Explore topic-wise InterviewSolutions in Current Affairs.

Correct Answer is \(\frac{\pi}{3}\)

Now, let x = \(sin^{-1}(sin\left(\frac{2\pi}{3}\right))\)

⇒ sin x =sin ( \(\frac{2\pi}{3}\)) 

Here range of principle value of sine is [\(-\frac{\pi}{2},\frac{\pi}{2}\) ]

⇒ \(x=\frac{2\pi}{3}\notin\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\)

Hence for all values of x in range [\(-\frac{\pi}{2},\frac{\pi}{2}\) ] ,the value of

\(sin^{-1}(sin\left(\frac{2\pi}{3}\right))\) is

⇒ sin x =sin ( \(\pi-\frac{\pi}{3}\)) ( \(\because\)sin ( \(\frac{2\pi}{3}\))= sin ( \(\pi-\frac{\pi}{3}\)) )

⇒ sin x =sin ( \(\frac{\pi}{3}\))

(\(\because\) sin (π - θ) = sin θ as here θ lies in II quadrant and sine is positive)

⇒ x = \(\frac{\pi}{3}\)

Correct Answer is \(\frac{\pi}{6}\)

Now, let x = \(cos^{-1}(cos\left(\frac{13\pi}{6}\right)\)

⇒ cos x =cos ( \(\frac{13\pi}{6}\)) 

Here ,range of principle value of cos is [0, π] 

⇒ x = \(\frac{13\pi}{6}\)∉ [0, π] 

Hence for all values of x in range [0, π] ,the value of 

\(cos^{-1}(cos\left(\frac{13\pi}{6}\right)\)is 

⇒ cos x =cos (2π - \(\frac{\pi}{6}\)) (\(\because\) cos ( \(\frac{13\pi}{6}\))= cos (2π - \(\frac{\pi}{6}\)) ) 

⇒ cos x =cos ( \(\frac{\pi}{6}\)) ( \(\because\)cos (2π - θ)= cosθ) 

⇒ x = \(\frac{\pi}{6}\)

The magnification of a plane mirror is 1.

The virtual image formed by a concave mirror is always magnified whereas the virtual image formed by a convex mirror is diminished.

Correct Answer is \(\frac{\pi}{6}\)

Now, let x = \(tan^{-1}\left(tan\frac{7\pi}{6}\right)\)

⇒ tan x =tan ( \(\frac{7\pi}{6}\)) 

Here range of principle value of tan is [ \(-\frac{\pi}{2},\frac{\pi}{2}\)] 

⇒ x = \(\frac{7\pi}{6}\)∉ [ \(-\frac{\pi}{2},\frac{\pi}{2}\)] 

Hence for all values of x in range [\(-\frac{\pi}{2},\frac{\pi}{2}\) ] ,the value of 

\(tan^{-1}\left(tan\frac{13\pi}{6}\right)\) is 

⇒ tan x =tan (π + \(\frac{\pi}{6}\) ) (\(\because\) tan ( \(\frac{7\pi}{6}\))= tan (π +\(\frac{\pi}{6}\)) ) 

⇒ tan x =tan ( \(\frac{\pi}{6}\)) (\(\because\) tan (π+ θ)= tan θ) 

⇒ x =\(\frac{\pi}{6}\)

Similarity:
(i) Both can form virtual images.
(ii) Both can form erect images.

Dissimilarity:
(i) A concave mirror can form a real as well as virtual image whereas convex mirror can form an only virtual image.
(ii) A concave mirror can form magnified as well as diminished image whereas convex mirror forms only diminished image.
(iii) A concave mirror can form erect as well as inverted image whereas convex mirror always forms an erect image.

We know that the image formed by a plane mirror is as much behind the mirror as object is in front. So, the speed of image will be same as object but in opposite direction. Thus, net velocity between man and his image will be 3 - (-3) = 6 m/s.

इस कविता में कवि ने संदेश दिया है कि हमें जाति-पात तथा धार्मिक भेदभाव के स्थान पर मनुष्यता को महत्व देना चाहिए। उसके अनुसार सभी मनुष्य भाई-भाई हैं कोई बढ़ा और कोई छोटा नहीं है।

The number of rays parallel to the principal axis are falling on a concave mirror which meat at a point is called principal focus of the concave mirror.

When the refractive index of a medium relative to lens is one, a convex lens will behave as an ordinary glass plate.

The refractive index of diamond is 2.42.It means that for a light ray travelling in air and entering in diamond, its speed is slowed and becomes  1/2.42 times than that in air.

Focal length of the concave mirror does not change because it is about half its radius of curvature and has nothing to do with the external medium. On the other hand, the focal length of the convex lens will increase because the refractive index of glass with respect to water is less than refractive index of glass with respect to air.

A point of the principal axis where the rays of light parallel to principal axis meet.

1 dioptre is defined as the power of a lens of focal length 1 metre.

1D=1 m^-1 

P=1/f(m)

1 dioptre is the power of a lens whose focal length is 1 metre.

The distance between the pole and the principal focus of the spherical mirror.

A right-angled prism is a better reflector because light incident on its hypotenuse is totally reflected, without absorption of light. On the other hand, in case of a plane mirror, there is a possibility of partial absorption of light.

The surface which reflects the light.

Bouncing back of light after striking any surface.

(i) Bending of light is more in the medium where refractive index is 1.50. 

(ii) Speed of light is more in the medium with refractive index 1.31

The ability of the medium to refract light is called optical density.

Group of parallel light rays emitted by the source of light.

It has no unit.

It is the path of light.

The light of single wavelength is called monochromatic light, e.g., Sodium lamp is a source of monochromatic light.

Concave mirror.

60° angle of reflection.

When medium 1 is vacuum, then refractive index of medium 2 is considered with respect to vacuum. This is called absolute refractive index.

Red is the component of white light that has the greatest wavelength.

The ratio of the height of an image to the height of an object is called magnification.

(a) Angle of incidence is equal to angle of emergence. 

(b) Incident ray is parallel to the emergent ray. 

(c) Lateral displacement is proportional to the thickness of glass slab. 

(d) Lateral displacement is proportional to the angle of incidence.

Refractive index is defined as the ratio of speed of light in medium 1 to the speed of light in medium 2 and is represented as n₂₁ and is read as refractive index of medium 2 with respect to medium 1. 

n₂₁ = speed of light in medium 1/speed of light in medium 2.

The phenomenon of lateral inversion occurs due to the reflection of light by plane mirror.

Lateral displacement is the perpendicular distance between the incident ray and the emergent ray.

If an object is placed in front of a plane mirror, then the right side of the object appears to be the left side of the image, and the left side of the object appears to be the right side of its image. This change of sides of an object and its mirror image is called lateral inversion.

Patrick never did his homework because he found it very boring. Instead of doing homework, he played hockey, basketball and Nintendo.

Patrick hated homework and loved sports. He called himself lucky when the tiny man agreed to do all his homework.

The little man was an elf. He was angry when he was called upon to do Patrick’s homework.

The little man’s tall hat is compared to the hat of a witch.

Correct option is C. a dishcloth thrown In a hamper.

Correct option is B. jacket.

Correct option is C. goggles

Correct option is A. Baseball

There are about 114 elements known at present.

(i) Mn (z = 25), Mn⁴⁺ (z = 21)

The electronic configuration of Mn⁴⁺ to Given by

1s² 2s² 2p⁶ 3s² 3p⁶ 3d³

As the outermost shell 3d has 3 electrons, thus the number of unpaired electrons is 3.

(ii) Fe (z = 26), Fe³⁺ (z = 23)

The electronic configuration of Fe³⁺ is given lay

1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵

The number of unpaired electron is 5.

(iii) Cr (z = 24), Cr²⁺ (z = 22)

The electronic configuration of Cr²⁺ is

1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁴

The number of unpaired electron is 4.

(iv) Zn (z = 30), Zn²⁺ (z = 28)

The electronic configuration of Zn²⁺ is

1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰

The number of unpaired electron is 0.

5³ = 5 × 5 × 5 = 125 

3⁵ = 3 × 3 × 3 × 3 × 3 = 243 is greater. 

125 < 243 (or) 243 > 125 

So, 5³ < 3⁵ (or) 3⁵ > 5³

When Kaki crept into the courtyard where guests were having dinner, one of the guests felt disgusted and raised an alarm that all should be careful of her. Looking at this, Pandit Buddhiram became furious. He caught Kaki with his hands and dragged her into the room.

When Rupa saw Kaki sitting close to the Kadhai, she became angry and shook Kaki with both her hands and shouted abuses. Kaki felt insulted.

One day a lion lay down under a shady tree to sleep. While he slept, a playful mouse ran over his body. The lion woke up. He put out his great paw and was just going to kill the mouse. The little mouse begged for mercy. The lion took pity on him and let him go. The mouse thanked the lion. “I will try to repay your kindness”, said the mouse. The lion laughed at this. 

Several days passed by. Then, while hunting in the forest, the lion was caught in a trap. He struggled and roared to get free. The little mouse heard the noise and ran to help him. At once he began nibbling at the massive ropes with his sharp teeth. After much hard work, he gnawed through the ropes. At last the lion was set free.