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Find the direction cosines of the line `(4-x)/2=y/2=(1-z)/3`

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SHARAM PUBLICATION-MODEL QUESTION PAPER -17-EXERCISE
  1. Write the order of the differential equation of the system of ellipse ...

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  2. If vectors vec(a) and vec(b) are such that vec(a) = 3, |vec(b)| = (2)/...

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  3. Find the direction cosines of the line (4-x)/2=y/2=(1-z)/3

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  4. For what valueof K is the following function continuous at x = 2 ?f(x)...

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  5. If x=acost,y= tsint then find (dy)/(dx)

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  6. Differentiate the function x^(cosx)w.r.t.x

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  7. Find the slope of the tangent to the curve y=sin 3t,x=2t at t=pi/4

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  8. If f(x) = a In x + bx^2 + x has extreme values at x= - 1 and x = 2 the...

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  9. Write the value of x-y+z from the relation [[x+y+z],[x+z],[y+z]]=[[4],...

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  10. Find the transpose of the matrix [[3,-2,-4],[3,-2,-5],[-1,1,2]].

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  11. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

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  12. Using the properties of determinants prove that |{:(a+b+2c,a,b),(c,b...

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  13. Evaluate int(x+sqrt(x^2+a^2))dx

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  14. Evaluate intcosec^2xsqrt(cotx)dx

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  15. Prove that int0^(pi/2)lnSinxdx=-pi/2ln2

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  16. Determine the area of the region between the curves y=cosx and y=sinx,...

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  17. Find the general solution of the differential equation (1+x^2) tan^-1y...

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  18. Prove that f:RrightarrowR such that f(x)=frac[2x^2][x^2+1] is neither ...

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  19. Let A={1, 2, 3, 5}, B={4, 6, 9}, A relation R form A to B is defined b...

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  20. Consider the binary operation ** on the set {1, 2, 3, 4 5} defined by ...

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