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Answers posted by rvidyagovindarajan_1

917
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dipanjanaalleaecolee
answered Jul 30, 2016
If ax^3+bx^2+cx^+d=0  is any equation  &  if Alpha, Beta,gama are roots of this c...
0 votes
Evaluate $\int\Large(\Large\frac{\sin^2x}{\cos^{\Large 14}x})^{\Large\frac{1}{3}} dx$
answered Aug 25, 2015
Toolbox:$sec^2x=1+tan^2x$Derivative of $tanx=sec^2x$$\int\Large(\Large\frac{\sin^2x}{\cos^{\Large 14...
0 votes
Find the particular solution of the differential equation $ log \bigg( \large\frac{dy}{dx} \bigg) =3x+4y,$ given that $ y=0$ when $x=0$
answered May 17, 2015
dy/dx=e^(3x+4y) Let 3x+4y=z ⇒3+4 dy/dx=dz/dx ⇒dy/dx=(dz/dx-3)/4 Substituting the value of dy/dx
0 votes
Write the statement "It is necessary to have a password to log on to the server." in the form if $p$ then $q$.
answered Aug 16, 2014
The given statement is "It is necessary to have a password to log on to the server." Here $p$ is Y...
0 votes
Write the converse and contra positive of the statement "If it is hot outside then you feel thirsty."
answered Aug 16, 2014
Toolbox:Converse of the statement "If $p$ then $q$." is "If $q$ then $p$." Contra positive o...
0 votes
Write the converse and contra positive of the statement "I go to the beach whenever it is sunny day."
answered Aug 16, 2014
Toolbox:Converse of the statement "If $p$ then $q$." is "If $q$ then $p$." Contra positive o...
0 votes
Write the converse and contra positive of the statement "A positive integer is prime only if it has no divisors other than 1 and itself."
answered Aug 14, 2014
Toolbox:Converse of the statement "If $p$ then $q$." is "If $q$ then $p$." Contra positive o...
0 votes
Write the negation of the statement " There exists a number $x$ such that 0<$x$<1."
answered Aug 4, 2014
The given statement is"There exists a number $x$ such that 0<$x$<1."The negation of this stat...
0 votes
Write the negation of the statement " For every real number $x$, either $x$ is >1 or <1."
answered Aug 4, 2014
The given statement is " For every real number $x$, either $x$ is >1 or <1."The negation ...
0 votes
Write the negation of "All cats scratch."
answered Aug 4, 2014
The given statement is"All cats scratch."The negation of this statement is There exist a cat which d...
0 votes
Write the negation of "For every positive real number $x$, the number $x+1$ is also positive."
answered Aug 4, 2014
The given statement is"For every positive real number $x$, the number $x+1$ is also positive."The n...
0 votes
State whether the statement "$\sqrt {11}$ is a rational number." is true or false. Give reason.
answered Jul 29, 2014
The given statement is :"$\sqrt {11}$ is a rational number." This statement is false.Because $11$ ...
0 votes
State whether the statement "If $x,\:y$ are integers such that $x>y$, then $-x<-y$" is true or false. Give reason.
answered Jul 29, 2014
The given statement is"If $x,\:y$ are integers such that $x>y$, then $-x<-y$" This stat...
0 votes
State whether the statement "Circle is a particular case of an ellipse." is true or false. Give reason.
answered Jul 29, 2014
The given statement is "Circle is a particular case of an ellipse." This statement is true. Because...
0 votes
State whether the statement "The centre of a circle bisects each chord of the circle." is true or false. Give reason.
answered Jul 29, 2014
The given statement is "The centre of a circle bisects each chord of the circle."This statement is f...
0 votes
State whether the statement "Each radius of a circle is a chord of the circle." is true or false. Give reason.
answered Jul 29, 2014
The given statement is"Each radius of a circle is a chord of the circle."This statement is false. B...
0 votes
By giving counter example show that the statement "The equation $x^2-1=0$ does not have a root lying between $0$ and $2$." is false.
answered Jul 29, 2014
The given statement is The equation $x^2-1=0$ does not have a root lying between $0$ and $2$." L...
0 votes
By giving counter example show that the statement "If all the angles of a triangle are equal then the triangle is an obtuse angled triangle" is not true.
answered Jul 29, 2014
The given statement is "If all the angles of a triangle are equal then the triangle is an obtuse ang...
0 votes
Show that the statement "If $x$ is an integer and $x^2$ is even, then $x$ is also even." using contrapositive method.
answered Jul 26, 2014
Toolbox:To prove a statement "if $p$ then $q$" using contrapositive method we have to prove ...
0 votes
Show that the statement "For any real numbers $a$ and $b$, $a^2=b^2$ implies that $a=b$" is not true by giving counter example.
answered Jul 26, 2014
The given statement is"For any real numbers $a$ and $b$, $a^2=b^2$ implies that $a=b$" To show...
0 votes
Show that the statement " If $x$ is real number such that $x^3+4x=0$, then $x$ is 0." is true using contra positive method.
answered Jul 26, 2014
Toolbox:Contrapositive method of proving a statement "if $p$ then $q$ is prove if ~$q$ then ...
0 votes
Show that the statement " If $x$ is real number such that $x^3+4x=0$, then $x$ is 0." is true using contradiction method.
answered Jul 26, 2014
The given statement is " If $x$ is real number such that $x^3+4x=0$, then $x$ is 0." Let $p...
0 votes
Show that the statement " If $x$ is real number such that $x^3+4x=0$, then $x$ is 0." is true using direct method.
answered Jul 26, 2014
The given statement is " If $x$ is real number such that $x^3+4x=0$, then $x$ is 0." Let $p...
0 votes
For the statement "If a quadrilateral is a parallelogram then its diagonals bisect each other"' is the statement "If the diagonals of a quadrilateral bisecyt then it is a parallelogram" contra positive or converse?
answered Jul 22, 2014
Toolbox:The contra positive of ' If $p$ then $q$ is If ~$q$ then ~$p$ The converse of ' If $p$ t...
0 votes
For the statement "If a quadrilateral is a parallelogram then its diagonals bisect each other"' is the statement "If the diagonals of a quadrilateral do not bisect then it is not a parallelogram" contra positive or converse?
answered Jul 22, 2014
Toolbox:The contra positive of ' If $p$ then $q$ is If ~$q$ then ~$p$ The converse of ' If $p$ t...
0 votes
For the statement "If you live in Delhi then you have winter clothes.' is the statement "If you have winter clothes then you live in Delhi" contra positive or converse?
answered Jul 22, 2014
Toolbox:The contra positive of ' If $p$ then $q$ is If ~$q$ then ~$p$ The converse of ' If $p$ t...
0 votes
For the statement "If you live in Delhi then you have winter clothes.' is the statement "If you do not have winter clothes then you do not live in Delhi" contra positive or converse?
answered Jul 22, 2014
Toolbox:The contra positive of ' If $p$ then $q$ is If ~$q$ then ~$p$ The converse of ' If $p$ t...
0 votes
Write the statement "To get 'A' in the class it is necessary that you do all the exercises of the book." in 'if-then' form.
answered Jul 22, 2014
The given statement is:To get 'A' in the class it is necessary that you do all the exercises of the...
0 votes
Write the statement "A quadrilateral is a parallelogram if its diagonals bisect each other" in 'if-then' form.
answered Jul 22, 2014
The given statement is:A quadrilateral is a parallelogram if its diagonals bisect each other.This st...
0 votes
Write the statement " The banana tree will bloom if it stays warm for a month.' in 'if-then' form
answered Jul 22, 2014
The given statement is:The banana tree will bloom if it stays warm for a month.This statement can be...
0 votes
Write the statement "You get a job implies that your credentials are good" in 'if-than' form.
answered Jul 22, 2014
The given statement is:You get a job implies that your credentials are good.This statement can be wr...
0 votes
Write the converse and contra positive statements of the statement "$x$ is an even number implies that $x$ is divisible by $4$.
answered Jul 21, 2014
Toolbox:Converse of if $p$ then $q$ is If $q$ then $p$.Contra positive of If $p$ then $q$ i...
0 votes
Write the converse and contra positive statements of the statement "You cannot comprehend geometry if you do not know how to reason deductively."
answered Jul 21, 2014
Toolbox:The converse of If $p$ then $q$ is If $q$ then $p$The contra positive of If $p$ th...
0 votes
Write the converse and contra positive statements of the statement "Something cold implies that it has low temperature."
answered Jul 21, 2014
Toolbox:The converse of If $p$ then $q$ is If $q$ then $p$.The contra positive of If $...
0 votes
Write the converse and contra positive statement of the statement " If the two lines are parallel then they do not intersect in the same plane."
answered Jul 21, 2014
Toolbox:The converse of If $p$ then $q$ is If $q$ then $p$.The contra positive of If $p...
0 votes
Write the contrapositive and converse of the statement: "If $x$ is prime then $x$ is odd."
answered Jul 21, 2014
Toolbox:Converse of: If $p$ then $q$ is If $q$ then $p.$Contra positive of If $p$ then $q$ is...
0 votes
Rewrite the the statement " $If\: a\:natural\:number\:is\:odd,\: then\:its\:square\:is\:also\:odd."$ in five different ways conveying the same meaning.
answered Jul 21, 2014
The given statement is$"If\: a\:natural\:number\:is\:odd,\: then\:its\:square\:is\:also\:odd."$Five...
0 votes
State whether 'or' used in the statement " All integers are positive or negative" is inclusive or or exclusive or. Give reason.
answered Jul 16, 2014
Toolbox:'or' is exclusive in the statement if only one of the the components occur at a time to m...
0 votes
State whether the 'or' in the statement "To apply for a driving licence, you should have a ration card or a passport." is inclusive or or exclusive or. Give reason.
answered Jul 16, 2014
Toolbox:'or' is inclusive in the statement if both the components can occur simultaneously to make...
0 votes
State whether 'or' used in the statement given "Sun rises or Moon sets" is exclusive or inclusive.
answered Jul 16, 2014
Toolbox:'or' is inclusive in the statement if both the components can occur simultaneously to make...
0 votes
Check whether the two statements given are negation of each other or not. Give reason " $p: x+y=y+x$ is true for every real number $x\:\:and\:\:y$. $q:$ There exists real numbers $x\:\:and\:\:y$ for which $x+y=y+x$.
answered Jul 16, 2014
The given statements are:$p: x+y=y+x$ is true for every real number $x\:\:and\:\:y$.$q:$ There exi...
0 votes
Identify the quantifier and and write the negation of the statement "There exists a capital for every state in India."
answered Jul 16, 2014
The given statement is:"There exists a capital for every state in India."The quantifier is 'there ex...
0 votes
Identify the quantifier and and write the negation of the statement "For every real number $x, \:\:x$ is less that $x+1$."
answered Jul 16, 2014
The given statement is: "For every real number $x, \:\:x$ is less that $x+1$."The quantifier is '...
0 votes
Identify the quantifier and write the negation of the statement "There exists a number which is equal to its square."
answered Jul 16, 2014
The given statement is:"There exists a number which is equal to its square."The quantifier of the st...
0 votes
Identify the connecting word and and write the components of the statement "$x=2\:\:and\:\:x=3$ are the roots of the equation $3x^2-x-10=0$."
answered Jul 16, 2014
The given statement is:"$x=2\:\:and\:\:x=3$ are the roots of the equation $3x^2-x-10=0$."the conne...
0 votes
Identify the connecting word and and write the components of the statement "The sand heats up quickly in the Sun and does not cool down fast at night"
answered Jul 16, 2014
The given statement is:"The sand heats up quickly in the Sun and does not cool down fast at night"Th...
0 votes
Identify the connecting word and and write the components of the statement "Square of an integer is positive or negative."
answered Jul 16, 2014
The given statement is: "Square of an integer is positive or negative."The connecting word is 'or'Th...
0 votes
Identify the connecting word and and write the components of the statement "All rational numbers are real and all real numbers are not complex."
answered Jul 16, 2014
The given statement is: "All rational numbers are real and all real numbers are not complex."The co...
0 votes
Write the components of the statement "$100$ is divisible by $3,\:11$ and $5$ Also check whether it is true or false.
answered Jul 14, 2014
The given statement is "$100$ is divisible by $3,\:11$ and $5$ The three components of this st...
0 votes
Write the component of the compound statement "All integers are positive or negative." Also check whether it is true of false.
answered Jul 14, 2014
The given statement is "All integers are positive or negative."The two components of this statemen...
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