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InterviewSolution
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.
| 951. |
If a,b,c are real numbers such that a + b + c = 0 and a2 + b2 + c2 = 1, then (3a + 5b – 8c)2 + (–8a + 3b + 5c)2 + (5a – 8b + 3c)2 is equal to (A) 49 (B) 98 (C) 147 (D) 294 |
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Answer» Correct Option :- (C) 147 Explanation :- Expanding are get 98 (a2 + b2 + c2 ) – 98 (ab + bc + ca) = 98 – 98 (-1/2) = 147 |
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| 952. |
The number of positive integers n in the set {2,3,....,200} such that 1/n has a terminating decimal expansion is (A) 16 (B) 18 (C) 40 (D) 100 |
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Answer» Correct Option :- (B) 18 Explanation :- The numbers will be 2, 4, 8, 16, 32, 64, 128, 5, 25, 125, 10, 20, 40, 50, 80, 100, 160, 200 |
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| 953. |
The number of positive integers n in the set {2,3,…,200} such that `(1)/(n)` has a terminating decimal expansion isA. 16B. 18C. 40D. 100 |
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Answer» Correct Answer - B The numbers will be 2,4,8,16,32,64,128, 5,25,125, 10,20,40,50,80,100,160,200 |
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| 954. |
`MnO_(4)^(-)` oxidizes (i) oxalate ion in acidic medium at 333 K and (ii) HCl. For balanced chemical equations, the rations `[MnO_(4)^(-) : C_(2)O_(4)^(2-)]` in (i) and `[MnO_(4)^(-) : HCl]` in (ii), respectively, are -A. 1 : 5 and 2 : 5B. 2 : 5 and 1 : 8C. 2 : 3 and 1 : 5D. 5 : 2 and 1 : 8 |
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Answer» Correct Answer - B `16H^(+)+2MnO_(4)^(-)+5C_(2)O_(4)^(2-) rarr 2Mn^(+2)+10CO_(2)+8H_(2)O` `MnO_(4)^(-) : C_(2)O_(4)^(2-) = 2: 5` `2KMnO_(4)+16 HCl rarr 2KCl+2MnCl_(2)+5Cl_(2)+8H_(2)O` `MnO_(4)^(-) : HCl =2 : 16 = 1 : 8` |
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| 955. |
`XeF_(6)` hydrolyses to give an oxide. The structure of `XeF_(6)` and the oxide, respectively, are -A. octahedral and tetrahedralB. distorted octahedral and pyramidalC. octahedral and pyramidalD. distorted octahedral and tetrahedral |
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Answer» Correct Answer - B `{:(ul(XeF_(6))+3H_(2)O,rarr,ul(XeO_(3))+6HF),(" "darr,," "darr),(Sp^(3) d^(3)" Hybridisation",,Sp^(3)" Hybridisation"),("(distorted octahedral)",,"(Pyramidal)"):}` |
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| 956. |
A liquid drop placed on a horizontal plane has a near spherical shape (slightly flattened due to gravity). Let R be the radius of its largest horizontal section. A small disturbance causes the drop to vibrate with frequency v about its equilibrium shape. By dimensional analysis the ratio `(v)/(sqrt(sigma//rho R^(3)))` can be (Here `sigma` is surface tension, `rho` is density, g is acceleration due to gravity, and k is arbitrary dimensionless constant)–A. `k rhog R^(2)//sigma`B. `k rho R^(2)//g sigma`C. `k rho R^(3)//g sigma`D. `k rho//g sigma` |
| Answer» Correct Answer - A | |
| 957. |
A ray of white light is incident on a spherical water drop whose center is C as shown below. When observed from the opposite side, the emergent light – A. Will be white and will emerge without deviatingB. Will be internally reflectedC.D. |
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Answer» Correct Answer - A |
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| 958. |
A ray of white light is incident on a spherical water drop whose center is C as shown below. When observed from the opposite side, the emergent light – (A) Will be white and will emerge without deviating (B) Will be internally reflected (C) Will split into different colors such that the angles of deviation will be different for all colors (D) Will split into different colors such that the angles of deviation will be the same for all colors |
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Answer» Correct option (A) Will be white and will emerge without deviating Perpendicular incidence so no deviation. |
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| 959. |
Two cars `S_(1)` and `S_(2)` are moving in coplanar concentric circular tracks in the opposite sense with the periods of revolution 3 min and 24 min, respectively. At time t = 0, the cars are farthest apart. Then, the two cars will beA. closest to each other at t = 12 min and farthest at t = 18 min.B. closest to each other at t = 3 min and farthest at t = 24 minC. closest to each other at t = 6 min and farthest at t = 12 minD. colsest to each other at t = 12 min and farthest at t = 24 min |
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Answer» Correct Answer - D |
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| 960. |
A cylindrical vessel of base radius R and height H has a narrow neck of height h and radius r at one end (see figure). The vessel is filled with water (density`rho_(w)`) and its neck is filled with immiscible oil (density `rho_(O)`). Then the pressure at A. M is `g(hrho_(0)+H rho_(w))`B. N is `g(hrho_(0)+Hrho_(w))(r^(2))/(R^(2))`C. M is g `Hrho_(w)`D. `"N is g"(rho_(w)HR^(2)+rho_(0)hr^(2))/(R^(2)+r^(2))` |
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Answer» Correct Answer - A |
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| 961. |
A point source of light is moving at a rate of `2 cm-s^(-1)` towards a thin convex lens of focal length 10 cm along its optical axis. When the source is 15 cm away from the lens the image is moving at -A. `4 cm-s^(-1)` towards the lensB. `8 cm-s^(-1)` towards the lensC. `4 cm-s^(-1)` away from the lensD. `8 cm-s^(-1)` away from the lens |
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Answer» Correct Answer - D |
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| 962. |
If the image formed by a thin convex lens of power P has agnification m then image distance v isA. `v=(1-m)/(P)`B. `v=(1+m)/(P)`C. `v=(m)/(P)`D. `v=(1+2m)/(P)` |
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Answer» Correct Answer - A |
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| 963. |
Two positively charged spheres of masses `m_(1), " and " m_(2)` are suspended from a common point at the ceiling by identical insulating massless strings of length l. Charged on the two spheres are `q_(1) " and " q_(2)`, respectively. At equilibrium both strings make the same angle `theta` with the vertical. ThenA. `q_(1) m_(1) = q_(2) m_(2)`B. `m_(1) = m_(2)`C. `m_(1) = m_(2) sin theta`D. `q_(2) m_(1)=q_(1)m_(2)` |
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Answer» Correct Answer - B |
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| 964. |
The radiu8s of `K^(+)` is 133 pm and that of CI is 181 pm. The volumne of the unit cell of KCI expressed in `10^(-22) cm^(3)` is :A. `0.31`B. `1.21`C. `2.48`D. `6.28` |
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Answer» Correct Answer - C `r_(K^(+))+r_(CI^(-))=(a)/(2)` `133+181=(a)/(2)` a=2(133+181) a=628pm or `a=628xx10^(-10)cm` and volume =`a^(3)=(6.28xx10^(-8))^(3)cm^(3)` `=2.4767xx10^(-22) cm^(2)` `~~2.48xx10^(-22)m^(3)` |
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| 965. |
A particle is acted upon by a force given by `F = - alphax^(3) -betax^(4)` where `alpha` and `beta` are positive constants. At the point x = 0, the particle is –A. In stable equilibriumB. In unstable equilibriumC. In neutral equilibriumD. Not in equilibrium |
| Answer» Correct Answer - C | |
| 966. |
the number of distinct primes dividing `12!+13!+14!` is -A. 5B. 6C. 7D. 8 |
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Answer» Correct Answer - A `12!+13!+14!` `=2!(1+13+14xx13)` `=13! (14+14xx13)` `=12! Xx196` prime nos are 2,3,4,5,,7,11 total =5 |
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| 967. |
Let `vecu = 2hati - hatj + hatk, vecv = -3hatj + 2hatk` be vectors in `R^(3)` and `vecw` be a unit vector in the xy-plane. Then the maximum possible value of `|(vecu xx vecv).vecw|` is-A. `sqrt(5)`B. `sqrt(12)`C. `sqrt(13)`D. `sqrt(17)` |
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Answer» Correct Answer - D `vecuxxvecv = (2hati - hatj + hatk)xx(-3hatj + 2hatk)` `-6hatk - 4hatj - 2hati + 3hati = hati - 4hatj - 6hatk` Let `vecw = a hati + bhatj , a^(2) + b^(2) = 1 , a cos theta , b = sintheta` `vecu xx vecv.vecw = a - 4b = costheta - 4 sin theta` max. value `= sqrt(1^(2) +(-4)^(2)) = sqrt(17)` |
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| 968. |
A stream of photons having energy 3 eV each impinges on a potassium surface. The work function of potassium is 2.3 eV. The emerging photo-electrons are slowed down by a copper plate placed 5 mm away. If the potential difference between the two metal plates is 1 V, the maximum distance the electrons can move away from the potassium surface before being turned back is–A. `3.5 mm`B. `1.5 mm`C. `2.5 mm`D. `5.0 mm` |
| Answer» Correct Answer - A | |
| 969. |
when 262 g of xenon (atomic mass = 131) receted completely with 152 g fluride (atomic mass = 19) ,a mixture of Xe `F_(2) ` and `XeF_(6) ` was produced , the molar `Xef_(2) : XeF_(6)` isA. `1:2`B. `1:4`C. `1:1`D. `1:3` |
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Answer» Correct Answer - C `{:(2Xe ,+,4F_(2) , to , XeF_(2) ,+ ,XeF_(6) ),(2,,8,,0,,0):}` `therefore` moles ofXe `F_(2)` formed =0.5 moles of `Xef_(6) ` formed = 0.5 `therefore ` moles ratio =1:1 |
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| 970. |
In a food chain such as grass → deer → lion, the energy cost of respiration as a proportion of total assimilated energy at each level would be – (A) 60% - 30 % - 20% (B) 20% - 30 % - 60% (C) 20% - 60 % - 30% (D) 30% - 30 % - 30% |
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Answer» Correct :- (A) 60% - 30 % - 20% Explanation :- Actually around one half of the energy is lost through respiration. Hence best option is 60% - 30% - 20% |
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| 971. |
Gaseous exchange of oxygen and carbon dioxide between alveolar air and capillaries takes place byA. Active transportB. DiffusionC. Carrier-mediated transportD. Imbibition |
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Answer» Correct Answer - B By diffusion along concentration gradient. |
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| 972. |
Scurvy is caused by the deficiency ofA. Nicotinic acidB. Ascorbic acidC. Pantothenic acidD. Retinoic acid |
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Answer» Correct Answer - B Ascorbic acid is required for a variety of biosynthetic pathway. It is required for collagen synthesis during wound healing. |
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| 973. |
Of the periods listed below, which ONE is the earliest period when Ostracoderms, the jawless and finless fishes, appeared?A. Devonian periodB. Cambrian periodC. Carboniferous periodD. Silurian period |
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Answer» Correct Answer - D Period is time |
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| 974. |
Of the periods listed below, which ONE is the earliest period when Ostracoderms, the jawless and finless fishes, appeared?(A) Devonian period (B) Cambrian period (C) Carboniferous period (D) Silurian period |
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Answer» Correct Option :- (D) Silurian period Explanation :- Period is time |
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| 975. |
A spiral galaxy can be approximated as an infinitesimally thin disk of a uniform surface mass density (mass per unit area) located at `z=0`. Two stars `A` and `B` start from rest from heights `2z_(0)` and `z_(0)` (`z_(0) lt lt` radial extent of the disk), respectively, and fall towards the disk, cross over to the other side, and execute periodic oscillations. The ratio of time periods of `A` and `B` isA. `2^(-1//2)`B. `2`C. `1`D. `2^(1//2)` |
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Answer» Correct Answer - D |
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| 976. |
Threee successive measurements in an experiment gave the values 10.9, 11.4042 and 11.42. The correct way of reporting the average value is -A. 11.208B. 11.21C. 11.2D. 11 |
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Answer» Correct Answer - C The convent wat of reporting the average value should have exactly exactly number of digit after decimal which has least digit after decimal among the data given. |
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| 977. |
The number of moles of `KMnO_(4)` required to oxidize one equivalent of Kl is the presence of sulfuric acid is-A. 5B. 2C. `1//2`D. `1//5` |
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Answer» Correct Answer - D `KMnO_(4)+Kl+H_(2)SO_(4)rarrMnSO_(4)+I_(2)+K_(2)SO_(4)+H_(2)O` `v.f=5 " " v.f=1` `:. (eq)_(KMnO_(4))=(eq)_(Kl)=I` Eq. =V.F `xx` mole 1=5 `xx` mole Mole =1/5 |
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| 978. |
The following two compounds are- A. geometrical isomersB. positional isomersC. functional group isomersD. optical isomers |
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Answer» Correct Answer - B `H_(3)C-C=C-CH_(3)("But-2-ene"),H_(3)C-CH_(2)=CH_(2)("But-1-ene")` |
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| 979. |
The following two compounds are – (A) geometrical isomers (B) positional isomers (C) functional group isomers (D) optical isomers |
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Answer» Correct option (B) positional isomers Explanation: H3C – C = C – CH3 (But-2-ene), H3C – CH2 – CH = CH2 (But-1-ene) |
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| 980. |
Upon fully dissolving 2.0 g of a metal in sulfuric acid, 6.8 g of the metal sulfate is formed. The equivalent weigth of the metal is-A. `13.6 g`B. `20.0g`C. `4.0g`D. `10.0g` |
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Answer» Correct Answer - B Equivalents of metal=Equivalents of metal sulphate `("wt.of metal")/("Eq. wt. of metal")("wt. of metal sulphate")/("Eq. wt. metal sulphate")` `(2)/(x)=(6.8)/(x +48)` `6.8x=2x+96` `4.8x=96` `x=(96)/(4.8)=20` |
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| 981. |
Two different liquids of same mass are kept in two identical vessels, which are placed in a freezer that extracts heat from them at the same rate causing each liquid to transform into a solid. The schematic figure below shows the temperature T vs time t plot for the two materials. We denote the specific heat of metrials in the liquid (solid) states to be `C_(L1) (C_(S1))` and `C_(L 2) (C_(S2))` respectively A. `C_(L1)ltC_(L2)` and `C_(S1)ltC_(S2)`B. `C_(L1)gtC_(L2)` and `C_(S1)gtC_(S2)`C. `C_(L1)gtC_(L2)` and `C_(S1)gtC_(S2)`D. `C_(L1)ltC_(L2)` and `C_(S1)gtC_(S2)` |
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Answer» Correct Answer - B |
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| 982. |
A man tosses a coin 10 times, scoring 1 point for each head and 2 points for each tail. Let P(K) be the probability of scoring at least K points. The largest value of K such that `P(K)gt1//2` is -A. 14B. 15C. 16D. 17 |
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Answer» Correct Answer - C Ways to make the sum K is coefficient of `x^(K)` in `(x+x^(2))^(10)` Coeffecient of `x^(K)` in `x^(10)(1+x)^(10)` Coefficient of `x^(K-10)` in `(1+x)^(10)` Which is `.^(10)C_(K-10)` So ways to make sum minimum K is `.^(10)C_(K-10)+.^(10)C_(K-9)+.^(10)C_(K-8)+......^(10)C_(10)` Probability `P(K)=(.^(10)C_(K-10 )+.^(10)C_(K-9)+.......+.^(10)C_(10))/(2^(10))` `P(K)=(2^(10)-(.^(10)C_(0)+.....+.^(10)C_(K-11)))/(2^(10))` `=I-(.^(10)C_(0)+....+.^(10)C_(K-11))/(2^(10))gt(1)/(2)` But K should be maximum so `.^(10)C_(K-11)=.^(10)C_(5)` (middle value) So that `.^(10)C_(0)+.....+.^(10)C_(K-11)` is max So K = 16 |
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| 983. |
Choose a number n uniformly at random from the set {,2,.....,100} . Choose one of the first seven days of the year 2014 at random and consider n consecutive days starting from the chosen day what is the probability that among the chosen n days , the number of Sundays is different from the number of Mondays?A. `(1)/(2)`B. `(2)/(7)`C. `(12)/(49)`D. `(43)/(175)` |
| Answer» Correct Answer - A | |
| 984. |
Let `f(x)=(x+1)/(x-1)` for all `xne1`. Let `f^(1)(x)=f(x),f^(2)(x)=f(f(x))` and generally `f^(n)(x)=f(f^(n-1)(x)) " for n"gt1` Let `P=f^(1)(2)f^(2)(3)f^(3)(4)f^(4)(5)` Which of the following is a multiple of P-(A) 125 (B) 375 (C) 250 (D) 147A. 125B. 375C. 250D. 147 |
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Answer» Correct Answer - B `f(x)=(x+1)/(x-1)` `f^(2)(x)=f(f(x))=f((x+1)/(x-1))=((x+1)/(x-1)+1)/((x+1)/(x-1)-1)=x` `f^(3)(x)=f(x)=(x+1)/(x-1)` `f^(4)(x)=x` `P=f(2).f^(3)(3)f^(3)(4)f^(4)(5)` `P=3xx3xx(5)/(3)xx5=75` Multiple of P is 375 |
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| 985. |
For a real number r we denote by [r] the largest integer less than or equal to r. If x,y are real numbers with `x,y ge 1` then which of the following statements is always true? A) `[x+y] le [x]+[y]` B) `[xy] le [x][y]` C) `[2^x] le 2^[x]` D)`[(x)/(y)] le [x]/[y]`A. `[x+y]le[x]+[y]`B. `[xy]le[x]+[y]`C. `[2^(x)]le2^([x])`D. `[(x)/(y)]le([x])/([y])` |
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Answer» Correct Answer - D (A) `[x+y]le[x]+[y]` let x=0.1 y=0.9 `[0.1+0.9]le[0.1]+[0.9]` `1 le 9+0` wrong (B) `[xy]le[x]+[y]` `x=2,y=(1)/(2)` `[2*(1)/(2)]le[2][(1)/(2)]` `rArr1le0` wrong (C) `[2^(x)]le2^([x])` `x=0.99[2^(0.99)]le2^([0.99])` `[2^(0.99)]le2^(@)=1` wrong (D) `[(x)/(y)]le([x])/([y])` given `x,yge1` if `xlty[(x]/(y)]=0" " 0le([x])/([y])` true if `xgey[(x]/(y)]le([x])/([y])` always true |
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| 986. |
Let S={(a,b)|a,b `in Z, 0 le a,b le 18}` . The number of lines in `R^(2)` passing though (0,0) and exactlu one other points in S is-A. 16B. 22C. 28D. 32 |
| Answer» Correct Answer - A | |
| 987. |
if n is the smallest natural number such that `n+2n+3n+* * * * * * *+99n` is a perfect squre , then the number of digits in `n^(2)` is -A. 1B. 2C. 3D. more than 3 |
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Answer» Correct Answer - C `n+2n+3n+** *+99n=k^(2)` `implies n(99.100)/(2)=k^(2) ` `implies n.99.50=k^(2)` `implies n.9.11.25.2=k^(2)` SO n=11.2=22 `n^(2) =484` No .of digits in `n^(2)`=3 . |
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