Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

The figure shown below is a system of two masses `3 kg` and `6 kg` and massless pulley accelerating upwards with `2 m//s^(2)`. If the value of `T_(2)` is `(288)/(x)N`, then the value of x is

Answer» Correct Answer - 3
`T_(1) - 30 = 3a_(1)`
`T_(1) - 60 = 6a_(2)`
`a_(1) + a_(2) = 2a_(3) = 2 xx 2`
`a_(1) + a_(2) = 4`
`(T_(1) - 30)/(3) + (T_(1) - 60)/(6) = 4`
`2T_(1) - 60 + T - 60 = 4 xx 6`
`3T_(1) - 120 = 24`
`T_(1) = (144)/(3) N`
`T_(2) = 2T_(1) = (288)/(3) N`
2.

What is an Interface?

Answer»

An interface is a list of methods that must be defined by any class which implements that interface. 

It may also define constants (public static final). In Java an interface is similar to an abstract class in that its members are not implemented.

3.

In the statement given below, which statement will be executed next if the value of a=5 and b=10? If ((a>4) || b<7) jlabel1.setText(“ Greater”); else jlavel1.setText(“ Lesser”);

Answer»

The statement is: jlavel1.setText(“ Greater”);

4.

What is the starting /first index value for a jList and a jCombobox control?

Answer»

The first item is added at index (); the next item is added at index 1 and so forth in case of a jComboBox and jList controls.

5.

At 6:20 when Ang Dorjee and I stepped out from the South Col, it was a perfect day. There was a gentle breeze but the cold was intense. I was, however, warm in my well-insulated (covered as not to allow heat to go out) climbing gear.We climbed unroped (without taking help of a rope). Ang Dorjee set a steady pace but I had no difficulty keeping up with him. The steep (a sharp slope) frozen slopes were as hard and brittle (easily breakable) as sheets of glass. We had to use the ice-axe and I had to kick really hard to get the front teeth of the crampons (boots with spikes) to bite into the frozen surface. I took every step very deliberately on the dangerous stretches.In less than two hours, we reached the Summit Camp. Ang Dorjee looked back and asked if I was tired. I replied, “No,” to his surprise and delight. He told me that the earlier Summit Party had taken four hours to reach the Summit Camp and added that if we could keep our present * pace, we would be on the Summit by 1:00 p.m.(1) How was Bachendri warm in spite of the intense cold ?(2) How did they start climbing?(3) How had she to use her ice-axe ?(4) Bachendri and Ang Dorjee climbed faster. How can you say so?(5) How would they be able to be on the Summit by 1:00 p.m.?

Answer»

(1) In spite of the intense cold Bachendri was warm because she was in her . well-insulated climbing gear.

(2) They started climbing unroped.

(3) Since the steep frozen slopes were hard and brittle, Bachendri had to kick the ice-axe hard to get the front teeth of the crampons to bite into the frozen surface.

(4) Bachendri and Ang Dorjee climbed faster.
We can say so because they took two hours to climb, while the earlier Summit Party had taken four hours to reach the Summit Camp.

(5) If they keep up their present pace (speed), they would be on the Summit by 1:00 p.m.

6.

Lhatoo was following us and caught up with (succeeded in reaching) us when we rested below the South Summit. After drinking some tea,’ we moved on. Lhatoo had brought a nylon rope so Ang Dorjee and I roped up while Lhatoo walked in the middle, holding the rope with one hand, more for balance than security.Lhatoo noticed that I had been climbing with oxygen at about two and a half litres per minute against the normal four for these heights. After he increased the oxygen flow on my regulator I found even the steeper stretches (distance) comparatively easy. (1) When did Lhatoo catch up with Bachendri and Ang Dorjee?(2) Why was Lhatoo holding the rope ?(3) At those heights what should be the normal amount of oxygen that one should breathe in?(4) Why did Lhatoo increase the flow of oxygen on Bachendri’s regulator?(5) What was the result of increase in the oxygen flow?

Answer»

(1) When Bachendri and Ang Dorjee were resting below the South Summit, Lhatoo caught up with them.

(2) Lhatoo was holding the rope more for balance than security for Bachendri and Ang Dorjee.

(3) At those heights the normal amount of oxygen that one should breathe in should be four litres per minute.

(4) Lhatoo increased the flow of oxygen on Bachendri’s regulator because it was just two and a half litres per minute against the normal four for those heights.

(5) As the result of increase in the oxygen flow, Bachendri found even the steeper stretches comparatively easy.

7.

The point defects that lower the density of crystal is called–(a) Schotty defects(b) Frankel fefects(c) Both (a) and (b)(d) None of them

Answer»

The point defects that lower the density of crystal is called Schotty defects

Shotty deffects
8.

In a lake, stream direction is as shown in the figure. A man starting from the point P on the bank wants to move to the A. along PQB. along PRC. In a direction in between PQ and PRD. in all cases he would reach at the same time

Answer» Correct Answer - A
the man must swim along the direction of shortest distance
9.

What is the difference between jComboBox and jListBox. Give one method of each of them?

Answer»

jComboBox is like a drop down box - you can click a drop-down arrow and select an option from a list whereas jList provides a scrollable set of items from which one or more may be selected. 

getSelectedItem() for combobox 

getSelectedValue() for list

10.

If a particle rotates along a circle of radius 3 m with an angular acceleration of `(pi)/(2) "rad"//s^(2)` starting from rest, then its average velocity over the time it covers quarter circle is :A. `1 m//s`B. `2 m//s`C. `3 m//s`D. `4 m//s`

Answer» Correct Answer - C
`theta = omega_(0) t + (1)/(2) alpha t^(2)`
`(pi)/(2) = 0 + (1)/(2) (pi)/(2) t^(2)`
`t = sqrt2`
average `v = (s)/(t) = (R sqrt2)/(sqrt2) = R = 3 ms^(-1)`
11.

A force F is applied to the initially, stationary cart. The variation of force with time is shown in the figure. The speed of cart at t = 5 s is A. 4B. `0.67`C. `3.75`D. `2`

Answer» Correct Answer - B
Here
`F = 5t^(2)`
`f_("max") = mu N = 5N`
`a = (5t^(2) - 5)/(10)`
`underset(0)overset(v)(int) dv = underset(1)overset(2)(int) (1)/(2) (t^(2) - 1) dt`
`v = (1)/(2)[(t^(3))/(3) - t]_(1)^(2)`
`v = (2)/(3) m//s`
12.

A light particle of mass m is connected to another very heavy particle by means of a light inextensible string that passes over a smooth pulley. The reading of the spring balance is approxinately A. `4 mg`B. `gt gt mg`C. zeroD. `2 mg`

Answer» Correct Answer - A
`T = (2m_(1)m_(2)g)/(m_(1) + m_(2))`
`m_(1) = m`
`m_(2) =` very heavy mass (M)
`T = (2mg)/((m+ M)/(M))`
`T = (2mg)/(1 + (m)/(M))`
`T ~~ 2mg" " m lt lt M`
spring balance will measure
`2T = 2 xx 2mg = 4 mg`
13.

The acceleration of a particle depends on displacement covered in a time as `a = s + 5`. It is given that initially `s = 0` and `v = 5 m//s`, then which of the following is possibly correct ?A. `v = s + 5`B. `v = sqrt(s + 5)`C. `v = "log"_(e) ((s + 5)/(5))^(2)`D. `v = "log"_(e) ((s + 5)/(s))`

Answer» Correct Answer - A
`a = s + 5`
`v (dv)/(ds) = + 5`
`underset(s)overset(v)(int) vdv = underset(0)overset(s)(int) v ds + underset(s)overset(s)(int) 5 ds`
`[(v)/(2)]_(s)^(v) = (s^(2))/(2) + 5s`
`(v^(2) - 2s)/(2) = (s^(2) + 10s)/(2)`
`v^(2) = s^(2) + 10s + 2s`
`v^(2) = (s + 5)^(2)`
`v = +- (s + 5)`
`v = s + 5`
14.

A particle is projected from point A on the ground at an angle `theta` with horizontal. Another particle is projected from point B simultaneously from height `4 H` above point A with same velocity A and B are in the same vertical plane, where H is the maximum height attained by the particle A, Both the particle collide at the same time on the ground. Find the angle at which particle B is projected with hoizontal.A. `theta` upwardsB. `theta` downwardsC. zeroD. None of these

Answer» Correct Answer - C
`T_(A) = (2v sin theta)/(g) = (2 sqrt2gh)/(g) = sqrt((2g 4H)/(g))`
`( :. H = (u^(2) sin^(2) theta)/(2g))`
`:. T_(A) = T_(B) = sqrt(2 xx ((4H))/(g))`
`rArr (u_(B))_(y) = 0`
Hence particle B is projected horizontally.
15.

The angle of rotation of a particle is given as a function of time as `theta = theta_(1) + at + bt^(2)` where `theta_(0)` is initial angular displacement and a and b are constants. If the initial angular velocity is `3 pi` radians per second and after 2 sec angulare velocity is `8 pi` radians per second, then a and b respectively in SI unit are:A. `3 pi, 3pi`B. `3pi, 1.25 pi`C. `1.2pi, 3pi`D. `1.25 pi, 1.25 pi`

Answer» Correct Answer - B
`omega = (d theta)/(dt) = a + 2bt`
`3 pi = a + 2b xx 0`
`8 pi = a + 4b`
Solving above, we get a and b.
16.

A block of mass `12 kg` moving on a rough horizontal surface having `(mu_(k) = 0.5, mu_(s) = 0.6)` with a speed `2 m//s` at any instant and a 12 N force is acting opposite to its motion as shown in figure. Friction force acting on the block is A. `72 hat(i) N`B. `-72 hat(i) N`C. `60 hat(i) N`D. `-60 hat(i) N`

Answer» Correct Answer - C
`f_("max") = mu_(k) N`
`= mu_(k) xx 12g`
`= 0.5 xx 120`
`60 N`
since block is in motion kinetic friction acts on it.
17.

Give any two methods of JOptionPane

Answer»

showMessageDialog() 

showConfirmDialog() 

showInputDialog()

18.

double c, x = 5,y = 10; int z = 51; c = x*y+z/2.5;What is the value now stored in c?

Answer»

Correct answer is 70.4

19.

5. Two particles P and Q are moving with constant velocities of (i + j) m/s and (-i + 2j) m/s respectively. At time t = 0, P is at origin and Q is at a point with position vector (2i + j)m. If the equation of the trajectory of Q as observed by P is x + 2y = n, then find n.6. A boat moves relative to water with a velocity half of the river flow velocity. If the angle from the direction of flow at which the boat must move relative to stream direction to minimize drift is 2π/n, then find n.7. A swimmer crosses the river along the line making an angle of 45 with the direction of flow. Velocity of the river water is 5m/s. Swimmer takes 6 second to cross the river of width 60m if the velocity of swimmer with respect to water is 5√n m/s. Then find n.

Answer»

5. The value of n will be 4.

Explanation:

As given, velocity of point P is Vp = (i + j)
The velocity of Point Q is Vq = (-i + 2j)
Displacement of point P is x1i + y1j = (i + j) × t 
Displacement of point Q is (x2 − 2)i + (y2 - 1)j =  (−2i + j) × t
Displacement of point Q with respect to P is
[(x2 − 2)i + (y2 - 1)j] - (x1i + y1j) = (-i + 2j) x t - (i + j) x t 
(x2 − x1)i + (y2 - y1)j - 2i - j = (-i + 2j) x t - (i + j) x t 
(x − 2)i + (y - 1)j = (−2 it + tj)      [as (x2 − x1) = x and (y2 − y1) = y]
x − 2 = −2t  _______(i)
and y − 1 = t _______(ii)

x − 2 = −2(y − 1)
x − 2 = −2y + 2 
2y + x = 4
comparing with the given eqn n = 4


6. The value of n will be 3.

Explanation:

Let the relative velocity of boat be 'v' m/s making an angle ϴ with vertical.

Then,the velocity of river is '2v' in hrizontal direction.
Now, break velocity of boat in respective components.
vx = 2v - vsinϴ
vy = vcosϴ
Let width of the river be d.
So, Time required to cross the river,t d/vcos(ϴ).
Drift ,x = vx x t = 2v - vsinϴ x  d/vcos(ϴ)
For min. drift,
dx/dϴ = 0
d/dϴ [d/v(2vsecϴ - v tanϴ)]
2vtanϴ - v secϴ = 0
sin ϴ = 1/2
ϴ = 30

This angle is the angle made with the vertical. Therefore the total angle made with the direction of river flow is 90+30=120 degree which is equal to 2π/3.

Hence, n = 3.

7. The value of n is 5.

Explanation:

Let the velocity of the swimmer be v m/s.
So, velocity along vertical direction is v sin45°
Total width = 60 m and time taken = 6 s
So, v sin45° = 60/6
v/√2 = 10
v = 10√2
or in the other way v = 10i + 100 
thus, velocity of swimmer w.r.t river = 10i + 10j - 5i
= |5i + 10j|
=√25 + 100

hence n = 5

20.

At an instant particle-A is at origin and moving with constant velocity (3i + 4j) m/s and particle B is at (4,4) m and moving with constant velocity (4i - 3j)m/s. Then at this instant:(A) Relative velocity of B w.r.t A is (i - 7j) m/s(B) approach velocity of A and B is 3√2 m/s(C) Relative velocity of B w.r.t A remains constant.(D) approach velocity of A and B remains constant.

Answer» If we are to choose the incorrect option the answer will be (b)
21.

An individual’s sole concern with the satisfaction of ...... needs would reduce him/her to the level of animals. a. survival b. esteem c. security d. belongingness

Answer»

Answer is a. survival

22.

Intelligence in the Indian tradition can be termed as, which gives emphasis on connectivity with the social and world environment.(1 Point)

Answer»

Four competencies of intelligence in Indian tradition are:

1. Cognitive capacity: sensitivity to context, understanding, discrimination, problem-solving and effective communication.
2. Social competence (respect for social, commitment to elders, they young and the needy, concern about others, recognising others Perspective.
3. Emotional competence: Emotional intelligence is a set of skills that underlie accurate appraisal, expression and regulation of emotions. It is the feeling side of intelligence. Some psychologists believe that the source of their difficulty may be a lack of emotional intelligence. This concept was first introduced by Shalvey and Mayer who 'considered emotional intelligence as the ability to monitor one's own and other's emotions, to discriminate among them, and to use the formation to guide one's thinking and actions." Emotional Quotient (IQ) is' used to express emotional intelligence in the same way as IQ is used to express intelligence.

Emotional intelligence is receiving increasing attention of educators for dealing with students who are affected by stresses and challenges of the outside world. They encourage cooperative behaviour and reduce their antisocial activities.

4. Entrepreneurial competence: commitment, persistence, patience, hardwork, vigilance and goal-directed behaviours.

23.

Ms. Reeta is designing an admission form for the college. She wants the user to select his stream from science, commerce and humanities. Help her select the most appropriate Swing Control in Net beans IDE.

Answer»

Radio button

24.

Hira wants to store values in a table but the command below is giving errors . Write correct MYSQL command for creating table. CREATE employee (name VARCHAR, id INTEGER)

Answer»

CREATE TABLE employee (name VARCHAR, id INTEGER);

25.

Give one limitation of switch case.

Answer»

1.It doesn't allow ranges. 

2. It requires either integers or characters and doesn't allow String.

26.

Aman is moving downward on an inclined plane (θ=37)with constant velocity v0 and rain drop appear to him moving in horizontal direction with velocity 2v0 towards him.If man increases his velocity to 2v0,the velocity of rain drops as observed by man is √n/5v0, then find n.

Answer»

The value of n is 41.

Explanation:

Let the relative velocity of man with respect to ground is  Vmg = Vm .
 Also, the relative velocity of rain w.r.t ground be Vrg = Vr .
And the relative velocity of rain with respect to man is Vrm .
We can say the relation between  Vm,  Vr,  Vrm as Vrm = Vr - Vm

Given,

V= v₀cos37°(-i) + v₀sin37°(-j) 

Vm = -4v₀/5 i - 3v₀/5 j 

and Vrm = 2v₀ i 

Hence, Vrm = Vr - Vm

Vr =2v₀i +(-4v₀/5 i - 3v₀/5 j) 

= 6v₀/5 i - 3v₀/5 j       ----(i)

Now, velocity of man with respect to ground, = -2v₀cos37° i - 2v₀sin37°j 

= -8v₀/5 i - 6v₀/5 j 

Vrm = 6v₀/5 i - 3v₀/5 j -(- 8v₀/5 i - 6v₀/5 j)

= 14v₀/5 i + 3v₀/5 j

Now, |Vrm | = √{(196 + 9)/25}v₀ = √{205/25}v₀ =√(41/5)v₀ 

Hence, from the above equation it is clear that  n =41

27.

A hydrogen like atom with atomic number Z is in an excited state of quantum number 2n. It can emit a maximum energy photon of 204 eV. If it makes a transition ot quantum state n, a photon of energy 40.8 eV is emitted. Find n, Z and the ground state energy (in eV) of this atom. Also calculate the minimum energy (in eV) that can be emitted by this atom during de-excitation. Ground state energy of hydrogen atom is – 13. 6 eV.A. 1B. 2C. 3D. 4

Answer» Correct Answer - B
Let ground state energy (in eV) be `E_(1)`
Then from the given condition
`E_(2n)-E_(1)=204eV` or `(E_(1))/(4n^(2))-E_(1)=204eV`
`rArr E_(1)((1)/(4n^(2))-1)=204eV`...(i)
and `E_(2n) -E_(n) = 40.8 eV`
`rArr (E_(1))/(4n^(2))-(E_(1))/(n^(2))=E_(1)(-(3)/(4n^(2)))=40.8eV`....(ii)
From equation (i) and (ii),
`(1-(1)/(4n^(2)))/((3)/(4n^(2)))=5 rArr n=2` .
28.

_________ displays slides on a page as seen when printed.a) View -> Slide Sorterb) View -> Slide Showc) View -> Notes Paged) View -> Handout Page

Answer»

(d) View -> Handout Page

View -> Handout Page displays slides on a page as seen when printed.

29.

Half lives of two isotopes X and Y of a material are known to be `2 xx 10^(9)` years and `4 xx 10^(9)` years respectively. If a planet was formed with equal number of these isotopes, then the current age of planet, given that currently the material has 20 % of X and 80 % of Y by number, will beA. `2 xx 10^(9)` yearsB. `4 xx 10^(9)` yearsC. `6 xx 10^(9)` yearsD. `8 xx 10^(9)` years

Answer» Correct Answer - D
`N=(N_(0))/(2).e^(-lamda_(1)t)=0.2 N_(0)`
`N_(y) =(N_(0))/(2) e^(-lamda_(2) t) = 0.8 N_(0)`
`e^((lamda_(1)-lamda_(2)))=4 rArr t=8xx10^(9)` years
30.

Which feature is used to make selected sentence to All Capital Letters or All Small Letters?a) Change Letterb) Change Sentencec) Change Cased) Change Word

Answer»

(c) Change Case

Change Case is used to make selected sentence to All Capital Letters or All Small Letters.

31.

An organization is planning to connect its new office in Delhi, which is more than 1250 km current location. Which type of network will be formed?a) LANb) MANc) WANd) Internet

Answer»

Correct answer is

(c) WAN

32.

Ravi received a mail from IRS department on clicking “Click –Here”, he was taken to a site designed to imitate an official looking website, such as IRS.gov. He uploaded some important information on it. Identify the cybercrime being discussed in the above scenario.a) Plagiarismb) Spamc) Cyber Theftd) Phishing

Answer»

Correct answer is

(d) Phishing

33.

Which of the following is NOT classified as nonverbal communication? a. Signs b. Eye Contactc. Body language d. Gestures

Answer»

b. Signs

Which of the following is NOT classified as nonverbal communication is Signs

a. signs







...



..

34.

A body of mass m, having momentum p, is moving on a rough horizontal surface. If it is stopped in a distance x, the coefficient of friction between the body and the surface is given byA. `mu=(p^(2))/(2gm^(2)x)`B. `mu=(p^(2))/(2mgx)`C. `mu=(p)/(2mgx)`D. `mu=(p)/(2gm^(2)x)`

Answer» Correct Answer - A
Force of friction = `mu`mg.
Therefore, retardation a = `mu`mg/m= `mu`g.
Also 2ax= `v^(2)or2am^(2)x=m^(2)v^(2)`. But p =mv
Therefore,
But `2am^(2)x=p^(2)`
But a = `mu`g. Therefore, 2`mugm^(2)x=p^(2)`
or `mu=(p^(2))/(2gm^(2)x)`
35.

A equilaterial triangle `ABC` formed from a uniform wire has two small identical beads initially located at `A`. The triangle is set rotating about the vertical axis `AO`. Then the beads are released from rest simultaneously and allowed to slide down. one long. `AB` and the other along `AC` as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down, are. .A. angular velocity and total energyB. angular velocity and moment of inertia about axis of rotationC. total angular momentum and moment of inertia about axis of rotationD. total angular momentum and total energy

Answer» Correct Answer - D
There is no external torque so angular momentum is conserved also force acting on system are conservative so mechanical energy of system is also conserved.
36.

Line is an element of design, commonly used on fashion products. Differentiate between horizontal and vertical line. a. horizontal line is passive and relaxed, a vertical line is strong and energetic. b. horizontal line is natural & dynamic, a vertical line is strong and energetic. c. horizontal line is passive and relaxed, a vertical line creates sense of movement and depth d. horizontal line is strong and energetic, a vertical line is passive and relaxed

Answer»

Correct answer is

a. horizontal line is passive and relaxed; a vertical line is strong and energetic.

37.

________ is historically associated with royalty and therefore, exclusivity. The lighter tints symbolize femininity while the darker shades symbolize aristocracy. a. Red b. Green c. Violet d. Yellow

Answer»

c. Violet

Violet is historically associated with royalty and therefore, exclusivity. The lighter tints symbolize femininity while the darker shades symbolize aristocracy.

38.

Distance between two image formed by upper and lower part of the point object placed at `30` cm from given lens is `(60+x)`cm, then the value of `x` is

Answer» Correct Answer - 6
`f/(f_(L))=(3/2-1)(1/20-1/20)`
`implies f_(L)=20cm`
`1/f=1/(-10)-2/20=-1/5`
`1/v+1/(-30)=1/(-5)implies1/v=1/30-1/5`
for lens `1/v-1/(-30)=1/20`
39.

The dispersive power of the material of a lens is `0.04` and the focal length of the lens is `10cm`. Find the difference in the focal length (in mm) of the lens for violet and red colour.

Answer» Correct Answer - 4
`1/f=(n-1)(1/(R_(1))-1/(R_(2)))implies-(df)/(f^(2))implies-(df)/(f^(2))=(1/(R_(1))-1/(R_(2)))dn`
(differentiating both sides)
`implies-(df)/f(n-1)(1/(R_(1))-1/(R_(2)))=(1/(R_(1))-1/(R_(2)))dn`
`=-df=f(dn)/(n-1)`
but `dn-v_(v)-n_(R):.-df=(n_(v)-n_(R))/(n-1)f`
`impliesdf=-wfimpliesf_(v)-f_(R)=-wf`
`=-0.04xx10=0.4cm`
`f_(R)-f_(v)=4mm`
40.

There are four tax slans namely 5 percent, 12 percent , 18 percent and _______ for all goods or services.

Answer» Correct Answer - 28 per cent
41.

All non-conventional sources of energy are clean true or false.

Answer»

Yes it is true that non conventional sources of energy are clean and non polluting. But it has exception also.

42.

Out of electric field vector E and magnetic field vectors B in an electromagnetic wave, which is move effective and why?

Answer»

(i) Electromagnetic wave consists of electric field vector E and magnetic field vector B vibrating transversly and sinusodly at right angle to each other.

(ii) The direction of propagation of electromagnetic (emf) wave is perpeandicular to the plane containing E and B vectors and is obtained by vector (E x B).

43.

A luminous point object is placed at `O`, whose image is formed at `I` as shown in the figure. `AB` is the optic axis. Which of the following statements are correct ? A. If a lens is used to obtain image, the lens must be converging.B. If a mirror is used to obtain image, the mirror must be a convex mirror having pole at the point of intersection of lines `OI` and `AB`.C. Position of principal focus of mirror cannot be found.D. `I` is real image.

Answer» Correct Answer - Use rays diagram
44.

A solid transparent sphere made of glass `(R.I.=mu gt 1)` has a small, opaque dot at its centre. When observed from outside, apparent position of dot will beA. closer to eye than its actual positionB. farther from eye than its actual positionC. same as its actual positionD. independent of refractive index of the sphere

Answer» Rays falls normally on the surface `rArr` refracted rays will go undeviated
45.

There is a uniformly charged ring having radius R. An infinite line charge (charge per unit length lambda) is placed along a diameter of the ring (in gravity free space). Total charge on the ring `Q=4sqrt(2lambda)R`. An electron of mass m is released from rest on the axis of the ring at a distance `x=sqrt(3) R` from the centre. Potential difference between points `A(x=sqrt(3)R)` and `B(x=R)i.e.(V_(A)-V_(B))` isA. `-lambda/(pivarepsilon_(0))[(1-1/sqrt(2))-(l n3)/4]`B. `-lambda/(pivarepsilon_(0))[(1-1/sqrt(2))-(l n3)/4]`C. `-lambda/(pivarepsilon_(0))[(1+1/sqrt(2))-(l n3)/4]`D. none

Answer» Correct Answer - A
Electricfield `E=-lambda/(2pivarepsilon_(0)x)+Q/(4pivarepsilon_(0)) x/((R^(2)+x^(2))^(3//2))` (considering right direction as positive)
`=lambda/(2pivarepsilon_(0))[-1/x+(x4sqrt(2)R)/(2(R^(2)+x^(2))^(3//2))]`
`=lambda/(2pivarepsilon_(0))[-1/x+(2sqrt(2)xxR)/((R^(2)+x^(2))^(3//2))]`
Initially`x=sqrt(3)R`
`E=lambda/(2pivarepsilon_(0)R)[-1/sqrt(3)+(2sqrt(2)sqrt(3))/8]`
`lambda/(2pivarepsilon_(0)R)[(-2sqrt(2)+3)/(sqrt(3)(2sqrt(2)))]=lambda/(2pivarepsilon_(0)R)((3-2sqrt(2))/(2sqrt(6)))`
a(acceleration)`=((-e)(E))/m=-(elambda)/(pivarepsilon_(0) mR) ((3-2sqrt(2))/(4sqrt(6)))`
Sol(2) Force on electron is zero at point where `E=0Rightarrow x=R`
Sol(3) Potential difference between two points
`DeltaV=-E dx`
P.d. due to line charge between
`x=R& x=sqrt(3)R`
`V_(A)-V_(B)=-underset(R)oversetsqrt((3)R)(int) -(lambda dx)/(2pivarepsilon_(0)x)=lambda/(pivarepsilon_(0))((l n3)/4)`
Potential difference due to ring between `x=sqrt(3) R and x=R`
`V_(A)-V_(B)=1/(4pivarepsilon_(0))((4sqrt(2)lambda R)/(2R)-(4sqrt(2)lambdaR)/(sqrt(2)R))=(-lambda)/(pivarepsilon_(0))(1-1/sqrt(2))`
Net `V_(A)-V_(B)=-lambda/(pivarepsilon_(0))[(1-1/sqrt(2))-(l n3)/4]`
46.

There is an insulator rod of length L and of negligible mass with two small balls of mass m and electric charge Q attached to its ends. The rod can rotate in the horizontal plane around a vertical axis crossing it at a `L//4` distance from one of its ends. In what position is the rod to be set so that if displaced a little from that position it begins a hormonic oscillation about the axisA?A. B. C. D.

Answer» Correct Answer - A::D
Position of option (A) is minimum PE position means stable equilibrium position. Any displacement from this position is opposed by restoring torque.
47.

The refracting angle of a prism is A and refractive index of the material of prism is `cot(A//2)` . The angle of minimum deviation will beA. `180^(@) - 3A`B. `180^(@)+2A`C. `90^(@)-A`D. `180^(@)-2A`

Answer» Correct Answer - D
`cot.(A)/(2) = (sin((delta_("min)+A)/(2)))/(sin((A)/(2)))`
`cos.(A)/(2) = sin ((delta_("min")+A)/(2))`
`sin((pi)/(2)-(A)/(2)) = sin ((delta_("min")+A)/(2))`
`rArr (pi)/(2)-(A)/(2) = (delta_("min"))/(2)+(A)/(2)`
`= (pi)/(2)-A = (delta_("min"))/(2)`
`Delta_("min") = pi - 2A`
48.

A man looks down on a fish of length 20 cm. His eye is 2m above the surface of the water `(mu = 4//3)` and the fish is 2m below the surface as shown in the figure the ratio of angular width `Delta theta` of the fish as seen by the man in presence of water to the `Delta theta` in the absence of water is `(Delta theta` is small) A. `6/5`B. `5//6`C. `7//8`D. `8//7`

Answer» Correct Answer - D
`theta = (Arc)/("radius")`
`(Delta theta_(w))/(Delta theta_(a)) = (r_(a))/(r_(w)) = (2+2)/(2+(2)/(4//3)) = (4)/((7)/(2)) = (8)/(7)`
49.

Find the cube of 46.1. 973362. 984563. 951364. 981965. None of these.

Answer» Correct Answer - Option 1 : 97336

Concept used:-

Trick for writing cube of a number.

Method & Calculation:-

  • Write the cube of 4 & 6 in three digit form i.e. (064216)
  • Now multiply all the digits within themselves i.e. (4 x 6) = 24
  • Now multiply the result obtained from step (2) by 3 i.e. 24 x 3 = 72
  • Now multiply 72 and 46 i.e. 72 x 46 = 331
  • Now keep the unit digit vacant and add 064216 & 3312 i.e. 064216 + 3312_ = 97336
50.

The sum of two numbers is 47 and their product is 550. Find the sum of their squares.1. 9862. 8763. 11094. 1209

Answer» Correct Answer - Option 3 : 1109

Given:

Sum of 2 numbers = 47

Product of 2 numbers = 550

Formula Used:

(a + b)2 = a2 + b2 + 2ab

Calculations:

Let the 2 numbers be x and y respectively.

x + y = 47

Squaring both sides, we get

(x + y)2 = (47)2

⇒ x2 + y2 + 2xy = 2209

⇒ x2 + y2 + 2 × 550 = 2209

⇒ x2 + y2 = 2209 – 1100

⇒ x2 + y2 = 1109

∴ The sum of squares of 2 number is 1109.