Straight Lines Test 10

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Straight Lines Test 10

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Weekly Quiz Competition

Question 1
1 / -0

Choose the correct statement(s):
$$A$$: Every sequence is a progression.
$$B$$: Every progression is a sequence.

A
Only $$A$$

B
Only $$B$$

C
Both $$A$$ and $$B$$

D
None

Solution

The difference between a progression and a sequence is that a progression has a specific rule to calculate its next term from its previous term, whereas a sequence can be based on a logical rule like 'a group of prime numbers'.
Thus, every progression is a sequence but every sequence is not a sequence.
Question 2
1 / -0

A sequence of numbers in which each term is related to its predecessor by same law is called

A
arithmetic series

B
progression

C
geometric series

D
none of these

Solution

A sequence of numbers in which each term is related to its predecessor by same law is called progression
Example: 1, 2, 3, 4.... is an example of sequence or progression.
Since the given sequence follows a same rule or law through out the sequence and there is a relation between each term and it's previous one.
Question 3
1 / -0

$$10,$$ __$$, 15, 15, 20, 20, 25, 25,...$$. What number should fill the blank?

A
7

B
8

C
10

D
15

Solution

Here addition with repetition series, each number in the series repeats itself, and then increases by $$5$$ to get the next number.
The next number is $$10$$.
Question 4
1 / -0

________ can be defined as arrangement of terms in which sequence of terms follow some conditions.

A
Series

B
Preceding sequence

C
Progression

D
Geometric progression

Solution

Progression can be defined as arrangement of terms in which sequence of terms follow some conditions.
Question 5
1 / -0

_______ is a series of successive events.

A
Series

B
Preceding sequence

C
Progression

D
Geometric progression

Solution

Progression is a series of successive events.
Question 6
1 / -0

Find the next number in the series.
$$3, 6, 9, 12, 15,....$$

A
$$17$$

B
$$18$$

C
$$19$$

D
$$20$$

Solution

The next number is $$18$$.
Since the numbers are multiple of $$3$$.
$$3, 6, 9, 12, 15, \underline {18 }$$.
Question 7
1 / -0

The area of triangle whose vertices are $$A (-3, -1), B(5, 3)$$ and $$C(2, -8)$$ is ____ $$\text{ sq. units}$$.

A
$$34\text{ sq. units}$$

B
$$36\text{ sq. units}$$

C
$$38\text{ sq. units}$$

D
$$32\text{ sq. units}$$

Solution

We know that the area of the triangle whose vertices are $$\displaystyle (x_{1},y_{1}),(x_{2},y_{2}),$$ and $$(x_{3},y_{3})$$ is $$\cfrac{1}{2}\left | x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1}) +x_{3}(y_{1}-y_{2})\right |$$

The given vertices of the triangle are $$A(-3,-1), B(5,3)$$ and $$C(2,-8)$$.
So, by using the above formula,
$$\begin{aligned}{}\text{Area of the triangle} &= \frac{1}{2} {[ - 3(3 - ( - 8)) + 5( - 8 - ( - 1)) + 2( - 1 - 3)]}\\ &= \frac{1}{2}{[ - 33 - 35 - 8]}\\ &= \frac{{[ - 76]}}{2}\\& = \frac{{76}}{2}\quad\quad\quad\quad\dots[\text{Area can never be negative so, we ignore negative sign}]\\& = 38\text{ sq. units}\end{aligned}$$

So, the area of the triangle is equal to $$38\text{ sq. units}$$.
Question 8
1 / -0

Based on this information answer the questions given below.
(i) $$\displaystyle ^{ n }{ C }_{ p }= r!^{ n }{ C }_{ r }$$
(ii) $$\displaystyle ^{ n }{ C }_{ r }+^{ n }{ C }_{ r-1 }=^{ n+1 }{ C }_{ r }$$
What is the value of $$\displaystyle ^{ 8 }{ C }_{ 4 }+^{ 8 }{ C }_{ 3 }$$?

A
$$\displaystyle ^{ 8 }{ c }_{ 5 }$$

B
$$63$$

C
$$35$$

D
$$\displaystyle ^{ 9 }{ c }_{ 4 }$$

Solution

$$ ^{n}C_{r}+^{n}C_{r-1} = ^{n+1}C_{r} $$
$$ \Rightarrow ^{8}C_{4}+^{8}C_{3} = \boxed{^{9}C_{4}} $$
Question 9
1 / -0

If there are five consecutive integer in a series and the first integer is $$1$$, what is the value of the last consecutive integer?

A
$$2$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

Let the five consecutive integers be $$x, x + 1, x + 2, x + 3$$ and $$x + 4$$.
Therefore, the value of first integer is $$1$$ i.e., $$x = 1$$
So, the last integer is $$x + 4$$
The value of last integer $$= 5$$.
Question 10
1 / -0

The area of the triangle formed by three vertices $$O(0, 0), A(1, 0), B(0, 1)$$ is _____ sq. units.

A
$$0$$

B
$$\dfrac{1}{2}$$

C
$$1$$

D
$$2$$

Solution

Points are given as $$O(0,0), A(1,0), B(0,1)$$.
When plotted on the cartesian plane, these points make a right angled triangle $$OAB$$ with
$$OA=1$$, $$OB=1$$
Area of this right angled triangle $$=\dfrac12\times OA\times OB$$
$$=\cfrac12\times1\times1\ sq.unit$$
$$=\cfrac12\ sq.unit$$

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Re-Attempt Weekly Quiz Competition

Straight Lines Test 10

Result

Straight Lines Test 10

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Rank

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SHARING IS CARING

Question 1

Only $$A$$

Only $$B$$

Both $$A$$ and $$B$$

None

Solution

Question 2

arithmetic series

progression

geometric series

none of these

Solution

Question 3

7

8

10

15

Solution

Question 4

Series

Preceding sequence

Progression

Geometric progression

Solution

Question 5

Series

Preceding sequence

Progression

Geometric progression

Solution

Question 6

$$17$$

$$18$$

$$19$$

$$20$$

Solution

Question 7

$$34\text{ sq. units}$$

$$36\text{ sq. units}$$

$$38\text{ sq. units}$$

$$32\text{ sq. units}$$

Solution

Question 8

$$\displaystyle ^{ 8 }{ c }_{ 5 }$$

$$63$$

$$35$$

$$\displaystyle ^{ 9 }{ c }_{ 4 }$$

Solution

Question 9

$$2$$

$$3$$

$$4$$

$$5$$

Solution

Question 10

$$0$$

$$\dfrac{1}{2}$$

$$1$$

$$2$$

Solution

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