The remainder when the determinant `|(999^999,1000^1000,1001^1001),(1002^1002,1003^1003,1004^1004),(1005^1005,1006^1006,1007^1007)|` is divided by 5 is

The remainder when the determinant [[999^(999),1000^(1000),1001^(1001)1002^(1002),1003^(1003),1004^(1004)1005^(1005),1006^(1006),1007^(1007)]| is divided by 5 is

The variance of the data 1001,1003,1006,1007,1009,1010 is

Find the remainder in expression– (1001 xx 1002 xx 1003 xx 1004)/(27)

Prove the following statements: (i) 1000 ^(1000) gt 1002^(999) (ii) 1000^(1002) gt 1002^(1000)

(1001xx1002xx1003)/(27) find R.

The unit's digit of 3^(1001)xx7^(1002)xx13^(1003)

Statement 1: The area of the triangle formed by the points A(1000,1002),B(1001,1004),C(1002,1003) is the same as the area formed by the point A'(0,0),B'(1,2),C'(2,1) statement 2: The area of the triangle is constant with respect to the translation of axes.

Statement 1 : The area of the triangle formed by the points A(1000 ,1002),B(1001 ,1004),C(1002 ,1003) is the same as the area formed by the point A^(prime)(0,0),B^(prime)(1,2),C^(prime)(2,1) Statement 2 : The area of the triangle is constant with respect to the translation of axes.