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Correct answer is (C) 1

Correct answer is (A) (15, 10)

Correct answer is (A) (9, 16)

A whole number is simply any positive number that does not include a fractional or decimal part. This means that, for example, the numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers. Numbers such as -3, 2.7, or 3 ½ are not whole numbers.

Correct answer is (C) √5

GIVEN:

Number = 77¹¹¹

CONCEPT:

Remainder

CALCULATION:

Remainder when 77¹ is divided by 5 = 2

Remainder when 77² is divided by 5 = 4

Remainder when 77³ is divided by 5 = 3

Remainder when 77⁴ is divided by 5 = 1

77¹¹¹ can be written as: (77⁴)²⁷ × 77³

Remainder when (77⁴)²⁷ is divided by 5 is 1 and remainder when 77³ is divided by 5 is 3.

Hence, required remainder is 3. 

(e) The series is as follows:
– 1², – 2², –3², – 4², – 5², – 6²
Hence, ? = 558 – 52 = 533

According to the question,

Original number : 7 1 3 3 6 1 4 5 8 9 3 2 7 2 4

New arrangement : 1 3 7 1 3 6 4 5 8 2 3 9 2 4 7

So, the second lowest number will be 137.

Highest number = 932

Second highest number = 724

So, the required difference

= (9 + 3 + 2) – (7 + 2 + 4)

= 14 – 13 = 1

Here,

5 × 3 = 15

15 × 3 = 45

45 × 3 = 135

So, the answer is 135 × 3 = 405

The series is as follows starting from second number

x × 1 + 1² , x × 2 + 2², x ×3 + 3², x × 4 + 4², x ×5 +5²

(x denotes the previous number in the series)
? = x × 4 + 4² = 45 × 4 + 16 = 196

(e) The given number series is based on the following pattern:
6417 – 713 = 5704
5704 – 713 = 4991
4991 – 713 = 4278
4278 – 713 = 3565
3565 – 713 = 2852
? = 2852 – 713 = 2139
Hence, 2139 will replace the question mark.

Here, the differences between two numbers are 

16 – 15 = 1 

19 – 16 = 3 

28 – 19 = 9 

55 – 28 = 27 

Here, the difference is multiplied by 3. 

So, the next difference will be 81. 

So, the answer is 55 + 81 = 136

Here, the difference between two consecutive terms are

10 – 2 = 8

26 – 10 = 16

50 – 26 = 24

82 – 50 = 32

Here, the difference is increased by 8 (or you can say the multiples of 8). 

So the next difference will be 40 (32 + 8). So, the answer is 82 + 40 = 122

(a) The given number series is based on the following pattern:
250_÷2.5 100_÷2.5 40_÷2.5 16_÷2.5 6.4_÷2.5 2.56
Hence, the number 16 will replace the question mark.

Here, starting from the third number 

1 × 2 = 2 

2 × 2 = 4 

2 × 4 = 8 

4 × 8 = 32 

So, the answer is 8 × 32 = 256

Here, the differnce of any term from its succeding term is 3. 

7 – 4 = 3 

10 – 7 = 3 

So,the answer is 19 + 3 = 22

(d) The given number series is based on the following
pattern:
7 + 6 = 13
13 + 8 = 21
21 + 10 = 31
31 + 12 = 43
Hence, the number 21 will replace the question mark.

GIVEN:

Statement related to fruits sold by a fruit seller.

CALCULATION:

Let purchased quantity of fruits on Mon = 4x

Sold in Mon morning = 4x/2 = 2x

Sold in Mon evening = (4x – 2x)/2 = x

Total quantity of fruits available to sell on Tue = (4x + x) = 5x

Sold quantity of fruits on Tue = 5x × (3/4) = 3.75x

Remaining quantity of fruits on Tue = 5x – 3.75x

⇒ 1.25x = 15

⇒ x = 12

So,

Purchased quantity of fruits by seller on Mon = 4x = 48 kg

GIVEN:

Number = 35³⁶⁶ + 35²³¹

CONCEPT:

Remainder

CALCULATION:

We know that:

When aⁿ is divided by (a + 1), then remainder-

a) When ‘n’ is even, then remainder will always be 1.

b) When ‘n’ is odd, the remainder will always be ‘a’.

Remainder when 35³⁶⁶ is divided by 36 is 1.

Remainder when 35²³¹ is divided by 36 is 35.

Required remainder = 1 + 35 = 36 or 0

Given:

The given conditions are 1 > a > 5 and -12 < b < -3

Concept Used:

(-ve)^odd = (-ve) and (-ve)^even = ( + ve)

Calculation:

From the given conditions it is clear that a is positive and b is negative

∴ The expression a³b, b is negative and a is positive so it will give negative value

Now, the second expression is ab³

∴ The expression ab³, b is negative with odd power and a is positive so it will give negative value

Now, the third expression is ab⁷

∴ The expression ab⁷, b is negative with odd and a is positive so it will give negative value

Now, the fourth expression is (ab)⁵

∴ The expression (ab)⁵, the product of ab will be negative

Here all the terms will give the negative value

∴ Order of expression from minimum to maximum will be a³b ≥ ab³ ≥ ab⁷ ≥ (ab)⁵

Hence, option (4) is correct

Given:

P is a prime number and P² + 7 is also gives a Prime number

Concept Used:

The numbers having exactly two factors, one and the number itself is called prime numbers

Calculation:

Let the P² + 7 is equal to x

∴ X should be prime number

If P is 2

∴ X = P² + 7 = (2)² + 7 = 11, where 11 is a prime number

If P is 3

∴ X = P² + 7 = (3)² + 7 = 16, where 16 is even number

If P is 5

∴ X = P² + 7 = (5)² + 7 = 32, where 32 is even number

So, all the values of P other than 2 give the values of X as the even number

∴ Only one value of P is possible which gives the X as a prime number

Hence, option (1) is correct

2 is the only even prime number, other are the odd prime number

P = 2,

P2 + 7 = 4 + 7 = 11.

Given:

Numbers are 3 and 5.

Concept used:

Firstly find LCM of (3, 5), then find its two digit multiples.

Explanation:

LCM of (3, 5) = 15

Two digit multiples of 15 are 15, 30, 45, 60, 75, 90.

∴ The number of two digit common multiples of 3 and 5 are 6.

Given:

The given progression is geometric progression

Formula used:

The geometric progression is as following

a, ar, ar², ar³, ar⁴, ar⁵………. arⁿ

Where a is the first term and r is the common ratio

Nth term of geometric progression = ar^{n - 1}

Calculation:

The first term of GP is x and common difference is y

∴ Geometric progression is as following

x, xy, xy², xy³, xy⁴, xy⁵… xyⁿ

Where x is the first term and y is the common ratio

Nth term of geometric progression = xy^{n - 1}

∴ LCM of this GP = xy^{n – 1}

And HCF of this GP = x

Now, the ratio of LCM to HCF of geometric progression

∴ LCM/HCF = xy^{n – 1}/x = y^{n – 1}

Hence, option (4) is correct

Given:

X and Y is multiple of 7

Concept Used:

If the number is a multiple of given number then the number is also divisible by the given number

Calculation:

It is given in the question that X and Y are multiples of 7

∴ X = 7m and Y = 7n

Now, let check first option (X² + Y²) is divisible by 7

∴ (X² + Y²) = ((7m)² + (7n)²) = 49 (m² + n²), which is divisible by 7

Now, let check second option (X² - Y²) is divisible by 7

∴ (X² - Y²) = ((7m)² - (7n)²) = 49 (m² - n²), which is divisible by 7

Now, let check third option (X + Y) is divisible by 14

∴ (X + Y) = ((7m) + (7n)) = 7 (m + n), which is divisible by 7 but not necessarily by 14

So, option third is incorrect

Hence, option (3) is correct

Given:

The given expression is (221)ⁿ + (221)^{n + 1}

Concept Used:

If the number is Divisible by the given number then it should be the multiple of that number

Calculation:

By using the exponential identity the given expression can be written as

∴ (221) ⁿ + (221) ^{n + 1} = (221) ⁿ + (221) ⁿ × 221

Now, by taking (221) ⁿ common we get

∴ (221) ⁿ × (221 + 1) = (221) ⁿ × 222

Now, if the value of n is 1

∴ (221) ¹ × 222 = 13 × 17 × 2 × 111

So, the given expression is divisible by 17, 13 and 2

Hence, option (4) is correct

Given:

The given number 1/x is terminating non repeating fraction

Concept Used:

Any terminating faction has the denominator is of the form of 2^m × 5ⁿ where both m and n are positive integer

Calculation:

From all the option given in the option only option three matches with the definition for the terminating decimal

Hence, option (3) is correct

Given:

x and y are prime numbers

Concept Used:

Prime numbers have exactly two factors one and the number itself

Calculation:

Let suppose x is 11 and y is 7

∴ (x + y) = (11 + 7) = 18 and (x - y) = (11 - 7) = 4

And HCF of (18 and 4) = 2

Again, Let suppose x is 3 and y is 2

∴ (x + y) = (3 + 2) = 5 and (x - y) = (3 - 2) = 1

And HCF of (5 and 1) = 1

Hence, option (1) is correct

Figures of speech used in the poem ' The Brook ' : 

Refrain:- is a repetition of a word or a phrase, for ex- 'for men may and men may go' .

Alliteration:- is the repetition of the initial consonant sound, for ex-'' I slip,I slide, I gloom, i glance.'

Onomatopoeia:- is a figure of speech that represents sound asssociated with the object,for ex- 'babble'.

Repetation:- means the repetation of a word , aphrase or  a clause to emphasise on a point, for ex- 'chatter,chatter'.

Imagery:- is a description which evokes readers senses of sight, smell, hearing,touch and taste. Metaphores and similes are also considered a imagery, for ex- "I babble on the pebbles".

Personification:- is a literary device that assigns human qualities to inanimate and abstract things, for example - 'I make a  netted sunbeam dance".

The magnetic quantum number specifies the orientation in space of an orbital of given energy and shape. This number divides the subshell into individual orbitals which hold the electrons; there are (2L+1) orbitals in each subshell. Thus, the s subshell has only one orbital, the p subshell has three orbitals, and so on.

For n=4, we have s,p,d,f subshells.

For s subshell, we have 2×0+1=1.
For p subshell, we have 2×1+1=3.
For d subshell, we have 2×2+1=5.
For f subshell, we have 2×3+1=7.

The total value of m will be 1+3+5+7=16

The principal quantum number is given as n=4

Thus the azimuthal quantum number has values, l=0 to (n−1).

∴l=0,1,2 and  3          

Electron orbitals having the same energy levels are called degenerate orbitals. As per the Aufbau principle, the lower energy levels are filled before higher energy levels. As per Hund's rule, degenerate orbitals are filled evenly before electrons are filled into higher energy levels.