Correct Answer:

Solution : In the given series, the small circle alternates shaded and unshaded and moves clockwise from one corner to another. Also, the figure at the centre of the box is moving 45° anticlockwise.
Thus, the answer figure is –

Therefore, the series becomes –

Hence, the fourth

Correct Answer: 4.2

Solution : The correct option is 4.2.

One calorie of heat energy is equivalent to approximately 4.2 joules of mechanical energy. The calorie is a unit of energy commonly used in the field of thermodynamics and represents the amount of heat required to raise the temperature

Correct Answer: $\frac{(x^{64}-\frac{1}{x^{64}})}{(x^2+\frac{1}{x^2})}$

Solution : Given:
$(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x-\frac{1}{x})(x^{16}+\frac{1}{x^{16}})(x+\frac{1}{x})(x^{4}+\frac{1}{x^{4}})$
$=(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^2-\frac{1}{x^2})(x^{16}+\frac{1}{x^{16}})(x^{4}+\frac{1}{x^{4}})$
Multiplying it by $\frac{(x^2+\frac{1}{x^2})}{(x^2+\frac{1}{x^2})}$, we get,
$= \frac{(x^2+\frac{1}{x^2})}{(x^2+\frac{1}{x^2})}×(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^2-\frac{1}{x^2})(x^{16}+\frac{1}{x^{16}})(x^{4}+\frac{1}{x^{4}})$
$= \frac{1}{(x^2+\frac{1}{x^2})}×(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^{16}+\frac{1}{x^{16}})(x^{4}+\frac{1}{x^{4}})(x^{4}-\frac{1}{x^{4}})$
$= \frac{1}{(x^2+\frac{1}{x^2})}×(x^{32}+\frac{1}{x^{32}})(x^{8}+\frac{1}{x^{8}})(x^{16}+\frac{1}{x^{16}})(x^{8}-\frac{1}{x^{8}})$
$= \frac{1}{(x^2+\frac{1}{x^2})}×(x^{32}+\frac{1}{x^{32}})(x^{16}+\frac{1}{x^{16}})(x^{16}-\frac{1}{x^{16}})$
$= \frac{1}{(x^2+\frac{1}{x^2})}×(x^{32}+\frac{1}{x^{32}})(x^{32}-\frac{1}{x^{32}})$
$= \frac{1}{(x^2+\frac{1}{x^2})}×(x^{64}-\frac{1}{x^{64}})$
$= \frac{(x^{64}-\frac{1}{x^{64}})}{(x^2+\frac{1}{x^2})}$
Hence, the correct answer is $\frac{(x^{64}-\frac{1}{x^{64}})}{(x^2+\frac{1}{x^2})}$.

Correct Answer: 7,400

Solution : Amount invested by A = INR 92,500
Amount invested by B = INR 1,12,500
B's share in profit = INR 9,000
Let the profit earned by A be INR $x$.
According to the question,
$(\frac{92500}{112500}) = (\frac{x}{9000})$
⇒ $x = \frac{(92500 × 9000)}{112500}$
⇒ $x

Correct Answer: Disipline

Solution : The correct choice is the second option.

The misspelt word among the options provided is "disipline", which should be spelt as discipline. The reason for the incorrect spelling is that it does not contain the letter "c", and it refers to a code

Correct Answer: $7 \mathrm{~cm}$

Solution :
Given,
AD is a diameter
AC is a chord
OB = 7
$\angle{OBA} = 60°$
$\angle{DOC} = 60°$
Now, $\angle{DOC} + \angle{AOC} = 180°$ (The sum of the angles on a straight line is 180°) 
⇒ $60° + \angle{AOC} = 180°$
⇒ $ \angle{AOC}=

Correct Answer: Mahmud of Ghazni

Solution : The correct option is Mahmud of Ghazni

Mahmud of Ghazni was the ruler of Afghanistan, and he resorted to attacks and raids to fulfil the economic requirements of his native kingdom. Under his rule, Ghazni achieved several conquests. When Ghazni invaded India, it

Correct Answer: a-3, b-1, c-4, d-2

Solution : The correct option is a-3, b-1, c-4, d-2.

The Chinook results from Pacific air rising, and descending over the Rocky Mountains, melting snow rapidly. Foehn occurs when moist air rises, cools and descends on the leeward side of mountains, creating a warm,

Correct Answer: 3 : 1

Solution : At a profit of 30%, the selling price (SP) is Rs. 39.
Let the cost price (CP) of the mixture be Rs. $x$.
So, $\frac{130x}{100} = 39$
$\therefore$ CP = 30
By using the alligation rule,

Required ratio = (Mean value – Lower

Correct Answer: OIGDMU

Solution : Given: 
FRIEND is written as IIFDME, and DEMAND is written as MVDDMA. 

FRIEND is written as IIFDME  –

And, DEMAND is written as MVDDMA –

Similarly, follow the same pattern for GROUND –

So, GROUND is written as OIGDMU in the code language. Hence, the