Sequences and Series Test 28

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Sequences and Series Test 28

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Weekly Quiz Competition

Question 1
1 / -0

Geometric mean of $$7,\ { 7 }^{ 2 },\ { 7 }^{ 3 }....{ 7 }^{ n }$$ is

A
$$\displaystyle { 7 }^{ \dfrac { \left( n+1 \right) }{ 2 } }$$

B
$${ 7 }^{ { n }/{ 2 } }$$

C
$${ 7 }^{ \dfrac { \left( n-1 \right) }{ 2 } }$$

D
$${ 7 }^{ \left( \dfrac { n+1 }{ 3 } \right) }$$

Solution

$$Gm$$ of two no $$a$$ & $$b=\sqrt {ab}$$
For $$aGP$$
$$GM=\sqrt {a_1. an}$$
$$\Rightarrow \ GM $$ of $$7, 7^2, ..... 7^n$$
$$=\sqrt {7.7^n}$$
$$=7\dfrac {(n+1)}{2}$$
Question 2
1 / -0

Sum of the three digit numbers (no digit being zero) having the property that all digits are perfect squares, is

A
$$3108$$

B
$$6216$$

C
$$13986$$

D
$$None\ of\ these$$

Solution

Perfect square digits from $$1 $$ to $$9 $$ are - $$1,4,9$$

The 3 digit nos. having the property that all digits are perfect squares are,

$$149, 194, 491, 419, 914, 941$$

The sum is,

$$149+194+491+419+914+941=3108$$
Question 3
1 / -0

The number of ways in which $$6$$ rings can be worn on the four fingers of one hand is

A
$$4^{6}$$

B
$$^{6}C_{4}$$

C
$$6^{4}$$

D
None of these

Solution

Each ring can be worn on $$4$$ fingers, means each have $$4$$ possibilities.
$$\therefore$$ Total ways$$=4\times4\times4\times4\times4\times4=4^{6}$$
Hence, $$(A)$$
Question 4
1 / -0

Choose the correct answer from the alternatives given.
A loss of $$20%$$ is incurred when $$6$$ articles are sold for a rupee. To gain $$20% $$ how many articles should be sold for a rupee?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

: Given that, SP = $$1$$. Loss$$ % = 20%$$ We know that, $$SP = 0.8$$ $$\times$$ $$CP$$
$$CP \, = \, \dfrac{5}{4}$$
To gain$$ 20%$$,SP=1.2 $$\displaystyle \times \, CP \, = \, \dfrac{120}{100} \, \times \, \dfrac{5}{4} \, = \, \dfrac{3}{2} \, \Rightarrow \, = \, \dfrac{3}{2}$$
For$$ Rs. 3/2$$ number of articles sold
For $$Rs. 1$$ number of articles to be sold $$= 6 $$ $$\times$$ $$ \dfrac{2}{3}$$ = $$ 4 $$ articles.
Question 5
1 / -0

If $$9@ 3 = 12, 15 @ 4 = 22, 16 @ 14 = 4$$, then what is the value of $$6 @ 2 = ?$$

A
$$26$$

B
$$1$$

C
$$30$$

D
$$8$$

Solution

$$(9 - 3) \times 2 = 12, (15 - 4) \times 2$$
$$= 22, (16 - 14) \times 2 = 4$$
Hence, $$(6 - 2) \times 2 = 8$$.
Question 6
1 / -0

5 2 7
? 3 1
4 5 2
-15 7 13
Select the missing number from the given alternatives.

A
$$1$$

B
$$5$$

C
$$9$$

D
$$7$$

Solution

Columnwise
First Number x Third Number - Second Number = Lowermost Number

First Column
$$5 \times 4 - ? = 15 \Rightarrow 20 - ? = 15$$
$$\therefore ? = 20 - 15 = 5$$

Second Column
$$ 2 \times 5 - 3 = 10 - 3 = 7$$

Third Column
$$ 7 \times 2 - 1 = 14 - 1 = 13$$
Question 7
1 / -0

Select the missing number from the given alternatives.
$$3$$ $$4$$ $$2$$ $$14$$
$$6$$ $$5$$ $$4$$ $$44$$
$$5$$ $$2$$ $$7$$ ?

A
$$58$$

B
$$14$$

C
$$49$$

D
$$4$$

Solution

$$3\times 2 + 4\times 2 = 6 + 8 = 14$$
$$6\times 4 + 5\times 4 = 24 + 20 = 44$$
Hence, $$5\times 7 + 2 \times 7 = 35 + 14 = 49$$.
Question 8
1 / -0

Directions for questions 1 to 3: Find the related word/ letters/numbers from given alternatives.
12:72::8:?

A
36

B
32

C
38

D
40

Solution

12 $$\times \, \frac{12}{2}$$ = 72 similarly, 8 $$\times \, \frac{8}{2}$$ = 32
Question 9
1 / -0

Select the missing number from the given alternatives.

A
110

B
115

C
121

D
54

Solution

48 $$\div$$ 2 = 24;
24 $$\times$$ 3 = 72: 72 $$\div$$ 2 = 36;
36 $$\div$$ 3 = 108; 108 $$\div$$ 2 = 54.
Question 10
1 / -0

Choose the correct answer from the alternatives given.
If $$1^2+2^2$$ +.... + $$x^2$$ = $$\frac{x(x + 1)(2x + 1)}{6}$$then $$1^2$$ + $$3^2$$+ $$5^2$$ + .... + $$19^2$$ is equal to

A
$$1330$$

B
$$2100$$

C
$$2485$$

D
$$2470$$

Solution

$$(1^2+3^2+5^2+...........+19^2)$$
= $$\displaystyle\, $$(1^2$$ \, + \, $$2^2$$ \, + \, $$3^2$$ \, + \, ........... \, + \, 20^2) \, - \, (2^2 \, + \, 4^2 \, + \, 6^2 \, + \, ........... \, + \, 20^2)$$
= $$\displaystyle\, (1^2 \, + \, 2^2 \, + \, 3^2 \, + \, .......... \, + \, 20^2) - 4(1 \, + \, 2^2 \, + \, 3^2 \, + \, .......... \, + \, 10^2)$$
Using the formula,
$$\displaystyle\, = \frac{20 \times 21 \times 41}{6} - 4 \left ( \frac{10 \times 11 \times 21}{6} \right ) = 2870 - 1540 = 1330$$

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Re-Attempt Weekly Quiz Competition

5	2	7
?	3	1
4	5	2
-15	7	13

$$3$$	$$4$$	$$2$$	$$14$$
$$6$$	$$5$$	$$4$$	$$44$$
$$5$$	$$2$$	$$7$$	?

Sequences and Series Test 28

Result

Sequences and Series Test 28

Score

-

Rank

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SHARING IS CARING

Question 1

$$\displaystyle { 7 }^{ \dfrac { \left( n+1 \right) }{ 2 } }$$

$${ 7 }^{ { n }/{ 2 } }$$

$${ 7 }^{ \dfrac { \left( n-1 \right) }{ 2 } }$$

$${ 7 }^{ \left( \dfrac { n+1 }{ 3 } \right) }$$

Solution

Question 2

$$3108$$

$$6216$$

$$13986$$

$$None\ of\ these$$

Solution

Question 3

$$4^{6}$$

$$^{6}C_{4}$$

$$6^{4}$$

None of these

Solution

Question 4

$$1$$

$$2$$

$$3$$

$$4$$

Solution

Question 5

$$26$$

$$1$$

$$30$$

$$8$$

Solution

Question 6

$$1$$

$$5$$

$$9$$

$$7$$

Solution

Question 7

$$58$$

$$14$$

$$49$$

$$4$$

Solution

Question 8

36

32

38

40

Solution

Question 9

110

115

121

54

Solution

Question 10

$$1330$$

$$2100$$

$$2485$$

$$2470$$

Solution

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