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Maths-

General

Easy

Question

The probability that 4th power of a positive integer ends in the digit 6 is:

10 %
20 %
25 %
40 %

The correct answer is: 40 %

Related Questions to study

Let A, B, C be pairwise independent events with P(C)> 0 and $P left parenthesis A intersection B intersection C right parenthesis equals 0$ . Then $P open parentheses A to the power of c end exponent intersection B to the power of c end exponent C close parentheses text is equal to: end text$

Let A, B, C be pairwise independent events with P(C)> 0 and $P left parenthesis A intersection B intersection C right parenthesis equals 0$ . Then $P open parentheses A to the power of c end exponent intersection B to the power of c end exponent C close parentheses text is equal to: end text$

Let A and B be two events such that $P left parenthesis stack A union B with bar on top right parenthesis equals fraction numerator 1 over denominator 6 end fraction comma P left parenthesis A intersection B right parenthesis equals fraction numerator 1 over denominator 4 end fraction$ and $P left parenthesis stack A with bar on top right parenthesis equals fraction numerator 1 over denominator 4 end fraction comma text where end text stack A with bar on top$ stands for complement of event A. Then events A and B are-

Let A and B be two events such that $P left parenthesis stack A union B with bar on top right parenthesis equals fraction numerator 1 over denominator 6 end fraction comma P left parenthesis A intersection B right parenthesis equals fraction numerator 1 over denominator 4 end fraction$ and $P left parenthesis stack A with bar on top right parenthesis equals fraction numerator 1 over denominator 4 end fraction comma text where end text stack A with bar on top$ stands for complement of event A. Then events A and B are-

A random variable X has the probability distribution :

For the events E = {X is a prime number} and F = {X < 4}, the probability $P left parenthesis E union F right parenthesis$ is-

A random variable X has the probability distribution :

For the events E = {X is a prime number} and F = {X < 4}, the probability $P left parenthesis E union F right parenthesis$ is-

parallel

A fair coin is tossed 3 times. Consider the events A : first toss is head ; B : second toss is head C : exactly two consecutive heads or exactly two consecutive tails
Statement - I A,B,C are independent events.
Statement - II A,B,C are pairwise independent.

A fair coin is tossed 3 times. Consider the events A : first toss is head ; B : second toss is head C : exactly two consecutive heads or exactly two consecutive tails
Statement - I A,B,C are independent events.
Statement - II A,B,C are pairwise independent.

An experiment resulting in sample space as S = {a, b, c, d, e, f} $text with end text P left parenthesis A right parenthesis equals fraction numerator 1 over denominator 16 end fraction comma P left parenthesis B right parenthesis equals fraction numerator 1 over denominator 16 end fraction comma P left parenthesis C right parenthesis equals fraction numerator 2 over denominator 16 end fraction comma P left parenthesis D right parenthesis equals fraction numerator 3 over denominator 16 end fraction comma P left parenthesis e right parenthesis equals fraction numerator 4 over denominator 16 end fraction text and end text P left parenthesis f right parenthesis equals fraction numerator 5 over denominator 16 end fraction text . end text$ Let three events A, B and C are defined as A = {a, c, e,}, B = {c, d, e, f} and C = {b, c, f}. $text If end text P left parenthesis A divided by B right parenthesis equals p subscript 1 end subscript comma P left parenthesis B divided by C right parenthesis equals p subscript 2 end subscript comma P open parentheses C divided by A to the power of c end exponent close parentheses equals p subscript 3 end subscript text and end text P open parentheses A to the power of c end exponent divided by C close parentheses equals p subscript 4 end subscript$ then the correct order sequance is

An experiment resulting in sample space as S = {a, b, c, d, e, f} $text with end text P left parenthesis A right parenthesis equals fraction numerator 1 over denominator 16 end fraction comma P left parenthesis B right parenthesis equals fraction numerator 1 over denominator 16 end fraction comma P left parenthesis C right parenthesis equals fraction numerator 2 over denominator 16 end fraction comma P left parenthesis D right parenthesis equals fraction numerator 3 over denominator 16 end fraction comma P left parenthesis e right parenthesis equals fraction numerator 4 over denominator 16 end fraction text and end text P left parenthesis f right parenthesis equals fraction numerator 5 over denominator 16 end fraction text . end text$ Let three events A, B and C are defined as A = {a, c, e,}, B = {c, d, e, f} and C = {b, c, f}. $text If end text P left parenthesis A divided by B right parenthesis equals p subscript 1 end subscript comma P left parenthesis B divided by C right parenthesis equals p subscript 2 end subscript comma P open parentheses C divided by A to the power of c end exponent close parentheses equals p subscript 3 end subscript text and end text P open parentheses A to the power of c end exponent divided by C close parentheses equals p subscript 4 end subscript$ then the correct order sequance is

An ellipse is drawn with major and minor axes of lengths 10 and 8 respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radius of the circle is

An ellipse is drawn with major and minor axes of lengths 10 and 8 respectively. Using one focus as centre, a circle is drawn that is tangent to the ellipse, with no part of the circle being outside the ellipse. The radius of the circle is

parallel

From a point P, perpendicular tangents PQ and PR are drawn to ellipse $x to the power of 2 end exponent plus 4 y to the power of 2 end exponent equals 4$ Locus of circumcentre of triangle PQR is

From a point P, perpendicular tangents PQ and PR are drawn to ellipse $x to the power of 2 end exponent plus 4 y to the power of 2 end exponent equals 4$ Locus of circumcentre of triangle PQR is

The least integral value that contained is the range of the function f defined by $f left parenthesis x right parenthesis equals fraction numerator x to the power of 2 end exponent plus 1 over denominator log invisible function application open parentheses x to the power of 2 end exponent plus 1 close parentheses end fraction$ is ___

The least integral value that contained is the range of the function f defined by $f left parenthesis x right parenthesis equals fraction numerator x to the power of 2 end exponent plus 1 over denominator log invisible function application open parentheses x to the power of 2 end exponent plus 1 close parentheses end fraction$ is ___

Let $f left parenthesis x right parenthesis equals L t stretchy sum from n rightwards arrow infinity to n minus 1 of fraction numerator x over denominator left parenthesis r x plus 1 right parenthesis left curly bracket left parenthesis r plus 1 right parenthesis x plus 1 right curly bracket end fraction comma$ then

Let $f left parenthesis x right parenthesis equals L t stretchy sum from n rightwards arrow infinity to n minus 1 of fraction numerator x over denominator left parenthesis r x plus 1 right parenthesis left curly bracket left parenthesis r plus 1 right parenthesis x plus 1 right curly bracket end fraction comma$ then

parallel

If m is the slope of tangent to the curve $e to the power of y end exponent equals 1 plus x to the power of 2 end exponent$ then

If m is the slope of tangent to the curve $e to the power of y end exponent equals 1 plus x to the power of 2 end exponent$ then

If $stack l i m with x rightwards arrow 0 below 1 plus x to the power of 2 end exponent plus fraction numerator f open parentheses x close parentheses over denominator x end fraction$ is equal to e⁷, then $stack l i m with x greater-than or slanted equal to 0 below fraction numerator f open parentheses x close parentheses over denominator x to the power of 3 end exponent end fraction equals horizontal ellipsis horizontal ellipsis$

If $stack l i m with x rightwards arrow 0 below 1 plus x to the power of 2 end exponent plus fraction numerator f open parentheses x close parentheses over denominator x end fraction$ is equal to e⁷, then $stack l i m with x greater-than or slanted equal to 0 below fraction numerator f open parentheses x close parentheses over denominator x to the power of 3 end exponent end fraction equals horizontal ellipsis horizontal ellipsis$

Set of all values of x such that $L t subscript x rightwards arrow infinity end subscript invisible function application fraction numerator 1 over denominator 1 plus open parentheses fraction numerator 4 t a n to the power of negative 1 end exponent invisible function application left parenthesis 2 pi x right parenthesis over denominator pi end fraction close parentheses to the power of 4 n end exponent end fraction$ is non-zero and finite number when n N $element of$ is

Set of all values of x such that $L t subscript x rightwards arrow infinity end subscript invisible function application fraction numerator 1 over denominator 1 plus open parentheses fraction numerator 4 t a n to the power of negative 1 end exponent invisible function application left parenthesis 2 pi x right parenthesis over denominator pi end fraction close parentheses to the power of 4 n end exponent end fraction$ is non-zero and finite number when n N $element of$ is

parallel

The period of the function $f left parenthesis x right parenthesis equals c o s e c to the power of 2 end exponent invisible function application 3 x plus c o t invisible function application 4 x$ is

The period of the function $f left parenthesis x right parenthesis equals c o s e c to the power of 2 end exponent invisible function application 3 x plus c o t invisible function application 4 x$ is

Let $g left parenthesis x right parenthesis equals left square bracket n plus p s i n invisible function application x right square bracket comma x element of left parenthesis 0 comma pi right parenthesis comma n element of Z comma p$ is a prime number and [x] = the greatest integer $less or equal than x$ The number of points at which f(x) is not differentiable is _______

Let $g left parenthesis x right parenthesis equals left square bracket n plus p s i n invisible function application x right square bracket comma x element of left parenthesis 0 comma pi right parenthesis comma n element of Z comma p$ is a prime number and [x] = the greatest integer $less or equal than x$ The number of points at which f(x) is not differentiable is _______

If the line $fraction numerator x minus 2 over denominator negative 1 end fraction equals fraction numerator y plus 2 over denominator 1 end fraction equals fraction numerator z plus k over denominator 4 end fraction$ is one of the angle bisectors of the lines $fraction numerator x over denominator 1 end fraction equals fraction numerator y over denominator negative 2 end fraction equals fraction numerator z over denominator 3 end fraction$ and $fraction numerator x over denominator negative 2 end fraction equals fraction numerator y over denominator 3 end fraction equals fraction numerator z over denominator 1 end fraction$ then the value of k is

If the line $fraction numerator x minus 2 over denominator negative 1 end fraction equals fraction numerator y plus 2 over denominator 1 end fraction equals fraction numerator z plus k over denominator 4 end fraction$ is one of the angle bisectors of the lines $fraction numerator x over denominator 1 end fraction equals fraction numerator y over denominator negative 2 end fraction equals fraction numerator z over denominator 3 end fraction$ and $fraction numerator x over denominator negative 2 end fraction equals fraction numerator y over denominator 3 end fraction equals fraction numerator z over denominator 1 end fraction$ then the value of k is

parallel

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