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Physics-

General

Easy

Question

Three point charges are placed at the corners of an equilateral triangle. Assuming only electrostatic forces are acting.

the system can never be in equilibrium
the system will be in equilibrium if the charges rotate about the centre of the triangle
the system will be in equilibrium if the charges have different magnitudes and different signs
the system will be in equilibrium if the charges have the same magnitude but different signs.

The correct answer is: the system can never be in equilibrium

Related Questions to study

Let $omega$ $not equal to 1$ be a cube root of unity and $S$ be the set of all non‐singular matrices of the form $open square brackets table row 1 a b row omega 1 c row cell omega to the power of 2 end exponent end cell omega 1 end table close square brackets$ , where each of a, b and $c$ is either $omega text or end text omega to the power of 2 end exponent$ Then the number of distinct matrices in the set $S$ is‐

Hence no of matrices formed = 2

Let $omega$ $not equal to 1$ be a cube root of unity and $S$ be the set of all non‐singular matrices of the form $open square brackets table row 1 a b row omega 1 c row cell omega to the power of 2 end exponent end cell omega 1 end table close square brackets$ , where each of a, b and $c$ is either $omega text or end text omega to the power of 2 end exponent$ Then the number of distinct matrices in the set $S$ is‐

Hence no of matrices formed = 2

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: $vertical line A vertical line equals 1.$

Hence option C is suitable option

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: $vertical line A vertical line equals 1.$

Hence option C is suitable option

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)

parallel

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 $left square bracket F left parenthesis alpha right parenthesis G left parenthesis beta right parenthesis right square bracket to the power of negative 1 end exponent equals$

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 $n greater or equal than 2 comma$ $A to the power of n end exponent equals$

parallel

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.

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:

parallel

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)

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‐

parallel

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

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

parallel

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