Using properties of determinants or otherwise evaluate `{:|(18, 40, 89), (40, 89, 198),(89, 198, 440)|:}`

Using the properties of determinants in Exercise 1 to 6, evaluate |{:(x+4,x,x),(x,x+4,x),(x,x,x+4):}|

Using the properties of determinants in Exercise 1 to 6, evaluate |{:(a+x,y,z),(x,a+y,z),(x,y,a+z):}|

Using the properties of determinants in Exercise 1 to 6, evaluate |{:(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b):}|

Using the properties of determinants in Exercise 1 to 6, evaluate |{:(3x,-x+y,-x+z),(x-y,3y,z-y),(x-z,y-z,3z):}|

Using the properties of determinants in Exercise 1 to 6, evaluate |{:(0,xy^2,xz^2),(x^2y,0,yz^2),(x^2z,y^2z,0):}|

Suppose three digit numbers A28 , 3B9 and 52C , where A,B and C are integers between 0 and 9 are divisble by a fixed integer K, prove that the determinant |{:(A,3,6),(8,9,C),(2,B,2):}| is also divisble by same integer K

A student performed the experiment of determination of focal length of a concave mirror by u-v method using an optical bench of length 1.5 meter. The focal length of the mirror used is 24 cm. The maximum error in the location of the image can be 0.2 cm. The 5 sets of (u,v) values recorded by the student (in cm) are: (42,56),(48,48),(60,40),(66,33),(78,39) . The data set (s) that cannot come from experiment and is (are) incorrectly recorded, is (are)

Find the median of the following frequency distribution : {:("Weekly wages (in ₹) ","Number of workers "),(" "60-69," "5),(" "70-79," "15),(" "80-89," "20),(" "90-99," "30),(" "100-109," "20),(" "110-119," "8):}

Find the LCM and HCF of the following integers by the prime factorization method. 8,9 and 25