Correct Answer: 8

Solution : If $\triangle \mathrm{A B C}$ is similar to $\triangle \mathrm{PQR}$
⇒ $\frac{\text{Ares of triangle ABC}}{AB^2}=\frac{\text{Area of triangle PQR}}{PQ^2}$
⇒ $\frac{32}{AB^2}=\frac{50}{10^2}$
⇒ $AB^2=\frac{32}{50}\times 100$
⇒ $AB^2=64$ cm
⇒ $AB=\sqrt{64}=8$ cm
Hence, the correct answer is 8 cm.

Correct Answer: power of a lens

Solution : The correct answer is the power of a lens.

The focal length determines the lens's power. The power of a lens will decrease with increasing focal length and increase with decreasing focal length. Light has less power if there is less bending

Correct Answer:

Solution : In the given series,
1. The triangle changes its position in each alternate box in the clockwise direction while it gets inverted. This shift happens at the corner of the box.
2. The arrow is fixed in its position and rotates in a clockwise direction as

Correct Answer: national park

Solution : The correct option is the national park.

A national park is a designated area for the conservation, preservation, and welfare of wildlife, and their natural ecosystems. National parks seek to protect biodiversity, ecosystems, and natural landscapes while also facilitating scientific study, education, and

Correct Answer: Sharavati

Solution : The correct option is Sharavati.

The drop of the Sharavati River is Jog Falls, one of the tallest waterfalls in India. It is situated in the Indian state of Karnataka. The Sharavathi River plunges from a height of about 830 feet (253 metres) into four

Correct Answer: DCEB

Solution : Let's check the options –
First option: DCEB; There is only one vowel and three consonants in this option.
Second option: PNQST; This option contains five consonants and no vowels.
Third option: VKHGM; This option contains five consonants and no vowels.
Fourth option: WPZLH; This

Correct Answer: 60°, 40°, 80°

Solution : The sum of all angles of the triangle should be 180°.
From the above-given options, only option 2 satisfies the condition.
Option 2: 60°, 40°, 80°
Sum of angles = 60° + 40° + 80° = 180°
Hence, the correct answer is 60°,

Correct Answer: 2

Solution : We know: $\sin (90^{\circ} -A) = \cos A$ and $\sin^2 A+\cos^2 A = 1$
$\frac{\sin^2 32^{\circ}+\sin^2 58^{\circ}}{\cos^2 32^{\circ}+\cos^2 58^{\circ}}+\sin^2 53^{\circ}+\cos 53^{\circ} \sin 37^{\circ}$
= $\frac{\sin^2 32^{\circ}+\sin^2 (90-32)^{\circ}}{\cos^2 32^{\circ}+\cos ^2 (90-32)^{\circ}}+\sin^2 53^{\circ}+\cos 53^{\circ} \sin (90-53)^{\circ}$
= $\frac{\sin^2 32^{\circ}+\cos^2 32^{\circ}}{\cos^2 32^{\circ}+\sin^2 32^{\circ}}+\sin^2 53^{\circ}+\cos 53^{\circ} \cos 53^{\circ}$
=

Correct Answer: 29 : 22

Solution : Given:
$\frac{x}{y} = \frac{5}{2}$
⇒ $x= \frac{5y}{2}$
We have to find $\frac{8x+9y}{8x +2y}$
Putting the value of x in the above equation,
$\frac{8\times \frac{5y}{2}+9y}{8\times \frac{5y}{2} +2y} = \frac{4\times 5y+9y}{4\times 5y +2y} = \frac{20y+9y}{20y +2y}=\frac{29y}{22y} = \frac{29}{22}$
$\therefore$ The ratio is 29 : 22

Correct Answer: They were irresponsible in performing their duties.

Solution : The correct choice is the fourth option.

The sentence with no spelling error is: They were irresponsible in performing their duties.

The first option contains the incorrect spellings "iresponsible" and "duties" whereas the correct spellings are irresponsible and duties