|(1990,1991,1992),(1991,1992,1993),(1992...

`|(1990,1991,1992),(1991,1992,1993),(1992,1993,1994)|=`

1992

1993

1994

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Match the following {:("(i) "3+1991+7 = 3+7+1991," [ ] a. Additive identity"),("(ii) "2xx68xx50 = 2xx50xx68,"[ ] b. Multiplicative identity"),("(iii) "1,"[ ] c. Commutative under addition"),("(iv) "0,"[ ] d. Distributive property of multiplication over addition "),("(v) " 879xx(100+30) = 879xx100+879xx30,"[ ] e. Commutative under multiplication"):}

How many books were sold from 1991 to 1993?

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Population growth in India during 1991-2001

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Find the product using suitable properties. 1991xx1005

AAKASH SERIES-MATRICES -DETERMINANTS- EXERCISE - II

If A=[(1,3),(2,1)] then the determinant of A^(2)-2A is
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|(1990,1991,1992),(1991,1992,1993),(1992,1993,1994)|=
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Show that |{:(x,a,a),(a,x,a),(a,a,x):}|=(x+2a)(x-a)^2
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Show that |(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b)|=2(a+b+c)^(3).
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Prove that |{:(y+z,x,x),(y,z+x,y),(z,z,x+y):}|=4xyz
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If|(a+b,b+c,c+a),(b+c,c+a,a+b),(c+a,a+b,b+c)|=k|(a,b,c),(b,c,a),(c,a,b...
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|{:(a-b-c,2b,2c),(2a,b-c-a,2c),(2a,2b,c-a-b):}|=
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If a!=6,b,c satisfy |(a,2b,2c),(3,b,c),(4,a,b)|=0 then abc
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If w is a complex cube root unity then |{:(1,1+w,1+w^(2)),(1+w,1+w^(2)...
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If alpha, beta, gamma are the roots of x^(3)+px+q=0 then |(alpha, beta...
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|(1,log(x)y,log(x)z),(log(y)x,1,log(y)z),(log(z)x,log(z)y,1)|=
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|(1//a,a^(2),bc),(1//b,b^(2),ca),(1//c,c^(2),ab)|=
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Let A=[(5,5 alpha, alpha),(0, alpha, 5 alpha),(0,0,5)] If |A|^(2)=25 t...
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If k gt1, and the determinant of the matrix A^(2), where A=[(k,kalpha,...
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If bc+ca+ab=18, and |(1,a^(2),a^(3)),(1,b^(2),b^(3)),(1,c^(2),c^(3))|=...
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If a,b,c are positive and not all equal then |(a,b,c),(b,c,a),(c,a,b)|
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|(a^(2)+x,ab,ac),(ab,b^(2)+x,bc),(ac,bc,c^(2)+x)|
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Show that A=|{:(-2a,a+b,c+a),(a+b,-2b,b+c),(c+a,c+b,-2c):}|=4(a+b)(b+c...
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If a+b+c=0 and |(a-x,c,b),(c,b-x,a),(b,a,c-x)|=0 then x=
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If |(lamda^(2)+3lamda, lamda-1, lamda+3),(lamda+1, 2-lamda,lamda-4),(l...
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