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Physics-

General

Easy

Question

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]

14.4×10^–19volt
7.2×10⁴volt
7.2×10⁸volt
14.4×10⁸volt

The correct answer is: 7.2×10⁴volt

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An electron which is initially at rest is accelerated through a potential difference of one volt. The energy acquired by the electron is

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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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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.

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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

parallel

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)

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

parallel

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

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.

parallel

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:

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

parallel

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