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Question

If ABCDEF is a regular hexagon and if $stack A B with bar on top plus stack A C with rightwards arrow on top plus stack A D with rightwards arrow on top plus stack A E with rightwards arrow on top plus stack A F with rightwards arrow on top equals lambda stack A D with bar on top comma text end text$ then $text end text lambda text is - end text$

0
1
2
3

The correct answer is: 3

Related Questions to study

If $text end text stack a with rightwards arrow on top plus stack b with rightwards arrow on top text end text$ is along the angle bisector of $stack a with rightwards arrow on top & stack b with rightwards arrow on top text end text$ then -

If $text end text stack a with rightwards arrow on top plus stack b with rightwards arrow on top text end text$ is along the angle bisector of $stack a with rightwards arrow on top & stack b with rightwards arrow on top text end text$ then -

If the solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator 1 over denominator x c o s invisible function application y plus s i n invisible function application 2 y end fraction text end text text is end text text end text x equals c o s i n invisible function application y minus k left parenthesis 1 plus s i n invisible function application y right parenthesis comma text then end text k equals$

If the solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator 1 over denominator x c o s invisible function application y plus s i n invisible function application 2 y end fraction text end text text is end text text end text x equals c o s i n invisible function application y minus k left parenthesis 1 plus s i n invisible function application y right parenthesis comma text then end text k equals$

A curve passes through the point $open parentheses 1 comma fraction numerator pi over denominator 6 end fraction close parentheses$ Let the slope of the curve at each point (x, y) be $fraction numerator y over denominator x end fraction plus s e c invisible function application open parentheses fraction numerator y over denominator x end fraction close parentheses comma x greater than 0$ Then the equation of the curve is

A curve passes through the point $open parentheses 1 comma fraction numerator pi over denominator 6 end fraction close parentheses$ Let the slope of the curve at each point (x, y) be $fraction numerator y over denominator x end fraction plus s e c invisible function application open parentheses fraction numerator y over denominator x end fraction close parentheses comma x greater than 0$ Then the equation of the curve is

parallel

The solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x plus y over denominator x end fraction$ $fraction numerator d y over denominator d x end fraction equals fraction numerator x plus y over denominator x end fraction$

The solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x plus y over denominator x end fraction$ $fraction numerator d y over denominator d x end fraction equals fraction numerator x plus y over denominator x end fraction$

Statement-I : Integral curves denoted by the first order linear differential equation $fraction numerator d y over denominator d x end fraction minus fraction numerator 1 over denominator x end fraction y equals negative x blank$ are family of parabolas passing through the origin.
Statement-II : Every differential equation geometrically represents a family of curve having some common property.

Statement-I : Integral curves denoted by the first order linear differential equation $fraction numerator d y over denominator d x end fraction minus fraction numerator 1 over denominator x end fraction y equals negative x blank$ are family of parabolas passing through the origin.
Statement-II : Every differential equation geometrically represents a family of curve having some common property.

A function f(x) satisfying $stretchy integral subscript 0 end subscript superscript 1 end superscript f left parenthesis t x right parenthesis d t equals n f left parenthesis x right parenthesis comma text end text$ where x>0 , is

A function f(x) satisfying $stretchy integral subscript 0 end subscript superscript 1 end superscript f left parenthesis t x right parenthesis d t equals n f left parenthesis x right parenthesis comma text end text$ where x>0 , is

parallel

$text If end text y equals fraction numerator x over denominator l n invisible function application vertical line c x vertical line end fraction$ (where c is an arbitrary constant) is the general solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y over denominator x end fraction plus$ $phi open parentheses fraction numerator x over denominator y end fraction close parentheses text end text$ then the function $text end text phi open parentheses fraction numerator x over denominator y end fraction close parentheses text is : end text$

$text If end text y equals fraction numerator x over denominator l n invisible function application vertical line c x vertical line end fraction$ (where c is an arbitrary constant) is the general solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y over denominator x end fraction plus$ $phi open parentheses fraction numerator x over denominator y end fraction close parentheses text end text$ then the function $text end text phi open parentheses fraction numerator x over denominator y end fraction close parentheses text is : end text$

A function y = f (x) satisfies the condition f '(x) sin x + f (x) cos x = 1, f (x) being bounded when x $rightwards arrow$ 0. If $I equals stretchy integral subscript 0 end subscript superscript there exists 2 end superscript f left parenthesis x right parenthesis d x text then end text$

A function y = f (x) satisfies the condition f '(x) sin x + f (x) cos x = 1, f (x) being bounded when x $rightwards arrow$ 0. If $I equals stretchy integral subscript 0 end subscript superscript there exists 2 end superscript f left parenthesis x right parenthesis d x text then end text$

Statement-I : In throwing of two dice, let the events A, B and C be 'the first dice shows an even number', 'the second dice shows an odd numbers' and 'both the dice show an odd numbers or both the dice show an even number’ respectively. Then $text end text P left parenthesis A right parenthesis equals P left parenthesis B right parenthesis equals P left parenthesis C right parenthesis equals fraction numerator 1 over denominator 2 end fraction text end text$ and $P left parenthesis A intersection B right parenthesis equals P left parenthesis B intersection C right parenthesis equals P left parenthesis C intersection A right parenthesis equals fraction numerator 1 over denominator 4 end fraction$ Therefore A, B and C are mutually independent events
Statement-II : Three events A, B and C are mutually independent if and only if P(A Ç B) = P(A) . P(B), P(B Ç C) = P(B) . P(C), $P left parenthesis C intersection A right parenthesis equals P left parenthesis C right parenthesis$ = P(C) . P(A) and $P left parenthesis A intersection B intersection C right parenthesis$ = P(A) . P(B) . P(C)

Statement-I : In throwing of two dice, let the events A, B and C be 'the first dice shows an even number', 'the second dice shows an odd numbers' and 'both the dice show an odd numbers or both the dice show an even number’ respectively. Then $text end text P left parenthesis A right parenthesis equals P left parenthesis B right parenthesis equals P left parenthesis C right parenthesis equals fraction numerator 1 over denominator 2 end fraction text end text$ and $P left parenthesis A intersection B right parenthesis equals P left parenthesis B intersection C right parenthesis equals P left parenthesis C intersection A right parenthesis equals fraction numerator 1 over denominator 4 end fraction$ Therefore A, B and C are mutually independent events
Statement-II : Three events A, B and C are mutually independent if and only if P(A Ç B) = P(A) . P(B), P(B Ç C) = P(B) . P(C), $P left parenthesis C intersection A right parenthesis equals P left parenthesis C right parenthesis$ = P(C) . P(A) and $P left parenthesis A intersection B intersection C right parenthesis$ = P(A) . P(B) . P(C)

parallel

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

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

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-

parallel

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-

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

parallel

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