image

    Have a query? Ask a Tutor!!

    Access to best educators and exclusive paper discussions

    Offsite CampusTurito Championship

    Can’t find what you’re looking for?

    Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

    • Homework- One to One Solutions
    • Understand concepts to solve better
    • Get your doubts solved instantly
    Mathematics
    Algebra
    Easy

    Question

    I f space t h e space s y s t e m space o f space l i n e a r space e q u a t i o n s space x space plus space y space plus space z space equals space 5 space x space plus space 2 y space plus space 2 z space equals space 6 straight x plus 3 straight y plus lambda straight z equals mu comma left parenthesis lambda comma mu element of straight R right parenthesis comma text  has infinitely many solutions, then the value of  end text lambda plus mu text  is :  end text

    1. 10
    2. 9
    3. 12
    4. 7

    The correct answer is: 10

    Related Questions to study

    Algebra
    Mathematics

    L e t space t h e space n u m b e r space 2 comma space b comma c space b e space i n space a n space A. P. space a n d space A equals open square brackets table attributes columnalign left left left columnspacing 1em rowspacing 4 pt end attributes row cell 1      1      1 end cell row cell 2      b      c end cell row cell 4      b squared      c squared end cell end table close square brackets. space I f space det invisible function application left parenthesis straight A right parenthesis element of left square bracket 2 comma 16 right square bracket space t h e n space c space l i e s space i n space t h e space i n t e r v a l space minus space

    L e t space t h e space n u m b e r space 2 comma space b comma c space b e space i n space a n space A. P. space a n d space A equals open square brackets table attributes columnalign left left left columnspacing 1em rowspacing 4 pt end attributes row cell 1      1      1 end cell row cell 2      b      c end cell row cell 4      b squared      c squared end cell end table close square brackets. space I f space det invisible function application left parenthesis straight A right parenthesis element of left square bracket 2 comma 16 right square bracket space t h e n space c space l i e s space i n space t h e space i n t e r v a l space minus space

    MathematicsAlgebra
    Algebra
    Mathematics

    I f space t h e space s y s t e m space o f space l i n e a r space e q u a t i o n s space x space – space 2 y space plus space k z space equals space 1 space 2 x space plus space y space plus space z space equals space 2 space 3 x space – space y space – space k z space equals space 3 h a s space a space s o l u t i o n space left parenthesis x comma space y comma space z right parenthesis comma space space z not equal to 0 comma space t h e n space left parenthesis x comma space y right parenthesis space l i e s space o n space t h e space s t r a i g h t space l i n e space w h o s e space e q u a t i o n space i s space minus

    I f space t h e space s y s t e m space o f space l i n e a r space e q u a t i o n s space x space – space 2 y space plus space k z space equals space 1 space 2 x space plus space y space plus space z space equals space 2 space 3 x space – space y space – space k z space equals space 3 h a s space a space s o l u t i o n space left parenthesis x comma space y comma space z right parenthesis comma space space z not equal to 0 comma space t h e n space left parenthesis x comma space y right parenthesis space l i e s space o n space t h e space s t r a i g h t space l i n e space w h o s e space e q u a t i o n space i s space minus

    MathematicsAlgebra
    Algebra
    Mathematics

    T h e space g r e a t e s t space v a l u e space o f space c space element of space R space f o r space w h i c h space t h e space s y s t e m space o f space l i n e a r space e q u a t i o n s x space – space c y space – space c z space equals space 0 space c x space – space y space plus space c z space equals space 0 space c x space plus space c y space – space z space equals space 0 space h a s space a space n o n minus t r i v i a l space s o l u t i o n comma space i s space minus

    T h e space g r e a t e s t space v a l u e space o f space c space element of space R space f o r space w h i c h space t h e space s y s t e m space o f space l i n e a r space e q u a t i o n s x space – space c y space – space c z space equals space 0 space c x space – space y space plus space c z space equals space 0 space c x space plus space c y space – space z space equals space 0 space h a s space a space n o n minus t r i v i a l space s o l u t i o n comma space i s space minus

    MathematicsAlgebra
    parallel
    Algebra
    Mathematics

    space If space the space system space of space equations space 2 x plus 3 y minus z equals 0 comma space x plus k y minus 2 z equals 0 space a n d space 2 x minus y plus z equals 0 space has space a space non minus trivial solution space left parenthesis straight x comma straight y comma straight z right parenthesis t h e n space x over y plus y over z plus z over x plus k space space is space equal space to :  space

    space If space the space system space of space equations space 2 x plus 3 y minus z equals 0 comma space x plus k y minus 2 z equals 0 space a n d space 2 x minus y plus z equals 0 space has space a space non minus trivial solution space left parenthesis straight x comma straight y comma straight z right parenthesis t h e n space x over y plus y over z plus z over x plus k space space is space equal space to :  space

    MathematicsAlgebra
    Algebra
    Mathematics

    L e t space alpha space a n d space beta space b e space t h e space r o o t s space o f space t h e space e q u a t i o n space x squared space plus space x space plus space 1 space equals space 0. space T h e n space f o r space y not equal to 0 space i n space R comma space open vertical bar table row cell y plus 1 end cell alpha beta row alpha cell y plus beta end cell 1 row beta 1 cell y plus alpha end cell end table close vertical bar space i s space e q u a l space t o space colon

    L e t space alpha space a n d space beta space b e space t h e space r o o t s space o f space t h e space e q u a t i o n space x squared space plus space x space plus space 1 space equals space 0. space T h e n space f o r space y not equal to 0 space i n space R comma space open vertical bar table row cell y plus 1 end cell alpha beta row alpha cell y plus beta end cell 1 row beta 1 cell y plus alpha end cell end table close vertical bar space i s space e q u a l space t o space colon

    MathematicsAlgebra
    Algebra
    Mathematics

    T h e space s u m space fraction numerator 3 cross times 1 cubed over denominator 1 squared end fraction plus fraction numerator 5 cross times open parentheses 1 cubed plus 2 cubed close parentheses over denominator 1 squared plus 2 squared end fraction plus fraction numerator 7 cross times open parentheses 1 cubed plus 2 cubed plus 3 cubed close parentheses over denominator 1 squared plus 2 squared plus 3 squared end fraction plus horizontal ellipsis horizontal ellipsis horizontal ellipsis text  upto  end text 10 to the power of th text  term is  end text

    T h e space s u m space fraction numerator 3 cross times 1 cubed over denominator 1 squared end fraction plus fraction numerator 5 cross times open parentheses 1 cubed plus 2 cubed close parentheses over denominator 1 squared plus 2 squared end fraction plus fraction numerator 7 cross times open parentheses 1 cubed plus 2 cubed plus 3 cubed close parentheses over denominator 1 squared plus 2 squared plus 3 squared end fraction plus horizontal ellipsis horizontal ellipsis horizontal ellipsis text  upto  end text 10 to the power of th text  term is  end text

    MathematicsAlgebra
    parallel
    Algebra
    Mathematics

    T h e space s u m stack space space sum with k equals 1 below and 20 on top k 1 over 2 to the power of k space i s space e q u a l space t o

    T h e space s u m stack space space sum with k equals 1 below and 20 on top k 1 over 2 to the power of k space i s space e q u a l space t o

    MathematicsAlgebra
    Algebra
    Mathematics

    text  The sum of all natural numbers 'n' such that  end text 100 less than n less than 200 space text  and H.C.F.  end text left parenthesis 91 comma n right parenthesis greater than 1 text  is  end text minus

    text  The sum of all natural numbers 'n' such that  end text 100 less than n less than 200 space text  and H.C.F.  end text left parenthesis 91 comma n right parenthesis greater than 1 text  is  end text minus

    MathematicsAlgebra
    Algebra
    Mathematics

    text  Let  end text A equals open parentheses table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row cell cos invisible function application alpha minus sin invisible function application alpha end cell blank row cell sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close parentheses comma left parenthesis a element of R right parenthesis text  such that  end text A to the power of 32 equals open parentheses table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 0 cell negative 1 end cell row 1 0 end table close parentheses. text  Then a value of  end text alpha text  is -  end text

    text  Let  end text A equals open parentheses table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row cell cos invisible function application alpha minus sin invisible function application alpha end cell blank row cell sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close parentheses comma left parenthesis a element of R right parenthesis text  such that  end text A to the power of 32 equals open parentheses table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 0 cell negative 1 end cell row 1 0 end table close parentheses. text  Then a value of  end text alpha text  is -  end text

    MathematicsAlgebra
    parallel
    Algebra
    Mathematics

    L e t space M equals open square brackets table attributes columnalign left end attributes row 0 1 a row 1 2 3 row 3 b 1 end table close square brackets space a n d space adj M equals open square brackets table row cell negative 1 end cell 1 cell negative 1 end cell row 8 cell negative 6 end cell 2 row cell negative 5 end cell 3 cell negative 1 end cell end table close square brackets space text  where a and b are real numbers. Which of the  end text text  following options is/are correct?  end text

    L e t space M equals open square brackets table attributes columnalign left end attributes row 0 1 a row 1 2 3 row 3 b 1 end table close square brackets space a n d space adj M equals open square brackets table row cell negative 1 end cell 1 cell negative 1 end cell row 8 cell negative 6 end cell 2 row cell negative 5 end cell 3 cell negative 1 end cell end table close square brackets space text  where a and b are real numbers. Which of the  end text text  following options is/are correct?  end text

    MathematicsAlgebra
    Algebra
    Mathematics

    L e t space M equals open square brackets table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row cell sin to the power of 4 theta end cell cell negative 1 minus sin squared theta end cell row cell 1 plus cos squared theta end cell cell cos to the power of 4 theta end cell end table close square brackets equals alpha I plus beta M to the power of negative 1 end exponent comma text where  end text alpha equals alpha left parenthesis theta right parenthesis text  and  end text beta equals beta left parenthesis theta right parenthesis space text  are real numbers, and I is the   end text 2 cross times 2 text  identity matrix. If  end text alpha to the power of ∗ text  is the minimum of the set   end text left curly bracket alpha left parenthesis theta right parenthesis colon theta element of left square bracket 0 comma 2 pi right parenthesis right curly bracket text  and  end text beta to the power of ∗ space text  is the minimum of the  end text set left curly bracket beta left parenthesis theta right parenthesis colon theta element of left square bracket 0 comma 2 pi right parenthesis right curly bracket space comma space text  then value of  end text alpha to the power of ∗ plus beta to the power of ∗ text  is -  end text

    L e t space M equals open square brackets table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row cell sin to the power of 4 theta end cell cell negative 1 minus sin squared theta end cell row cell 1 plus cos squared theta end cell cell cos to the power of 4 theta end cell end table close square brackets equals alpha I plus beta M to the power of negative 1 end exponent comma text where  end text alpha equals alpha left parenthesis theta right parenthesis text  and  end text beta equals beta left parenthesis theta right parenthesis space text  are real numbers, and I is the   end text 2 cross times 2 text  identity matrix. If  end text alpha to the power of ∗ text  is the minimum of the set   end text left curly bracket alpha left parenthesis theta right parenthesis colon theta element of left square bracket 0 comma 2 pi right parenthesis right curly bracket text  and  end text beta to the power of ∗ space text  is the minimum of the  end text set left curly bracket beta left parenthesis theta right parenthesis colon theta element of left square bracket 0 comma 2 pi right parenthesis right curly bracket space comma space text  then value of  end text alpha to the power of ∗ plus beta to the power of ∗ text  is -  end text

    MathematicsAlgebra
    Algebra
    Mathematics

    text  The sum of the series   end text 1 plus 2 cross times 3 plus 3 cross times 5 plus 4 cross times 7 plus horizontal ellipsis text  upto  end text 11 to the power of th text  term is :  end text

    text  The sum of the series   end text 1 plus 2 cross times 3 plus 3 cross times 5 plus 4 cross times 7 plus horizontal ellipsis text  upto  end text 11 to the power of th text  term is :  end text

    MathematicsAlgebra
    parallel
    Algebra
    Mathematics

    I f space t h e space s u m space a n d space p r o d u c t space o f space t h e space f i r s t space t h r e e space t e r m s space i n space a n space A. P. space a r e space 33 space a n d space 1155 comma space r e s p e c t i v e l y comma space t h e n space a space v a l u e space o f space i t s space 11 t h space t e r m space i s space colon

    I f space t h e space s u m space a n d space p r o d u c t space o f space t h e space f i r s t space t h r e e space t e r m s space i n space a n space A. P. space a r e space 33 space a n d space 1155 comma space r e s p e c t i v e l y comma space t h e n space a space v a l u e space o f space i t s space 11 t h space t e r m space i s space colon

    MathematicsAlgebra
    Algebra
    Mathematics

    text  The total number of matrices   end text A equals open parentheses table attributes columnalign center center center columnspacing 1em rowspacing 4 pt end attributes row 0 cell 2 y end cell 1 row cell 2 x end cell y cell negative 1 end cell row cell 2 x end cell cell negative y end cell 1 end table close parentheses comma left parenthesis x comma y element of R comma x not equal to y right parenthesis space text  for which   end text straight A to the power of straight T straight A equals 3 straight I subscript 3 is colon

    text  The total number of matrices   end text A equals open parentheses table attributes columnalign center center center columnspacing 1em rowspacing 4 pt end attributes row 0 cell 2 y end cell 1 row cell 2 x end cell y cell negative 1 end cell row cell 2 x end cell cell negative y end cell 1 end table close parentheses comma left parenthesis x comma y element of R comma x not equal to y right parenthesis space text  for which   end text straight A to the power of straight T straight A equals 3 straight I subscript 3 is colon

    MathematicsAlgebra
    Algebra
    Mathematics

    text  Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball,  end text text  the second row consists of two balls and so on. If 99  more identical balls are added to the total number of  end text text  balls used in forming the equilateral triangle, then all these balls can be arranged in a square whose each side  end text text  contains exactly  end text 2 text  balls less than the number of balls each side of the triangle contains. Then the number of  end text text  balls used to form the equilateral triangle is:  end text

    text  Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball,  end text text  the second row consists of two balls and so on. If 99  more identical balls are added to the total number of  end text text  balls used in forming the equilateral triangle, then all these balls can be arranged in a square whose each side  end text text  contains exactly  end text 2 text  balls less than the number of balls each side of the triangle contains. Then the number of  end text text  balls used to form the equilateral triangle is:  end text

    MathematicsAlgebra
    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.