Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

If $A equals left curly bracket p colon p equals fraction numerator open parentheses n plus 2 close parentheses open parentheses 2 n to the power of 5 end exponent plus 3 n to the power of 4 end exponent plus 4 n to the power of 3 end exponent plus 5 n to the power of 2 end exponent plus 6 close parentheses over denominator n to the power of 2 end exponent plus 2 n end fraction comma n comma p element of Z to the power of plus end exponent right curly bracket$ then the number of elements in the set $A comma$ is

2
3
4
6

The correct answer is: 4

We have,
$p equals fraction numerator left parenthesis n plus 2 right parenthesis left parenthesis 2 n to the power of 5 end exponent plus 3 n to the power of 4 end exponent plus 4 n to the power of 3 end exponent plus 5 n to the power of 2 end exponent plus 6 right parenthesis over denominator n to the power of 2 end exponent plus 2 n end fraction$
$rightwards double arrow p equals 2 n to the power of 4 end exponent plus 3 n to the power of 3 end exponent plus 4 n to the power of 2 end exponent plus 5 n plus fraction numerator 6 over denominator n end fraction$
Clearly, $p element of Z to the power of plus end exponent blank i f f blank n equals 1 comma blank 2 comma blank 3 comma blank 6.$ So, $A$ has 4 elements

Related Questions to study

For any three sets $A subscript 1 end subscript comma A subscript 2 end subscript comma A subscript 3 end subscript comma$ let $B subscript 1 end subscript equals A subscript 1 end subscript comma B subscript 2 end subscript equals A subscript 2 end subscript minus A subscript 1 end subscript$ and $B subscript 3 end subscript equals A subscript 3 end subscript minus open parentheses A subscript 1 end subscript union A subscript 2 end subscript close parentheses comma$ then which one of the following statement is always true

For any three sets $A subscript 1 end subscript comma A subscript 2 end subscript comma A subscript 3 end subscript comma$ let $B subscript 1 end subscript equals A subscript 1 end subscript comma B subscript 2 end subscript equals A subscript 2 end subscript minus A subscript 1 end subscript$ and $B subscript 3 end subscript equals A subscript 3 end subscript minus open parentheses A subscript 1 end subscript union A subscript 2 end subscript close parentheses comma$ then which one of the following statement is always true

If $n left parenthesis A intersection B equals 10 comma n open parentheses B intersection C close parentheses equals 20 right parenthesis$ and $n open parentheses A intersection C close parentheses equals 30 comma$ then the greatest possible value of $n left parenthesis A intersection B intersection C right parenthesis$ is

If $n left parenthesis A intersection B equals 10 comma n open parentheses B intersection C close parentheses equals 20 right parenthesis$ and $n open parentheses A intersection C close parentheses equals 30 comma$ then the greatest possible value of $n left parenthesis A intersection B intersection C right parenthesis$ is

Let $R$ be a relation from a set $A$ to a set $B comma$ then

Let $R$ be a relation from a set $A$ to a set $B comma$ then

parallel

In a town of $10000$ families $blank$ it was found that 40% families buy newspaper $A comma 20 percent sign$ families buy newspaper $B$ and 10% families buy newspaper $C comma blank 5 percent sign$ families buy $A$ and $B comma$ 3% buy $B$ and $C$ and 4% buy $A$ and $C.$ If 2% families buy all the three newspapers, then the number of families which buy $A$ only is

In a town of $10000$ families $blank$ it was found that 40% families buy newspaper $A comma 20 percent sign$ families buy newspaper $B$ and 10% families buy newspaper $C comma blank 5 percent sign$ families buy $A$ and $B comma$ 3% buy $B$ and $C$ and 4% buy $A$ and $C.$ If 2% families buy all the three newspapers, then the number of families which buy $A$ only is

Let $R$ be a reflexive relation on a finite set $A$ having $n$ elements, and let there be $m$ ordered pairs in $R.$ Then,

Let $R$ be a reflexive relation on a finite set $A$ having $n$ elements, and let there be $m$ ordered pairs in $R.$ Then,

For any two sets $A$ and $B$ , if $A intersection X equals B intersection X equals ϕ$ and $A union X equals B union X$ for some set $X$ , then

For any two sets $A$ and $B$ , if $A intersection X equals B intersection X equals ϕ$ and $A union X equals B union X$ for some set $X$ , then

parallel

Let $A equals open curly brackets 1 comma blank 2 comma blank 3 close curly brackets comma B equals open curly brackets 3 comma blank 4 close curly brackets comma C equals left curly bracket 4 comma blank 5 comma blank 6 right curly bracket$ . Then, $A union left parenthesis B intersection C right parenthesis$ is

Let $A equals open curly brackets 1 comma blank 2 comma blank 3 close curly brackets comma B equals open curly brackets 3 comma blank 4 close curly brackets comma C equals left curly bracket 4 comma blank 5 comma blank 6 right curly bracket$ . Then, $A union left parenthesis B intersection C right parenthesis$ is

If $A subscript 1 end subscript comma A subscript 2 end subscript comma horizontal ellipsis comma A subscript 100 end subscript$ are sets such that $n open parentheses A subscript i end subscript close parentheses equals i plus 2 comma A subscript 1 end subscript subset of A subscript 2 end subscript subset of A subscript 3 end subscript horizontal ellipsis subset of A subscript 100 end subscript$ and $not stretchy ⋂ from i equals 3 to 100 of A subscript i end subscript equals A comma$ then $n open parentheses A close parentheses equals$

If $A subscript 1 end subscript comma A subscript 2 end subscript comma horizontal ellipsis comma A subscript 100 end subscript$ are sets such that $n open parentheses A subscript i end subscript close parentheses equals i plus 2 comma A subscript 1 end subscript subset of A subscript 2 end subscript subset of A subscript 3 end subscript horizontal ellipsis subset of A subscript 100 end subscript$ and $not stretchy ⋂ from i equals 3 to 100 of A subscript i end subscript equals A comma$ then $n open parentheses A close parentheses equals$

If $A equals left curly bracket x blank colon x blank$ is a multiple of $blank 3 right curly bracket$ and,
$B equals left curly bracket x blank colon x blank$ is a multiple of $blank 5 right curly bracket$ , then $A minus B$ is

If $A equals left curly bracket x blank colon x blank$ is a multiple of $blank 3 right curly bracket$ and,
$B equals left curly bracket x blank colon x blank$ is a multiple of $blank 5 right curly bracket$ , then $A minus B$ is

parallel

Let $A$ be the set of all students in a school. A relation $R$ is defined on $A$ as follows:
$" a R b$ iff $a$ and $b$ have the same teacher”

Let $A$ be the set of all students in a school. A relation $R$ is defined on $A$ as follows:
$" a R b$ iff $a$ and $b$ have the same teacher”

In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation, it is sufficient, if $R$

In order that a relation $R$ defined on a non-empty set $A$ is an equivalence relation, it is sufficient, if $R$

Which of the following is an equivalence relation?

Which of the following is an equivalence relation?

parallel

Let $n open parentheses U close parentheses equals 700 comma blank n open parentheses A close parentheses equals 200 comma blank n open parentheses B close parentheses equals 300$ and $n open parentheses A intersection B close parentheses equals 100.$ Then, $n open parentheses A to the power of c end exponent intersection B to the power of c end exponent close parentheses equals$

Let $n open parentheses U close parentheses equals 700 comma blank n open parentheses A close parentheses equals 200 comma blank n open parentheses B close parentheses equals 300$ and $n open parentheses A intersection B close parentheses equals 100.$ Then, $n open parentheses A to the power of c end exponent intersection B to the power of c end exponent close parentheses equals$

The shaded region in the figure represents

The shaded region in the figure represents

Consider the following statements:
$p blank colon$ Every reflexive relation is symmetric relation
$q blank colon$ Every anti-symmetric relation is reflexive
Which of the following is/are true?

Consider the following statements:
$p blank colon$ Every reflexive relation is symmetric relation
$q blank colon$ Every anti-symmetric relation is reflexive
Which of the following is/are true?

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.