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Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+...

Prove that `abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c],[p,q,r],[x,y,z]]`

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Prove that the following. [[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2[[a,b,c],[p,q,r],[x,y,z]]

Prove that: |[y+z, z, y],[z, z+x, x], [y, x, x+y]|= 4 xyz

Prove that the following. [[a,b,c],[x,y,z],[p,q,r]]=[[y,b,q],[x,a,p],[z,c,r]]=[[x,y,z],[p,q,r],[a,b,c]]

Simplify: "[x y z]"xx[[a,h,g],[h,b,f],[g,f,c]]xx[[x],[y],[z]]

Prove that |[x, y, z],[x^2, y^2, z^2], [x^3, y^3, z^3]|=xyz(x-y)(y-z)(z-x)

Using properties of the determinants, prove that: |[2y, y-z-x, 2y],[2z, 2z, z-x-y], [x-y-z, 2x, 2x]| = (x+y+z)^3

Prove that |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|=|{:(1,1,1),(x^2,y^2,z^2),(x^3,y^3,z^3):}|=(x-y) (y-z) (z-x) (xy+yz+zx)

Evaluate the following determinants: [[a-b,b-c,c-a],[x-y,y-z,z-x],[p-q,q-r,r-p]]

Express as a sum of a symmetric and a skew symmetric matrix: [[x,a,b],[a,y,c],[b,c,z]]

Show that |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

ARIHANT PRAKASHAN-VERY SIMILAR TEST 9-Section B
  1. Let R be a relation on the set A of ordered pairs of positive integers...

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  2. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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  3. Two persons A and B throw a die alternately till one of them gets a th...

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  4. A = [(1, 0), (0, 1)], B = [(1, 0), (0, -1)] and C = [(0, 1), (1, 0)], ...

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  5. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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  6. An urn contains 4 white and 6 red balls. Four balls are drawn at rando...

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  7. Using differentials, find approximate value (3.968)^(3//2)

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  8. Prove that: y = (4 sin theta)/(2 +cos theta)- theta is an increasing f...

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  9. If xy log(x + y) = 1, then prove that (dy)/(dx) = -(y(x^(2)y + x +...

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  10. If sin 2x = (2t)/(1 + t^(2)), tan y = (2t)/(1 - t^(2)) then find (dy)/...

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  11. Using mean value theorem, prove that sin xltx,in(0.pi//2).

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  12. Solve (dy)/(dx)+y=cos x-sin x

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  13. Find the equation of the curve passing through the point (1, 1) whose ...

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  14. Evaluate int(x^(2))/(x^(4)-x^(2)+12)dx.

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  15. Evaluate int(0)^(pi//2) (sin2x)/(sin^(4)x + cos^(4)x) dx.

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  16. Find the area bounded by the curve y = x abs(x), X-axis and ordinates ...

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  17. The plane lx+my=0 is rotated about its line of intersection with the p...

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  18. Find the distance of the plane 2x - 3y + 4z - 6 = 0 from the origin an...

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  19. Prove that |veca xx vecb|^(2) = abs(veca)^(2)abs(vecb)^(2) - (veca * v...

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  20. Find the cartesian equation of a plane which is at a distance of 6 uni...

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