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Using properties of determinants, pro...

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

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Using properties of determinants, prove the following: |3"a"-"a"+"b"-"a"+"c""a"-"b"3"b""c"-"b""a"-"c""b"-"c"3"c"|=3("a"+"b"+"c")("a b"+"b c"+"c a")

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

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

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 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

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 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 properties of determinants, prove that |{:(,a,b,b+c),(,c,a,c+a),(,b,c,a+b):}|=(a+b+c) (a-c)^2

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, Find |(b+c,a,a),(b,c+a,b),(c,c,a+b)|

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Find the points on the curve y=x^3 at which the slope of the tangen...

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  2. Using integration, find the area of the region enclosed between the...

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  3. Using properties of determinants, prove that following: |"a"+"b"+2...

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  4. Find the values of x for which f(x)=[x(x-2)]^2 is an increasing func...

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  5. Find the particular solution of the differential equation x(x^2-a)...

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  6. Form the differential equation of the family of circles in the seco...

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  7. A dealer wishes to purchase a number of fans and sewing machines. He h...

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  8. Find the area of the region included between the parabola y^2=x and...

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  9. Coloured bills are distributed in three bags as shown in the follow...

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  10. The scalar product of the vector hat i+\ hat j+\ hat k\ with the ...

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  11. Find the equation of the plane determined by the points (A(3,-1,\ 2...

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  12. Evaluate: int0^pi(xtanx)/(secx+tanx)\ dxdot

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  13. Find the equation of line through the intersection of lines 3x+4y=7 an...

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  14. Differentiate the following with respect to x : x^(sinx)+(sinx)^(cosx)

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  15. Write the differential equation formed from the equation y=m x+c , ...

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  16. If vec a is a unit vector and ( vec x- vec a)dot( vec x+ vec a)=24 , ...

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  17. If A is a square matrix and |A| =2, then write the value of |A A '|,...

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  18. If A=|[3, 10],[ 2, 7]|, then write A^(-1)

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  19. Write the value of sin(2sin^(-1)(3/5)) .

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  20. If A is a 3xx3 matrix, whose elements are given by a(i j)=1/3|-3i+j...

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