Tag: maths

Questions Related to maths

The conditional $( p \wedge q ) \Rightarrow p$ is 

maths mathematical reasoning special words/phrases duality mathematical logic

  1. neither tautology nor contradiction

  2. a tautology

  3. a contradiction

  4. both tautology and contradiction

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Correct Option: B

Boolean algebra is also called

maths mathematical reasoning special words/phrases duality mathematical logic

  1. switching algebra

  2. arithmetic algebra

  3. linear algebra

  4. algebra

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Correct Option: A
Explanation:

Boolean algebra is also called switching algebra..


It was invented by mathematician George Boole in 1849.Boolean algebra or 

switching algebra ia a system of mathematical logic to perform different 

mathematical operation in binary system.

$e*x=x*e=x$ is the

maths mathematical reasoning special words/phrases duality mathematical logic

  1. commutative property

  2. inverse property

  3. associative property

  4. identity element

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Correct Option: D
Explanation:

Given, $e\times x=x\times e=x$

This is possible when $e=1$
This is an identity element.

A Boolean function may be transformed into

maths mathematical reasoning special words/phrases duality mathematical logic

  1. logical diagram

  2. logical graph

  3. map

  4. matrix

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Correct Option: A
Explanation:

Boolean function:

        It can be represented in the form of diagram with logic gates.

Boolean algebra theorem, gives   $x\cdot (x+y)$   equal to

maths mathematical reasoning special words/phrases duality mathematical logic

  1. $x'$

  2. $1$

  3. $x$

  4. $0$

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Correct Option: C
Explanation:

    $x\cdot \left( x+y \right) $

$=x\cdot x+xy$
$=x$

To perform product of maxterms Boolean function must be brought into

maths mathematical reasoning special words/phrases duality mathematical logic

  1. and terms

  2. or terms

  3. not terms

  4. nand terms

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Correct Option: B
Explanation:

For performing Product of Maxterms, it has to be brought into POS, i.e; Product of Sum form. For this, the Boolean Function must be brought into OR terms.

Minterms are also called

maths mathematical reasoning special words/phrases duality mathematical logic

  1. standard sum

  2. standard product

  3. standard division

  4. standard subtraction

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Correct Option: B
Explanation:

A product is called a minterm because it has minimum-satisfiability where as a sum is called a maxterm because it has maximum-satisfiability among all practically interesting boolean functions.

The ratio of the present age of Manoj to that of Wasim is $3:11$. Wasim is $12\ yr$ younger than Rehana. Rehanas age after $7\ yr$ will be $85\ yr$. What is thepresent age of Manojs father, who is $25\ yr$ older than Manoj?

maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

  1. $43\ yr$

  2. $67\ yr$

  3. $45\ yr$

  4. $69\ yr$

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Correct Option: A
Explanation:

 the present age of Wasim $=11x$

 present age of Manoj $=3x$

 present age of Rehana $=11x+12$
 present age of Manoj's father $=3x+25$

 after $7$ years, Rehana's age is $85$ years. 
 $11x+12+7=85$
 $ 11x=66$
 $x=6$
 
age of Manoj's father $=3 \times  6 + 25 = 43$ years. 

The sum of three consecutive odd numbers is $38$ more than the average of these numbers. What is the first number

maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

  1. $13$

  2. $17$

  3. $19$

  4. Data inadequate

  5. None of these

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Correct Option: B
Explanation:
let $'a'$ be the first odd number

As per Question

$ a+a+2+a+4 = 38 +\dfrac{a+a+2+a+4}{3}$

$ \Rightarrow 3a+6 = 38+a+2 $

$ \Rightarrow 2a = 34$

$ \Rightarrow a = 17 $

Solve $3x-450=2x-240$.

maths equations and simple functions further equations solving linear equations with variable on both sides solution of linear equations in one variable

  1. $210$

  2. $230$

  3. $220$

  4. $200$

Show answer
Correct Option: A
Explanation:

We have,

$3x-450=2x-240$

$3x-2x=450-240$

$x=210$

Hence, this is the answer.