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If tan^(-1)x, tan^(-1)y and tan^(-1)z ar...

If `tan^(-1)x`, `tan^(-1)y` and `tan^(-1)z` are in A.P, find the algebric relation between x,y and z. If x,y,z be also in A.P. then show that `x = y = z(y ne 0)`.

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UNITED BOOK HOUSE-SET 12-EXERCISE
  1. Find the intercept form of a plane with intercepts 2,3 and 4 on the x,...

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  2. A and B are two independent events with P(A) = 2/5 and P(B) = 1/3, eva...

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  3. The mean and variance of a binomial distribution are 4 and 3 respectiv...

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  4. If tan^(-1)x, tan^(-1)y and tan^(-1)z are in A.P, find the algebric re...

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  5. Prove that, the inverse of a given square matrix, if its exists, is un...

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  6. Prove that, |(2a, a-b-c,2a),(2b,2b,b-c-a),(c-a-b,2c,2c)|=(a + b+c)^3

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  7. If sqrt(1 -x^2) + sqrt(1-y^2) = a(x-y), show that, (dy)/(dx) = sqrtfra...

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  8. Evaluate: int (xdx)/[(x^2 - a^2)(b^2-x^2)] (b^2>a^2).

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  9. Evaluate: int(sqrt x dx)/sqrt(a^3 - x^3)

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  10. Solve:(dy)/(dx)-y/x + cosec (y/x)=0, given y = 0 when x = 1

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  11. Solve: y^2 + (x - 1/y)(dy)/(dx) = 0.

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  12. The position vectors of the points A and B are 2 veca + vecb and veca...

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  13. Evaluate: underset(0)overset(pi)int |sinx + cosx|dx

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  14. evaluate underset(0)overset(1)int e^(-x) dx

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  15. A packet, of 10 electronic components is known to include 3 defectives...

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  16. A random variable x follows binomial distribution with mean 3 and stan...

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  17. (b)answer any two questions : (i) a circular ink blot grows at the rat...

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  18. answer any two questions :(iii) if the straight line lx+my=n be a norm...

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  19. Find the vector equation of a line which passes throught the point wit...

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  20. Let vec n be a vector of magnitude 2sqrt 3 such that it makes equal ac...

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