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General

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Question

If the independent variable $x$ is changed to $y$ , then the differential equation $x fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction plus left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 3 end exponent minus fraction numerator d y over denominator d x end fraction equals 0$ is transformed to $x fraction numerator d to the power of 2 end exponent x over denominator d y to the power of 2 end exponent end fraction plus left parenthesis fraction numerator d x over denominator d y end fraction right parenthesis to the power of 2 end exponent equals k$ , k being a number Then k equals

$0$
1
$- 1$
2

The correct answer is: 1

$fraction numerator d y over denominator d x end fraction equals fraction numerator 1 over denominator d divided by to the power of x subscript d y end subscript end exponent end fraction comma fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals negative fraction numerator negative 1 over denominator left parenthesis d x divided by d y right parenthesis to the power of 3 end exponent end fraction fraction numerator d to the power of 2 end exponent x over denominator d y to the power of 2 end exponent end fraction$
then $x fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction plus left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 3 end exponent minus left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis equals 0$ changes to
$x fraction numerator d to the power of 2 end exponent x over denominator d y to the power of 2 end exponent end fraction plus left parenthesis fraction numerator d x over denominator d y end fraction right parenthesis to the power of 2 end exponent minus 1 equals 0$

Related Questions to study

The differential equation $e to the power of y end exponent d x plus left parenthesis e to the power of y end exponent. x plus 2 y right parenthesis d y equals 0$ has the particular solution $y left parenthesis O right parenthesis equals 1$ The value of $x$ , when $y equals 0$ , is

The differential equation $e to the power of y end exponent d x plus left parenthesis e to the power of y end exponent. x plus 2 y right parenthesis d y equals 0$ has the particular solution $y left parenthesis O right parenthesis equals 1$ The value of $x$ , when $y equals 0$ , is

If a, b, $c$ , are real numbers, and $D equals open vertical bar table row a cell 1 plus 2 i end cell cell 3 minus 5 i end cell row cell 1 minus 2 i end cell b cell negative 7 minus 3 i end cell row cell 3 plus 5 i end cell cell negative 7 plus 3 i end cell c end table close vertical bar$ then D is

If a, b, $c$ , are real numbers, and $D equals open vertical bar table row a cell 1 plus 2 i end cell cell 3 minus 5 i end cell row cell 1 minus 2 i end cell b cell negative 7 minus 3 i end cell row cell 3 plus 5 i end cell cell negative 7 plus 3 i end cell c end table close vertical bar$ then D is

The value of $lambda$ for which the system ofequations 2x-y-z=12, x-2y+z=-4, x+y+λz=4 has no solution is

Hence λ=−2 for no solution.

The value of $lambda$ for which the system ofequations 2x-y-z=12, x-2y+z=-4, x+y+λz=4 has no solution is

Hence λ=−2 for no solution.

parallel

The number of values of $k$ for which the linear equations 4x+ky+2z=0 kx+4y+z=0 2x+2y+z=0 possess a non‐zero solution is :‐

The number of values of $k$ for which the linear equations 4x+ky+2z=0 kx+4y+z=0 2x+2y+z=0 possess a non‐zero solution is :‐

If $a subscript 1 end subscript comma$ $a subscript 2 end subscript comma horizontal ellipsis horizontal ellipsis. a subscript n end subscript comma$ $a subscript n plus 1 end subscript$ are in $G P blank a n d blank a subscript i end subscript greater than 0 for all i comma$ then $open vertical bar table row cell l o g invisible function application a subscript n end subscript end cell cell l o g invisible function application a subscript n plus 2 end subscript end cell cell l o g invisible function application a subscript n plus 4 end subscript end cell row cell l o g invisible function application a subscript n plus 6 end subscript end cell cell l o g invisible function application a subscript n plus 8 end subscript end cell cell l o g invisible function application a subscript n plus 10 end subscript end cell row cell l o g invisible function application a subscript n plus 12 end subscript end cell cell l o g invisible function application a subscript n plus 14 end subscript end cell cell l o g invisible function application a subscript n plus 16 end subscript end cell end table close vertical bar$ is equal to

If $a subscript 1 end subscript comma$ $a subscript 2 end subscript comma horizontal ellipsis horizontal ellipsis. a subscript n end subscript comma$ $a subscript n plus 1 end subscript$ are in $G P blank a n d blank a subscript i end subscript greater than 0 for all i comma$ then $open vertical bar table row cell l o g invisible function application a subscript n end subscript end cell cell l o g invisible function application a subscript n plus 2 end subscript end cell cell l o g invisible function application a subscript n plus 4 end subscript end cell row cell l o g invisible function application a subscript n plus 6 end subscript end cell cell l o g invisible function application a subscript n plus 8 end subscript end cell cell l o g invisible function application a subscript n plus 10 end subscript end cell row cell l o g invisible function application a subscript n plus 12 end subscript end cell cell l o g invisible function application a subscript n plus 14 end subscript end cell cell l o g invisible function application a subscript n plus 16 end subscript end cell end table close vertical bar$ is equal to

If $a comma$ $b comma$ $c$ are real then the value of determinant $open vertical bar table row cell a to the power of 2 end exponent plus 1 end cell cell a b end cell cell a c end cell row cell a b end cell cell b to the power of 2 end exponent plus 1 end cell cell b c end cell row cell a c end cell cell b c end cell cell c to the power of 2 end exponent plus 1 end cell end table close vertical bar equals 1$ if

If $a comma$ $b comma$ $c$ are real then the value of determinant $open vertical bar table row cell a to the power of 2 end exponent plus 1 end cell cell a b end cell cell a c end cell row cell a b end cell cell b to the power of 2 end exponent plus 1 end cell cell b c end cell row cell a c end cell cell b c end cell cell c to the power of 2 end exponent plus 1 end cell end table close vertical bar equals 1$ if

parallel

The system of linear equations x+y-z=6, x+2y-3z=14 and $2 x plus 5 y minus lambda z equals 9 left parenthesis lambda element of R right parenthesis$ has a unique solution if

Hence option B is the correct option

The system of linear equations x+y-z=6, x+2y-3z=14 and $2 x plus 5 y minus lambda z equals 9 left parenthesis lambda element of R right parenthesis$ has a unique solution if

Hence option B is the correct option

If $D equals$ $open vertical bar table row cell a to the power of 2 end exponent plus 1 end cell cell a b end cell cell a c end cell row cell b a end cell cell b to the power of 2 end exponent plus 1 end cell cell b c end cell row cell c a end cell cell c b end cell cell c to the power of 2 end exponent plus 1 end cell end table close vertical bar$ then $D equals$

If $D equals$ $open vertical bar table row cell a to the power of 2 end exponent plus 1 end cell cell a b end cell cell a c end cell row cell b a end cell cell b to the power of 2 end exponent plus 1 end cell cell b c end cell row cell c a end cell cell c b end cell cell c to the power of 2 end exponent plus 1 end cell end table close vertical bar$ then $D equals$

Let $A equals open curly brackets table attributes columnalign left end attributes row cell c o s to the power of negative 1 end exponent x end cell cell c o s to the power of negative 1 end exponent y end cell cell c o s to the power of negative 1 end exponent end cell z row cell c o s to the power of negative 1 end exponent y end cell cell c o s to the power of negative 1 end exponent z end cell cell c o s to the power of negative 1 end exponent x end cell blank row cell c o s to the power of negative 1 end exponent z end cell cell c o s to the power of negative 1 end exponent x end cell cell c o s to the power of negative 1 end exponent y end cell blank end table close curly brackets$ such that $vertical line A vertical line equals 0$ , then maximum value of $x plus y plus z$ is

Let $A equals open curly brackets table attributes columnalign left end attributes row cell c o s to the power of negative 1 end exponent x end cell cell c o s to the power of negative 1 end exponent y end cell cell c o s to the power of negative 1 end exponent end cell z row cell c o s to the power of negative 1 end exponent y end cell cell c o s to the power of negative 1 end exponent z end cell cell c o s to the power of negative 1 end exponent x end cell blank row cell c o s to the power of negative 1 end exponent z end cell cell c o s to the power of negative 1 end exponent x end cell cell c o s to the power of negative 1 end exponent y end cell blank end table close curly brackets$ such that $vertical line A vertical line equals 0$ , then maximum value of $x plus y plus z$ is

parallel

Statement‐I : The inverse of the matrix $A equals left square bracket a subscript i j end subscript right square bracket subscript n cross times n end subscript$ where $a subscript i j end subscript equals 0 comma$ $i greater or equal than j$ is $B equals left square bracket a subscript i j to the power of negative 1 end exponent end subscript right square bracket subscript n cross times n end subscript$
Statement‐II : The inverse of singular matrix does not exist.

Hence option D is the suitable option

Statement‐I : The inverse of the matrix $A equals left square bracket a subscript i j end subscript right square bracket subscript n cross times n end subscript$ where $a subscript i j end subscript equals 0 comma$ $i greater or equal than j$ is $B equals left square bracket a subscript i j to the power of negative 1 end exponent end subscript right square bracket subscript n cross times n end subscript$
Statement‐II : The inverse of singular matrix does not exist.

Hence option D is the suitable option

Let $P equals open square brackets a subscript i j end subscript close square brackets$ be a $3 cross times 3$ matrix and let $Q equals left square bracket b subscript i j end subscript right square bracket$ , where $b subscript i j end subscript equals 2 to the power of i plus j end exponent a subscript i j end subscript$ for $1 less than i comma$ $j less than 3$ If the determinant of $P$ is 2, then the determinant of the matrix $Q$ is ‐

Let $P equals open square brackets a subscript i j end subscript close square brackets$ be a $3 cross times 3$ matrix and let $Q equals left square bracket b subscript i j end subscript right square bracket$ , where $b subscript i j end subscript equals 2 to the power of i plus j end exponent a subscript i j end subscript$ for $1 less than i comma$ $j less than 3$ If the determinant of $P$ is 2, then the determinant of the matrix $Q$ is ‐

The power factor of the circuit is $1 divided by square root of 2$ The capacitance of the circuit is equal to

The power factor of the circuit is $1 divided by square root of 2$ The capacitance of the circuit is equal to

physics-General

parallel

In a L–R decay circuit, the initial current at t = 0 is I. The total charge that has flown through the resistor till the energy in the inductor has reduced to one–fourth its initial value, is

In a L–R decay circuit, the initial current at t = 0 is I. The total charge that has flown through the resistor till the energy in the inductor has reduced to one–fourth its initial value, is

physics-General

The current in the given circuit is increasing with a rate a = 4 amp/s. The charge on the capacitor at an instant when the current in the circuit is 2 amp will be :
<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/610610/1/1102617/Picture43.png" alt=""

The current in the given circuit is increasing with a rate a = 4 amp/s. The charge on the capacitor at an instant when the current in the circuit is 2 amp will be :
<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/610610/1/1102617/Picture43.png" alt=""

physics-General

The radius of curvature of the left and right surface of the concave lens are 10cm and 15cm respectively. The radius of curvature of the mirror is 15cm

The radius of curvature of the left and right surface of the concave lens are 10cm and 15cm respectively. The radius of curvature of the mirror is 15cm

physics-General

parallel

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