Correct Answer: 2 cm

Solution :
AC = $2 \sqrt{2}$ cm
Also, $\angle$B = 90°, and $\angle$C = 45°
Applying angle sum property in triangle ABC,
$\angle$ A + $\angle$ B + $\angle$ C = 180°
or, $\angle$A + 90° + 45° = 180°
or, $\angle$A = 45°
Since, $\angle$A

Correct Answer:

Solution : Brother and Husband come under the category of men. They cannot be women. So, their circles will lie inside that of men.
Also, a brother can be a husband and a husband can be a brother. So, they will have some areas in common in the

Correct Answer: The President

Solution : The correct answer is The President.

The President has the authority to convoke and prorogue either House of Parliament or dissolve the Lok Sabha. The Lower House is dissolved when five years have passed since the first day of its sessions, by Article 83(2)

Correct Answer: Polyamide polymer

Solution : The correct answer is Polyamide polymer.

Nylon polymers are synthetic polymers derived from polyamide polymers. Polymerization produces Nylon polymers, such as Nylon-6, and forms repeating units known as monomers. Because of their strength and adaptability, These synthetic polymers have many applications in textiles, plastics

Correct Answer: 8

Solution : Given: Whole surface area = 340 cm²
Area of each lateral face = 30 cm²
Area of base = 100 cm²
Whole surface area = lateral surface area + area of the base
⇒ 340 = lateral surface area + 100
$\therefore$

Correct Answer: 2

Solution : $\frac{a^{2}-bc}{a^{2}+bc}+\frac{b^{2}-ca}{b^{2}+ca}+\frac{c^{2}-ab}{c^{2}+ab}=1$
Adding 3 on both sides,
$⇒(\frac{a^{2}-bc}{a^{2}+bc}+1)+(\frac{b^{2}-ca}{b^{2}+ca}+1)+(\frac{c^{2}-ab}{c^{2}+ab}+1)=1+3$
$⇒(\frac{a^{2}-bc+a^{2}+bc}{a^{2}+bc})+(\frac{b^{2}-ca+b^{2}+ca}{b^{2}+ca})+(\frac{c^{2}-ab+c^{2}+ab}{c^{2}+ab})=4$
$⇒(\frac{2a^{2}}{a^{2}+bc})+(\frac{2b^{2}}{b^{2}+ca})+(\frac{2c^{2}}{c^{2}+ab})=4$
$⇒\frac{a^{2}}{a^{2}+bc}+\frac{b^{2}}{b^{2}+ac}+\frac{c^{2}}{c^{2}+ab}=2$
Hence, the correct answer is 2.

Correct Answer: $-21\sqrt{5}$

Solution : Given: $x^2-7 x+1=0$
⇒ $x+\frac{1}{x}=7$
Squaring the equation, we get,
$(x+\frac{1}{x})^2=7^2$
⇒ $x^2+\frac{1}{x^2}+2=49$
⇒ $x^2+\frac{1}{x^2}=47$
And we know, $(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-2$
⇒ $(x-\frac{1}{x})^2=47-2=45$
⇒ $x-\frac{1}{x}=\pm\sqrt{45}$
⇒ $x=-\sqrt{45}$ [As $0<x<1$]
Now consider, $x^2-\frac{1}{x^2}$
Using $a^2-b^2=(a-b)(a+b)$
$=(x+\frac{1}{x})(x-\frac{1}{x})$
$=7\times (-\sqrt{45})$
$=-7\times 3\sqrt5=-21\sqrt5$
Hence, the correct answer is $-21\sqrt5$.

Correct Answer: Only conclusion III follows

Solution : The possible Venn diagram according to the given statements is as follows –

Let's analyse the conclusions –
Conclusion I: All desks are plates – From the above diagram, it is clear that only some parts of the circle that are desks

Correct Answer: We demand an enquiry

Solution : The first option is correct.

Active voice is the voice in which the subject performs the action expressed by the verb. In an active voice construction, the subject is the doer of the action, and the recipient of the action, if there

Correct Answer: Rs. 2000

Solution : Given: A man invested a sum of money at compound interest. It amounted to Rs. 2420 in 2 years and Rs. 2662 in 3 years.
Let the sum be p and the rate of interest per annum be r%.
Here, Rs. 2420 yield interest