Which of the following is (are) NOT the square of a 3×3 matrix with real entries? (a)⎣⎡10001000−1⎦⎤ (b) ⎣⎡−1000−1000−1⎦⎤ (c)⎣⎡100010001⎦⎤ (d) ⎣⎡1000−1000−1⎦⎤
Let n1,andn2, be the number of red and black balls, respectively, in box I. Let n3andn4,be the number one red and b of red and black balls, respectively, in box II. One of the two boxes, box I and box II, was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probablity that this red ball was drawn from box II is 31 then the correct option(s) with the possible values of n1,n2,n3,andn4, is(are)
Let n be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number in which 5 boys and 5 girls stand in such a way that exactly four girls stand consecutively in the queue. Then the value of nm is ____
Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 27 on y-axis is (are)
A box B1, contains 1 white ball, 3 red balls and 2 black balls. Another box B2, contains 2 white balls, 3 red balls and 4 black balls. A third box B3, contains 3 white balls, 4 red balls and 5 black balls.
Let Mbe a 2×2symmetric matrix with integer entries. Then Mis invertible ifThe first column of Mis the transpose of the second row of MThe second row of Mis the transpose of the first column of MMis a diagonal matrix with non-zero entries in the main diagonalThe product of entries in the main diagonal of Mis not the square of an integer
Let −61<θ<−12π Suppose α1andβ1, are the roots of the equation x2−2xsecθ+1=0 and α2andβ2 are the roots of the equation x2+2xtanθ−1=0. If α1>β1 and α2>β2, then α1+β2 equals