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Show that by mathematical- induction :`x^3+(x+1)^3+(x+2)^3`is divisible by 9.

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UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 5-EXERCISE
  1. If 13theta=pi,show that costhetacos2theta cos3theta cos4theta cos5thet...

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  2. Solve:sinx-sin2x=cos2x-cosx

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  3. Show that by mathematical- induction :x^3+(x+1)^3+(x+2)^3is divisible ...

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  4. If z = x + iy and arg ((z-1)/(z+1))=(pi)/(4), then the locus of (x, y)...

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  5. If the co-efficient of the (3r+1) th term is equal to the co-efficient...

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  6. Find the sum of 1 + 5 + 12 + 22 + 35 +….upto n term.

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  7. A straight line passes through A(1, 2) and makes an angle theta with t...

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  8. Find the equations of the lines, which cut-off intercepts on the axes ...

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  9. The equation of circum circle of an equilateral triangle is x^2+y^2+2g...

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  10. A straight line passes through (h, k) and the middle point of the also...

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  11. Evaluate :lim(xrarr0)(tan2x-x)/(3x-sinx)

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  12. From definition, differentiate cos4x at 'x=pi/6,will respect to x.

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  13. Prove the following by contradiciton ."The sum of a rational and an ir...

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  14. Show that sqrt7 is an irrational, (use the method of contradiction)

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  15. If the variance of lst.n even natural numbers is 65, find the value of...

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  16. In on examination the probability of a student passed in physics is 2/...

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  17. If p sin (alpha+beta) = cos (alpha -beta), show that1/(1-p sin 2alpha)...

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  18. Solve :sqrt(2cos^2x+1)+sqrt(2sin^2x+1)=2sqrt2

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  19. Exhibit graphically the solution region of the following system of 'in...

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  20. If the roots of the equation qx^2 + 2px + 2q =.0 are real and unequal ...

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