2-x,1lexle2):}, then what is the value of int0^2...

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  18. Solve sin^(-1)x +sin^(-1)(1-x) =(pi)/(2).

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  19. Let f be a real function. Show that h(x) =f(x)=f(-x) is always an even...

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  20. Minimize:Z=6x1+7x2 "Subject to":x1+2x2 ge 4 x1,x2 ge 0

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