Correct Answer: $5\frac{1}{2}$

Solution : $\sin^{2}1^{\circ}+\sin^{2}11^{\circ}+\sin^{2}21^{\circ}+\sin^{2}31^{\circ}+\sin^{2}41^{\circ}+\sin^{2}45^{\circ}+\sin^{2}49^{\circ}+\sin^{2}59^{\circ}+\sin^{2}69^{\circ}+\sin^{2}79^{\circ}+\sin^{2}89^{\circ}$
Using the identity $\sin(90^{\circ} - \theta) = \cos\theta$, we get,
$\sin^{2}49^{\circ}=\sin^{2}(90^\circ-41^{\circ}) = \cos^2{41}^\circ$
$\sin^{2}59^{\circ}=\sin^{2}(90^\circ-31^{\circ}) = \cos^2{31}^\circ$
$\sin^{2}69^{\circ}=\sin^{2}(90^\circ-21^{\circ}) = \cos^2{21}^\circ$
$\sin^{2}79^{\circ}=\sin^{2}(90^\circ-11^{\circ}) = \cos^2{11}^\circ$
$\sin^{2}89^{\circ}=\sin^{2}(90^\circ-1^{\circ}) = \cos^2{1}^\circ$
$=\sin^{2}1^{\circ}+\sin^{2}11^{\circ}+\sin^{2}21^{\circ}+\sin^{2}31^{\circ}+\sin^{2}41^{\circ}+\sin^{2}45^{\circ}+\cos^{2}41^{\circ}+\cos^{2}31^{\circ}+\cos^{2}21^{\circ}+\cos^{2}11^{\circ}+\cos^{2}1^{\circ}$Each pair adds up to $1$ because $\sin^{2}\theta + \cos^{2}\theta = 1$
$=5+\sin^{2}45^{\circ}$
$=5+\frac{1}{2}$
$=\frac{11}{2}=5\frac{1}{2}$
Hence, the correct answer

Correct Answer: Recessionary gap
    

Solution : The correct answer is (a) Recessionary gap.

A recessionary gap occurs when the equilibrium level of output in an economy is below the potential level of output. When aggregate supply exceeds aggregate demand, it means that businesses are producing more goods and services than

Correct Answer: Daughter's son

Solution : Given:
P – Q ⇒ P is the wife of Q
P ÷ Q ⇒ P is the husband of Q
P × Q ⇒ P is the son of Q
P + Q ⇒ P is the daughter of Q

As per the

Correct Answer: (3)

Solution : The error lies in the third part of the sentence.

The reason for the error is the incorrect usage of subject-verb agreement. "User" is a singular noun, so the verb should be "is" instead of "are" to match in singular form.

So, the correct sentence

Correct Answer: Tire

Solution : The correct choice is the third option.

Explanation: Invigorate means to fill with energy or vitality, to refresh and stimulate. The word typically conveys a sense of renewal and increased vigour. On the other hand, the antonym tire refers to the state of becoming

Correct Answer: $0$

Solution : $x = \sqrt[3]{3} + 2$
⇒ $x - 2 = \sqrt[3]{5}$
By cubing on both the sides,
$⇒x^3-6x^2+3x (-2)^2-2^3=5$ [since $(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$]
$⇒x^3-6x^2+12x-8-5=0$
$⇒x^3-6x^2+12x-8-5=0$
$⇒x^3-6x^3+12x-13=0$
Hence, the correct answer is $0$.

Correct Answer: It provides insights into social and cultural aspects 

Solution : The Mahabharata is considered a significant text for studying ancient Indian society because it provides insights into social and cultural aspects, reflecting the values and beliefs of the time.

Correct Answer: buy a pair of scissors

Solution : The correct choice is the third option.

Explanation: The sentence needs "a pair of scissors" because "scissors" is a plural noun. "Pair" is used to indicate two connected objects functioning together. The sentence means she's purchasing a tool with

Correct Answer: 14

Solution : The correct answer is 14.

The President can appoint up to 12 Rajya Sabha members with exceptional expertise or practical experience in sectors such as literature, science, art, and social service. If the President considers that the Anglo-Indian community is underrepresented in the Lok Sabha,

Correct Answer: Rural poor

Solution : The 'Garibi Hatao' campaign primarily targeted the rural poor, aiming to address their needs and alleviate poverty through various social welfare programs.