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General

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Question

Let A be a $2 cross times 2$ matrix with non‐zero entries and let $A to the power of 2 end exponent equals I$ , where I is $2 cross times 2$ identity matrix Defi ne Tr(A) $equals s u m$ of diagonal elements $o f A$ and $vertical line A vertical line equals$ determinant of matrix A
Statement 1: Tr(A) $equals 0.$
Statement 2: $vertical line A vertical line equals 1.$

Statement1 is true, Statement2 is true; Statement2 is a correct explanation for Statement1.
Statement1 is true, Statement2 is true; Statement2 is not a correct explanation for statement1
Statement1 is true, Statement2 is false.
Statement1 is false, Statement2 is true.

The correct answer is: Statement1 is true, Statement2 is false.

Let A be a $2 cross times 2$ matrix with non‐zero entries and let $A to the power of 2 end exponent equals I$ , where I is $2 cross times 2$ identity matrix Defi ne Tr(A) $equals s u m$ of diagonal elements $o f A$ and $vertical line A vertical line equals$ determinant of matrix A
From the given statements
Statement 1: Tr(A) $equals 0.$
Statement 2: $vertical line A vertical line equals 1.$
It is clearly observed that Statement 1 is true and Statement 2 is false

Hence option C is suitable option

Related Questions to study

If A $equals left square bracket subscript 1 end subscript superscript 1 end superscript$ $01 right square bracket$ and I $equals left square bracket subscript 0 end subscript superscript 1 end superscript$ $01 right square bracket$ , then which one of the following holds for all $n greater or equal than 1$ , (by the principal of mathematical induction)

If A $equals left square bracket subscript 1 end subscript superscript 1 end superscript$ $01 right square bracket$ and I $equals left square bracket subscript 0 end subscript superscript 1 end superscript$ $01 right square bracket$ , then which one of the following holds for all $n greater or equal than 1$ , (by the principal of mathematical induction)

The equation $open curly brackets table attributes columnalign left end attributes row 1 2 2 row 1 3 4 row 3 4 k end table close curly brackets open curly brackets table attributes columnalign left end attributes row x row y row z end table close curly brackets equals open curly brackets table attributes columnalign left end attributes row 0 row 0 row 0 end table close curly brackets$ has a solution for (x, y, z) besides (0,0,0) The value of k equals

The equation $open curly brackets table attributes columnalign left end attributes row 1 2 2 row 1 3 4 row 3 4 k end table close curly brackets open curly brackets table attributes columnalign left end attributes row x row y row z end table close curly brackets equals open curly brackets table attributes columnalign left end attributes row 0 row 0 row 0 end table close curly brackets$ has a solution for (x, y, z) besides (0,0,0) The value of k equals

If $F left parenthesis alpha right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell c o s alpha end cell cell negative s i n alpha end cell 0 row cell s i n alpha end cell cell c o s alpha end cell 0 row 0 0 1 end table close curly brackets a n d G left parenthesis beta right parenthesis equals open square brackets table row cell c o s invisible function application beta end cell 0 cell s i n invisible function application beta end cell row 0 1 0 row cell negative s i n invisible function application beta end cell 0 cell c o s invisible function application beta end cell end table close square brackets$ , then $left square bracket F left parenthesis alpha right parenthesis G left parenthesis beta right parenthesis right square bracket to the power of negative 1 end exponent equals$

If $F left parenthesis alpha right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell c o s alpha end cell cell negative s i n alpha end cell 0 row cell s i n alpha end cell cell c o s alpha end cell 0 row 0 0 1 end table close curly brackets a n d G left parenthesis beta right parenthesis equals open square brackets table row cell c o s invisible function application beta end cell 0 cell s i n invisible function application beta end cell row 0 1 0 row cell negative s i n invisible function application beta end cell 0 cell c o s invisible function application beta end cell end table close square brackets$ , then $left square bracket F left parenthesis alpha right parenthesis G left parenthesis beta right parenthesis right square bracket to the power of negative 1 end exponent equals$

parallel

Matrix A is such that $A to the power of 2 end exponent equals 2 A minus I$ , where I is the identity matrix The for $n greater or equal than 2 comma$ $A to the power of n end exponent equals$

Matrix A is such that $A to the power of 2 end exponent equals 2 A minus I$ , where I is the identity matrix The for $n greater or equal than 2 comma$ $A to the power of n end exponent equals$

Statement‐I:: If $f left parenthesis x right parenthesis$ is increasing function with concavity upwards, then concavity of $f to the power of negative 1 end exponent left parenthesis x right parenthesis$ is also upwards
Statement‐II:: If $f left parenthesis x right parenthesis$ is decreasing function with concavity upwards, then concavity of $f to the power of negative 1 end exponent left parenthesis x right parenthesis$ is also upwards.

Statement‐I:: If $f left parenthesis x right parenthesis$ is increasing function with concavity upwards, then concavity of $f to the power of negative 1 end exponent left parenthesis x right parenthesis$ is also upwards
Statement‐II:: If $f left parenthesis x right parenthesis$ is decreasing function with concavity upwards, then concavity of $f to the power of negative 1 end exponent left parenthesis x right parenthesis$ is also upwards.

Statement‐I:: $fraction numerator 2 e to the power of x subscript 1 end subscript end exponent plus e to the power of x subscript 2 end subscript end exponent over denominator 3 end fraction greater than e left parenthesis fraction numerator 2 x subscript 1 to the power of plus X end exponent 2 end subscript over denominator 3 end fraction right parenthesis$ , where $e$ is Napier $’$ sconstant.
Statement‐II:: If f $e subscript i left parenthesis x right parenthesis end subscript$ and $f C C left parenthesis x right parenthesis$ is positive $for all x element of R$ , then $f left parenthesis x right parenthesis$ increases with concavity up $for all x element of R$ and any chord lies above the curve.

Statement‐I:: $fraction numerator 2 e to the power of x subscript 1 end subscript end exponent plus e to the power of x subscript 2 end subscript end exponent over denominator 3 end fraction greater than e left parenthesis fraction numerator 2 x subscript 1 to the power of plus X end exponent 2 end subscript over denominator 3 end fraction right parenthesis$ , where $e$ is Napier $’$ sconstant.
Statement‐II:: If f $e subscript i left parenthesis x right parenthesis end subscript$ and $f C C left parenthesis x right parenthesis$ is positive $for all x element of R$ , then $f left parenthesis x right parenthesis$ increases with concavity up $for all x element of R$ and any chord lies above the curve.

parallel

The beds of two rivers (within a certain region) are a parabola $y equals x to the power of 2 end exponent$ and a straight line y=x-2 These rivers are to be connected by a straight canal The coordinates of the ends of the shortest canal can be:

The beds of two rivers (within a certain region) are a parabola $y equals x to the power of 2 end exponent$ and a straight line y=x-2 These rivers are to be connected by a straight canal The coordinates of the ends of the shortest canal can be:

If f(x) is twice differentiable function f((1)=1, f(2)=4, f(3)=9

If f(x) is twice differentiable function f((1)=1, f(2)=4, f(3)=9

If f(x) $equals x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d comma$ $0 less than b to the power of 2 end exponent less than c$ , then f(x)

If f(x) $equals x to the power of 3 end exponent plus b x to the power of 2 end exponent plus c x plus d comma$ $0 less than b to the power of 2 end exponent less than c$ , then f(x)

parallel

The set of value (s) of $a$ ’for which the function $f left parenthesis x right parenthesis equals fraction numerator a x to the power of 3 end exponent over denominator 3 end fraction plus left parenthesis a plus 2 right parenthesis x to the power of 2 end exponent plus left parenthesis a minus 1 right parenthesis x plus 2$ possess anegative point of inflection‐

The set of value (s) of $a$ ’for which the function $f left parenthesis x right parenthesis equals fraction numerator a x to the power of 3 end exponent over denominator 3 end fraction plus left parenthesis a plus 2 right parenthesis x to the power of 2 end exponent plus left parenthesis a minus 1 right parenthesis x plus 2$ possess anegative point of inflection‐

The greatest, the least values of the function, $f left parenthesis x right parenthesis equals 2 minus square root of 1 plus 2 x plus x to the power of 2 end exponent end root comma$ $x element of left square bracket 21 right square bracket$ are respectively

Hence the final answer is (2,0)

The greatest, the least values of the function, $f left parenthesis x right parenthesis equals 2 minus square root of 1 plus 2 x plus x to the power of 2 end exponent end root comma$ $x element of left square bracket 21 right square bracket$ are respectively

Hence the final answer is (2,0)

Suppose that $f$ is differentiable for allx and that $f to the power of ’ end exponent left parenthesis x right parenthesis less or equal than 2$ for all x If $f left parenthesis 1 right parenthesis equals 2$ and f(4)=8 then f(2) has the value equal to

Hence f(2)=4 is the suitable option

Suppose that $f$ is differentiable for allx and that $f to the power of ’ end exponent left parenthesis x right parenthesis less or equal than 2$ for all x If $f left parenthesis 1 right parenthesis equals 2$ and f(4)=8 then f(2) has the value equal to

Hence f(2)=4 is the suitable option

parallel

$f left parenthesis x right parenthesis equals not stretchy integral subscript blank superscript left parenthesis end superscript left parenthesis 2 minus fraction numerator 1 over denominator 1 plus x to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator square root of 1 plus x to the power of 2 end exponent end root end fraction right parenthesis right parenthesis$ dxthenfis‐

$f left parenthesis x right parenthesis equals not stretchy integral subscript blank superscript left parenthesis end superscript left parenthesis 2 minus fraction numerator 1 over denominator 1 plus x to the power of 2 end exponent end fraction minus fraction numerator 1 over denominator square root of 1 plus x to the power of 2 end exponent end root end fraction right parenthesis right parenthesis$ dxthenfis‐

The tangent to the curve $3 x y to the power of 2 end exponent minus 2 x to the power of 2 end exponent y equals 1$ at (1,1) meets the curve again at the point‐

The final answer is option B

The tangent to the curve $3 x y to the power of 2 end exponent minus 2 x to the power of 2 end exponent y equals 1$ at (1,1) meets the curve again at the point‐

The final answer is option B

If the number of images that are formed between two mirrors are 6, then the angle between them is:

If the number of images that are formed between two mirrors are 6, then the angle between them is:

physics-General

parallel

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