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If a line makes angle 90o , 60o and 3...

If a line makes angle `90o` , `60o` and `30o` with the positive direction of x, y and z-axis respectively, find its direction cosines.

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To find the direction cosines of a line that makes angles of \(90^\circ\), \(60^\circ\), and \(30^\circ\) with the positive directions of the x, y, and z axes respectively, we can follow these steps: ### Step 1: Identify the angles Let: - \(\alpha = 90^\circ\) (angle with the x-axis) - \(\beta = 60^\circ\) (angle with the y-axis) - \(\gamma = 30^\circ\) (angle with the z-axis) ...
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XII BOARD PREVIOUS YEAR PAPER ENGLISH-XII Boards-All Questions
  1. Determine the value of the constant k, so that the function f(x) ={(kx...

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  2. Evaluate int2^3 3^x dx

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  3. If a line makes angle 90o , 60o and 30o with the positive direct...

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  4. Show that the elements on the main diagonal of a skew-symmetric matrix...

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  5. Find the distance between the parallel planes 2x-y+2z+3=0a n d4x-2y+4z...

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  6. Find (dy)/(dx) at x=1, y=pi/4 if sin^2 y+cos xy=k

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  7. The volume of a sphere is increasing at the rate of 3 cubic centimeter...

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  8. Show that the functionf(x) = 4x^3-18x^2+ 27x – 7 is always increasing ...

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  9. Find the vector equation of the line passing through the point A(1, 2,...

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  10. If A is a skew-symmetric matrix of order 3, then prove that det A = 0...

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  11. Prove that if E and F are independent events, then so are the events E...

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  12. A small firm manufactures necklaces and bracelets. The total number of...

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  13. int1/(x^2-4x+8)dx

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  14. Prove that tan(pi/4+1/2 cos^-1(a/b))+tan(pi/4-1/2 cos^-1(a/b))=(2b)/a

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  15. Using properties of determinants, prove the following: |xx+y x+2y\...

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  16. Find the value of c in Rolle’s theorem for the function f(x) = x^3– 3...

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  17. Differentiate the function (sin x)^x+ sin^(-1) sqrtx with respect to...

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  18. The volume of a cube is increasing at the rate of 9cm3/sec. How fas...

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  19. Evaluate: int(2x)/((x^2+1)(x^2+2))dx

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  20. Evaluate: int0^pi(xsinx)/(1+cos^2x)\ dx

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