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If x/(lm-n^2)=y/(mn-l^2)=z/(nl-m^2), the...

If `x/(lm-n^2)=y/(mn-l^2)=z/(nl-m^2)`, then show that lx+my+nz=0

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If l,m and n are real numbers such that l^2+m^2+n^2=0 , then show that |{:(1+l^2,lm,ln),(lm,1+m^2,mn),(ln,mn,1+n^2):}|=1

If the straight line lx+my+n=0 be a normal to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then by the application of calculus, prove that (a^2)/(l^2)-(b^2)/(m^2)=((a^2+b^2)^2)/(n^2) .

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If x,y,z be variable quantities such that (x+y+z) is constant and (z+x-2y)(x+y-2z) prop yz then show that [2(y+z)-x]propyz .

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UNITED BOOK HOUSE-KANACHI HIGH SCHOOL-EXERCISE
  1. If a alpha b and b alpha c, show that a^3+b^3+c^3 alpha 5 abc.

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  2. If a^2/(b+c)=b^2/(c+a)=c^2/(a+b)=1, show that 1/(1+a)+1/(1+b)+1/(1+c)=...

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  3. If x/(lm-n^2)=y/(mn-l^2)=z/(nl-m^2), then show that lx+my+nz=0

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  4. Answer any One queation : Prove that, if a perpendicular is draw on t...

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  5. Prove that if two tangents are drawn to a circle from a point outside ...

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  6. ABCD is a cyclic quadrilaterla. Extended AB and DC intersect at P. Pr...

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  7. A straight line intersects one of the two concentric circles at the po...

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  8. Draw the incircle of an equilateral triangle of side 7 cm.

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  9. Geometrically find the value of sqrt(21),

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  10. Sum of two angles is 135^@ and their difference is pi^c/12. Find the s...

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  11. If sin theta+ sin^2 theta = 1, prove that cos^2 theta+ cos^4 theta = ...

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  12. If x tan 30^@ + y cot 60^@ = 0,2x-y tan 45^@ = 1, then find the value ...

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  13. The height of two towers are 180 metres and 60 metres respectively. If...

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  14. A telegraph post is bent at a point above the ground due to storm. Its...

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  15. The length of radius of cross-section of a solid circular rod is 3.2 d...

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  16. The ratio of length breadth and height of a cuboid is 3:2:1 and its vo...

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  17. Three spheres made of copper having the lengths of 3 cm. 4 cm and 5 cm...

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  18. Ages of 100 patients in a hospital of Mahidual's locaity are given bel...

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  19. Find the median of heights of the students from the following frequenc...

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  20. Calculate the mode of the following frequency distribution table.

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