Sequences and Series Test 13

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Sequences and Series Test 13

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is $$GP?$$

A
$$2, 4, 8, 16$$

B
$$2, -2, 2, 3, 1$$

C
$$0, 3, 6, 9, 12$$

D
$$10, 20, 30, 40$$

Solution

The sequence $$2, 4, 8, 16$$ is $$GP$$
Because here common ration between the consecutive terms is same. That is illustrated below.
$$\dfrac {4}{2}=2, \dfrac {8}{4}=2, \dfrac {16}{8}=2$$
Here the common ratio is $$2$$.
Question 2
1 / -0

The common ratio is calculated in

A
A.P.

B
G.P.

C
H.P.

D
I.P.

Solution

The common ratio is calculated in G.P.
For example: $$2,4,8,16,....$$
Here the common ratio is $$2$$.
Question 3
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 $$=\dfrac12\times OA\times OB$$
$$=\cfrac12\times1\times1\ sq.unit$$
$$=\cfrac12\ sq.unit$$
Question 4
1 / -0

A garrison of '$$n$$' men had enough food to last for $$30$$ days. After $$10$$ days, $$50$$ more men joined them. If the food now lasted for $$16$$ days, what is the value of $$n$$?

A
$$200$$

B
$$240$$

C
$$280$$

D
$$320$$

Solution

After $$10$$ days, the food for n men is there for $$20$$ days.
This food can be eaten by $$(n + 50)$$ men in $$16$$ days.
$$\therefore 20n = 16(n + 50)$$
$$\therefore n = 200$$
Question 5
1 / -0

The sum of two numbers is $$80$$. If the larger number exceeds four times the smaller by $$5$$, what is the smaller number?

A
$$5$$

B
$$15$$

C
$$20$$

D
$$25$$

Solution

Given, sum of two numbers is $$80$$.
Let the smaller number be $$x$$
Thus the larger will be $$80 - x$$.
Also given, larger number exceeds four times the smaller number by $$5$$.
Therefore, $$ 80 - x = 4x + 5$$
$$\Rightarrow 5x = 75$$
$$\Rightarrow x = 15$$
Thus the smaller number is $$15$$.
Question 6
1 / -0

A man has 9 friends, 4 boys and 5 girls. In how many ways can be invite them, if there have to be exactly three girls in the invites?

A
$$320$$

B
$$160$$

C
$$80$$

D
$$200$$

Solution

He can select three girls in $$^5C_3$$ ways = 10 ways
He can select boys in $$ [^4C_0+^4C_1 +^4C_2 +^4C_3 + ^4C_4]$$ ways = 16 ways
Total number of ways $$= 10\times16$$ $$ = 160$$
Question 7
1 / -0

Complete the addition square by finding the missing numbers.
Find $$(A-B)-(C-D)$$
$$+$$ $$10,923$$ $$8,473$$
$$18,732$$ $$A$$ $$B$$
$$9,018$$ $$C$$ $$D$$

A
$$0$$

B
$$450$$

C
$$1000$$

D
$$300$$

Solution

From the given table, we have
$$A=18,732+10,923=29,655$$
$$B=18,732+8,473=27,205$$
$$C=10,923+9,018=19,941$$
and $$D=8473+9,018=17,491$$
Now $$A-B=29,655-27,205=2,450$$
$$C-D=19,941-17,491=2,450$$
$$\therefore$$ $$(A-B)-(C-D)=2,450-2,450=0$$
Question 8
1 / -0

The models are shaded to show which of the following?

A
$$\cfrac { 1 }{ 3 } =\cfrac { 2 }{ 4 } $$

B
$$\cfrac { 1 }{ 4 } >\cfrac { 1 }{ 3 } $$

C
$$\cfrac { 2 }{ 3 } <\cfrac { 2 }{ 4 } $$

D
$$\cfrac { 2 }{ 4 } <\cfrac { 2 }{ 3 } $$

Solution

Fraction of shaded part in upper rectangle $$=2\times\dfrac{1}{3}=\dfrac{2}{3}$$
Fraction of shaded part in lower rectangle $$=2\times\dfrac{1}{4}=\dfrac{2}{4}$$
In upper rectangle shaded part is greater
So, $$\dfrac { 2 }{ 4 } <\dfrac { 2 }{ 3 } $$
Option D is correct.
Question 9
1 / -0

Fathom is a unit once used by sailors to measure the depth of water. If a sunken ship was located underwater at $$240$$ feet, which expression would describe the location of the ship in fathoms?
$$ { 1\ fathom=6\ feet } $$

A
$$240\times 6$$

B
$$240\div 6$$

C
$$240-6$$

D
$$240+6$$

Solution

We have $$1fathom=6feet$$
$$1feet=\cfrac{1}{6}fathom$$
Ship was located underwater at $$240$$ feet
$$\therefore$$ location of ship underwater in fathoms $$=240\div6$$
Question 10
1 / -0

A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices given below. The columns and rows of Matrix I are numbered from $$0$$ to $$4$$ and that of Matrix $$I$$ are numbered from $$5$$ to $$9$$. A letter from these matrices can be represented first by its row and next by its column, e.g. $$'A'$$ can be represented by $$00, 12, 23$$ etc., and $$'P'$$ can be represented by $$58, 69, 75$$ etc. Similarly, you have to identify the set for the word 'POET'.
Matrix I
$$0$$ $$1$$ $$2$$ $$3$$ $$4$$
$$0$$ $$A$$ $$R$$ $$S$$ $$N$$ $$C$$
$$1$$ $$N$$ $$C$$ $$A$$ $$R$$ $$S$$
$$2$$ $$S$$ $$N$$ $$C$$ $$A$$ $$R$$
$$3$$ $$R$$ $$S$$ $$N$$ $$C$$ $$A$$
$$4$$ $$C$$ $$A$$ $$R$$ $$S$$ $$N$$
Matrix II
$$5$$ $$6$$ $$7$$ $$8$$ $$9$$
$$5$$ $$O$$ $$E$$ $$L$$ $$P$$ $$T$$
$$6$$ $$T$$ $$O$$ $$E$$ $$L$$ $$P$$
$$7$$ $$P$$ $$T$$ $$O$$ $$E$$ $$L$$
$$8$$ $$L$$ $$P$$ $$T$$ $$O$$ $$E$$
$$9$$ $$E$$ $$L$$ $$P$$ $$T$$ $$O$$

A
$$69, 88, 67, 65$$

B
$$75, 56, 65, 67$$

C
$$77, 88, 98, 78$$

D
$$75, 66, 76, 78$$

Solution

From matrix,
$$P\Rightarrow 58, 69, 75, 86, 97$$
$$O\Rightarrow 55, 66, 77, 88, 99$$
$$E\Rightarrow 56, 67, 78, 87, 98$$
$$T\Rightarrow 69, 88, 67, 65$$
$$\therefore POET\Rightarrow 69, 88, 67, 65$$.

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$$+$$	$$10,923$$	$$8,473$$
$$18,732$$	$$A$$	$$B$$
$$9,018$$	$$C$$	$$D$$

		Matrix I
	$$0$$	$$1$$	$$2$$	$$3$$	$$4$$
$$0$$	$$A$$	$$R$$	$$S$$	$$N$$	$$C$$
$$1$$	$$N$$	$$C$$	$$A$$	$$R$$	$$S$$
$$2$$	$$S$$	$$N$$	$$C$$	$$A$$	$$R$$
$$3$$	$$R$$	$$S$$	$$N$$	$$C$$	$$A$$
$$4$$	$$C$$	$$A$$	$$R$$	$$S$$	$$N$$

		Matrix II
	$$5$$	$$6$$	$$7$$	$$8$$	$$9$$
$$5$$	$$O$$	$$E$$	$$L$$	$$P$$	$$T$$
$$6$$	$$T$$	$$O$$	$$E$$	$$L$$	$$P$$
$$7$$	$$P$$	$$T$$	$$O$$	$$E$$	$$L$$
$$8$$	$$L$$	$$P$$	$$T$$	$$O$$	$$E$$
$$9$$	$$E$$	$$L$$	$$P$$	$$T$$	$$O$$

Sequences and Series Test 13

Result

Sequences and Series Test 13

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Rank

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SHARING IS CARING

Question 1

$$2, 4, 8, 16$$

$$2, -2, 2, 3, 1$$

$$0, 3, 6, 9, 12$$

$$10, 20, 30, 40$$

Solution

Question 2

A.P.

G.P.

H.P.

I.P.

Solution

Question 3

$$0$$

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

$$1$$

$$2$$

Solution

Question 4

$$200$$

$$240$$

$$280$$

$$320$$

Solution

Question 5

$$5$$

$$15$$

$$20$$

$$25$$

Solution

Question 6

$$320$$

$$160$$

$$80$$

$$200$$

Solution

Question 7

$$0$$

$$450$$

$$1000$$

$$300$$

Solution

Question 8

$$\cfrac { 1 }{ 3 } =\cfrac { 2 }{ 4 } $$

$$\cfrac { 1 }{ 4 } >\cfrac { 1 }{ 3 } $$

$$\cfrac { 2 }{ 3 } <\cfrac { 2 }{ 4 } $$

$$\cfrac { 2 }{ 4 } <\cfrac { 2 }{ 3 } $$

Solution

Question 9

$$240\times 6$$

$$240\div 6$$

$$240-6$$

$$240+6$$

Solution

Question 10

$$69, 88, 67, 65$$

$$75, 56, 65, 67$$

$$77, 88, 98, 78$$

$$75, 66, 76, 78$$

Solution

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