Cardinality of Sets

Q. $Thevalueof(1^3+2^3+3^3+\dots +{15}^3)–(1+2+3+\dots +15)is$

1. 14280
2. 14400
3. 14520
4. 14200

Q. Question 7
In a city, $30\%$ are females, $40\%$ are males and remaining are children .What percent are children?

Q. Cardinal number of the set A = {x : x is an even prime number} is ____ .

1. 1

2. 2

3. Infinite

4. 0

Q.

Divide the following:

$600÷3$

Q.

Divide the following:

$550÷5$

Q.

What is the cardinal number of following sets?

$K=\left\{lettersinthewordMADAM\right\}$

Q. Set A = {Letters of the word "PARALLELOGRAM" }.
The cardinality of set A is ________.

1. 13
2. 8
3. 10
4. 7

Q.

Write the following set in the tabular form and find their cardinal numbers$.$

$B=\{x:x$ is a prime number of one digit$\}$

Q.

Divide the following:

$333÷3$

Q.

$\text{If}U=\{x:x\in N\},$ $A=\{x:x=2n,n\in N\}$ and $B=\{x:x\text{is a prime number}\},$ then $A\cap B$ is a set with cardinality ________.

1. infinity

2. zero

3. one

4. two

Q.

Assertion : The opposite sides of a parallelogram are a+b and 3a – 2b. Then the ratio a: b = 3:2.

Reason : The opposite sides of a parallelogram are equal.

Chose from the following alternatives:

1. Both Assertion and Reason are true and reason is required to solve the assertion.

2. Both Assertion and Reason are true but Reason is not required to solve the Assertion.

3. Assertion is false, Reason is true.

4. Both Assertion and Reason are false.

Q. In the Venn diagram given below, what is the cardinality of the set $A\cap B$?

1. 3
2. 0
3. 2
4. 4

Q. If $P=\{x:xisaletterintheword"PERMANENT"\}$, then n(P) is _____________.

1. 8
2. 10
3. 6
4. 7

Q. Let $f:R\to R$ be a function such that $f(x+y)=f\left(x\right)+f\left(y\right),\forall x,y\in R.$
If $f\left(x\right)$ is differentiable at $x=0$, then

1. $f\left(x\right)$ is differentiable only in a finite interval containing zero
2. $f\left(x\right)$ is continuous $\forall x\in R$
3. $f^{\prime }\left(x\right)$ is constant $\forall x\in R$
4. $f\left(x\right)$ is differentiable except at finitely many points

Q.

Divide the following:

$402÷2$

Q.

Divide the following:

$404÷2$

Q.

Divide the following:

$800÷4$

Q.

Divide the following:

$286÷2$

Q.

Find the value of each of the following.

$\left|-4\right|+\left|-6\right|$

Q.

Find the value of each of the following.

$\left|5\right|+\left|-5\right|$

Q.

Find the value of each of the following.

$\left|6\right|-\left|-6\right|$

Q. If $P=\{x:xisletterintheword"PERMANENT"\}$, then find n(P).