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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 151. |
The equation `2x^2 + (a - 10)x + 33/2 = 2a` has real roots. Find least possible value of a. |
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Answer» Correct Answer - 8 |
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| 152. |
The area that is enclosed in the circle `x^(2)+y^(2)=2` which is not common enclosed by `y=x & y^(2)-x` isA. `(1)/(12)(24pi-1)`B. `(1)/(6)(12pi-1)`C. `(1)/(12)(6pi-1)`D. `(1)/(12)(12pi-1)` |
| Answer» Correct Answer - B | |
| 153. |
The six digit numbers that can be formed using digits 1,3,5,7,9 such that each digit is used at least once. |
| Answer» Correct Answer - 1800 | |
| 154. |
A sphere of density `rho` is half submerged in a liquid of density `sigma` and surface tension T. The sphere remains in equilibrium. Find radius of the sphere (assume the force due to surface tension acts tangentially to surface of sphere)A. `r=sqrt((T)/((d-rho)g))`B. `r=sqrt((T)/((d+rho)g))`C. `r=sqrt((2T)/(3(d+rho)g))`D. `r=sqrt((3T)/((2d-rho)g))`a |
| Answer» Correct Answer - 4 | |
| 155. |
In YDSE pattern with light of wavelength `lambda_1 = 500nm`, 15 fringes are obtained on a certain segment of screen. If number of fringes for light of wavelength `lambda_2` on same segment of screen is 10, then the value of `lambda_2` (in nm) is- |
| Answer» Correct Answer - 750 nm | |
| 156. |
An electric field `vecE=4xhati-(y^(2)+1)hatjN//C` passes through the box shown in figure. The flux of the electric field through surface ABCD and BCGF are marked as `phi_1)and phi_(11)` respecticvely. The differentce between `(phi_(1)-phi_(1))` is in `Nm^(2)`/C) |
| Answer» Correct Answer - -48 | |
| 157. |
Find the power loss in each diode (in mW), if potential drop across the zener diode is 8V |
| Answer» Correct Answer - 40 | |
| 158. |
Find the greatest value of k for which `49^(k)+1` is a factor of `1+49+49^(2)….(49)^(125)`A. 63B. 65C. 2D. 5 |
| Answer» Correct Answer - A | |
| 159. |
An ideal gas at initial temperature 300 K is compressed adiabatically (`gamma = 1.4`) to `(1/16)^(th)` of its initial volume. The gas is then expanded isobarically to double its volume. Then final temperature of gas round to nearest integer is: |
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Answer» Correct Answer - 1819K |
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| 160. |
1 litre of a gas at STP is expanded adiabatically to 3 litre. Find work done by the gas. Given `gamma` = 1.40 and` 3^(1.4)= 4.65 `A. ` 60.7 ` JB. ` 90.5 ` JC. `100.8 ` JD. `48 ` J |
| Answer» Correct Answer - B | |
| 161. |
Flocculation value for `As_2S_3` sol by HCl is 30 m mole `L^( –1)` . Calcualte mass of `H_2SO_4` required in gram for 250 mL sol. |
| Answer» Correct Answer - 0.37 g | |
| 162. |
3 gram of acetic acid is mixed in 250 mL of 0.1 M HCl. This mixture is now diluted to 500 mL. 20 mL of this solution is now taken is another container `1/2` mL of 5M NaOH is added to this. Find the pH of this solution. (`pK_a = 4.74`) |
| Answer» Correct Answer - 5.22 | |
| 163. |
When two non reactive samples at different temperatures are mixed in an isolated container of negligible heat capacity the final temperature of the mixture can be: |
| Answer» Correct Answer - 50 | |
| 164. |
If the wavelength of the first line of the Balmer series of hydrogen is `6561 Å`, the wavelngth of the second line of the series should be |
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Answer» Correct Answer - A 486 |
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| 165. |
Purest form of commercial iron is :A. Wrought ironB. Cast ironC. Pig ironD. Iron scrap + pig iron |
| Answer» Correct Answer - A | |
| 166. |
Planet A has massa M and radius R. Planet B has half the mass and half the radius of Planet A.If the escape velocities from the Planets A and B are `v_(A) and v_(B),` respectively , then `(v_(A))/(v_(B))=n/4.` The vlaue of n is :A. 2B. 3C. 1D. 4 |
| Answer» Correct Answer - 4 | |
| 167. |
If distance between the foci of an ellipse is 6 and distance between its directionces is 12, then length of its latus rectum isA. `3sqrt(2)`B. `sqrt(3)`C. `2sqrt(3)`D. `(3)/(sqrt(2))` |
| Answer» Correct Answer - A | |
| 168. |
Let `(x)^(k) + (y)^(k) = (a)^(k)` where a, k > 0 and `(dy/dx) +(y/x)^(1/3) = 0` then find kA. `(1)/(3)`B. `(2)/(3)`C. `(4)/(3)`D. 2 |
| Answer» Correct Answer - B | |
| 169. |
If distance between the foci of an ellipse is 6 and distance between its directionces is 12, then length of its latus rectum isA. 4B. `3sqrt2`C. 9D. `2sqrt2` |
| Answer» Correct Answer - B | |
| 170. |
If `g(x)=x^(2)+x+x-1 and g(f(x))=4x^(2)-10x+5` then find `f((5)/(4))`A. `(1)/(2)`B. `-(1)/(2)`C. `-(1)/(3)`D. `(1)/(3)` |
| Answer» Correct Answer - B | |
| 171. |
If z=x+iy and real part `((z-1)/(2z+1))=1` then locus of z isA. Straight line with slope 2B. Straight line with slope -`(1)/(2)`C. circle with diameter `(sqrt5)/(2)`D. circle with diameter `(1)/(2)` |
| Answer» Correct Answer - C | |
| 172. |
If z=x+iy and real part `((z-1)/(2z+1))=1` then locus of z isA. circle whose diameter is `(sqrt(5))/(2)`B. straight line whose slope is `3/2`C. straight line whose slope is `-2/3`D. circle whose centre is at `(-(1)/(2), -(3)/(2))` . |
| Answer» Correct Answer - A | |
| 173. |
Two liquids isohexane and 3-methylpentane has boiling point `60^@C` and `63^@C`. They can be separated byA. FIGUREractional distillation, isohexaneB. simple distillation, 3-methylpentaneC. FIGUREraction distillation 3-methylpentaneD. simple distillation, isohexane |
| Answer» Correct Answer - A | |
| 174. |
Mean and standard deviations of 10 observations are 20 and 2 respectively. If p `(p ne 0)` is multiplied toeach observation and then q `(q ne 0)` is subtracted then new mean and standard deviation becomes halfof original value . Then find qA. 10B. `-10`C. `-20`D. `5` |
| Answer» Correct Answer - C | |
| 175. |
A carnot engine operates between two reservoirs of temperature 900K and 300K. The engine performs 1200 J of work per cycle. The heat energy delivered by the engine to the low temperature reservoir in a cycle is: |
| Answer» Correct Answer - 600 J | |
| 176. |
There is a potentiometer wire of length 1200 cm and 60 mA current is flowing in it. A battery of emf 5V and internal resistance of `20 ohm` is balanced on potentiometer wire with balancing length 1000 cm. The resistance of potentiometer wire isA. `60Omega`B. `100Omega`C. `120Omega`D. `80Omega` |
| Answer» Correct Answer - 2 | |
| 177. |
H-like atom with ionization energy of 9R. Find the wavelength of light emitted (in nm) when electron jumps from second excited state to ground state. (R is Rydberg constant)A. 11.39B. 12.86C. 8.02D. 2.19 |
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Answer» Correct Answer - A |
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| 178. |
A charge particle of mass m and charge q is released from rest in uniform electric field. Its graph between velocity (v) and distance travelled (x) will be :A. B. C. D. |
| Answer» Correct Answer - 3 | |
| 179. |
An electron `(-|e|, m)` is released in Electric field E from rest. rate of change of de-Broglie wavelength with time will be.A. `-h/(2|e|)`B. `-h/(2|e|t)`C. `-h/(|e|Et^2)`D. `-(2ht^2)/(|e|E)` |
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Answer» Correct Answer - C |
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| 180. |
A block of mass m is suspended from a pulley in form of a circular disc of mass m & radius R. The system is released from rest, find the angular velocity of disc when block has dropped by height h. (there is no slipping between string & pulley) A. ` rsqrt ( ( 3) /( 4 gh ) ) `B. ` ( 1 ) /(r ) sqrt ( (4gh ) /( 3 ) ) `C. ` r sqrt ( ( 3 ) /( 2gh)) `D. ` ( 1 ) /(r ) sqrt ( (2gh)/( 3 )) ` |
| Answer» Correct Answer - B | |
| 181. |
5 g of Zn reacts with (I) Excess of NaOH (II) Dilute HCl, then volume ratio of `H_2` gas evolved in (I) and (II) isA. `2:1`B. `1:2`C. `1:1`D. `1:3` |
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Answer» Correct Answer - C |
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| 182. |
0.1 ml of an ideal gas has volume `1 dm^3` in a locked box with friction less piston. The gas is in thermal equilibrium with excess of 0.5 m aqueous ethylene glycol at its freezing point. If piston is released all of a sudden at 1 atm then determine the final volume of gas in `dm^3` `(R = 0.08 atm L mol^(–1) K ^(–1) K_f = 2.0 K molal ^(–1) )`. |
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Answer» Correct Answer - `2.176 dm^3 , 2.18` |
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| 183. |
If 10% of intensity is passed from analyser, then, the angle by which analyser should be rotated such that transmitted intensity becomes zero. (Assume no absorption by analyser and polarizer).A. ` 90 ^(@) `B. ` 71.6 ^(@) `C. ` 18.4 ^(@) `D. ` 45^(@)` |
| Answer» Correct Answer - 3 | |
| 184. |
If a point source is placed at a depth `h` in a liquid of refractive index `4/3` . Find percentage of energy of light that escapes from liquid. (assuming `100%` transmission of emerging light)A. `15%`B. `17%`C. `21%`D. `34%` |
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Answer» Correct Answer - B |
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| 185. |
In the given circuit both diodes are ideal having zero forward resistance and built-in potential of 0.7 V. Find the potential of point E in volts. |
| Answer» Correct Answer - 12 V | |
| 186. |
A particle moves so that its position vector is given by `vec r = cos omega t hat x + sin omega t hat y`, where `omega` is a constant which of the following is true ?A. `vecv` and `veca` both are perpendiculart to `vecr`B. `vecv ` and `veca` both are parallel to `vecr`C. `vecv` is perpendicular to `vecr` and `veca` is directed aways form the origin.D. velocity is perpendicular to`vecr` and `acceleration is directed towards origin |
| Answer» Correct Answer - D | |
| 187. |
Find the current supplied by the battery ? A. `0.1A`B. `0.3A`C. `0.4A`D. `0.5A` |
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Answer» Correct Answer - B |
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| 188. |
Find centre of mass of given rod of linear mass density `lambda=(a+b(x/l)^2)` , x is distance from one of its end. Length of the rod is `l`.A. `(3l)/4((3a+b)/(2a+b))`B. `(3l)/4((2a+b)/(3a+b))`C. `(l)/4((2a+b)/(3a+b))`D. `l((2a+b)/(3a+b))` |
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Answer» Correct Answer - B |
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| 189. |
Position of a particle as a function of time is given as `x^2 = at^2 + 2bt + c`, where a, b, c are constants. Acceleration of particle varies with `x^(-n) then value of n is. |
| Answer» Correct Answer - 3 | |
| 190. |
A loop of radius R and mass m is placed in a uniform magnetic field B with its plane perpendicular to the field. Current I is flowing in it. Now loop is slightly rotated about its diameter and released. Find time period of oscillation.A. `T=sqrt((pim)/(IB))`B. `T=sqrt((pim)/(IB))`C. `T=sqrt((2pim)/(IB))`D. `T=sqrt((pim)/(2IB))` |
| Answer» Correct Answer - 3 | |
| 191. |
Ratio of energy density of two steel rods is `1 : 4` when same mass is suspended from the rods. If length of both rods is same then ratio of diameter of rods will be.A. `sqrt2:1`B. `1:2`C. `2:1`D. `1:sqrt2` |
| Answer» Correct Answer - `sqrt2:1` | |
| 192. |
Find centre of mass of given rod of linear mass density `lambda=(a+b(x/l)^2)` , x is distance from one of its end. Length of the rod is `l`.A. `4/3((a+b)/(2a+3b))L`B. `3/2((a+b)/(2a+b))L`C. `3/2((2a+b)/(3a+b))L`D. `3/4((2a+b)/(3a+b))L.` |
| Answer» Correct Answer - 4 | |
| 193. |
An AC source is connected to the LC series circuit with `V = 10 sin (314t)`. Find the current in the circuit as function of time ? (`L = 40 mH, C = 100 mu F`)A. `10 sin (314t)`B. `5.2 sin (314t)`C. `0.52 sin (314t)`D. `0.52 cos (314t)` |
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Answer» Correct Answer - D |
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| 194. |
The system of equation `3x + 4y + 5z = mu` `x + 2y + 3z = 1` `4x + 4y + 4z = delta` is inconsistent, then (`delta,mu`) can beA. (4,3)B. (4,6)C. (3,4)D. (1,0) |
| Answer» Correct Answer - 3 | |
| 195. |
A loop of radius R and mass m is placed in a uniform magnetic field B with its plane perpendicular to the field. Current I is flowing in it. Now loop is slightly rotated about its diameter and released. Find time period of oscillation.A. `2sqrt((pim)/(IB))`B. `sqrt((2pim)/(IB))`C. `2sqrt((m)/(pi IB))`D. `sqrt((m)/(pi IB))` |
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Answer» Correct Answer - B |
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| 196. |
Ratio of energy density of two steel rods is `1 : 4` when same mass is suspended from the rods. If length of both rods is same then ratio of diameter of rods will be.A. `sqrt(2):1`B. `1:sqrt(2)`C. `1:2`D. `2:1` |
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Answer» Correct Answer - A |
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| 197. |
An AC source is connected to the LC series circuit with `V = 10 sin (314t)`. Find the current in the circuit as function of time ? (`L = 40 mH, C = 100 mu F`)A. `5.2 cos 314t`B. `0.52cos 314t`C. `0.52sin 314t`D. `10 cos 314t` |
| Answer» Correct Answer - `0.52sin 314t` | |
| 198. |
A string of mass per unit length `mu = 6 × 10^(-3)` kg/m is fixed at both ends under the tension 540 N. If the string is in resonance with consecutive frequencies 420 Hz and 490 Hz. Then find the length of the string?A. `8.1 m`B. `5.1m`C. `2.1m`D. `1.1m` |
| Answer» Correct Answer - `2.1m` | |
| 199. |
A string of mass per unit length `mu = 6 xx 10^(-3)` kg/m is fixed at both ends under the tension 540 N. If the string is in resonance with consecutive frequencies 420 Hz and 490 Hz. Then find the length of the string?A. 2.1 mB. 1.1 mC. 4.8 mD. 4.2 m |
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Answer» Correct Answer - A |
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| 200. |
Match the coloumn `{:(,A to Q, B to R, C to P, D to S),(,A to Q, B to R, C to S, D to P),(,A to R, B to Q, C to S, D to P),(,A to R, B to Q, C to P, D to S):}` |
| Answer» Correct Answer - B | |