100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS Page 124 InterviewSolution

6151.	Pipes P and Q can fill a tank in 12 hours and 16 hours respectively, and R can empty it in 8 hours. If all three are opened at 8:00 am, at what time will one-fourth of the tank be filled? 1. 1:00 pm2. 3:00 pm3. 8:00 pm4. 10:00 pm
Answer» Correct Answer - Option 3 : 8:00 pm Given: P and Q can fill a tank in 12 hours and 16 hours respectively, R can empty in 8 hours. Calculation: Take capacity of tank is LCM of (12, 16, and 8) = 48 unit P fill in one hour = 48/12 = 4 unit Q fill in one hour = 48/16 = 3 unit R empty in one hour = 48/8 = 6 unit Now, All work together then fill in one hour = 4 + 3 - 6 = 1 unit Then, Time taken to fill 1/4th of tank by P, Q and R together ⇒ (48 × 1/4) ÷ 1 ⇒ 12 hour ∴ The 1/4th part of tank filled at 8:00 pm.

6151.

Pipes P and Q can fill a tank in 12 hours and 16 hours respectively, and R can empty it in 8 hours. If all three are opened at 8:00 am, at what time will one-fourth of the tank be filled? 1. 1:00 pm2. 3:00 pm3. 8:00 pm4. 10:00 pm

Answer» Correct Answer - Option 3 : 8:00 pm

Given:

P and Q can fill a tank in 12 hours and 16 hours respectively, R can empty in 8 hours.

Calculation:

Take capacity of tank is LCM of (12, 16, and 8) = 48 unit

P fill in one hour = 48/12 = 4 unit

Q fill in one hour = 48/16 = 3 unit

R empty in one hour = 48/8 = 6 unit

Now,

All work together then fill in one hour = 4 + 3 - 6 = 1 unit

Then, Time taken to fill 1/4th of tank by P, Q and R together

⇒ (48 × 1/4) ÷ 1

⇒ 12 hour

∴ The 1/4th part of tank filled at 8:00 pm.

Discussion

6152.	Which two signs should be interchanged to make the given equation correct?(580 ÷ 80) + 90 × 8 - 30 = 5241. ÷ and –2. + and ÷3. + and –4. × and +
Answer» Correct Answer - Option 1 : ÷ and – Using option 1 ÷ and – (580 - 80) + 90 × 8 ÷ 30 According to BODMAS rule: 500 + 90 × 0.266 500 + 24 524 = 524 L.H.S = R.H.S Using option 2 + and ÷ (580 + 80) ÷ 90 × 8 - 30 According to BODMAS rule: 660 ÷ 90 × 8 - 30; 7.33 × 8 - 30 ≠ 524 Using option 3 + and – (580 ÷ 80) - 90 × 8 + 30 According to BODMAS rule: 7.25 - 90 × 8 + 30 ≠ 524 Using option 4 × and + (580 ÷ 80) × 90 + 8 - 30 According to BODMAS rule: 7.25 × 90 + 8 - 30 ≠ 524 Hence, interchanging ÷ and – will make equation correct.

6152.

Which two signs should be interchanged to make the given equation correct?(580 ÷ 80) + 90 × 8 - 30 = 5241. ÷ and –2. + and ÷3. + and –4. × and +

Answer» Correct Answer - Option 1 : ÷ and –

Using option 1

÷ and –

(580 - 80) + 90 × 8 ÷ 30

According to BODMAS rule:

500 + 90 × 0.266

500 + 24

524 = 524

L.H.S = R.H.S

Using option 2

+ and ÷

(580 + 80) ÷ 90 × 8 - 30

According to BODMAS rule:

660 ÷ 90 × 8 - 30;

7.33 × 8 - 30 ≠ 524

Using option 3

+ and –

(580 ÷ 80) - 90 × 8 + 30

According to BODMAS rule:

7.25 - 90 × 8 + 30 ≠ 524

Using option 4

× and +

(580 ÷ 80) × 90 + 8 - 30

According to BODMAS rule:

7.25 × 90 + 8 - 30 ≠ 524

Hence, interchanging ÷ and – will make equation correct.

Discussion

6153.	EXAMPLE 1. The radius of earth's orbit is \( 1.5 \times 10^{8} km \) and that of mars is \( 2.5 \times 10^{11} m \). In how many years does the mars complete one revolution?
Answer» Answer sumit please

Discussion

6154.	when beats are formed between sound waves of slightly different frequencies, the intensity of the sound heard changes form maximum to minimum in `0.2 s`. The difference in frequencies of the two sound waves isA. `5 Hz`B. `4 hz`C. `2.5 Hz`D. `2 Hz`
Answer» Correct Answer - C

Discussion

6155.	STATEMENT-1: When two sounds of equal frequencies and slightly different intensities are heard together, beats are heard. STATEMENT-2: Beats are caused by alternate constructive and destructive interferences between two sounds. (a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1. (c) Statement-1 is True, Statement-2 is False. (d) Statement-1 is False, Statement-2 is True.
Answer» Correct Answer is: (d) Statement-1 is False, Statement-2 is True.

Discussion

6156.	STATEMENT-1: When two sounds of slightly different frequecies are heard together, periodic variations in intensity (called beats) are observed. Similar phenomenon is not observed when two lights of slightly different wavelengths reach a point together. STATEMENT-2: Sound waves are longitudinal in nature, while light waves are transverse in nature.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation, for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is a False, Statement-2 is True.
Answer» Correct Answer - B

Discussion

6157.	STATEMENT-1: It is not possible for a charged particle to move in a circular path around a long straight conductor carrying current. STATEMENT-2: The electromagntic force on a moving particle is normal to its plane of rotation.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation, for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is a False, Statement-2 is True.
Answer» Correct Answer - C

Discussion

6158.	STATEMENT-1: It is possible for a charged particle to move in a circular path around a uniformly charged long conductor. STATEMENT-2: The electrostatic force on the moving particle is directed towards the conductor. (a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (b) Statement-1 is True, Statement-2 is True; Statement-2 is not a correct explanation for Statement-1. (c) Statement-1 is True, Statement-2 is False. (d) Statement-1 is False, Statement-2 is True.
Answer» Correct Answer is: (a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Discussion

6159.	A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 ms-1. What is the trajectory of the bob if the string is cut when the bob is1. at one of its extreme positions.2. at its mean position.
Answer» 1. At the extreme position, the speed of the bob is zero. If the string is cut, it will fall vertically down wards. 2. At the mean position, the bob has a horizontal velocity. If the string is cut, it will fall along a parabolic path.

6159.

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 ms-1. What is the trajectory of the bob if the string is cut when the bob is1. at one of its extreme positions.2. at its mean position.

Answer»

1. At the extreme position, the speed of the bob is zero. If the string is cut, it will fall vertically down wards.

2. At the mean position, the bob has a horizontal velocity. If the string is cut, it will fall along a parabolic path.

Discussion

6160.	A ladder leans against a wall, with its foot 2 metres away from the wall and the angle with the floor 40°. How high is the top end of the ladder from the ground?
Answer» tan 40 = \(\frac{QR}{2}\) QR = 2 × tan 40 = 2 × 0.8391 = 1.6782 Height of the ladder from ground = 1.68m

6160.

A ladder leans against a wall, with its foot 2 metres away from the wall and the angle with the floor 40°. How high is the top end of the ladder from the ground?

Answer»

tan 40 = \(\frac{QR}{2}\)

QR = 2 × tan 40

= 2 × 0.8391 = 1.6782

Height of the ladder from ground = 1.68m

Discussion

6161.	A boy hits a baseball with a bat and imparts and impulse J to the ball. And if the boy hits the ball again with the same force, except that the ball and the bat are in contact for twice the amount of time as in the first hit. The new impulse equals.A. half the original impulseB. the original impulseC. twice the original impulseD. four times the original impulse
Answer» Correct Answer - `J=F Deltat`

Discussion

6162.	A ball is projected towards right from point A at an angle `theta` with vertical. A system imparts an acceleration `g tan theta` to the ball towards left along negative x-axis. The ball will return to ground at : A. at point A.B. left to poin AC. right to point AD. information is not suffcient
Answer» Correct Answer - 1

Discussion

6163.	A mass m moving with a constant velocity along a line parallel to the axis, away from the origin. Its anguarl momentum with respect to the originA. is zeroB. remains constantsC. goes on increasingD. goes on decreasing
Answer» Correct Answer - D

Discussion

6164.

Table below given analogy between translational and rotational motions. Match the following.Linear motionRelation motionvelocityAngular momentummass1/2 τω2\(\frac{1}{2}\) mv2τ = \(\frac{dL}{dt}\)a = \(\frac{dv}{dt}\)Moment of inertiaF = \(\frac{dp}{dt}\)1/2 lω2F = \(\frac{dl}{dt}\)Torque a =\(\frac{dω}{c^"}\)

Answer»

Linear motion	Relation motion
velocity	Angular momentum
mass	Momentum of inertia
Force	Torque
\(\frac{1}{2}\) mv²	1/2 τω²
a = \(\frac{dv}{dt}\)	a =\(\frac{dω}{c^"}\)
F = \(\frac{dp}{dt}\)	τ = \(\frac{dL}{dt}\)

Discussion

6165.	The radioactivity of a given sample of whisky due to tritium (half life `12.3` years) was found to be only `3 %` of that measured in a recently purchased bottle marked `'7` years old'. The sample must have been prepared about.A. Before 70 yearsB. Before 220 yearsC. Before 420 yearsD. Before 300 years
Answer» Correct Answer - A We have `N_(1)=N_(0)e^(-lamda xx7)and N_(2)=N_(0)e^(-lamdax)` `(N_(2))/(N_(1))=(3)/(100) = e^(lamda(7-x))or e^(lamda(x+7))=(100)/(3)` `lamda(x-7)= "ln" (100)/(3)~~2.3 log_(10)2.3` `"log"_(10)(100)/(3)=2.3 [2-0.4771]=2.3 xx1.5229` But `lamda =(0.693)/(T_(1//2))=(0.693)/(12.5)` `:. x-7=(12.5)/(0.693)xx2.3 xx1.5229` `~~ (125)/(3)xx1.52 ~~ 63` `:. xx =(63+7)` years = 70 years

Discussion

6166.	The above configuration isA. plane of symmetryB. axis of symmetryC. centre of symmetryD. not any type of symmetry
Answer» Correct Answer - 3 Centre of Symmmetry

Discussion

6167.	Two indentical cylinders have a hole of radius a `(aleleR)` at its bottom a ball of radius R is kept on the hole and water is filled in the cylinder sucj that there is no water leakage from bottom in case1 water is filled upto height h and in second case it is filled upto height 2h if `F_(1)` is net force by liquid on sphere in case1 and `F_(2)` is net force by liquid on sphere in case-2 then A. `F_(1) = F_(2) = 0`B. `F_(1) ge F_(2)`C. `F_(2)geF_(1)`D. `F_(1)=F_(2)ne0`
Answer» Correct Answer - B `F_(1) = F_(B)-(pia^(2))rhogh` `F_(2) = F_(B)-(pia^(2))rhog(2h)`

Discussion

6168.	Figure shows two block `A` and `B`, each having a mass of 320 g connected by a light string passing over a smooth light pulley. The horizontal surface on which the block `A` can slide is smooth. The block `A` is attached to spring constant `40 N//m` whose other end is fixed to a support 40 cm above the horizontal surface. Initially, the spring is vertical and unstretched when the system is released to move. Find the velocity of the block A at the instant it breaks off the surface below it. Take `g = 10 m//s^(2)` . A. `sqrt((19)/(8))`B. `sqrt((3)/(2))`C. `sqrt((9)/(4))`D. None of these
Answer» Correct Answer - A When block A breaks off it has moved 0.3 m by energy conservation `0.32 g 0.3 - 20 (0.01) + 0.32 v_(2)` therefore `v = sqrt((19)/(8))`

Discussion

6169.	For a particle moving along `x-`axis, speed must be increasing for the following graph `:`A. B. C. D.
Answer» Correct Answer - D For `(1)` `:` For speeding up, signs of `v` and a must be same and for speeding down signs of `v` and a must be opposite. For `(2)` `:` speed`=`[velocity] `:.` speed first`darr` then `uarr` For `(3)` & `(4)` `:` speed `=`[slope of `x-t` graph]

Discussion

6170.	The kinetic energy of a particle continuously icreses with timeA. The resultant force on the particle must be parallel to the velocity at all instants.B. The resultant force on the particle must be at an angle greater then `90^(@)` with velocity all the timeC. Its height above the ground level must continuously decrease.D. The magnitude of its linear momentum is increasing continuously
Answer» Correct Answer - A

Discussion

6171.	A car of mass `1000kg` moves from point `A` to `B`. If kinetic energy of car at point `A` is `100KJ` and at `B` is `220 Kj`. Then find work done by friction force on the car ? A. `-100kJ`B. `100kJ`C. `-20kJ`D. `20 kJ`
Answer» Correct Answer - D By using work energy theorm,`W=DeltaKE` `rArrW_(gravity)+W_(f riction)=DeltaKE` `rArrmgh+W_(f riction)=120xx10^(3)rArrW_(f riction)=20kJ`

Discussion

6172.	A particle with total energy `E` moves in one direction in a region where, the potential energy is `U` The acceleration of the particle is zero, where,A. `U=E`B. `U=0`C. `(dU)/(dx)=0`D. `(d^(2)U)/(dx^(2))=0`
Answer» Correct Answer - C For acceleration `=0`so `F_(n et)=0` `rArr(dU)/(dx)=0`

Discussion

6173.	The graph given below shows how the force on a mass depends on the position of the mass. What is the change in the kinetic energy of the mass as it moves from `x=0.0m` to `x=3.0m` ? A. 0.0 JB. 20 JC. 50 JD. 60 J
Answer» Correct Answer - A

Discussion

6174.	The graph given below shows how the force on a mass depends on the position of the mass. What is the change in the kinetic energy of the mass as it moves from `x=0.0m` to `x=3.0m` ? A. `0.0J`B. `20J`C. `50 J`D. `60 J`
Answer» Correct Answer - C Area `=` work done `=(1)/(2)xx20xx1+2xx20=50=` change in `KE`

Discussion

6175.	Two bodies of masses `m_(1)` and `m_(2)` are acted upon by a constant force `F` for a time `t` . They start from rest and acquire kinetic energies `K_(1)` and `K_(2)` respectively. Then `(K_(1))/(K_(2))` is `:`A. `m_(1)/m_(2)`B. `m_(2)/m_(1)`C. `1`D. `sqrt(m_(1)m_(2))/(m_(1)+m_(2))`
Answer» Correct Answer - B `K=(1)/(2)mv^(2)=(1)/(2)m(at)^(2)=(1)/(2)m((Ft)/m)^(2)rArrKprop(1)/(m)`

Discussion

6176.	A body starts falling under gravity from rest. When it loses a gravitational potential energy by u, its speed is v. The mass of the body will beA. `(2U)/(V)`B. `(U)/(2V)`C. `(2U)/(V^(2))`D. `(U)/(2V^(2))`
Answer» Correct Answer - C `U=(1)/(2)MV^(2)` `M=(2U)/(V^(2))`

Discussion

6177.	A body (intially at rest is falling under gravity. When it loses a gravitational potential energy by `U`, its speed is `v`.The mass of the body shall be `:`A. `(2U)/(v)`B. `(U)/(2v)`C. `(2U)/(v^(2))`D. `(U)/(2v^(2))`
Answer» Correct Answer - C By COME loss is `PE=`gain in `KE` `:` `U=(1)/(2)mv^(2)rArrm=(2U)/(v^(2))`

Discussion

6178.	A cubic solid is made up of two elements P and Q. Atom Q is present at corners of the cube and atom P at the body centre. What is the formula of the compound? What are the coordination numbers of P and Q ?
Answer» Number of Q atoms per unit cell = 1/8 X 8 = 1 Number of P atoms per unit cell = 1x1=1 Ratio of atoms P : Q = 1:1 Hence, the formula of the compound is PQ. As it is a bcc lattice therefore, coordination number is 8 for both P and Q.

6178.

A cubic solid is made up of two elements P and Q. Atom Q is present at corners of the cube and atom P at the body centre. What is the formula of the compound? What are the coordination numbers of P and Q ?

Answer»

Number of Q atoms per unit cell = 1/8 X 8 = 1 Number of P atoms per unit cell = 1x1=1

Ratio of atoms P : Q = 1:1 Hence, the formula of the compound is PQ.

As it is a bcc lattice therefore, coordination number is 8 for both P and Q.

Discussion

6179.	In L-R circit, the A.C. source has voltage `220V`. If potential difference across inductor is `176V`, the potential difference across the resistor (in Volts) is `Kxx33`. Find the value of `K`
Answer» Correct Answer - 4 4 `220V=sqrt((176)^(2)+V_(0)^(2))impliesV_(0)=sqrt((220)^(2)-(176)^(2))V=132V`

Discussion

6180.	For a given velocity of projection from a point on the inclined plane, the maximum range down the plane is three times the maximum range up the incline. Then find the angle of inclination of the inclined plane.
Answer» Correct Answer - 3 3 `(u^(2))/(g[1-sinbeta])=(3u^(2))/(g[1+sin beta])implies1+sinbeta=3-3sinbetaimpliessinbeta=1/2impliesbeta=30^(@)`

Discussion

6181.	A particle is rotated in a vertical circle by connecting it to a string of length `l` and keeping the other end of the string fixed. The minimum speed of the particle when the string is horizontal for which the particle will complete the circle isA. `sqrt(gl)`B. `sqrt(2gl)`C. `sqrt(3gl)`D. `sqrt(5gl)`
Answer» Correct Answer - C `V_(min) = sqrt(3 gl)`.

Discussion

6182.	Assertion For looping a verticla loop of radius, r the minimum velocity at lowest point should be `sqrt(5gr).` Reason In this event the velocityh at the highest point will be zero.A. Both assertion and reson are true and reason is the correct explanation of assertionB. Both assetion and reason are true but reason is not the correct explanation of assertionC. Assertion is true but reason is falseD. Both assetion and reason are flase
Answer» Correct Answer - C

Discussion

6183.	A particle of mass `2kg` starts to move at position `x=0` and time `t=0` under the action of force `F=(10+4x)N` along the `x- ` axis on a frictionless horizontal track . Find the power delivered by the force in watts at the instant the particle has moved by distance `5m`.
Answer» Correct Answer - 300 According to `W.E.` theorem `(1)/(2)mV^(2)-0=underset(0)overset(5)int(10+4x)dx` `V=10m//s` Force at that moment `=(10+20)=30N` Instataneous power `= vec(F).vec(V)` `=30xx10=300W`

Discussion

6184.	Choose the correct option(s) for the given sitution. A. The maximum horizontal force `F` which can be applied such that sliding does not occur between `A` and `B` is `24 N`B. The maximum horizontal force `F` which can be applied such that sliding does not occur between `A` and `B` is `30 N`C. The maximum horizontal force `F` which can be applied such that sliding does not occur between `A` and `B` is `20 N`D. There will be no sliding between `A` and `B`, if `F = 5N`.
Answer» Correct Answer - A::D No sliding between `A` and `B`. Hence both move together `F - 0.1 xx 3 xx g = 3a`……(i) `F = 2T` …….(ii) `T - 0.5 xx 1.g = 1 . a`……..(iii) On solving `F - 0.3g = ((F)/(2)-0.5g)` `:. F = 2 xx (1.5 - 0.3) xx 10 = 24 N`

Discussion

6185.	A metallic disc of radius `r` is made of a material of negligible resistance and can rotate about a conducting horizontal shaft. A smaller non conducting disc of radius a is fixed onto the same shaft and has a massless cord wrapped around it, which is attached to a small object of mass `m` as shown. Two ends of a resistor of resistance `R` are connected to the perimeter of the disc and to the shaft by sliding contacts. The system is then placed into a uniform horizontal magnetic field `B` and the mass `m` is released. Find the terminal angular velocity with which the disc will rotate finally. (Take `r=10 cm `, `a=2cm`, `R=(1)/(100)Omega`, `B=0.2 T`, `m=50 gm`, `g=10m//s^(2)`) A. `200 rad//s`B. `300 rad//s`C. `100 rad//s`D. `10 rad//s`
Answer» At terminal stage, torque applied on the smaller disc by the rope `=mga` current to the disc `=(Bomega r^(2))/(2R)`(where `omega` is terminal angular velocity) torque applied by magnetic field `=(B^(2)omega r^(4))/(4R)` So, `(B^(2)omega r^(4))/(4R)=mga` `omega=100 rad//sec`

Discussion

6186.	In a certain region of space a uniform and constant electric field and a magnetic field parallel to each other are present. A proton is fired from a point `A` in the field with speed `v=4xx10^(4)m//s` at an angle of `alpha` with the field direction. The proton reaches a point `B` in the field where its velocity makes an angle `beta` with the field direction. If `(sinalpha)/(sinbeta)=sqrt(3)`. Find the electric potential difference between the points `A` and `B`. Take `m_(p)`(mass of proton) `=1.6xx10^(-27)kg` and `c`(magnitude of electronic charge)`=1.6xx10^(19)C`.A. `16 V`B. `16//3 V`C. `90 V`D. `30 V`
Answer» Work done by magnetic force is zero so from work energy theorem `(1)/(2)m_(p)v_(B)^(2)=(1)/(2)m_(p)v_(A)^(2)+qDeltaV` and simultaneously there is no change of velocity component along the direction of perpendicular to electric and magnetic field. `v_(A)sinalpha=v_(B)sinbeta` After solving `Deltav=16` Volt

Discussion

6187.	In a region of space, a uniform magnetic field B exists in the y-direction. A proton is fired from the origin, with its initial velocity v making a small angle α with the y-direction in the yz-plane. In the subsequent motion of the proton,(a) its x-coordinate can never be positive (b) its x- and z-coordinates cannot both be zero at the same time (c) its z-coordinate can never be negative (d) its y-coordinate will be proportional to the square of its time of flight
Answer» Correct Answer is: (a) its x-coordinate can never be positive

Discussion

6188.	Analyse the graph showing the diseases that affected the crops in John’s-field and answer the following questions.a) Identify the most affected crop based on the inference on most prevalent disease. b) Name the causative agents of the diseases A and C. c) Which type of insects spread the disease B and D.
Answer» a) Paddy b) Quickwilt- Fungus, Blight disease – Bacteria c) Aphids

6188.

Analyse the graph showing the diseases that affected the crops in John’s-field and answer the following questions.a) Identify the most affected crop based on the inference on most prevalent disease. b) Name the causative agents of the diseases A and C. c) Which type of insects spread the disease B and D.

Answer»

a) Paddy

b) Quickwilt- Fungus, Blight disease – Bacteria

c) Aphids

Discussion

6189.	Find the word which is out of the logic list:A) placard B) brochure C) leaflet D) catalogue
Answer» Correct option is A) placard

Discussion

6190.	Complete the following sentences using the correct degree of the adjective given in the brackets.1. My brother’s handwriting is (bad) mine2. Health is wealth, (important)3. Blood is water, (thick)4. Everest is peak in the world, (high)5. This is play I have ever heard on the radio, (interesting)6. Sushila is of all the four sisters, (beautiful)7. The planet Mars is from the earth than the satellite Moon, (far)8. The elephant is animal in the world, (large)9. An ocean is certainly a sea. (big)10. Iam in cricket than in football, (interested)
Answer» 1. worse than 2. more important than 3. thicker than 4. the highest peak 5. the most interesting 6. the most beautifu 7. farther 8. the largest 9. An ocean is certainly a sea. (big) 10. Iam in cricket than in football, (interested)

6190.

Complete the following sentences using the correct degree of the adjective given in the brackets.1. My brother’s handwriting is (bad) mine2. Health is wealth, (important)3. Blood is water, (thick)4. Everest is peak in the world, (high)5. This is play I have ever heard on the radio, (interesting)6. Sushila is of all the four sisters, (beautiful)7. The planet Mars is from the earth than the satellite Moon, (far)8. The elephant is animal in the world, (large)9. An ocean is certainly a sea. (big)10. Iam in cricket than in football, (interested)

Answer»

1. worse than

2. more important than

3. thicker than

4. the highest peak

5. the most interesting

6. the most beautifu

7. farther

8. the largest

9. An ocean is certainly a sea. (big)

10. Iam in cricket than in football, (interested)

Discussion

6191.	Analyse the slogan given in the placard and answer the questions.Health individuals are the wealth of a societya) What is health? b) What should be our attitude to patients?
Answer» a) The complete physical, mental and social wellbeing of a person. b) Compassion, mercy, sympathy, empathy, pity, service mindedness and helping mentality etc.

6191.

Analyse the slogan given in the placard and answer the questions.Health individuals are the wealth of a societya) What is health? b) What should be our attitude to patients?

Answer»

a) The complete physical, mental and social wellbeing of a person.

b) Compassion, mercy, sympathy, empathy, pity, service mindedness and helping mentality etc.

Discussion

6192.	Electrons used in an electron microscope are accelerated by a voltage of `25 kV`. If the voltage is increased to `100 kV` then the de - Broglie wavelength associated with the electrons wouldA. increase by 2 timesB. decrease by 2 timesC. decrease by 4 timesD. increase by 4 times
Answer» Correct Answer - B `lambdaprop(1)/sqrt(v)`

Discussion

6193.	The product of two numbers is 6300 and their HCF is 15. If none of the numbers is less than 30, what is the sum of these two numbers?1. 752. 1003. 1504. 165
Answer» Correct Answer - Option 4 : 165 Calculation: HCF of these number is 15 So, let assume that number is 15x and other number is 15 y According to question ⇒ 15x × 15y = 6300 ⇒ xy = 28 Factors of 28 are 28 × 1 = 28 14 × 2 = 28 7 × 4 = 28 So, Numbers are 15 × 7 = 105 15 × 4 = 60 ∴ Sum of numbers is 105 + 60 = 165 The correct option is 4 i.e. 165

6193.

The product of two numbers is 6300 and their HCF is 15. If none of the numbers is less than 30, what is the sum of these two numbers?1. 752. 1003. 1504. 165

Answer» Correct Answer - Option 4 : 165

Calculation:

HCF of these number is 15

So, let assume that number is 15x

and other number is 15 y

According to question

⇒ 15x × 15y = 6300

⇒ xy = 28

Factors of 28 are

28 × 1 = 28

14 × 2 = 28

7 × 4 = 28

So,

Numbers are

15 × 7 = 105

15 × 4 = 60

∴ Sum of numbers is 105 + 60 = 165

The correct option is 4 i.e. 165

Discussion

6194.	Find the number of prime factors of 6300.1. 42. 53. 74. 3
Answer» Correct Answer - Option 3 : 7 Given: Number is 6300 Concept used: If a number N = x^a × y^b × z^c, where x, y, z are distinct prime numbers & a, b, c are natural numbers. ⇒ Number of prime factors = (a + b + c) Explanation: 6300 = 2² × 3² × 5² × 7¹ ⇒ prime factors = 2, 3, 5, 7 ⇒ Number of prime factors = 2 + 2 + 2 + 1 = 7 ∴ The number of prime factors of 6300 is 7

6194.

Find the number of prime factors of 6300.1. 42. 53. 74. 3

Answer» Correct Answer - Option 3 : 7

Given:

Number is 6300

Concept used:

If a number N = x^a × y^b × z^c, where x, y, z are distinct prime numbers & a, b, c are natural numbers.

⇒ Number of prime factors = (a + b + c)

Explanation:

6300 = 2² × 3² × 5² × 7¹

⇒ prime factors = 2, 3, 5, 7

⇒ Number of prime factors = 2 + 2 + 2 + 1 = 7

∴ The number of prime factors of 6300 is 7

Discussion

6195.	The HCF and the product of two numbers are 21 and 2205 respectively then find the LCM of that numbers.1. 1892. 1263. 1054. 147
Answer» Correct Answer - Option 3 : 105 Given: HCF is 21 and the product of two numbers is 2205 Concept: HCF × LCM = Product of two numbers Calculation: Let the LCM of that numbers is 'y' Now, ⇒ 21 × y = 2205 ⇒ y = 2205/21 ⇒ y = 105 ∴ The required LCM is 105.

6195.

The HCF and the product of two numbers are 21 and 2205 respectively then find the LCM of that numbers.1. 1892. 1263. 1054. 147

Answer» Correct Answer - Option 3 : 105

Given:

HCF is 21 and the product of two numbers is 2205

Concept:

HCF × LCM = Product of two numbers

Calculation:

Let the LCM of that numbers is 'y'

Now,

⇒ 21 × y = 2205

⇒ y = 2205/21

⇒ y = 105

∴ The required LCM is 105.

Discussion

6196.	The Product of LCM and HCF of two numbers is 2500. The ratio of two numbers is 4 : 1. What is the difference of the two numbers?1. 1252. 503. 844. 75
Answer» Correct Answer - Option 4 : 75 Given: LCM × HCF = 2500 The ratio of two numbers is 4 : 1 Concept used: LCM × HCF = product of two numbers Calculation: Let the numbers is 4x and x By formula, 2500 = 4x × x ⇒ 2500 = 4x² ⇒ x² = 625 ⇒ x = 25 The difference of the two numbers = 4x - x = 3x ∴ Difference is 3 × 25 is 75.

6196.

The Product of LCM and HCF of two numbers is 2500. The ratio of two numbers is 4 : 1. What is the difference of the two numbers?1. 1252. 503. 844. 75

Answer» Correct Answer - Option 4 : 75

Given:

LCM × HCF = 2500

The ratio of two numbers is 4 : 1

Concept used:

LCM × HCF = product of two numbers

Calculation:

Let the numbers is 4x and x

By formula,

2500 = 4x × x

⇒ 2500 = 4x²

⇒ x² = 625

⇒ x = 25

The difference of the two numbers = 4x - x = 3x

∴ Difference is 3 × 25 is 75.

Discussion

6197.	A father and his son decide to sum their age. The sum is equal to six ty yedr. Six years. ago the age of father was five timeas the age of son sixy ears from Now the son age willbe.
Answer» let son's age be x therefore father's age: 60-x 6 years ago: sons age- x-6, father's age: 60-x-6= 54-x 6 years ago, given: 54-x= 5(x-6) 54-x=5x-30 6x= 84 x=14 therefore, sons age sixty years from now= x+60= 14+60 = 74.

6197.

A father and his son decide to sum their age. The sum is equal to six ty yedr. Six years. ago the age of father was five timeas the age of son sixy ears from Now the son age willbe.

Answer»

let son's age be x

therefore father's age: 60-x

6 years ago: sons age- x-6, father's age: 60-x-6= 54-x

6 years ago, given: 54-x= 5(x-6)

54-x=5x-30

6x= 84

x=14

therefore, sons age sixty years from now= x+60= 14+60 = 74.

Discussion

6198.	If the refractive index of water for light going from air to water be 1.33 what will be the refractive index for light going from water to air.
Answer» The refractive index is the ration between seed of in vacuum to the speed of light in medium. The refractive index of water for light going from air to water is 1.33. So the refractive index for beam of light going from water to air will be the inverse of 1.33. n = 1/ 1.33 n = 0.75 Thus the refractive index will be 0.75

6198.

If the refractive index of water for light going from air to water be 1.33 what will be the refractive index for light going from water to air.

Answer»

The refractive index is the ration between seed of in vacuum to the speed of light in medium.

The refractive index of water for light going from air to water is 1.33.

So the refractive index for beam of light going from water to air will be the inverse of 1.33.

n = 1/ 1.33

n = 0.75

Thus the refractive index will be 0.75

Discussion

6199.	Using property of determinants show that \( \left\|\begin{array}{ccc}(b+c)^{2} & a^{2} & a^{2} \\ b^{2} & (c+a)^{2} & b^{2} \\ c^{2} & c^{2} & (a+b)^{2}\end{array}\right\|=2 a b c(a+b+c)^{3} \).
Answer» \(\begin{vmatrix}(b+c)^2&a^2&a^2\\b^2&(c+a)^2&c^2\\c^2&c^2&(a+b)^2\end{vmatrix}\) Applying C₂→C₂ - C₁, C₃→ C₃ - C₁ \(\begin{vmatrix}(b+c)^2&(a-(b+c))(a+b+c)&(a-(b+c))(a+b+c)\\b^2&(c+a-b)(c+a+b)&0\\c^2&0&(a+b-c)(a+b+c)\end{vmatrix}\) Applying C₂ → \(\frac{C_2}{a+b+c}\), C₃ → \(\frac{C_3}{a+b+c}\) = (a + b + c)²\(\begin{vmatrix}(b+c)^2&a-b-c&a-b-c\\b^2&c+a-b&0\\c^2&0&a+b-c\end{vmatrix}\) Applying R₁ → R₁ - R₂ - R₂ - R₃ = (a + b + c)²\(\begin{vmatrix}2bc&-2c&-2b\\b^2&c+a-b&0\\c^2&0&a+b-c\end{vmatrix}\) Applying R₁ → R₂/2 = 2(a + b + c)²\(\begin{vmatrix}bc&-c&-b\\b^2&c+a-b&0\\c^2&0&a+b-c\end{vmatrix}\) Expanding determinant along row R₃ = 2(a + b + c)²(c²(ab + bc - b²) + (a + b - c)(abc + bc² - b²c + b²c)) = 2(a + b + c)² c(abc + a²b + ab²) = 2abc (a + b + c)²(a + b + c) = 2abc (a + b + c)³

6199.

Using property of determinants show that \( \left|\begin{array}{ccc}(b+c)^{2} & a^{2} & a^{2} \\ b^{2} & (c+a)^{2} & b^{2} \\ c^{2} & c^{2} & (a+b)^{2}\end{array}\right|=2 a b c(a+b+c)^{3} \).

Answer»

\(\begin{vmatrix}(b+c)^2&a^2&a^2\\b^2&(c+a)^2&c^2\\c^2&c^2&(a+b)^2\end{vmatrix}\)

Applying C₂→C₂ - C₁, C₃→ C₃ - C₁

\(\begin{vmatrix}(b+c)^2&(a-(b+c))(a+b+c)&(a-(b+c))(a+b+c)\\b^2&(c+a-b)(c+a+b)&0\\c^2&0&(a+b-c)(a+b+c)\end{vmatrix}\)

Applying C₂ → \(\frac{C_2}{a+b+c}\), C₃ → \(\frac{C_3}{a+b+c}\)

= (a + b + c)²\(\begin{vmatrix}(b+c)^2&a-b-c&a-b-c\\b^2&c+a-b&0\\c^2&0&a+b-c\end{vmatrix}\)

Applying R₁ → R₁ - R₂ - R₂ - R₃

= (a + b + c)²\(\begin{vmatrix}2bc&-2c&-2b\\b^2&c+a-b&0\\c^2&0&a+b-c\end{vmatrix}\)

Applying R₁ → R₂/2

= 2(a + b + c)²\(\begin{vmatrix}bc&-c&-b\\b^2&c+a-b&0\\c^2&0&a+b-c\end{vmatrix}\)

Expanding determinant along row R₃

= 2(a + b + c)²(c²(ab + bc - b²) + (a + b - c)(abc + bc² - b²c + b²c))

= 2(a + b + c)² c(abc + a²b + ab²)

= 2abc (a + b + c)²(a + b + c)

= 2abc (a + b + c)³

Discussion

6200.

Simplify:|x - 3| + 2|x + 1| = 4.

Answer»

|x - 3| + |x + 1| = 4

⇒ |x - 3| + 2|x + 1| - 4 = 0 f(x) (Let)

f(x) = \(\begin{cases}-(x-3)-2(x+1)-4&;x\leq-1\\-(x-3)+2(x+1)-4&;-1\leq x\leq 3\\ x-3+2(x+1)-4&;x\geq3\end{cases}\)

= \(\begin{cases}-3x-3&;x\leq-1\\x+1&;-1\leq x\leq3\\3x-6&;x\geq3\end{cases}\)

∵ -3x - 3 = 0 ⇒ x = -1 which satisfies x \(\leq-1\)

x + 1 = 0 ⇒ x = -1 which satisfies -1 \(\leq x\leq3\)

3x - 6 = 0 ⇒ x = 2 which does not satisfy x \(\geq\) 3.

∴ x = -1 is only zero of f(x).

Hence, |x - 3| + 2 |x + 1| = 4 satisfies by x = -1

Discussion

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