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Without expanding show that |{:(1,a,b...

Without expanding show that
`|{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0`

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Without expanding , show that |{:(x,a,x+a),(y,b,y+b),(z,c,z+a):}|=0

Without expanding show that |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Show that without expanding at any stage |{:(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab):}|=0

Using properties of determinants , prove that |{:(1,a,bc),(1,b,ca),(1,c,ab):}|=(a-b)(b-c)(c-a)

Without expanding prove that |[1,a,a^(2),-bc],[1,b,b^(2),-ca],[1,c,c^(2),-ab]|=0

Without expanding the determinants prove that |{:(a,a^2,bc),(b,b^2,ca),(c,c^2,ab):}| = |{:(1,a^2,a^3),(1,b^2,b^3),(1,c^2,c^3):}|

Show that abs{:(b-c,c-a,a-b),(c-a,a-b,b-c),(a-b,b-c,c-a):}=0.

Without expanding prove abs((bc, a, a^2),(ca, b, b^2),(ab, c, c^2))=abs((1, a^2, a^3),(1, b^2, b^3),(1, c^2, c^3))

Evaluate [[1,a,b+c],[1,b,c+a],[1,c,a+b]]

Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

ARIHANT PRAKASHAN-VERY SIMILAR TEST 9-Section C
  1. Without expanding show that |{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|=0

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  2. If e^(x) + e^(y) = e^(x + y), then prove that (dy)/(dx) = (e^(x)(e^...

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  3. Find a point on the curve f(x)=(x-3)^2, where the tangent is parallel ...

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  4. Find the area of the region included between the parabolas y^(2) = 4ax...

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  5. Solve (dy)/(dx) = ysin 2x: y(0) = 1.

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  6. Evaluate int (1)/(sinx(2cos^(2) x -1)) dx.

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  7. Prove analytically : The perpendicular bisector of the sides of a tria...

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  8. Find the foot of the perpendicular drawn from the point 2hati - hatj +...

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  9. Solve the following LPP graphically. Maximise Z = 5x + 3y Su...

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  10. Let f : N to R be a function defined as f(x)=4x^(2)+12x +15. Show tha...

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  11. If A = [(1, -1, 1),(2, 1, -3), (1, 1, 1)], find A^(-1) and hence solve...

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  12. A dice is thrown thrice. Find the probability of getting an odd number...

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  13. Find the inverse of the following matrix using elementary transformati...

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  14. If e^(x) + e^(y) = e^(x + y), then prove that (dy)/(dx) = (e^(x)(e^...

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  15. Find a point on the curve f(x)=(x-3)^2, where the tangent is parallel ...

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    |

  16. Find the area of the region included between the parabolas y^(2) = 4ax...

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  17. Solve (dy)/(dx) = ysin 2x: y(0) = 1.

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  18. Evaluate int (1)/(sinx(2cos^(2) x -1)) dx.

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  19. Prove analytically : The perpendicular bisector of the sides of a tria...

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  20. Find the foot of the perpendicular drawn from the point 2hati - hatj +...

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  21. Solve the following LPP graphically. Maximise Z = 5x + 3y Su...

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