Correct Answer: $2–\sqrt{2}: \sqrt{2}$

Solution :
Given: ABC is an isosceles right-angle triangle. $\angle ABC = 90 ^{\circ}$ and AB = 12 cm.
In $\triangle ABC$, $H^2=B^2+P^2$ (Using Pythagoras theorem).
⇒ $H^2=12^2+12^2$
⇒ $H^2=144+144=288$
⇒ $H=\sqrt{288}=12\sqrt2$ cm
Inradius of inscribed circle of right angled triangle = $\frac{(P + B –

Correct Answer: 14

Solution : Given:
(2, 2, 4); (1, 6, 6); (7, 2, ?)

Like, (2, 2, 4)→2 × 2 = 4
(1, 6, 6)→1 × 6 = 6
Similarly, (7, 2, ?)→7 × 2 = 14

So, 14 is the required answer. Hence, the first option is correct.

Correct Answer: $\frac{3816}{325}$

Solution : Given: The series is $\frac{7}{2}+\frac{11}{3}+\frac{7}{6}+\frac{11}{15}+\frac{7}{12}+\frac{11}{35}+\ldots \ldots+\frac{7}{156}+\frac{11}{575}$.
Determine the value of the series by solving two distinct series independently.
The sum of the first series = $\frac{7}{2}+\frac{7}{6}+\frac{7}{12}+...+\frac{7}{156}$
⇒ Sum = $7[1–(\frac{1}{2})+(\frac{1}{2}–\frac{1}{3})+(\frac{1}{3}–\frac{1}{4})+...+(\frac{1}{12}–\frac{1}{13})]$
⇒ Sum = $7[1–\frac{1}{13}]$
⇒ Sum = $7\times\frac{12}{13}=\frac{84}{13}$
The sum of the second series =

Correct Answer: $3\sqrt{5}-7$

Solution : Given: $x+[\frac{1}{(x+7)}]=0$
Adding both sides 7, we get,
⇒ $x+7+[\frac{1}{(x+7)}]=7$
Squaring both sides, we get,
⇒ $(x+7)^{2}+(\frac{1}{x+7})^{2}+2=49$
⇒ $(x+7)^{2}+(\frac{1}{x+7})^{2}=47$
Subtracting 2 from both sides,
$(x+7)^{2}+(\frac{1}{x+7})^{2}–2=47-2$
⇒ $[(x+7)-(\frac{1}{x+7})]^{2}=45$
⇒ $[(x+7)-(\frac{1}{x+7})]=\sqrt{45}$
⇒ $[(x-\frac{1}{x+7})]=\sqrt{45}-7=\sqrt{9 \times5}-7=3\sqrt{5}–7$
Hence, the correct answer is $3\sqrt{5}-7$.

Correct Answer: 26

Solution : $27^{27}+27$ can written as $27^{27}+1^{27}-1+27=(27^{27}+1^{27})+26$
We know that Aⁿ + Bⁿ is divisible by A + B when n is odd.
Here n = 27 is an odd number.
When $(27^{27}+1^{27})$ is divided by 28, the remainder will be 0.
And, when $(27^{27}+1^{27})+26$

Correct Answer:

Solution : As there is no restriction on the rotation of the figure, we will check all possible angles where the question figure can fit itself in all the given option figures.
The question figure is embedded only in the first option figure.

Hence, the first option is

Correct Answer: Metres

Solution : Given:
Weight : Pound :: Height : ?

Like, a Pound is a unit used to measure Weight.
Similarly, the unit used to measure Height is metre.

Hence, the second option is correct.

Correct Answer: 1056

Solution : Given:

156, 506, ?, 1806

Here,

12² + 12 = 156

22² + 22 = 506

32² + 32 = 1056

42² + 42 = 1806

So, the missing number is 1056.

Hence, the first option is correct.

Correct Answer: Enthusiastic

Solution : The correct choice is the second option.

The word keen has a few potential synonyms, but the most appropriate one among the options provided would be enthusiastic.

The meanings of other words are as follows:

• Happy refers to a feeling of pleasure, contentment,

Correct Answer: 69

Solution : Total number of students = 40 + 52 = 92
⇒ $75 = \frac{\text{(Sum of scores of all students)}}{92}$
⇒ Total score in mathematics = 75 × 92 = 6900
Now,
Let the average score of section B students be $x$
⇒ Average score of