(b) answer any one question : (i) prove...

(b) answer any one question : (i) prove that `|[1,a,a^2],[1,b,b^2],[1,c,c^2]|`=(a-b)(b-c)(c-a)

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Prove that . |[1,a,a^2-bc],[1,b,b^2-ca],[1,c,c^2-ab]|=0

Without expanding the determinant, prove that |{:(1,a,a^2),(1,b,b^2),(1,c,c^2):}|=(a-b)(b-c)(c-a) .

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

By using properties of determinants , show that : (i) {:|( 1,a,a^(2)),( 1,b,b^(2)),( 1,c,c^(2))|:}=(a-b)(b-c) (c-a) (ii) {:|( 1,1,1),( a,b,c) ,(a^(3) , b^(3), c^(3))|:} =( a-b) (b-c)( c-a) (a+b+c)

Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)(c- a)

Prove that: |[-2a, a+b,a+c],[ b+a,-2b,b+c],[c+a, c+b,-2c]|=4(a+b)(b+c)(c+a)

Prove |{:(1,a^2+bc,a^3),(1,b^2+ca,b^3),(1,c^2+ab,c^3):}|=-(a-b)(b-c)(c-a)(a^2+b^2+c^2)

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)

Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a b c(a+b+c)^3

prove that : |{:(1,a,b),(-a,1,c),(-b,-c,1):}|=1+a^2+b^2+c^2

UNITED BOOK HOUSE-HIGHER SECONDARY QUESTION 2018-EXERCISE

1 (a) answer any one question :(i) suppose IR be the set of all real ...
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answer any one question :(ii) if sin^(-1) x=tan^(-1)y , then show that...
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(b) answer any one question : (i) prove that |[1,a,a^2],[1,b,b^2],[1,...
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answer any one question A=[[1,0],[-1,7]] and I be the unit matrix of s...
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(c)answer any three questions: (i) if the function , f(x)={((1- cos(ax...
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If xsqrt(1+y)+ysqrt(1+x)=0, prove that dy/dx=(-1)/((1+x)^2
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answer any three questions: (iii) if x>0 ,y>0 and xy=25, then find the...
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answer any three questions: (iv) a particle moves along the parabola y...
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verify lagrange's mean value of theorem in the interval 4lexle6 for fu...
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int (e^x (1+x))/(cos^2(xe^x)) dx is
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(d) answer any one question : (i) if the three vectors vec a, vec b, v...
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answer any one question : (ii) find the equation of the plane passing ...
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e) answer any one question : (i) if P(A/B)=0.8 , P(B/A)=0.6 and P(A^c ...
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answer any one question : (ii) an unbiased coin is tossed 6 times . Us...
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A relation R is defined on the set of natural numbers N as follows: R=...
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answer any one question : (ii) prove that , tan(pi/4 +1/2 (cos ^(-1) (...
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(b) answer the foll. Questions: (i) express the matrix A=[[3,2,3],[4,5...
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if |[x-1,1,1],[1,x+1,-1],[-1,1,x+1]| =0 , find the value of x.
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answer the foll. Questions: (i) if y=(sin^(-1)x)/(sqrt(1-x^2)) , then ...
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or,find the derivatives of tan^(-1) ((sqrt(1+x^2)-1)/x) with respect t...
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