If the matrix M_r is given by M_r = $open square brackets table row r cell r minus 1 end cell row cell r minus 1 end cell r end table close square brackets$ , r = 1, 2, 3 .... Then the value of det (M₁) + det(M₂) + .... + det (M₂₀₀₉) is

Helium was discovered by:

For a general reaction given, below the value of solubility product can be given as :

$K subscript s p end subscript equals left parenthesis x s right parenthesis to the power of X end exponent times left parenthesis y s right parenthesis to the power of y end exponent$ or $K subscript s p end subscript equals x to the power of x end exponent y to the power of y end exponent left parenthesis S right parenthesis to the power of x plus y end exponent$
Solubility product gives us not only an idea about the solubility of an electrolyte in a solvent but also helps in explaining concept of precipitation and calculation of H⁺ ion, OH^- ion. It is also useful in qualitative analysis for the identification and separation of basic radicals.
Which metal sulphides can be precipitated from a solution that is 0.01 M in Na⁺ , Zn²⁺, Pb²⁺ and Cu²⁺ and 0.10 M in H₂S at a pH of 1.0 ?

A weak acid (or base) is titrated against a strong base (or acid), volume v of strong base (or acid) is plotted against pH of the solution. The weak protolyte i.e acid (or base) could be

Let A = $open square brackets table row 0 cell 2 y end cell z row x y cell negative z end cell row x cell negative y end cell z end table close square brackets$ and A' . A = I, then the value of $x to the power of 2 end exponent plus y to the power of 2 end exponent plus z to the power of 2 end exponent$ is -

If A is a n rowed square matrix, A = [a_ij] where a_ij = $open square brackets fraction numerator i over denominator j end fraction close square brackets$ , [ ] denotes greatest integer, then det (A) =

If A = $open square brackets table row 0 5 row 0 0 end table close square brackets$ and f(x) = 1 + x + x² + … + x¹⁶, then f(A) =

Assertion : The expression n!(20 – n)! is minimum when n = 10.
Reason : $blank to the power of 2 straight m end exponent C subscript r$ is maximum when r = m.

Let a matrix A = $open square brackets table row 1 1 row 0 1 end table close square brackets$ & P = $open square brackets table row cell fraction numerator square root of 3 over denominator 2 end fraction end cell cell fraction numerator 1 over denominator 2 end fraction end cell row cell negative fraction numerator 1 over denominator 2 end fraction end cell cell fraction numerator square root of 3 over denominator 2 end fraction end cell end table close square brackets$ Q = PAP^T where P^T is transpose of matrix P. Find P^T Q²⁰⁰⁵ P is

an invertible matrix gives identity matrix as the product when multiplied with its inverse.

Let a matrix A = $open square brackets table row 1 1 row 0 1 end table close square brackets$ & P = $open square brackets table row cell fraction numerator square root of 3 over denominator 2 end fraction end cell cell fraction numerator 1 over denominator 2 end fraction end cell row cell negative fraction numerator 1 over denominator 2 end fraction end cell cell fraction numerator square root of 3 over denominator 2 end fraction end cell end table close square brackets$ Q = PAP^T where P^T is transpose of matrix P. Find P^T Q²⁰⁰⁵ P is

an invertible matrix gives identity matrix as the product when multiplied with its inverse.

Let A = $open square brackets table row 1 0 0 row 0 1 1 row 0 cell negative 2 end cell 4 end table close square brackets$ & I = $open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets$ and A^-1= $fraction numerator 1 over denominator 6 end fraction$ [A²+CA+dI], find ordered pair (c,d) ?

the roots of the characteristic equation give us the eigenvalues of the matrix.

Let A = $open square brackets table row 1 0 0 row 0 1 1 row 0 cell negative 2 end cell 4 end table close square brackets$ & I = $open square brackets table row 1 0 0 row 0 1 0 row 0 0 1 end table close square brackets$ and A^-1= $fraction numerator 1 over denominator 6 end fraction$ [A²+CA+dI], find ordered pair (c,d) ?

the roots of the characteristic equation give us the eigenvalues of the matrix.

Which of the following is an intermolecular redox reaction?

In which of the following processes is nitrogen oxidised?

Which one of the following statements, is true-

A square matrix is one whose number of rows are equal to the number of columns.

Which one of the following statements, is true-

A square matrix is one whose number of rows are equal to the number of columns.

If A = $open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets$ and A adj A = $open square brackets table row k 0 row 0 k end table close square brackets$ , then k is equal to -

adjoint of a matrix is the transpose of the cofactor matrix of that matrix. cofactors are the resultant numbers when the corresponding row and column of an element is removed from the matrix.

If A = $open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets$ and A adj A = $open square brackets table row k 0 row 0 k end table close square brackets$ , then k is equal to -

adjoint of a matrix is the transpose of the cofactor matrix of that matrix. cofactors are the resultant numbers when the corresponding row and column of an element is removed from the matrix.

If A_αβ= $open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets$ , then which of following statement is true -