Maths-
General
Easy

Question

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

  1. purely real    
  2. purely imaginary    
  3. non real    
  4. integer    

The correct answer is: purely real



    Related Questions to study

    General
    Maths-

    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

    Maths-General

    Hence λ=2 for no solution.

    General
    maths-

    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 :‐

    maths-General
    General
    maths-

    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

    maths-General
    parallel
    General
    maths-

    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

    maths-General
    General
    Maths-

    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

    Maths-General

    Hence option B is the correct option

    General
    Maths-

    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

    Maths-General
    parallel
    General
    maths-

    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

    maths-General
    General
    Maths-

    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.

    Maths-General

    Hence option D is the suitable option

    General
    maths-

    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 ‐

    maths-General
    parallel
    General
    physics-

    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
    General
    physics-

    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
    General
    physics-

    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
    parallel
    General
    physics-

    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
    General
    physics-

    An object O is kept infront of a converging lens of focal length 30cm behind which there is a plane mirror at 15cm from the lens

    An object O is kept infront of a converging lens of focal length 30cm behind which there is a plane mirror at 15cm from the lens

    physics-General
    General
    physics-

    A diminished image of an object is to be obtained on a large screen 1 m from it. This can be achieved by

    A diminished image of an object is to be obtained on a large screen 1 m from it. This can be achieved by

    physics-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.