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Using properties of determinants, show that `|b+c a a b c+a b cc a+b|=4a b c`

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Using properties of determinants, show that |1 a a^2 -b c 1 b b^2 -c a 1 c c^2 -a b|=0

Using properties of determinant show that: |[1 , a , bc] , [1 , b , ca] , [1 , c , a b]|=(a-b)(b-c)(c-a)

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, a +b, a+b+c),(2a, 3a + 2b, 4a + 3b + 2c),(3a, 6a+3b, 10a + 6b + 3c):}| = a^(3)

Using properties of determinants, prove that |[a, a+b, a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]|=a^3

Using properties of determinant, prove that |(2a, a-b-c, 2a), (2b, 2b, b-c-a), (c-a-b,2c,2c)|=(a+b+c)^(3) .

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

Using properties of determinants, Find |(b+c,a,a),(b,c+a,b),(c,c,a+b)|

Using properties of determinant prove that |a+b+c-c-b-c a+b+c-a-b-a a+b+c|=2(a+b)(b+c)(c+a)

Using the properties of determinants, find the value of | 0 a -b -a 0 -c b c 0 | ​

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Solve the differential equation x(dy)/(dx)+y=xcosx+sinx , given y(pi/2...

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  2. Two schools, P and Q, want to award their selected students for the...

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  3. Using properties of determinants, show that |b+c a a b c+a b cc a+b|=...

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  4. Let f,g: R-R be two functions defined as f(x)=|x|+x and g(x)=|x|-x , f...

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  5. Write the equation of the straight line through the point (alpha,beta,...

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  6. If y=tan^(-1)(a/x)+logsqrt((x-a)/(x+a)) , Prove that (dy)/(dx)=(2a^3)/...

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  7. Find the value of the constant k so that the function f , defined belo...

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  8. The sides of an equilateral triangle are increasing at the rate of 2...

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  9. Find intervals in which the function given by f(x)=3/(10)x^4-4/5x^3-3x...

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  10. Find the particular solution of the differential equation x(dy)/(dx)-y...

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  11. Differentiate tan^(-1)((sqrt(1-x^2))/x) with respect to cos^(-1)(2xsqr...

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  12. Using properties of determinants, prove that |2yy-z-x2y2z2z z-x-y x-y...

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  13. Write the vector equation of the plane, passing through the point (...

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  14. Let A={1,\ 2,\ 3,\ ,\ 9} and R be the relation on AxxA defined by (a ...

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  15. Evaluate: int(x-3)sqrt(x^2+3x-18)\ dx

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  16. Evaluate : int(sin^6x+cos^6x)/(sin^2xdotcos^2x)dx

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  17. Find the particular solution of the differential equation e^xsqrt(1-y^...

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  18. A dealer in rural area wishes to purchase a number of sewing machin...

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  19. From a lot of 15 bulbs which include 5 defectives, a sample of 4 bu...

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  20. A card from a pack of 52 playing cards is lost. From the remaining car...

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