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:

Solution : Because there is no restriction on the rotation of the figure, we will check all possible orientations of the option figures to determine which one may fit in the question figure. By comparison of all the option figures, only the third option figure is embedded in

Correct Answer: neither loss nor profit

Solution : As per the graph,
The total income of companies M and N = 35 + 50 = Rs. 85 crore
The total expenditure of companies M and N = 45 + 40 = Rs. 85 crore
Since both the income and expenditure

Correct Answer: Zero

Solution : The correct option is zero.

Bacterial cells lack mitochondria for various reasons, including bacteria being prokaryotic cells, which implies their structures are significantly simpler than those of eukaryotic cells. Bacteria did not form mitochondria since they did not obtain these organelles through endosymbiosis.

Correct Answer: Golf

Solution : The correct answer is Golf.

Ryder Cup is a prestigious golf championship which is held every two years. It happens between the teams of the United States of America and Europe only. It was established in 1927 in the USA by Samuel Ryder. He

Correct Answer: 2197

Solution : Given:
13 : ? :: 8 : 512 :: 11 : 1331

Like, (8 : 512)→(8³ = 512
(11 : 1331)→(11)³ = 1331
Similarly, follow the same pattern for (13 : ?)→(13)³ = 2197

Therefore, 2197 is the required answer. Hence, the

Correct Answer: 57.14%

Solution : As per the given table,
The total yearly expenses = Rs. 28 lakhs
The combined expense of raw materials and interest = Rs. 12 lakh + Rs. 4 lakh = Rs. 16 lakhs
$\therefore$ The required percentage of total expenses
$=\frac{\text{Combined expenses of raw materials

Correct Answer: Blade

Solution : Given:
Car : Steering :: Fan : ?

Like, a Car is controlled or operated by using its steering wheel.
Similarly, for Fan, its operation is facilitated by its blades.

Hence, the fourth option is correct.

Correct Answer: Each candidate was making tall promises.

Solution : The correct choice is the fourth option.

Active voice emphasises the doer of the action, while passive voice emphasises the receiver. To convert passive to active, we make the subject perform the action and rephrase the verb.

The structure of

Correct Answer: cyclic trapezium

Solution :
$\angle$BAP = $\angle$ABQ and AB $\neq$ PQ
Now, $\angle$BAP + $\angle$BQP = 180°
⇒ $\angle$ABQ + $\angle$BQP = 180°
⇒ AB || PQ
So, ABQP is a cyclic trapezium.
Hence, the correct answer is cyclic trapezium.