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Physics-

General

Easy

Question

Two identical conductors of copper and aluminium are placed in an identical electric fields. The magnitude of induced charge in the aluminium will be

Zero
Greater than in copper
Equal to that in copper
Less than in copper

The correct answer is: Equal to that in copper

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Four charges are arranged at the corners of a square ABCD. as shown in the adjoining figure. The force on the charge kept at the centre O is

Four charges are arranged at the corners of a square ABCD. as shown in the adjoining figure. The force on the charge kept at the centre O is

physics-General

There is an electric field E in X-direction. If the work done on moving a charge 0.2 C through a distance of 2 m along a line making an angle 60° with the X-axis is 4.0, what is the value of E.

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As shown in the fig. charges +q and –q are placed at the vertices B and C of an isosceles triangle. The potential at the vertex A is

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A tin nucleus has charge +50e. If the proton is at a distance 10^–12m from the nucleus, then the potential V at this position is [charge on the proton = 1.6×10^–19C]

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A charge q is placed at the centre of the open end of a cylindrical vessel. The flux of the electric field through the surface of the vessel is

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Fig. shows a distribution of charges. The flux of electric field due to these charges through the surface S is

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As per fig. a point charge +q is placed at the origin O. Work done in taking another point charge –Q from the point A [Co-ordinates (0,a)] to another point B [Co-ordinates (a, 0)] along the straight path AB is :

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

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

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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

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