Sequences and Series Test 2

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Sequences and Series Test 2

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Weekly Quiz Competition

Question 1
1 / -0

How many combinations of two-digit numbers having 8 can be made from the following numbers?
8, 5, 2, 1, 7, 6

A
$$9$$

B
$$10$$

C
$$11$$

D
$$12$$

Solution

The possible two-digit number are
88, 85, 82, 81, 87, 86, 58, 28, 18, 78, 68
These are 11 in number
Question 2
1 / -0

The positions of the first and the fifth digits in the number 83256479 are interchanged. Similarly the positions of the second and the sixth digits are interchanged and so on. Which of the following will be the third to the right of the seventh digit from the right end after rearrangement?

A
3

B
4

C
7

D
8

Solution

In the given number 83256479, the first and the fifth digits are interchanged.The number becomes 63258479.
Then second and the sixth digit are interchanged. The number becomes 64258379.
The third and the seventh digit are interchanged. The number becomes 64758329.
The fourth and the eighth digit are interchanged. The number becomes 64798325.
The seventh digit from the right end after rearrangement is 4.The third digit to the right of 4 is 8.
Answer is Option D
Question 3
1 / -0

The spread sheet on the right contains 20 cells. A cell In a spread sheet can be identified fIrst by the column letter and then by the row number. For example,. the number 10 is found in cell C4. If the number in cell A3 =B4-3(E2 +D4) then which of the following must be the number in cell E2?

A
-21

B
-15

C
-4

D
-12

Solution

Its given
A3=B4-3(E2+D4)
Substituting the values from the grid
$$18=-6-3(E2+4)$$
$$24=-3(E2+4)$$
$$-8-4=E2$$
$$E2=-12$$
Answer is Option D
Question 4
1 / -0

In numbers from $$1 \ to\ 100$$ the digit "$$0$$" appears ____________times.

A
$$9$$

B
$$10$$

C
$$11$$

D
$$12$$

Solution

$$10, 20, 30, 40, 50, 60, 70, 80, 90, 100$$
Thus the digit $$0$$ appears $$11$$ times.
Question 5
1 / -0

The greatest number that can be formed by the digits $$7,0,9,8,6,3$$

A
$$9,87,360$$

B
$$9,87,063$$

C
$$9,87,630$$

D
$$9,87,603$$

Solution

The greatest number that can be formed by the digits $$7,0,9,8,6,3$$ is $$9 8 7 6 3 0$$
To achieve this arrange the given numbers in descending order.
Question 6
1 / -0

The area of a triangle whose vertices are $$(a, c+a), (a, c) $$ and $$(-a, c-a) $$ are

A
$$\displaystyle a^{2}$$

B
$$\displaystyle b^{2}$$

C
$$\displaystyle c^{2}$$

D
$$\displaystyle a^{2}+c^{2}$$

Solution

Area of a triangle with vertices $$({ x }_{ 1 },{ y }_{ 1 })$$ ; $$({ x }_{ 2 },{ y

}_{ 2 })$$ and $$({ x }_{ 3 },{ y }_{ 3 })$$ is $$ \left| \frac { {

x }_{ 1 }({ y }_{ 2 }-{ y }_{ 3 })+{ x }_{ 2 }({ y }_{ 3 }-{ y }_{ 1 })+{ x }_{

3 }({ y }_{ 1 }-{ y }_{ 2 }) }{ 2 } \right| $$
Hence, area of the triangle with given vertices is $$ \left| \frac { { a }(c-c+a)+a(c-a-c-a)-a(c+a-c) }{ 2 } \right| = \left| \frac { { a }^{ 2 }-2{ a }^{ 2 }-{ a }^{ 2 } }{ 2 } \right| = { a }^{ 2 } $$
Question 7
1 / -0

In the series given below. count the number of 9s, each of which Is not immediately preceded by 5 but is immediately followed by either 2 or 3. How many such 9s are there?
1 9 2 6 5 9 3 8 3 9 3 2 5 9 2 9 3 4 8 2 6 9 8

A
One

B
Three

C
Five

D
Six

Solution

There are 3 such 9s that are not immediately preceded by 5 and immediately followed by 2 or 3 in the given series. They are marked in bold.
1 9 2 6 5 9 3 8 3 9 3 2 5 9 2 9 3 4 8 2 6 9 8
Answer is Option B
Question 8
1 / -0

How many numbers amongst the numbers 9 to 54 are there which are exactly divisible by 9 but not by 3?

A
8

B
6

C
5

D
Nil

Solution

Any number divisible by 9 is also divisible by 3
Question 9
1 / -0

Arrange the given words in the sequence in which they occur in the dictionary and then choose the correct sequence.
1. Page 2. Pagan 3. Palisade 4. Pageant 5. Palate

A
$$1,4,2,3,5$$

B
$$2,4,1,3,5$$

C
$$2,1,4,5,3$$

D
$$1,4,2,5,3$$

Solution

Words 1,2 and 4 have first 3 letter as "pag" and words "3 and 5 have first 3 letters as "pal". So words starting with "pal" will come later than words starting with "pag" as in Alphabet set the letter "g" comes after letter "a".

The fourth letter of word 5 is "a" and of word 3 is "i" hence word 3 will be the last in order.
So choice A and B are incorrect and the answer will be either C or D.

Simply arranging the 4th letter of words 1,2 and 4 will give the correct sequence choice as C.
Question 10
1 / -0

Refer Diagram

A
8

B
9

C
7

D
12

E
10

Solution

The number inside the triangle is equal to the sum of the numbers obtained by multiplying number o either side of the triangle with the base number.
Thus, $$3 \times 1 + 3 \times 2 = 9$$
$$5 \times 2 + 3 \times 2 = 16$$
Hence, the missing term is: $$4 \times 1 + 5 \times 1 = 9$$

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Re-Attempt Weekly Quiz Competition

Sequences and Series Test 2

Result

Sequences and Series Test 2

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SHARING IS CARING

Question 1

$$9$$

$$10$$

$$11$$

$$12$$

Solution

Question 2

3

4

7

8

Solution

Question 3

-21

-15

-4

-12

Solution

Question 4

$$9$$

$$10$$

$$11$$

$$12$$

Solution

Question 5

$$9,87,360$$

$$9,87,063$$

$$9,87,630$$

$$9,87,603$$

Solution

Question 6

$$\displaystyle a^{2}$$

$$\displaystyle b^{2}$$

$$\displaystyle c^{2}$$

$$\displaystyle a^{2}+c^{2}$$

Solution

Question 7

One

Three

Five

Six

Solution

Question 8

8

6

5

Nil

Solution

Question 9

$$1,4,2,3,5$$

$$2,4,1,3,5$$

$$2,1,4,5,3$$

$$1,4,2,5,3$$

Solution

Question 10

8

9

7

12

10

Solution

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