(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

If `"x"/("b + c - a") =" y" /("c + a - b") = "z"/("a + b - c")` , then prove that each ratio is equal to the ratio of `("x + y+z")/("a + b + c")`

If `"a"/("b + c") = "b"/("c + a") = "c"/("a + b")` , then prove that a(b - c) + b(c-a) + c (a - b) = 0

If x = `"pab"/("a + b")`, then prove that `("x + pa")/("x - pa") + ("x + pb")/("x - pb") = (2("a"^2 - "b"^2))/"ab"`

Show that the value of x is 11, when `("x"^3 + "3x")/(3"x"^2 + 1) = 341/91`

Classify the following rnatrix : 

`|(2,1),(0 , 6),(8 , 7) |`

Classify the following matrix :

`[(7, 0)]`

Classify the following matrix :

`|(800),(521)|`

Classify the following matrix :

`|(1 , 1),(0,9)|`

Classify the following matrix :

`|(11 , 3 , 0),(21 , 8 , 4),(15,5,2)|`

Find the values of a and b) if [2a + 3b a - b] = [19  2]. 

Find the values of x and y, if  `|(3"x" - "y"),(5)| = |(7) , ("x + y")|`

Find the values of a, b, c and d, if `|("a + 3b", 3"c" + "d"),(2"a" - "b" , "c" - 2"d")| = |(5 , 8),(3 , 5)|`

If M =`|(8,3),(9,7),(4,3)|` and N = `|(4,7),(5,3),(10,1)|` find M - N

If A = `|(1,9,4),(5 , 0 , 3)|`  find A'

If P= (8,5),(7,2) find : P + P^t

If P = `|(8,5),(7,2)|` find  P - P^t

If B = `|(15 , 13),(11,12),(10,17)|` , find the transpose of matrix Band If possible find the sum of the two matrices. If not possible state the reason.

If A = `|(5,"r"),("p",7)|` , c and if A + B = (9,7),(5,8) , find the values of p,q,r and s.

If A = `|("p","q"),(8,5)|` , B = `|(3"p",5"q"),(2"q" , 7)|` and if A + B = `|(12,6),(2"r" , 3"s")|` , find the values of p,q,r and s.

Evaluate the following :

`|(1 , 1),(2 , 3)|  |(2 , 1),(1 , 4)|`