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Mathematics

Algebra

Easy

Question

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

$3221$
$3303$
$3203$
$3121$

The correct answer is: $3121$

Related Questions to study

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

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

MathematicsAlgebra

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

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

MathematicsAlgebra

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

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

MathematicsAlgebra

parallel

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

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

MathematicsAlgebra

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

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

MathematicsAlgebra

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

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

MathematicsAlgebra

parallel

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

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

MathematicsAlgebra

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

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

MathematicsAlgebra

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

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

MathematicsAlgebra

parallel

$I f space t h e space f u n c t i o n space straight f colon straight R minus left curly bracket 1 comma negative 1 right curly bracket not stretchy rightwards arrow straight A space defined space by space straight f left parenthesis straight x right parenthesis equals fraction numerator straight x squared over denominator 1 minus straight x squared end fraction comma space is space surjective comma space then space straight A space is space equal space to space colon$

$I f space t h e space f u n c t i o n space straight f colon straight R minus left curly bracket 1 comma negative 1 right curly bracket not stretchy rightwards arrow straight A space defined space by space straight f left parenthesis straight x right parenthesis equals fraction numerator straight x squared over denominator 1 minus straight x squared end fraction comma space is space surjective comma space then space straight A space is space equal space to space colon$

MathematicsAlgebra

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

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

MathematicsAlgebra

If $left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 1 row 0 1 end table right square bracket left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 2 row 0 1 end table right square bracket left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 3 row 0 1 end table right square bracket horizontal ellipsis horizontal ellipsis. left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 cell n minus 1 end cell row 0 1 end table right square bracket equals left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 78 row 0 1 end table right square bracket$ then the inverse of $left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 n row 0 1 end table right square bracket$ is

If $left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 1 row 0 1 end table right square bracket left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 2 row 0 1 end table right square bracket left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 3 row 0 1 end table right square bracket horizontal ellipsis horizontal ellipsis. left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 cell n minus 1 end cell row 0 1 end table right square bracket equals left square bracket table attributes columnalign center center columnspacing 1em rowspacing 4 pt end attributes row 1 78 row 0 1 end table right square bracket$ then the inverse of $left square bracket table attributes columnalign left left columnspacing 1em rowspacing 4 pt end attributes row 1 n row 0 1 end table right square bracket$ is

MathematicsAlgebra

parallel

Tell the time the clock shows.

Tell the time the clock shows.

MathematicsGrade-1

Find the time the clock shows.

Find the time the clock shows.

MathematicsGrade-1

Choose the clock which shows the time 9 o’clock.

Choose the clock which shows the time 9 o’clock.

MathematicsGrade-1

parallel

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