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

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.

chemistry-

Which of the following is an intermolecular redox reaction?

chemistry-General

chemistry-

In which of the following processes is nitrogen oxidised?

chemistry-General

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 -

If $f left parenthesis x right parenthesis equals vertical line vertical line sin left parenthesis vertical line x vertical line minus 1 right parenthesis vertical line minus 2 vertical line space$ then

chemistry-

Which of following is not a disproportionation reaction?

chemistry-General

Consider a continuous function $f colon left square bracket 0 comma infinity right parenthesis rightwards arrow left square bracket 0 comma infinity right parenthesis space i f space f left parenthesis a b right parenthesis equals f left parenthesis a right parenthesis f left parenthesis b right parenthesis space$ for all a, b in the domain of ‘f’ and $L i m left parenthesis x rightwards arrow infinity right parenthesis space f left parenthesis x right parenthesis$ is a non zero finite number then