Correct Answer: 4 cm

Solution :
Let $OB$ be the radius of the circle and $OD$ be the distance from the centre to the chord $AB$.
The radius of a circle, $OB$ = 5 cm
Length of chord $AB$ = 6 cm
Now, we know altitude from the centre of

Correct Answer: South Africa

Solution : The correct answer is South Africa.

In January 1915, Gandhi Ji returned to India from South Africa. They were encouraged to free themselves from decades of slavery by Mahatma Gandhi, who also taught them the value of freedom and gave them Satyagrah, the greatest

Correct Answer: famous

Solution : The correct choice is the third option.

Explanation:
The passage discusses various comic book superheroes introduced by different publishers. The context implies that the superheroes introduced by Raj comics—Nagraj, Tiranga, and Shakti—are being referred to. The word famous fits well here, as it suggests

Correct Answer: Rs. 16,400

Solution : The difference between the Simple Interest and Compound Interest on a certain sum of money $P$ for 2 years at $R$% per annum is given by:
$(CI - SI) = \frac{PR^{2}}{100^{2}}$
According to Question,
The difference between CI and SI for 2 years is

Correct Answer:

Solution : As per mirror image properties, closer things appear closer to the mirror in reflection.
According to the information provided, if the mirror is placed on the right side of the figure (on line AB), the right of the reflected image will appear as the

Correct Answer: 1,456

Solution : The demand of P, Q, and R companies is $(3800 + 4532 + 5318) = 13650$
Production of P, Q, and R companies is $(3620 + 2829 + 2833) = 9282$
Average = $\frac{\text{Sum of all the observations}}{{\text{Total number of observations}}}$
The average demand of

Correct Answer: $\frac{1}{2}$

Solution : Given: $\frac{a^2+b^2}{c^2}=\frac{b^2+c^2}{a^2}=\frac{c^2+a^2}{b^2}=\frac{1}{k}$
Solving the expressions, we get:
$k(a^2+b^2)=c^2$ (equation 1).
$k(b^2+c^2)=a^2$ (equation 2).
$k(c^2+a^2)=b^2$ (equation 3).
On adding all the equations, we get–
$(a^2+b^2+c^2)​​​​​=k(a^2+b^2+b^2+c^2+c^2+a^2)$
⇒ $(a^2+b^2+c^2)​​​​​=2k(a^2+b^2+c^2)$
⇒ $k=\frac{1}{2}$
Hence, the correct answer is $\frac{1}{2}$.

Correct Answer: $\frac{6600}{7}$ cm²

Solution : Length of minute hand = 20 cm
As we know the 1 minute angle made by the minute hand is $6^\circ$
In 45 minutes, the minute hand will make = $45(6^\circ)= 270^\circ$
Area swept by minute hand in 45 minutes
= $\frac{\theta}{360^{\circ}}\times \pi

Correct Answer: $\frac{x}{2\sqrt{2}}$

Solution :
Let BD be the distance between two posts is $x$ metres.
$\therefore$ OB = OD = $\frac{x}{2}$
From $\triangle$OCD
$\tan\theta$ = $\frac{CD}{OD}$
$\tan\theta$ = $\frac{h}{\frac{x}{2}}$= ${\frac{2h}{x}}$............(equation 1)
From $\triangle$OAB
$\tan(90–\theta)=\frac{AB}{OB}$
$\cot\theta$ = $\frac{2h}{\frac{x}{2}}$= ${\frac{4h}{x}}$............(equation 2)
Multiplying both equations, we get:
$\tan\theta×\cot\theta$ = ${\frac{2h}{x}}×{\frac{4h}{x}}$
⇒ 1

Correct Answer: 112 kg

Solution : Given:
The average weight of three men is increased by 4 kg.
One of them, whose weight is 100 kg, is replaced by another man.
According to the question,
⇒ Weight of new man = increase weight $×$ number of persons + weight of