Maths-
General
Easy

Question

A square matrix open square brackets a subscript i j end subscript close square brackets equals 0 for i space not equal to j and a subscript i j end subscript equals K (constant) for i equals j is called a

  1. unit matrix
  2. scalar matrix
  3. Null matrix
  4. Diagonal matrix

Hint:

Matrix of size n in n cross times n square matrix with1 on the main diagonal and zero elsewhere is Unit matrix. A diagonal matrix is a matrix having non-zero elements only in the diagonal running from the upper left to the lower right. A scalar matrix is the special case diagonal matrix with all the diagonals elements equal and all off-diagonals element not equal. Null matrix is the matrix with all the elements zero.

The correct answer is: scalar matrix


    L e t space A equals open square brackets a subscript i j end subscript close square brackets space i s space a space s q u a r e space m a t r i x
a subscript i j end subscript equals open curly brackets table attributes columnalign left columnspacing 1.4ex end attributes row cell 0 comma end cell cell i f space i not equal to j end cell row cell k comma end cell cell i f space i equals j end cell end table close
A equals open square brackets table row cell a subscript 11 end cell cell a subscript 12 end cell row cell a subscript 21 end cell cell a subscript 22 end cell end table close square brackets equals space open square brackets table row k 0 row 0 k end table close square brackets
T h u s comma space A space i s space s c a l a r space m a t r i x.

    Book A Free Demo

    +91

    Grade*

    Related Questions to study

    General
    chemistry-

    DS for the reaction: MgCO3(s) → MgO(s) + CO2(g) will be -

    DS for the reaction: MgCO3(s) → MgO(s) + CO2(g) will be -

    chemistry-General
    General
    physics-

    A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length s equals t to the power of 3 end exponent plus 5 comma where s is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly

    G i v e n comma blank s equals t to the power of 3 end exponent plus 5
    S p e e d comma blank v equals fraction numerator d s over denominator d t end fraction equals 3 t to the power of 2 end exponent
    a n d blank r a t e blank o f blank c h a n g e blank o f blank s p e e d comma blank a subscript t end subscript equals fraction numerator d v over denominator d t end fraction equals 6 t
    therefore T a n g e n t i a l blank a c c e l e r a t i o n blank a t blank t equals 2 blank s comma
    a subscript t end subscript equals 6 cross times 2 equals 12 blank m s to the power of negative 2 end exponent
    a n d blank a t blank t equals 2 s comma blank v equals 3 left parenthesis 2 right parenthesis to the power of 2 end exponent equals 12 m s to the power of negative 1 end exponent
    therefore C e n t r i p e t a l blank a c c e l e r a t i o n comma blank a subscript c end subscript equals fraction numerator v to the power of 2 end exponent over denominator R end fraction equals fraction numerator 144 over denominator 20 end fraction m s to the power of negative 2 end exponent
    therefore N e t blank a c c e l e r a t i o n equals a subscript t end subscript superscript 2 end superscript plus a subscript i end subscript superscript 2 end superscript almost equal to 14 m s to the power of negative 2 end exponent

    A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of P is such that it sweeps out length s equals t to the power of 3 end exponent plus 5 comma where s is in metre and t is in second. The radius of the path is 20 m. The acceleration of P when t =2s is nearly

    physics-General
    G i v e n comma blank s equals t to the power of 3 end exponent plus 5
    S p e e d comma blank v equals fraction numerator d s over denominator d t end fraction equals 3 t to the power of 2 end exponent
    a n d blank r a t e blank o f blank c h a n g e blank o f blank s p e e d comma blank a subscript t end subscript equals fraction numerator d v over denominator d t end fraction equals 6 t
    therefore T a n g e n t i a l blank a c c e l e r a t i o n blank a t blank t equals 2 blank s comma
    a subscript t end subscript equals 6 cross times 2 equals 12 blank m s to the power of negative 2 end exponent
    a n d blank a t blank t equals 2 s comma blank v equals 3 left parenthesis 2 right parenthesis to the power of 2 end exponent equals 12 m s to the power of negative 1 end exponent
    therefore C e n t r i p e t a l blank a c c e l e r a t i o n comma blank a subscript c end subscript equals fraction numerator v to the power of 2 end exponent over denominator R end fraction equals fraction numerator 144 over denominator 20 end fraction m s to the power of negative 2 end exponent
    therefore N e t blank a c c e l e r a t i o n equals a subscript t end subscript superscript 2 end superscript plus a subscript i end subscript superscript 2 end superscript almost equal to 14 m s to the power of negative 2 end exponent
    General
    chemistry-

    FothreactioN2(g)+3H2(g)→2NH3(g),DH is-

    FothreactioN2(g)+3H2(g)→2NH3(g),DH is-

    chemistry-General
    General
    physics-

    Three identical spheres of mass Meach are placed at the corners of an equilateral triangle of side 2m. Taking one of the corner as the origin, the position vector of the centre of mass is

    The x coordinate of centre of mass is
    stack x with minus on top equals fraction numerator not stretchy sum m subscript i end subscript x subscript i end subscript over denominator not stretchy sum m subscript i end subscript end fraction
    equals fraction numerator m cross times 0 plus m cross times 1 plus m cross times 2 over denominator m plus m plus m end fraction equals 1
    stack y with minus on top equals fraction numerator not stretchy sum m subscript i end subscript y subscript i end subscript over denominator not stretchy sum m subscript i end subscript end fraction
    equals fraction numerator m cross times 0 plus m left parenthesis 2 sin invisible function application 60 degree right parenthesis plus m cross times 0 over denominator m plus m plus m end fraction
    stack y with minus on top equals fraction numerator square root of 3 m over denominator 3 m end fraction equals fraction numerator 1 over denominator square root of 3 end fraction
    Position vector of centre of mass is open parentheses stack i with hat on top plus fraction numerator stack j with hat on top over denominator square root of 3 end fraction close parentheses.

    Three identical spheres of mass Meach are placed at the corners of an equilateral triangle of side 2m. Taking one of the corner as the origin, the position vector of the centre of mass is

    physics-General
    The x coordinate of centre of mass is
    stack x with minus on top equals fraction numerator not stretchy sum m subscript i end subscript x subscript i end subscript over denominator not stretchy sum m subscript i end subscript end fraction
    equals fraction numerator m cross times 0 plus m cross times 1 plus m cross times 2 over denominator m plus m plus m end fraction equals 1
    stack y with minus on top equals fraction numerator not stretchy sum m subscript i end subscript y subscript i end subscript over denominator not stretchy sum m subscript i end subscript end fraction
    equals fraction numerator m cross times 0 plus m left parenthesis 2 sin invisible function application 60 degree right parenthesis plus m cross times 0 over denominator m plus m plus m end fraction
    stack y with minus on top equals fraction numerator square root of 3 m over denominator 3 m end fraction equals fraction numerator 1 over denominator square root of 3 end fraction
    Position vector of centre of mass is open parentheses stack i with hat on top plus fraction numerator stack j with hat on top over denominator square root of 3 end fraction close parentheses.
    General
    physics-

    Four bodies of equal mass start moving with same speed are shown in the figure. In which of the following combination the centre of mass will remain at origin?

    Four bodies of equal mass start moving with same speed are shown in the figure. In which of the following combination the centre of mass will remain at origin?

    physics-General
    General
    chemistry-

    From threactions: C(s)+2H2(g)→CH4(g)DH=–Xcal C(g)+4H(g)→CH4(g),DH=–X1Kcal CH4(g)→CH3(g)+H(g)DH=+Y(Kcal) Bond energof C–H bond is-

    From threactions: C(s)+2H2(g)→CH4(g)DH=–Xcal C(g)+4H(g)→CH4(g),DH=–X1Kcal CH4(g)→CH3(g)+H(g)DH=+Y(Kcal) Bond energof C–H bond is-

    chemistry-General
    General
    physics-

    From a circular disc of radius R and mass 9 M, a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

    I subscript r e m a i n i n g end subscript equals I subscript w h o l e end subscript minus I subscript r e m o v e d end subscript
    or I equals fraction numerator 1 over denominator 2 end fraction open parentheses 9 M close parentheses open parentheses R to the power of 2 end exponent close parentheses minus open square brackets fraction numerator 1 over denominator 2 end fraction m open parentheses fraction numerator R over denominator 3 end fraction close parentheses to the power of 2 end exponent plus fraction numerator 1 over denominator 2 end fraction m open parentheses fraction numerator 2 R over denominator 3 end fraction close parentheses to the power of 2 end exponent close square brackets (i)
    Here, m equals fraction numerator 9 M over denominator pi R to the power of 2 end exponent end fraction cross times pi open parentheses fraction numerator R over denominator 3 end fraction close parentheses to the power of 2 end exponent equals M
    Substituting in Eq. (i), we have
    I equals 4 M R to the power of 2 end exponent

    From a circular disc of radius R and mass 9 M, a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

    physics-General
    I subscript r e m a i n i n g end subscript equals I subscript w h o l e end subscript minus I subscript r e m o v e d end subscript
    or I equals fraction numerator 1 over denominator 2 end fraction open parentheses 9 M close parentheses open parentheses R to the power of 2 end exponent close parentheses minus open square brackets fraction numerator 1 over denominator 2 end fraction m open parentheses fraction numerator R over denominator 3 end fraction close parentheses to the power of 2 end exponent plus fraction numerator 1 over denominator 2 end fraction m open parentheses fraction numerator 2 R over denominator 3 end fraction close parentheses to the power of 2 end exponent close square brackets (i)
    Here, m equals fraction numerator 9 M over denominator pi R to the power of 2 end exponent end fraction cross times pi open parentheses fraction numerator R over denominator 3 end fraction close parentheses to the power of 2 end exponent equals M
    Substituting in Eq. (i), we have
    I equals 4 M R to the power of 2 end exponent
    General
    physics-

    The instantaneous velocity of a point B of the given rod of length 0.5 m is 3 m s to the power of negative 1 end exponent in the represented direction. The angular velocity of the rod for minimum velocity of end A is

    If rod is rotated about end A, then vertical component of velocity v subscript perpendicular end subscript of end A will be zero.
    therefore omega equals fraction numerator v cos invisible function application 60 degree over denominator l end fraction equals fraction numerator square root of 3 v over denominator 2 l end fraction
    equals fraction numerator square root of 3 cross times 3 over denominator 2 cross times 0.5 end fraction equals 5.2 blank r a d s to the power of negative 1 end exponent

    The instantaneous velocity of a point B of the given rod of length 0.5 m is 3 m s to the power of negative 1 end exponent in the represented direction. The angular velocity of the rod for minimum velocity of end A is

    physics-General
    If rod is rotated about end A, then vertical component of velocity v subscript perpendicular end subscript of end A will be zero.
    therefore omega equals fraction numerator v cos invisible function application 60 degree over denominator l end fraction equals fraction numerator square root of 3 v over denominator 2 l end fraction
    equals fraction numerator square root of 3 cross times 3 over denominator 2 cross times 0.5 end fraction equals 5.2 blank r a d s to the power of negative 1 end exponent
    General
    biology

    The backbone of RNA consists of which of the following sugar?

    Each spindle is a bipolar fibrous structure composed mainly of microtubules. The spindle fibres are mainly composed of tubulin protein.

    The backbone of RNA consists of which of the following sugar?

    biologyGeneral
    Each spindle is a bipolar fibrous structure composed mainly of microtubules. The spindle fibres are mainly composed of tubulin protein.
    General
    biology

    Consider the following statements and choose the correct one

    In protoplasm, fat store in the form oftriglycerides. Polypeptides, polysaccharides and nucleoside are proteins, carbohydrates ad nucleic acid, respectively

    Consider the following statements and choose the correct one

    biologyGeneral
    In protoplasm, fat store in the form oftriglycerides. Polypeptides, polysaccharides and nucleoside are proteins, carbohydrates ad nucleic acid, respectively
    General
    biology

    Identify A to F in the sectional view of a chloroplast showing the different parts

    70 S ribosomes are found in prokaryotes, i. e. comma bacteria and blue green algae. The 70 S ribosomes have 2 subunits, i. e., 50 S and 30 S. The ribosomes of mitochondria are smallcomma blank i. e., 55-60 S type, which are comparable to 70 S than 80 S type.

    Identify A to F in the sectional view of a chloroplast showing the different parts

    biologyGeneral
    70 S ribosomes are found in prokaryotes, i. e. comma bacteria and blue green algae. The 70 S ribosomes have 2 subunits, i. e., 50 S and 30 S. The ribosomes of mitochondria are smallcomma blank i. e., 55-60 S type, which are comparable to 70 S than 80 S type.
    General
    biology

    Organelle important in spindle formation during nuclear division is

    DNA multiplication or duplication of DNA takes place by replication. It takes place during S-phase of interphase in cell-cycle

    Organelle important in spindle formation during nuclear division is

    biologyGeneral
    DNA multiplication or duplication of DNA takes place by replication. It takes place during S-phase of interphase in cell-cycle
    General
    biology

    A widely accepted, improved model of cell membrane is

    The ability to distinguish different neighbouring cells is important for organism’s function
    Glycolipids are lipids with attached carbohydrate, which acts as recognition sites during cell-cell interaction, as well as sites of attachment in a tissue
    Glycoproteins are often integral membrane proteins and are also important for cell recognition

    A widely accepted, improved model of cell membrane is

    biologyGeneral
    The ability to distinguish different neighbouring cells is important for organism’s function
    Glycolipids are lipids with attached carbohydrate, which acts as recognition sites during cell-cell interaction, as well as sites of attachment in a tissue
    Glycoproteins are often integral membrane proteins and are also important for cell recognition
    General
    biology

    Rough endoplasmic reticulum differs from smooth walled endoplasmic reticulum due to the presence of

    In eukaryotes, DNA is tightly bound to histones which form a DNA protein particle called nucleosome

    Rough endoplasmic reticulum differs from smooth walled endoplasmic reticulum due to the presence of

    biologyGeneral
    In eukaryotes, DNA is tightly bound to histones which form a DNA protein particle called nucleosome
    General
    biology

    Middle lamella is present

    Steps of Gram’s staining technique
    (i) Staining with weak alkaline solution of crystal violet
    (ii) Treatment with 0.5% iodine solution
    (iii) Washing with water
    (iv) Treatment with absolute alcohol/acetone

    Middle lamella is present

    biologyGeneral
    Steps of Gram’s staining technique
    (i) Staining with weak alkaline solution of crystal violet
    (ii) Treatment with 0.5% iodine solution
    (iii) Washing with water
    (iv) Treatment with absolute alcohol/acetone