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Using properties of determinants, prove the following: `|[a^2 + 1,ab, ac], [ab,b^2 + 1,b c],[ca, cb, c^2+1]|=1+a^2+b^2+c^2`

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Using properties of determinants, prove the following |(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2 .

Using properties of determinants, prove the following |(a^2,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2 .

By using properties of determinants. Show that: |[a^2+1,a b, a c],[ a b,b^2+1,b c],[c a, c b, c^2+1]|=(1+a^2+b^2+c^2)

Using properties of determinants, prove that |[a^2, bc, ac+c^2] , [a^2+ab, b^2, ac] , [ab, b^2+bc, c^2]| = 4a^2b^2c^2

Prove that |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]|=1+a^2+b^2+c^2

Using properties of determinants, prove the following : |[a, a^2,bc],[b,b^2,ca],[c,c^2,ab]|=(a-b)(b-c)(c-a)(b c+c a+a b)

Using properties of determinant prove that |(a^(2)+1, ab, ac),(ab, b^(2)+1, bc),(ca, cb,c^(2)+1)|=(1+a^(2)+b^(2)+c^(2)) .

Using properties of determinants, prove that : |{:(a^(2)+1,ab,ac),(ba,b^(2)+1,bc),(ca,cb,c^(2)+1):}|=a^(2)+b^(2)+c^(2)+1

abs([-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]) = 4a^2.b^2.c^2

Using properties of determinants, prove that following |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^3

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find the point on the curve y=x^3-11 x+5 at which the equation of tang...

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  2. Using differentials, find the approximate value of sqrt(49. 5)

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  3. Using properties of determinants, prove the following: |[a^2 + 1,ab, ...

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  4. Show that the lines vec r=3 hat i+2 hat j-4 hat k+lambda( hat i+2 ha...

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  5. Find the particular solution of the differential equation satisfyin...

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  6. Find the general solution of the differential equation xlogx\ (dy)/...

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  7. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

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  8. If y="sin"(logx), then prove that (x^2d^2y)/(dx^2)+x(dy)/(dx)+y=0

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  9. Find the value of k , for which f(x)={(sqrt(1+k x)-\ sqrt(1-k x))/(x)...

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  10. Two cards are drawn simultaneously (or successively without replace...

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  11. One kind of cake requires 200 g of flour and 25 g of fat, and anoth...

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  12. If vec a ,\ vec b ,\ vec c are three vectors such that vec a. v...

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  13. The probability that A hits a target is 1/3 and the probability tha...

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  14. Solve the following system of equations by matrix method. 3x-2y + 3z=...

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  15. Show that the lines (x+3)/(-3)=y-1/1=(z-5)/5;(x+1)/(-1)=(y-2)/2=(z-5)/...

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  16. Using integration, find the area of the region: {(x , y):9x^2+y^2l...

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  17. Consider the binary operations ** \: R\ xx\ R -> R and o\ : R\ xx\ R ...

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  18. Evaluate: intx^2\ cos^(-1)\ x\ dx

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  19. Evaluate : int1/(x+xlogx)\ dx

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  20. Find the area of the greatest rectangle that can be inscribed in an...

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