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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`

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

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

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

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

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. Show that: int0^(pi/2) "sqrt(tanx) +sqrt(cotx)=sqrt(2)pi

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  2. Prove that the curves "x"="y"^2 and "x y"="k" intersect at right ang...

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

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  4. If |[x+2, 3],[x+5, 4]|=3 , find the value of x

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  5. Show that the points (1,0), (6,0), (0,0) are collinear.

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  6. If "f"("x")=sqrt((sec"x"-1)/(secx+1))" " find "f '"("x")dot Also fin...

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  7. If xsqrt(1+y)+ysqrt(1+x)=0, find ("dy")/("dx") . To prove (dy)/(dx)=...

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  8. Show that the semi vertical angle of a right circular cone of given ...

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  9. If the equation of a line "A B" is ("x"-3)/1=("y"+2)/(-2)=("z"-5)/4...

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  10. If "f"("x") is an invertible function, find the inverse of "f"("x")...

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  11. If [[(x+3y),y],[7-x,4]]=[(4,-1),(0,1)], find the values of x and y.

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  12. Solve for x: tan^-1((1-x)/(1+x))=1/2 tan^-1 x, x > 0

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  13. Evaluate: int("x"+cos6"x")/(3"x"^2+sin6"x")" dx"

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  14. If int("e"^("a x")+"bx")"dx"=1/4"e"^(4"x")+(3"x"^2)/2" find the values...

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  15. A and B throw a pair of die turn by turn. The first to throw 9 is a...

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  16. Find the equation of the line passing through the point "P"(4,6,2) ...

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  17. Evaluate: int0^pi(xtanx)/(secx+tanx)\ dx

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  18. Find the area of that part of the circle "x"^2+" y"^2=16 which is ex...

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  19. A man is known to speak truth 3 out of 4 times. He throws a die and...

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  20. An aeroplane can carry a maximum of 200 passengers. A profit of Rs. 80...

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