Statement 1: if `a ,b ,c ,d` are real numbers and `A=[a b c d]a n dA^3=O ,t h e nA^2=Odot` Statement 2: For matrix `A=[a b c d]` we have `A^2=(a+d)A+(a d-b c)I=Odot`

If a,b,c,d ,e are +ve real numbers such that a+b+c+d+e=8 and a^2 + b^2 +c^2 + d^2 +e^2 = 16 , then the range of 'e' is

If a,b,c,d are distinct numbers such that : a + C = 2d and b+d = 2c , which of the following statements must be ture ? I. a cannot be the average of a,b,c,d. II b can be the average of a,b,c,d . III d can be the average of a,b,c,d.

If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0, then prove that a ,b ,c , d are in G.P.

Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4 Then the sum of all possible values of |a-d|=

Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: If A is obtuse angle I A B C , then tanB\ t a n C<1 because Statement II: In A B C ,\ t a n A=(t a n B+t a n C)/(t a n B t a n C-1)\ a. A b. \ B c. \ C d. D

If B is an idempotent matrix, and A=I-B , then a. A^2=A b. A^2=I c. A B=O d. B A=O

If a, b, c, d and p are different real numbers such that (a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0 , then show that a, b, c and d are in G.P.

If A=[(a,b),(c,d)] , where a, b, c and d are real numbers, then prove that A^(2)-(a+d)A+(ad-bc) I=O . Hence or therwise, prove that if A^(3)=O then A^(2)=O

if a : b = e : d , show that : 3a + 2b : 3a - 2b = 3c + 2d : 3c - 2d .

If a , b , c ,d and p are distinct real numbers such that (1987, 2M) (a^2+b^2+c^2)p^2-2(a b+b c+c d)P+(b^2+c^2+d^2)geq0,t h e na , b , c , d are in AP (b) are in GP are in HP (d) satisfy a b=c d