Tag: maths

Question 1

Reciprocal of $\displaystyle \frac{7}{5}$

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

$\displaystyle 1\frac{2}{5}$
$\displaystyle \frac{5}{7}$
$\displaystyle 5\frac{2}{3}$
$\displaystyle \frac{12}{5}$

Answer

Correct Option: B

Question 2

$\displaystyle \frac{1}{9}$ of ___ $= 5$

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

$5$
$9$
$14$
$45$

Answer

Correct Option: D

Question 3

Find the product:

$\displaystyle 1\frac{1}{3}\times 3\frac{1}{4}\times \frac{7}{8}$

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

$\displaystyle 3\frac{18}{24}$
$\displaystyle 2\frac{19}{24}$
$\displaystyle 3\frac{19}{24}$
$\displaystyle 2\frac{18}{24}$

Answer

Correct Option: C

Question 4

If $\displaystyle 40-\frac{1}{5}\times $ ____ $= 0$, then the missing value is

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

$0$
$\displaystyle \frac{1}{5} $
$\displaystyle \frac{199}{5} $
$200$

Answer

Correct Option: D

Question 5

If the reciprocal of $y - 1$ is $y + 1$, then $y$ equals

maths parts and whole multiplication of a fraction multiplication of a fractions multiplication of fraction finding the whole when a fraction is given

$-1$
$+1$
$0$
$\pm$ 1
none of these

Answer

Correct Option: E

Question 6

Without using truth , whether
$\left[ {p\Delta \left( { \sim q\Delta r} \right)} \right]V\left[ { \sim r\Delta \sim q\Delta p} \right] \equiv p$

maths principle of mathematical induction implications proofs in mathematics different forms of theoretical statements

True
False

Answer

Correct Option: B

Question 7

Solve it:-
$\left( {p \to q} \right) \to [\left( { \sim p \to q} \right) \to q]$

maths principle of mathematical induction implications proofs in mathematics different forms of theoretical statements

Tautology
Contradiction
Contingent
Not statement

Explanation:

$Y=\left( p\longrightarrow q \right) \longrightarrow \left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$

Method : TRUTH TABLE [ ALWAYS PREFERABLE]

$p$	$q$	$p\longrightarrow q$	$\left( \sim p\longrightarrow q \right) $	$\left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$	$Y$
$1$	$0$	$0$	$1$	$1$	$1$
$1$	$1$	$1$	$1$	$1$	$1$
$0$	$0$	$1$	$0$	$1$	$1$
$0$	$1$	$1$	$1$	$1$	$1$

As the result is always TRUE $\left(i.e. 1\right)$;

$\left( p\longrightarrow q \right)\longrightarrow \left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$ is Tautology.

A. Tautology

Answer

Correct Option: A

Question 8

Which of the following is true

maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

$a _{r}=a _{n-r}$
$a _{2r}=a _{n-r}$
$a _{r}=a _{2n-r}$
$None\ of\ these$

Answer

Correct Option: A

Question 9

Let $p$ and $q$ be two propositions given by
$p$ : The sky is blue.
$q$ : The milk is white.
Then $p\wedge q$ will be

maths principle of mathematical induction implications proofs in mathematics different forms of theoretical statements

The sky if blue or milk is white
The sky is blue and milk is white
The sky is white and milk is blue
If the sky is blue then milk is white

Answer

Correct Option: B

Question 10

Let $p$ and $q$ be two propositions. Then the contrapositive the implication $p\rightarrow q$

maths principle of mathematical induction implications proofs in mathematics different forms of theoretical statements

$\sim q\rightarrow \sim p$
$\sim p\rightarrow \sim q$
$q\rightarrow p$
$p\leftrightarrow q$

Answer

Correct Option: A

$p$	$q$	$p\longrightarrow q$	$\left( \sim p\longrightarrow q \right) $	$\left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$	$Y$
$1$	$0$	$0$	$1$	$1$	$1$
$1$	$1$	$1$	$1$	$1$	$1$
$0$	$0$	$1$	$0$	$1$	$1$
$0$	$1$	$1$	$1$	$1$	$1$

$p$	$q$	$p\longrightarrow q$	$\left( \sim p\longrightarrow q \right) $	$\left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$	$Y$
$1$	$0$	$0$	$1$	$1$	$1$
$1$	$1$	$1$	$1$	$1$	$1$
$0$	$0$	$1$	$0$	$1$	$1$
$0$	$1$	$1$	$1$	$1$	$1$

Tag: maths

Questions Related to maths

$p$	$q$	$p\longrightarrow q$	$\left( \sim p\longrightarrow q \right) $	$\left[ \left( \sim p\longrightarrow q \right) \longrightarrow q \right]$	$Y$
$1$	$0$	$0$	$1$	$1$	$1$
$1$	$1$	$1$	$1$	$1$	$1$
$0$	$0$	$1$	$0$	$1$	$1$
$0$	$1$	$1$	$1$	$1$	$1$