Solution for the question - the sum sum_(k=1)^(20)k(1)/(2^(k)) is equal to 2-(11)/(2^(19)) '/> 2-(3)/(2^(17)) '/> 1-(11)/(2^(20)) '/> 2-(21)/(2^(20))'/>

Mathematics

Algebra

Easy

Question

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

$2 - \frac{21}{2^{20}}$
$1 - \frac{11}{2^{20}}$
$2 - \frac{3}{2^{17}}$
$2 - \frac{11}{2^{19}}$

The correct answer is: $2 minus 11 over 2 to the power of 19$

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

MathematicsAlgebra

Algebra

Mathematics

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

With Turito Academy.

With Turito Foundation.

Get an Expert Advice From Turito.

Turito Academy

With Turito Academy.

Test Prep

With Turito Foundation.

About Turito

Turito is a revolutionary learning platform for quality online and on-campus education from the most experienced faculty. We offer two years integrated classroom coaching for IIT-JEE and NEET aspirants at our Hyderabad campus. We provide online coaching for all kinds of competitive exams such as IIT-JEE, NEET, SAT, ACT, PSAT, Subjective SAT, AP & Olympiads, and Foundation Courses for students of Class 6 to 10 (CBSE, ICSE & State Syllabus).

Turito's faculty has 30+ years of experience with a proven track record in teaching English, Maths, Physics, Chemistry, Botany, Zoology, Reading Comprehension, and so on. Turito is driven to provide the best online and on-campus programs to students across India, US, Singapore, and Middle East regions.