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.
| 22351. |
Find the equation of the line whose distance from origin is 2 and the normal ray through origin makes an angle π/4 with the positive direction of the x-axis measured in counter clock sense. |
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Answer» We have p = 2 at α = π/4 = 2 Hence, the equation of the line is x cos π/4 + y sin π/4 = 2 or x + y = 2√2 |
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| 22352. |
The values of `k` for which the system of equations `kx+y+z=0,x-ky+z=0` and `x+y+z=0` possesses non-trivial solution. AreA. `1,2`B. `-1,1`C. `1,-2`D. `-1,-2` |
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Answer» Correct Answer - B `Delta=0` `implies|{:(k,1,1),(1,-k,1),(1,1,1):}|=0` `impliesk(-k-1)-1(1-1)+1(1+k)=0` `implies-k^(2)-k+1+k=0` `k=+-1` |
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| 22353. |
if `f(x)={{:(2+x,xge0),(2-x,xlt0):}` then `lim_(x to 0) f(f(x))` is equal to |
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Answer» Correct Answer - B Let `phi(x)=f(f(x))` `thereforephi(0^(+))=underset(xto0^(+))limf(f(x))=f(f(0^(+)))=f^(2^(+))=4` `phi(0^(-))=underset(xto0)limf(f(x))=f(f(0^(-)))=f(2^(-))=4` |
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| 22354. |
If `f:RtoR` is a function which satisfies the condition `f(x)+f(y)=f((x+y)/(1+xy))` for all `x, y in R` except `xy=-1`, then range of `f(x)` isA. `[0,infty)`B. `{0,1}`C. `R`D. `{0}` |
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Answer» Correct Answer - D `f(1)+f(1)=f(1)impliesf(1)=0` `f(x)+f(1)=f((1+x)/(1+x))=f(1)` for `x ne-1` `impliesf(x)=0` for all `x ne -1` also `f(-1)+f(-1)=f(-1)impliesf(-1)=0` `thereforef(x)=0` for all `x ne R` `thereforef(x)` is odd as well as even function. |
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| 22355. |
If `|a|=|b|=1 and |a+b|=sqrt(3)`, then the value of `(3a-4b)(2b+5b)` isA. `-21`B. `-(21)/(2)`C. `21`D. `(21)/(2)` |
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Answer» Correct Answer - B Given ,`|a|=|b|=1 and |a+b|=sqrt(3)` `rArr |a|^2+|b|^2+2a.b=3` `a.b=(1)/(2)[because|a|^2=1|b|^2=1]` `therefore(3a-4b).(2a+5b)=6|a|^2+15a.b-8a.b-20|b|^2` `=6+7a.b-20=-(21)/(2)[becausea.b=(1)/(2)]` |
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| 22356. |
If `A={x:x in N and xlt6(1)/(4)}` and `B={x: x in N and x^(2)le5)` the number of subsets of set `Axx(AcapB)` which contains exactly 3 elements isA. 126B. 280C. 220D. 144 |
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Answer» Correct Answer - C `thereforea=[1,2,3,4,5,6},B={1,2}` `thereforeAcapB={1,2}` `thereforen(Axx(AcapB))=12` `therefore` required `=.^(12)C_(3)=220` |
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| 22357. |
The differential equation for which `sin^(-1) x + sin^(-1) y = c` is given byA. `sqrt(1-x^2)dx+sqrt(1-y^2)-dx=0`B. `sqrt(1-x^2)dy+sqrt(1-y^2)-dx=0`C. `sqrt(1-x^2)dy-sqrt(1-y^2)-dx=0`D. `sqrt(1-x^2)dx-sqrt(1-y^2)-dx=0` |
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Answer» Correct Answer - B Given , `sin^(-1)x+sin^(-1)y=c` `rArr (1)/(sqrt(1-x^2))+(1)/(sqrt(1-y^2))(dy)/(dx)=0` `rArr sqrt(1-x^2)dy+sqrt(1-y^2)dx=0` Which is required differential equation . |
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| 22358. |
A particle moves in a straight line so that `s=sqrt(t)`, then its acceleration is proportional toA. `("velocity")^3`B. velocityC. `("velocity")^2`D. `("velocity")^(3//2)` |
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Answer» Correct Answer - A Given, `s=sqrt(t)` On differenting w.r.t., we get `(ds)/(dt)=(1)/(2sqrt(1))rArrv=(1)/(2sqrt(t))` Again differentiating. We get `(dv)/(dt)=-(1)/(2.2t^(3//2))` `rArr a=-(2)/((2sqrt(t))^3)` `rArr a=-2v^3rArr a prop v^3` . |
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| 22359. |
Scandium forms no coloured ions, yet it is regarded as a transition elements. Explain why? |
| Answer» Scandium in the ground state has one electron in the 3d-subshell. Hence, it is regarded as a transition elements. However, in its common oxidation state `+3` it has no electron in `3d` subshell `(3d^(0))` Hence, it does not form coloured red ions. | |
| 22360. |
The natural world and the study of life and plant forms is called ___ |
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Answer» Correct answer is Biology |
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| 22361. |
Money, banking, the country’s growth patterns and taxation are all studies in _ |
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Answer» Correct answer is Economics |
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| 22362. |
The subject of what has happened to the cultures and countries of the world is ___ |
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Answer» Correct answer is History |
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| 22363. |
Write the name of the worm that causes intestinal parasitic infection. |
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Answer» Round worm that causes intestinal parasitic infection. |
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| 22364. |
If `100 mL "of" 1 M H_(2) SO_(4)` solution is mixed with `100 mL` of 98% `(W//W)` of `H_(2)SO_(4)` solution `(d = 0.1 g mL^(-1))`, thenA. concentration of solution remains sameB. volume of solution become 200 mlC. mass of `H_2SO_4` in the solution is 98 gmD. mass of `H_2SO_4` in the solution is 19.6 gm |
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Answer» Correct Answer - A,B,D (A)Molarity of second solution is `=(10xxdxxx)/M=1M` (B)Volume=100+100=200 ml ( D)Mass of `H_2SO_4=(200xx1)/1000xx98=19.6` gm |
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| 22365. |
Which of the following samples of reducing agents is /are chemically equivalent to 25mL of 0.2 N `KMnO_(4)` to be reduced to `Mn^(2+)` and water?A. 25 ml of 0.2 M `FeSO_4` to be oxidized to `Fe^(3+)`B. 50 ml of 0.1 M `H_3AsO_3` to be oxidized to `H_3AsO_4`C. 25 ml of 0.1 M `H_2O_2` to be oxidized to `H^+ and O_2`D. 25 ml of 0.1 M `SnCl_2` to be oxidized to `Sn^(4+)` |
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Answer» Correct Answer - A,D meq. Of `KMnO_4=25xx0.2=5` meq. Of `FeSO_4`=meq. Of `SnCl_2=5` hence (A) and (D) are correct |
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| 22366. |
The solubility of CH3COOAg in buffer solution with pH=4, whose Ksp=10-12 and Ka=10-4/3 is |
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Answer» When CH3COOAg(s) is dissolved in water an equilibrium is established with the solid salt at a given temperature forming ions as follows. CH3COOAg(s) ⇋ CH3COO- + Ag+ ...[1] If the salt is dissolved in buffer solution of pH=4 ie [H+]=10-4 then acetate ions in the solution goes to combine with H+ ions as follows and proceeds towards another equilibrium state CH3COO- + H+ ⇋ CH3COOH.....[2] Both the reactions establish a overall equilibrium state. Let at the final equilibrium state the concentration of [Ag+] be x(M). This will represent the solubility of the salt in buffer solution. If a(M) be the concentration of acetic formed at equilibrium then concentration of acetate ion will be (x-a) (M) Concentration of H+ ion remains unaltered due to buffer action. So for equation(1) Ksp=(x-a)*x. =>(x-a)*x=10-12 ......(3) And for equation (2) 1/ka=a/((x-a)*10-4) =>3/10-4=a/((x-a)×10-4) =>3=a/(x-a) =>3x-3a=a =>a=(3/4)x...(4) Combining (3) and (4) we get (x-3x/4)*x=10-12 =>x2=4×10-12 =>x=2×10-6 M |
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| 22367. |
Two samples of HCl having 1M and 0.25 M are mixed. Find the volumes of these samples respectively taken in order to prepare 0.75 M HCl solution.A. 20 ml, 10 mlB. 100 ml, 50 mlC. 40 ml, 20 mlD. 50 ml, 25ml |
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Answer» Correct Answer - A,B,C,D Final molarity =`(V_1xx1+V_2xx0.25)/((V_1+V_2))` `0.75(V_1+V_2)=V_1+V_2xx0.25` `0.75 V_1+0.75 V_2=V_1+V_2xx0.25` `0.5 V_2=0.25V_1` `V_1/V_2=2` |
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| 22368. |
Two samples of HCl having 1M and 0.25 M are mixed. Find the volumes of these samples respectively taken in order to prepare 0.75 M HCl solution.A. 20 ml, 10 mlB. 100 ml, 50 mlC. 40 ml, 10 mlD. 20 ml, 40 ml |
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Answer» Correct Answer - A::B `0.75 = (1xx V_(1)+0.25xxV_(2))/(V_(1)+V_(2))` `0.75 = (V_(1))/(V_(2))=0.75 = (V_(1))/(V_(2))+0.25` `(V_(1))/(V_(2))(0.25)=0.5,(V_(1))/(V_(2))=(2)/(1)` |
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| 22369. |
Which of the following compounds form salt with `NaHCO_3`?A. B. C. D. |
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Answer» Correct Answer - C Carbxylic acid from salt with `NaHCO_3` |
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| 22370. |
Complex forming tendency is more for the metal ion a) \( K^{+} \) b) \( Co ^{2+} \) c) \( Ce ^{2+} \) d) \( Mg ^{2+} \) |
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Answer» d-block elements have very high tendency to complex farming than other blocks of elements of periodic table. Therefore, CO+2 has very high tendency to complex forming |
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| 22371. |
Which of the following statement is true about \( \pi \)-acid ligands a) they are capable of accepting an appreciable amount of \( \pi \) electron density from the metal atom into \( \pi \) or \( \pi^{*} \) orbitals of their ownb) CO, NO, ferrocene, ethylene and cyclopentadienyl act as \( p \)-acid ligandsc) both \( a \) and \( b \) are correctd) neither A or B is correct |
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Answer» π -acid ligands are capable of accepting an appreciable amount of π electron density from the metal atom into π* or σ* orbital( LUMO) of their own. CO, No, ethylene and cyclopentadienyl act as \(P\hat t\)- acid ligand while ferrocene does not because it is a complex not a ligand. Hence option (d) is right answer |
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| 22372. |
LEAST COORDINATION NUMBERA)Co2(CO)8 B)MN(CO)10 |
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Answer» A) Co2(CO)8 is known as dicobalt octacarbonyl and its structure is:
B) Mn may bind itself with CO ligand as [Mn(CO)5]- carbonylate ion, [Mn(CO)6]+ or polynuclear dimeric non-bridged complex, [Mn2(CO)10].
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| 22373. |
what happens if conc `H_(2)SO_(4)` is used in preparing hydrogen by its reaction with a metal? |
| Answer» Nascent hydrogen `[H]` produced will reduce `H_(2)SO_(4)` to `SO_(2)`. | |
| 22374. |
Explain why is sodium less reactive than potassium. |
| Answer» Down the group `(darr)`, `IE_(1)` decreases, hence `IE_(1)` of potassium `(496 kJ "mol"^(-1))` is less that of sodium `(520 kJ "mol"^(-1))`. Moreover, `E^(ө)K_(aq)^(o+)//K_((s))=-2.925 V` is more negative than `E^(ө)Na_(aq)^(o+)//Na_((s))=-2.714 V`. Hence sodium is less reactive than potassium. | |
| 22375. |
An assumption of Steady State Approximation is ____(a) Reaction occurs without the formation of intermediates(b) Catalyst does not accelerate reaction rate(c) One of the intermediates in the reaction is consumed as quickly as it is generated(d) Equilibrium state is attained at the end of a reaction |
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Answer» The correct option is (c) One of the intermediates in the reaction is consumed as quickly as it is generated Explanation: The steady-state approximation is a method used to derive the rate expression. It is based on the assumption that one intermediate in the reaction mechanism is consumed as fast as it is generated. |
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| 22376. |
Explain the following temperature vs time graph. |
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Answer» During heating ice the change in temperature with time is shown in the graph Seg AB: Seg AB represents conversion of ice in to water at constant temperature. During melting of ice at 0oC, ice absorb heat energy and this continues till all the ice converts into water. Seg BC: once all ice is transformed into water, temperature of water starts rising it increases up to 100oC. Seg BC represents rise in temperature of water from 0oC to 100oC. Seg CD: even though the heat energy is supplied to the water after 100oC its temperature does not rise. The heat energy absorbed by water is used to break the bonds between molecules of the liquid to convert it into gaseous state. |
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| 22377. |
Write the proper name of the orbits of satellites shown in the following figure with their height from the earth’s surface. |
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Answer» a) low earth orbits height above the earth’s surface: 180 km to 2000 km b) Medium earth orbits height above the earth’s surface: 2000 km to 35780 km c) high earth orbits height from the earth’s surface > 35780 km |
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| 22378. |
Study the radius of the element given below and answer the following questions.elementsKNaRbCsLiAtomic radius (pm)231186244262151a) Which of above element have smallest atom? b) In which group of modern periodic table the above element are belongs? c) What is the periodic trend observed in the variation of atomic radii down a group? |
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Answer» a) Li b) first group c) while going down a group atomic radius goes on increasing. As a result, atomic size increases. |
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| 22379. |
The oxidation number of \( P t \) in the complex \( \left[ Pt \left( C _{2} H _{4}\right) Cl _{3}\right] \) is1) \( +1 \)2) \( +2 \)3) \( +3 \)4) \( +4 \) |
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Answer» Oxidation no of pt will be +3 C2 will be -2 in each carbon H4 will bhi +1 in each carbon Cl3 will bhi -1 in each carbon Pt -4 +4-3=0 Pt=3
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| 22380. |
Write the IUPAC names of the following structural formula.i. CH3- CH2- CH2- CH3 ii. CH3- CH2- COOH iii. CH3 – CO- CH2- CH3 |
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Answer» i. butane ii. propanoic acid iii. butan-2-one |
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| 22381. |
Assertion: In general, for an element, `IE_(1) lt IE_(2) lt IE_(3)....` Reason: After the removal of each succesive electron remaining electrons are held more tightly by the nucleus so removal of next electorn becomes difficult.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True. |
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Answer» Correct Answer - A (A)Statement-1 and Statement-2 are correct. Statement-2 is correct explanation of Statement -1 |
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| 22382. |
Statement-1: Third ionisation energy of phosphorous is larger than sulphur. Statement-2: There is a larger amount of stability associated with filled s-and p-sub-shells (a noble gas electron configuration) which corresponds to having eight electrons in the valence shell of an atom or ion.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True. |
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Answer» Correct Answer - D Statement-1 is false. Electrons configuration`._16S^(2+)=1s^2 2s^2 2p^6 3s^2 3p^2 and ._15P^(2+)=1s^2 2s^2 2p^6 3s^2 3p^1` Sulphur has higher nuclear charge and smaller size than that of phosphorus so `IE_3` of `SgtP` `E_3(P)=2,912 kJ//mol,(S)=3,361 kJ//mol` Statement-2 is true statement. |
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| 22383. |
What is molar conductance? |
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Answer» Molar Conductivity: Molar conductivity of a solution at a given concentration is the conductance of the volume V of solution containing on mole of electrolyte kept between two electrodes with area of cross section A and distance of unit length. Therefore, lm = (kA/l) = k |
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| 22384. |
What happen when- Ethyl alcohol is oxidised? |
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Answer» Ethyl alchol is oxidised, it gives ethanol. CH3 — CH2 — OH + [O] → CH3CHO |
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| 22385. |
Define 'Peptization'. |
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Answer» Peptization: The process of converting a precipitate into a colloidal solution by shaking it with dispersion medium in the presence of a small amount of electrolyte is called peptization. |
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| 22386. |
Which of the following precaution to be taken to dilute a concentrated acid ? (a) Add water to acid (b) Add acid to water |
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Answer» (b) Add acid to water. |
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| 22387. |
In metallurgy , flux is a substance used to convert_________.A. mineral into silicateB. Fusible impurities to infusible impuritiesC. Infusible impurities to soluble impuritiesD. Soluble impurities into infusible impurities |
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Answer» Correct Answer - B Gangue + flux =slag |
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| 22388. |
Which apparatus is mainly required to avoid heat loss to find the specific heat of given solid ? |
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Answer» Calorimeter.. |
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| 22389. |
Metallurgy involves steps :(A) Concentration of ore (B) Reduction of ore (C) Purification (D) Alloy formation |
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Answer» Correct option (A,B,C) Explanation: Steps of metallurgy are : Concentration of ore, reduction of ore and purification |
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| 22390. |
Minerals of lead are : (A) Cerussite (B) Pyrolusite (C) Galena (D) Calamine |
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Answer» Correct option (A,C) Explanation: Cerussite – PbCO3 Pyrolusite – MnO2 Galena – PbS Calamine – ZnCO3 |
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| 22391. |
What happens when a current carrying wire is placed in a magnetic field ? |
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Answer» It experiences magnetic force. |
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| 22392. |
What is the maximum value of 'l' for n = 4? |
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Answer» '3' is the maximum value of 'l' for n = 4. |
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| 22393. |
How does a glass marble behaves in water ? |
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Answer» Convergent lens. |
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| 22394. |
Expand VSEPRT. |
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Answer» Valence Shell Electron Pair Repulsion Theory. |
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| 22395. |
The most abundant metal in the earth's crust is (A) silver (B) aluminium (C) zinc (D) iron |
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Answer» (B) aluminium. |
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| 22396. |
K4 [Fe(CN)]6 is a/an– (a) Double salt(b) Complex salt(c) Acid(d) Base |
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Answer» K4 [Fe(CN)]6 is a Complex salt. |
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| 22397. |
Most abundant metal on the surface of earth is- (a) Iron(b) Aluminium(c) Calcium(d) Sodium |
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Answer» Most abundant metal on the surface of earth is Aluminium. |
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| 22398. |
With respect to the formation of Ethane molecule mention. (i) hybridation of Carbon.(ii) number of sigma bonds in the molecule. |
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Answer» (i) sp2 (ii) 5 |
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| 22399. |
Define the terms: (i) Bond order (ii) Bond length (iii) Bond enthalpy |
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Answer» (i) It is the number of covalent bonds holding the atoms in the molecule. Example: If the bond is formed by the sharing of two electron pairs, then the bond order is 2. O = O or C = C bond in alkenes. (ii) Bond length: It is the equilibrium distance between nuclei of two bonded atoms in a molecule. (iii) Bond enthalpy: It is the amount of energy required to break one mole of bonds of a particular type between two atoms in a gaseous state. |
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| 22400. |
What is Empirical formula ? Give an example for a compound whose Empirical formula and molecular formula are the same |
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Answer» Empirical formula represents the simplest whole-number ratio of various atoms present in a compound. Example: C2H8. |
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