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Maths-

General

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Question

Matrix Ais given by $A equals open curly brackets table attributes columnalign left end attributes row 3 11 row 2 8 end table close curly brackets$ then the determinant of $A to the power of 2011 end exponent minus 5 A to the power of 2010 end exponent$ is

$- 7 . 2^{2012}$
$2^{2012}$
$- 7 . 2^{2010}$
$7 . 2^{2010}$

The correct answer is: $negative 7.2 to the power of 2012 end exponent$

$vertical line A vertical line equals 2$ $A to the power of 2011 end exponent minus 5 A to the power of 2010 end exponent$ $equals A to the power of 2010 end exponent left parenthesis A minus 5 I right parenthesis$
$vertical line A to the power of 2011 end exponent minus 5 A to the power of 2010 end exponent vertical line equals 2 to the power of 2010 end exponent open vertical bar table row cell negative 2 end cell 11 row 2 3 end table close vertical bar equals 2 to the power of 2010 end exponent left parenthesis negative 28 right parenthesis equals negative 2 to the power of 2012 end exponent 7$

Related Questions to study

If $A open parentheses table row 1 3 4 row 3 cell negative 1 end cell 5 row cell negative 2 end cell 4 cell negative 3 end cell end table close parentheses equals open parentheses table row 3 cell negative 1 end cell 5 row 1 3 4 row cell plus 4 end cell cell negative 8 end cell 6 end table close parentheses$ then $A equals negative times$

If $A open parentheses table row 1 3 4 row 3 cell negative 1 end cell 5 row cell negative 2 end cell 4 cell negative 3 end cell end table close parentheses equals open parentheses table row 3 cell negative 1 end cell 5 row 1 3 4 row cell plus 4 end cell cell negative 8 end cell 6 end table close parentheses$ then $A equals negative times$

If $open vertical bar table row cell a blank b blank 1 end cell row cell b blank c blank 1 end cell row cell c blank a blank 1 end cell end table close vertical bar equals 2010 text andif end text open vertical bar table row cell c minus a end cell cell c minus b end cell cell a b end cell row cell a minus b end cell cell a minus c end cell cell b c end cell row cell b minus c end cell cell b minus a end cell cell c a end cell end table close vertical bar minus open vertical bar table row cell c minus a end cell cell c minus b end cell cell c to the power of 2 end exponent end cell row cell a minus b end cell cell a minus c end cell cell a to the power of 2 end exponent end cell row cell b minus c end cell cell b minus a end cell cell b to the power of 2 end exponent end cell end table close vertical bar equals p$ then the number of positive divisors of the number p is

If $open vertical bar table row cell a blank b blank 1 end cell row cell b blank c blank 1 end cell row cell c blank a blank 1 end cell end table close vertical bar equals 2010 text andif end text open vertical bar table row cell c minus a end cell cell c minus b end cell cell a b end cell row cell a minus b end cell cell a minus c end cell cell b c end cell row cell b minus c end cell cell b minus a end cell cell c a end cell end table close vertical bar minus open vertical bar table row cell c minus a end cell cell c minus b end cell cell c to the power of 2 end exponent end cell row cell a minus b end cell cell a minus c end cell cell a to the power of 2 end exponent end cell row cell b minus c end cell cell b minus a end cell cell b to the power of 2 end exponent end cell end table close vertical bar equals p$ then the number of positive divisors of the number p is

The number of positive integral solutions of the equation $open vertical bar table row cell y to the power of 3 end exponent plus 1 end cell cell y to the power of 2 end exponent z end cell cell y to the power of 2 end exponent x end cell row cell y z to the power of 2 end exponent end cell cell z to the power of 3 end exponent plus 1 end cell cell z to the power of 2 end exponent x end cell row cell y x to the power of 2 end exponent end cell cell X to the power of 2 end exponent Z end cell cell x to the power of 3 end exponent plus 1 end cell end table close vertical bar equals 11$ is

The number of positive integral solutions of the equation $open vertical bar table row cell y to the power of 3 end exponent plus 1 end cell cell y to the power of 2 end exponent z end cell cell y to the power of 2 end exponent x end cell row cell y z to the power of 2 end exponent end cell cell z to the power of 3 end exponent plus 1 end cell cell z to the power of 2 end exponent x end cell row cell y x to the power of 2 end exponent end cell cell X to the power of 2 end exponent Z end cell cell x to the power of 3 end exponent plus 1 end cell end table close vertical bar equals 11$ is

parallel

If $A comma$ $B comma$ $C comma$ $D$ be real matrices (not necessasrily square) such that $A to the power of T end exponent equals B C D comma$ $B to the power of T end exponent equals C D A comma$ $C to the power of T end exponent equals D A B comma$ $D to the power of T end exponent equals A B C$ forthematrix $S equals A B C D$ consider the statements $I colon S to the power of 3 end exponent equals S$ $capital pi colon S to the power of 2 end exponent equals S to the power of 4 end exponent$

If $A comma$ $B comma$ $C comma$ $D$ be real matrices (not necessasrily square) such that $A to the power of T end exponent equals B C D comma$ $B to the power of T end exponent equals C D A comma$ $C to the power of T end exponent equals D A B comma$ $D to the power of T end exponent equals A B C$ forthematrix $S equals A B C D$ consider the statements $I colon S to the power of 3 end exponent equals S$ $capital pi colon S to the power of 2 end exponent equals S to the power of 4 end exponent$

If $l o g subscript 4 end subscript left parenthesis x plus 2 y right parenthesis plus l o g subscript 4 end subscript left parenthesis x minus 2 y right parenthesis equals 1$ , then
Statement $negative 1 colon left parenthesis vertical line x vertical line minus vertical line y vertical line right parenthesis subscript blank m i n blank end subscript equals square root of 3$ because
Statement $negative 2$ :A.M $greater or equal than G. M$ for $R to the power of plus end exponent.$

If $l o g subscript 4 end subscript left parenthesis x plus 2 y right parenthesis plus l o g subscript 4 end subscript left parenthesis x minus 2 y right parenthesis equals 1$ , then
Statement $negative 1 colon left parenthesis vertical line x vertical line minus vertical line y vertical line right parenthesis subscript blank m i n blank end subscript equals square root of 3$ because
Statement $negative 2$ :A.M $greater or equal than G. M$ for $R to the power of plus end exponent.$

If $alpha element of left parenthesis negative fraction numerator pi over denominator 2 end fraction comma 0 right parenthesis$ , then the value of $t a n to the power of negative 1 end exponent left parenthesis blank c o t blank alpha right parenthesis minus c o t to the power of negative 1 end exponent left parenthesis blank t a n blank alpha right parenthesis$ is equal to

If $alpha element of left parenthesis negative fraction numerator pi over denominator 2 end fraction comma 0 right parenthesis$ , then the value of $t a n to the power of negative 1 end exponent left parenthesis blank c o t blank alpha right parenthesis minus c o t to the power of negative 1 end exponent left parenthesis blank t a n blank alpha right parenthesis$ is equal to

parallel

The minimum value of $left parenthesis s e c to the power of negative 1 end exponent x right parenthesis to the power of 2 end exponent plus left parenthesis blank c o s blank e c to the power of negative 1 end exponent x right parenthesis to the power of 2 end exponent$ is

The minimum value of $left parenthesis s e c to the power of negative 1 end exponent x right parenthesis to the power of 2 end exponent plus left parenthesis blank c o s blank e c to the power of negative 1 end exponent x right parenthesis to the power of 2 end exponent$ is

If $5 f left parenthesis x right parenthesis plus 3 f left parenthesis fraction numerator 1 over denominator x end fraction right parenthesis equals x plus 2$ andy $equals x f$ (x)then $fraction numerator d y over denominator d x end fraction$ at x=1 is

If $5 f left parenthesis x right parenthesis plus 3 f left parenthesis fraction numerator 1 over denominator x end fraction right parenthesis equals x plus 2$ andy $equals x f$ (x)then $fraction numerator d y over denominator d x end fraction$ at x=1 is

Statement 1:Degree of differential equation $2 x minus 3 y plus 2 equals blank l o g blank left parenthesis fraction numerator d y over denominator d x end fraction 1$ is not defined
Statement 2: In the given D.E, the power of highest order derivative when expressed as a polynomials of derivatives is called degree

Statement 1:Degree of differential equation $2 x minus 3 y plus 2 equals blank l o g blank left parenthesis fraction numerator d y over denominator d x end fraction 1$ is not defined
Statement 2: In the given D.E, the power of highest order derivative when expressed as a polynomials of derivatives is called degree

parallel

The solution of $e to the power of x y end exponent left parenthesis x y to the power of 2 end exponent d y plus y to the power of 3 end exponent d x right parenthesis plus e to the power of x divided by y end exponent left parenthesis y d x minus x d y right parenthesis equals 0$ is

The solution of $e to the power of x y end exponent left parenthesis x y to the power of 2 end exponent d y plus y to the power of 3 end exponent d x right parenthesis plus e to the power of x divided by y end exponent left parenthesis y d x minus x d y right parenthesis equals 0$ is

Solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y to the power of 2 end exponent minus y minus 2 over denominator x to the power of 2 end exponent plus 2 x minus 3 end fraction$ is $minus$ ( where c is arbitrary constant)

Solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y to the power of 2 end exponent minus y minus 2 over denominator x to the power of 2 end exponent plus 2 x minus 3 end fraction$ is $minus$ ( where c is arbitrary constant)

Assertion (A) : If (2, 3) and (3,2) are respectively the orthocenters of $capital delta A B C$ and $capital delta D E F$ where D, E, F are mid points of sides of $capital delta A B C$ respectively then the centroid of either triangle is $Error converting from MathML to accessible text.$
Reason (R) :Circumcenters of triangles formed by mid‐points of sides of $capital delta A B C$ and pedal triangle of $capital delta A B C$ are same

Assertion (A) : If (2, 3) and (3,2) are respectively the orthocenters of $capital delta A B C$ and $capital delta D E F$ where D, E, F are mid points of sides of $capital delta A B C$ respectively then the centroid of either triangle is $Error converting from MathML to accessible text.$
Reason (R) :Circumcenters of triangles formed by mid‐points of sides of $capital delta A B C$ and pedal triangle of $capital delta A B C$ are same

parallel

Two metallic strings A and B of different materials are connected in series forming a joint. The strings have similar cross-sectional area. The length of A is $l subscript A end subscript equals 0.3 m$ and that of B is $l subscript B end subscript equals 0.75 m$ . One end of the combined string is tied with a support rigidly and the other end is loaded with a block of mass m passing over a frictionless pulley. Transverse waves are setup in the combined string using an external source of variable frequency. The total number of antinodes at this frequency with joint as node is (the densities of A and B are $6.3 cross times 10 to the power of 3 end exponent k g m to the power of negative 3 end exponent text and end text 2.8 cross times 10 to the power of 3 end exponent k g m to the power of negative 3 end exponent$ respectively)

Two metallic strings A and B of different materials are connected in series forming a joint. The strings have similar cross-sectional area. The length of A is $l subscript A end subscript equals 0.3 m$ and that of B is $l subscript B end subscript equals 0.75 m$ . One end of the combined string is tied with a support rigidly and the other end is loaded with a block of mass m passing over a frictionless pulley. Transverse waves are setup in the combined string using an external source of variable frequency. The total number of antinodes at this frequency with joint as node is (the densities of A and B are $6.3 cross times 10 to the power of 3 end exponent k g m to the power of negative 3 end exponent text and end text 2.8 cross times 10 to the power of 3 end exponent k g m to the power of negative 3 end exponent$ respectively)

physics-General

A rod PQ of length ‘L’ is hung from two identical wires A and B. A block of mass ‘m’ is hung at point R of the rod as shown in figure. The value of ‘x’ so that the fundamental mode in wire A is in resonance with first overtone of B is

A rod PQ of length ‘L’ is hung from two identical wires A and B. A block of mass ‘m’ is hung at point R of the rod as shown in figure. The value of ‘x’ so that the fundamental mode in wire A is in resonance with first overtone of B is

physics-General

The length of the wire shown in figure between the pulley is 1.5m and its mass is 12 gm. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest

The length of the wire shown in figure between the pulley is 1.5m and its mass is 12 gm. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest

physics-General

parallel

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