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Maths-

General

Easy

Question

$404 C subscript 4 end subscript minus C subscript 4 end subscript. C subscript 1 end subscript plus 2024 minus 1014 equals$

$(101)^{3}$
$(101)^{4}$
$(202)^{3}$
$(202)^{4}$

The correct answer is: $left parenthesis 101 right parenthesis to the power of 4 end exponent$

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If $2 to the power of 2006 end exponent minus 2006$ divided by 7, the remainder is

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The remainder when $2 3 to the power of 23 end exponent$ is divided by 53 is

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If $C subscript r end subscript equals 32 C subscript r end subscript$ , then $not stretchy sum subscript r equals 0 end subscript superscript 5 end superscript C subscript 6 r end subscript equals$

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$bullet$ If $C subscript r end subscript equals to the power of 30 end exponent C subscript r end subscript$ , then $C subscript 0 end subscript plus C subscript 4 end subscript plus C subscript 8 end subscript plus$ $plus C subscript 28 end subscript equals$

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A particle goes from point A to B. Its displacement is X and pathlength is y. So $x over y$

A particle goes from point A to B. Its displacement is X and pathlength is y. So $x over y$

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A particle moves from A to P and then it moves from P to B as shown in the figure. Find path length and displacement.

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physics-General

proportional to pi r to the power of 2 end exponent

If thickness (radius) of wire is doubled then breaking force will become four times

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The Young’s modulus of the material of a wire is $2 cross times 10 to the power of 10 end exponent N m to the power of negative 2 end exponent.$ If the elongation strain is $1 percent sign$ , then the energy stored in the wire per unit volume in $J m blank to the power of negative 3 end exponent$ is

Per unit volume energy stored

equals fraction numerator 1 over denominator 2 end fraction cross times Y cross times left parenthesis s t r a i n right parenthesis to the power of 2 end exponent equals fraction numerator 1 over denominator 2 end fraction cross times Y cross times open parentheses fraction numerator l over denominator L end fraction close parentheses to the power of 2 end exponent

l equals L cross times 1 percent sign

l equals fraction numerator L over denominator 100 end fraction cross times s t o r e d blank e n e r g y

Y equals fraction numerator 1 over denominator 2 end fraction cross times 2 cross times 10 to the power of 10 end exponent cross times open parentheses fraction numerator L over denominator 100 L end fraction close parentheses to the power of 2 end exponent equals 10 to the power of 6 end exponent J m to the power of negative 3 end exponent

The Young’s modulus of the material of a wire is $2 cross times 10 to the power of 10 end exponent N m to the power of negative 2 end exponent.$ If the elongation strain is $1 percent sign$ , then the energy stored in the wire per unit volume in $J m blank to the power of negative 3 end exponent$ is

physics-General

Per unit volume energy stored

equals fraction numerator 1 over denominator 2 end fraction cross times Y cross times left parenthesis s t r a i n right parenthesis to the power of 2 end exponent equals fraction numerator 1 over denominator 2 end fraction cross times Y cross times open parentheses fraction numerator l over denominator L end fraction close parentheses to the power of 2 end exponent

l equals L cross times 1 percent sign

l equals fraction numerator L over denominator 100 end fraction cross times s t o r e d blank e n e r g y

Y equals fraction numerator 1 over denominator 2 end fraction cross times 2 cross times 10 to the power of 10 end exponent cross times open parentheses fraction numerator L over denominator 100 L end fraction close parentheses to the power of 2 end exponent equals 10 to the power of 6 end exponent J m to the power of negative 3 end exponent

The following data were obtained when a wire was stretched within the elastic region Force applied to wire 100 N
Area of cross-section of wire $10 to the power of negative 6 end exponent m to the power of 2 end exponent$
Extensional of wire $2 cross times 10 to the power of negative 9 end exponent m$
Which of the following deductions can be correctly made from this data?
I. The value of Young’s Modulus is $10 to the power of 11 end exponent N blank m to the power of negative 2 end exponent$
II. The strain is $10 to the power of negative 3 end exponent$
III. The energy stored in the wire when the load is applied is 10 J

fraction numerator 100 N over denominator 10 to the power of negative 6 end exponent m to the power of 2 end exponent end fraction equals 10 to the power of 8 end exponent blank N m to the power of negative 2 end exponent

equals blank fraction numerator 2 cross times 10 to the power of negative 3 end exponent over denominator 2 end fraction equals 10 to the power of negative 3 end exponent

Young modulus
=

fraction numerator 10 to the power of 8 end exponent over denominator 10 to the power of negative 3 end exponent end fraction blank N m to the power of negative 2 end exponent equals 10 to the power of 11 end exponent blank N m to the power of negative 2 end exponent

Energy stored =

fraction numerator 1 over denominator 2 end fraction cross times 100 blank cross times 2 cross times 10 to the power of negative 3 end exponent blank J

minus

The following data were obtained when a wire was stretched within the elastic region Force applied to wire 100 N
Area of cross-section of wire $10 to the power of negative 6 end exponent m to the power of 2 end exponent$
Extensional of wire $2 cross times 10 to the power of negative 9 end exponent m$
Which of the following deductions can be correctly made from this data?
I. The value of Young’s Modulus is $10 to the power of 11 end exponent N blank m to the power of negative 2 end exponent$
II. The strain is $10 to the power of negative 3 end exponent$
III. The energy stored in the wire when the load is applied is 10 J

physics-General

fraction numerator 100 N over denominator 10 to the power of negative 6 end exponent m to the power of 2 end exponent end fraction equals 10 to the power of 8 end exponent blank N m to the power of negative 2 end exponent

equals blank fraction numerator 2 cross times 10 to the power of negative 3 end exponent over denominator 2 end fraction equals 10 to the power of negative 3 end exponent

Young modulus
=

fraction numerator 10 to the power of 8 end exponent over denominator 10 to the power of negative 3 end exponent end fraction blank N m to the power of negative 2 end exponent equals 10 to the power of 11 end exponent blank N m to the power of negative 2 end exponent

Energy stored =

fraction numerator 1 over denominator 2 end fraction cross times 100 blank cross times 2 cross times 10 to the power of negative 3 end exponent blank J

minus

Which of the following relations is true

Y equals 2 eta open parentheses 1 plus sigma close parentheses rightwards double arrow sigma equals fraction numerator 0.5 Y minus eta over denominator eta end fraction

Which of the following relations is true

physics-General

Y equals 2 eta open parentheses 1 plus sigma close parentheses rightwards double arrow sigma equals fraction numerator 0.5 Y minus eta over denominator eta end fraction

parallel

A particle moves from A to B and then it moves from to as shown in figure. Calculate the ratio between path length and displacement.

A particle moves from A to B and then it moves from to as shown in figure. Calculate the ratio between path length and displacement.

If $A equals open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell 1 0 1 end cell row cell 2 1 0 end cell row cell 3 2 1 end cell end table close square brackets$ then det A=

A equals open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell 1      0      1 end cell row cell 2      1      0 end cell row cell 3      2      1 end cell end table close square brackets

open vertical bar table row 1 0 1 row 2 1 0 row 3 2 1 end table close vertical bar equals open square brackets 1 left parenthesis 1 cross times 1 minus 2 cross times 0 right parenthesis close square brackets minus open square brackets 0 left parenthesis 2 cross times 1 minus 3 cross times 0 right parenthesis close square brackets plus open square brackets 1 left parenthesis 2 cross times 2 minus 3 cross times 1 right parenthesis close square brackets space space space space space space space space space space space space space space space equals open square brackets 1 cross times 1 close square brackets minus 0 plus open square brackets 1 cross times 1 close square brackets space space space space space space space space space space space space space space space equals 1 minus 0 plus 1 equals 2

If $A equals open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell 1 0 1 end cell row cell 2 1 0 end cell row cell 3 2 1 end cell end table close square brackets$ then det A=

A equals open square brackets table attributes columnalign left left left columnspacing 1em end attributes row cell 1      0      1 end cell row cell 2      1      0 end cell row cell 3      2      1 end cell end table close square brackets

open vertical bar table row 1 0 1 row 2 1 0 row 3 2 1 end table close vertical bar equals open square brackets 1 left parenthesis 1 cross times 1 minus 2 cross times 0 right parenthesis close square brackets minus open square brackets 0 left parenthesis 2 cross times 1 minus 3 cross times 0 right parenthesis close square brackets plus open square brackets 1 left parenthesis 2 cross times 2 minus 3 cross times 1 right parenthesis close square brackets space space space space space space space space space space space space space space space equals open square brackets 1 cross times 1 close square brackets minus 0 plus open square brackets 1 cross times 1 close square brackets space space space space space space space space space space space space space space space equals 1 minus 0 plus 1 equals 2

$open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row 1 w cell w squared end cell row w cell w squared end cell 1 row cell w squared end cell 1 w end table close vertical bar equals$

space space space space open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row 1 w cell w squared end cell row w cell w squared end cell 1 row cell w squared end cell 1 w end table close vertical bar equals open vertical bar table row cell 1 plus w plus w squared end cell w cell w squared end cell row cell 1 plus w plus w squared end cell cell w squared end cell 1 row cell 1 plus w plus w squared end cell 1 w end table close vertical bar space space space space space space space open square brackets C subscript 1 rightwards arrow C subscript 1 plus C subscript 2 plus C subscript 3 close square brackets equals open parentheses 1 plus w plus w squared close parentheses open vertical bar table row 1 w cell w squared end cell row 1 cell w squared end cell 1 row 1 1 w end table close vertical bar space space space space space space space space equals open parentheses 1 plus w plus w squared close parentheses cross times 0 space space space space space space space space space space space space space open square brackets C o l l i n e a r i t y close square brackets equals 0

$open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row 1 w cell w squared end cell row w cell w squared end cell 1 row cell w squared end cell 1 w end table close vertical bar equals$

space space space space open vertical bar table attributes columnalign center center center columnspacing 1em end attributes row 1 w cell w squared end cell row w cell w squared end cell 1 row cell w squared end cell 1 w end table close vertical bar equals open vertical bar table row cell 1 plus w plus w squared end cell w cell w squared end cell row cell 1 plus w plus w squared end cell cell w squared end cell 1 row cell 1 plus w plus w squared end cell 1 w end table close vertical bar space space space space space space space open square brackets C subscript 1 rightwards arrow C subscript 1 plus C subscript 2 plus C subscript 3 close square brackets equals open parentheses 1 plus w plus w squared close parentheses open vertical bar table row 1 w cell w squared end cell row 1 cell w squared end cell 1 row 1 1 w end table close vertical bar space space space space space space space space equals open parentheses 1 plus w plus w squared close parentheses cross times 0 space space space space space space space space space space space space space open square brackets C o l l i n e a r i t y close square brackets equals 0

parallel

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