Tag: business maths

Questions Related to business maths

If adj $B=A$ and $|P|=|Q|=1$, then $adj (\left( { Q }^{ -1 }{ BP }^{ -1 } \right)$ is equal ?

business maths inverse of a matrix and linear equations non singular matrix singular & non-singular matrix determinants

  1. $APQ$

  2. $PAQ$

  3. $B$

  4. $A$

Show answer
Correct Option: A
Explanation:

$adj\left| { A }^{ -1 } \right| =\frac { A }{ \left| A \right|  } $


$adj\left| { Q }^{ -1 }{ BP }^{ -1 } \right| =adj\left| { P }^{ -1 } \right| \ast adj\left| { B } \right| \ast adj\left| { Q }^{ -1 } \right| =\frac { P }{ \left| P \right|  } \ast A\ast \frac { Q }{ \left| Q \right|  } =PAQ$

What is true about the statement "If two angles are right angles the angles have equal measure" and its converse "If two angles have equal measure then the two angles are right angles"?

business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. The statement is true but its converse is false

  2. The statement is false but its converse is true

  3. Both the statement and its converse are false

  4. Both the statement and its converse are true

Show answer
Correct Option: A
Explanation:

Two right angles are always equal, each measuring 90 degrees.

However,  two equal angles can be anything not necessarily equal to 90 degrees always.
Hence $A$ is correct.

The converse of "if $x\in A\cap B$ then $x\in A$ and $x\in B$", is

business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. If $x\in A$ and $x\in B$, then $x\in A\cap B$.

  2. If $x\not\in A\cap B$, then $x\not\in A$ or $x\not\in B$.

  3. If $x\not\in A$ or $x\not\in B$, then $x\not\in A\cap B$.

  4. If $x\not\in A$ or $x\not\in B$, then $x\in A\cap B$.

Show answer
Correct Option: A
Explanation:

The converse of "If P then Q" is "If Q then P"
Hence, Option A

The converse of "If in a triangle $ABC, AB=AC$, then $\angle B=\angle C$", is

business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. lf in a triangle $ABC, \angle B=\angle C$, then $AB=AC$.

  2. lf in a triangle$ABC, AB\neq AC$, then $\angle B\neq\angle C$.

  3. lf in a triangle $ABC, \angle B\neq\angle C$, then $AB\neq AC$.

  4. lf in a triangle $ABC, \angle B\neq\angle C$, then $AB=AC$ .

Show answer
Correct Option: A
Explanation:

Take $p:AB=AC$

and $q:\angle B=\angle C$
So the given statement is symbolically represented as $p\rightarrow q$
Now by definition, Converse of a conditional statement $p\rightarrow q$ is $q\rightarrow p$
So $q\rightarrow p$ is given by 
"If in a triangle $ABC, \angle B=\angle C,$ then $AB=AC.$"

Which of the following is the converse of the statement: "If x>4 then x+2>5"?

business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. If x+2<5 then x<4

  2. If x is not greater than 4 then x+2 is not greater than 5

  3. If x+2>5 then x>4

  4. If x+2 is not greater than 5 then x is not greater than 4

Show answer
Correct Option: C
Explanation:
Converse of  "If  $A$  then  $B$"   is   "If  $B$  then  $A$".    Hence,
Converse of  "If  $x>4$  then  $x+2>5$"  will be  "If  $x+2>5$   then  $x>4$"
So, $C$ is correct.

The converse of "If $x$ has courage, then $x$ will win", is

business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. If $x$ wins, then $x$ has courage.

  2. If $x$ has no courage, then $x$ will not win.

  3. If $x$ will not win, then $x$ has no courage.

  4. If $x$ will not win, then $x$ has courage.

Show answer
Correct Option: A
Explanation:

Take $p:x$ has courage

and $q:x$ will win
So the given conjugation is $p\Rightarrow q$

Now we need to find converse of this.
Be definition, Converse will be $q\Rightarrow p$
This is symbolic for "If $x$ wins then $x$ has courage

The converse of "if in a triangle $ABC, AB>AC$, then $\angle C=\angle B$", is

business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. lf in a triangle $ABC, \angle C=\angle B$, then $AB>AC$.

  2. lf in a triangle$ABC, AB\not\simeq AC$, then $\angle C\not\simeq \angle B$.

  3. lf in a triangle $ABC, \angle C\not\simeq \angle B$, then $ AB\not\simeq AC$.

  4. lf in a triangle $ABC, \angle C\not\simeq \angle B$, then $AB>AC$.

Show answer
Correct Option: A
Explanation:

Take $p:AB>AC$

and $q: \angle C=\angle B$
So the given statement is symbolically represented as $p\rightarrow q$
Now by definition, Converse of a conditional statement $p\rightarrow q$ is $q\rightarrow p$
Thus $q\rightarrow p$ is given by
"If in a $\triangle ABC, \angle C=\angle B$ then $AB>AC$."

Which of the following statements is the converse of "If the moon is full, then the vampires are prowling."?

business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. If the vampires are prowling, then the moon is full.

  2. If the moon is not full, then the vampires are prowling

  3. If the vampires are not prowling, then the moon is not full.

  4. None of these

Show answer
Correct Option: A
Explanation:

Converse of  "If $P$, then $Q$"  is  "If $Q$, then $P$"

Similarly, option "$A$" is converse of the given statement  "If the moon is full, then the vampires are prowling."

Which of the following statements is the converse of "You cannot skateboard if you do not have a sense of balance."?

business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. If you cannot skateboard, then you do not have a sense of balance.

  2. If you do not have a sense of balance, then you cannot skateboard.

  3. If you skateboard, then you have a sense of balance.

  4. None of these

Show answer
Correct Option: B
Explanation:

Converse of "If $P$, then $Q$"  is  "If $Q$, then $P$". 

Now, the given statement  "You cannot skateboard if you do not have a sense of balance." can be re-written as "If you do not have a sense of balance, then you cannot skateboard."
The converse of this statement is option $B$.

Which of the following statements is the contrapositive of the statement, You win the game if you know the rules but are not overconfident.

business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

  1. If you lose the game then you dont know the rules or you are overconfident.

  2. A sufficient condition that you win the game is that you know the rules or you are not overconfident.

  3. If you dont know the rules or are overconfident you lose the game

  4. If you know the rules and are overconfident then you win the game.

Show answer
Correct Option: A
Explanation:

Contrapositive is the inverse of the converse of the statement.

It is obtained by first interchanging the hypothesis and conclusion and then adding "not" to both
In this case, converse is "If you win the game, then you know the rules but are not overconfident."
Inverse of this statement gives answer as A.