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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.
| 201. |
Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between them is F. A third identical conducting spheres, C,is uncharged. Sphere C is first touched to A, then to B, and then removed. As a result, the force between A and B would be equal to :A. FB. `(3F)/(8)`C. `(3F)/(4)`D. `(F)/(2)` |
| Answer» Correct Answer - B | |
| 202. |
Two particles of de-broglie wavelength `lamda_(x)` and `lamda_(y)` are moving in opposite direction. Find debroglie wavelength after perfectly inelastic collision:A. `(lamda_(x)lamda_(y))/(|lamda_(x)-lamda_(y)|)`B. `(2lamda_(x)lamda_(y))/(lamda_(x)-lamda_(y))`C. `(lamda_(x)lamda_(y)^(2))/(lamda_(y)-lamda_(x))`D. `lamda_(y)-lamda_(x)` |
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Answer» Correct Answer - A |
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| 203. |
Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths `lambda_(N) ,lambda_(A)` respectively. The ratio `(lambda_(N))/(lambda_(A))` is closest to :A. `10^(-6)`B. `10^(-1)`C. `10^(-10)`D. 10 |
| Answer» Correct Answer - C | |
| 204. |
Two particles A,B are moving on two concentric circles of radii `R_1)` and `R_2` with equal angular speed `omega`. At`t=0`,their positions and direction fo motion are shown in the figure : A. `omega(R_1+R_2)hati`B. `-omega(R_1+R_2)hati`C. `omega(R_2-R_1)hati`D. `omega(R_1-R_2)hati` |
| Answer» Correct Answer - A | |
| 205. |
A particle executes simple harmonic motion and is located at ` x = a`, b at times `t_(0),2t_(0) and3t_(0)` respectively. The frequency of the oscillation is :A. `(1)/(2pit_(0))cos^(-1)((2a+3c)/(b))`B. `(1)/(2pit_(0))cos^(-1)((a+c)/(2b))`C. `(1)/(2pit_(0))cos^(-1)((a+b)/(2c))`D. `(1)/(2pit_(0))cos^(-1)((a+2b)/(3c))` |
| Answer» Correct Answer - B | |
| 206. |
Statement -1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement -2 : Principle of conservation of momentum holds true for all kinds of collisions.A. Statement-1 is true, Statement-2 is true, Statement-2 is the correct explanation of Statement-1.B. Statement-1 is true, Statement-2 is true, Statement-2 is not the correct explanation of Statement-1.C. Statement-1 is false, Statement-2 is true.D. Statement-1 is true, Statement-2 is false. |
| Answer» Correct Answer - A | |
| 207. |
A carrier wave of peak voltage 14 V is used for transmitting a message signal. The peak voltage of modulating signal given to achieve a modulation index of 80% will be :A. 7 VB. 11.2 VC. 28 VD. 22.4 V |
| Answer» Correct Answer - B | |
| 208. |
Two particles of the same mass m are moving in circular orbits because of force, given by `F(r)=(-16)/(r)-r^(3)` The first particle is at a distance r =1 , and the second, at r = 4. The best estimate for the ratio of kinetic energies of the first and the second particle is closet to :A. `3xx10^(-3)`B. `6xx10^(2)`C. `10^(-1)`D. `6xx10^(-2)` |
| Answer» Correct Answer - D | |
| 209. |
A power transmission line feeds input power at 2300 V a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5A and its efficiency is `90%`, the output current would be :A. 20 AB. 50 AC. 25 AD. 45 A |
| Answer» Correct Answer - D | |
| 210. |
An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume `V_1` and contains ideal gas at pressure `P_1` and temperature `T_1`.The other chamber has volume `V_2` and contains ideal gas at pressure `P_2` and temperature `T_2`. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will beA. `(T_(1)T_(2)(P_(1)V_(1) + P_(2)V_(2)))/(P_(1)V_(1)T_(2) + P_(2)V_(2)T_(1))`B. `(P_(1)V_(1)T_(1) + P_(2)V_(2)T_(2))/(P_(1)V_(1) + P_(2)V_(2))`C. `(P_(1)V_(1) T_(2) + P_(2) V_(2)T_(1))/(P_(1)V_(1) + P_(2)V_(2))`D. `(T_(1)T_(2) (P_(1)V_(1) + P_(2)V_(2)))/(P_(1)V_(1) T_(1) + P_(2)V_(2)T_(2))` |
| Answer» Correct Answer - A | |
| 211. |
The locus of the mid points of the chords of the circle `x^2+y^2+4x-6y-12=0` which subtends an angle of `pi/3` radians at its centre is |
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Answer» Equation of the circle, `x^2+y^2+4x-6y -12 = 0` Here, `g = 2, f = -3, c = -12` `:.` Center of the circle will be `(-2,3)`. Radius of the circle ` = sqrt(g^2+f^2-c) = sqrt(4+9+12) = 5` Let `AB` is the chord and `C(h,k)` is the midpoint of `AB`. We have to find locus of point `C`. Let `O(-2,3)` is the center of the circle. Then, `/_AOB = pi/3 =>/_AOC = 1/2/_AOB = pi/6`. Now, `(OC)/(OA) = cos (pi/6)` `=>OC = 5**sqrt3/2 = 5sqrt3/2`...(As OA = radius) `:. sqrt((h+2)^2+(k-3)^2) = (5sqrt3)/2` Squaring both sides, `=>((h+2)^2+(k-3)^2) = ((5sqrt3)/2)^2` `=>(h+2)^2+(k-3)^2 = 75/4` Replacing `(h,k)` with `(x,y)`, `(x+2)^2+(y-3)^2 = 75/4`, which is the required locus. |
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| 212. |
The equation of the circle whose diameter is the common chord of thecircles; `x^2+y^2+3x+2y+1=0`& `x^2+y^2+3x+4y+2=0`is:`x^2+y^2+8x+10 y+2=0``x^2+y^2-5x+4y+7=0``2x^2+2y^2+6x+2y+1=0`None of these |
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Answer» Here, S1 is `x^2+y^2+3x+2y+1=0`. S2 is `x^2+y^2+3x+4y+2=0` As both circles have common chord, we can have `x^2+y^2+3x+2y+1 = x^2+y^2+3x+4y+2``=>y=-1/2->Eq(1)` Now, equation of the required circle can be generate by: `S1+lambdaS2 = 0` (From, family of circles equation) `=>x^2+y^2+3x+2y+1+lambda(x^2+y^2+3x+4y+2) = 0` `=>(1+lambda)x^2+(1+lambda)y^2+3(1+lambda)x+2(1+2lambda)y+(1+2lambda) = 0->Eq(2)` Now, we can find centre of the circle from the above equation. Centre will be `(-3/2(1+lambda),-(1+2lambda))` As `y=-1/2`, we can say that `-(1+2lambda) = -1/2` `lambda = -1/4` So, putting above value of ` lambda` in Eq(2), we get the required equation. |
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| 213. |
The copolymer formed by addition polymerization of styrene and acrylonitrile in the presence of peroxide is :A. B. C. D. |
| Answer» Correct Answer - C | |
| 214. |
If `(2+iota)(2+2iota)(2+3iota).....(2+9iota)=x+iotay`, then 5.8.13.....85= |
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Answer» `|z|=|x+iy|=sqrt(x^2+y^2)` `|x+iy|=|(2+i)(2+2i)(2+3i)...(2+9i)|` `=|2+i||2+2i||2+3i|...|2+9i|` `=sqrt(4+1)*sqrt(2^2+2^2)...sqrt(2^2+9^2)` `sqrt(x^2+y^2)=sqrt5*sqrt8*sqrt13...sqrt85` `x^2+y^2=5*8*13*...*85` option 1 is correct. |
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| 215. |
The points of intersection of the two curves `|z-3|=2` and `|z|=2` in an argand plane are: |
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Answer» `Z=x+iy` `|z|=sqrt(x^2+y^2)=2` `x^2+y^2=2` `Z-3=x+iy-3=(x-3)+iy` `|z-3|=sqrt((x-3)^2+y^2)=2` `(x-3)^2+y^2=4-(2)` `cx^2-(x-3)^2=0` `x^2=(x-3)^2` `x=pm(x-3)` `x=x-3` `x=-x+3` `2x=3` `x=3/2` `y^2=4-9/4` `y=sqrt7/2` Intersection=`3/2+sqrt7/2i` and `3/2-sqrt7/2i` `1/2(3pmisqrt7)` option 2 is corrrect. |
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| 216. |
If `|z_1-1| |
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Answer» `|z-1|<1` center(1,0) and` r_1=1` `|z_2-2|<2` `C_2(2,0) and r_2=2` `|z_3-3|<3` `c_3(3,0) and r_3=3` `|Z_1| in(0,2)` `|Z_2| in (0,4)` `|Z_3| in(0,6)` `|z_1+z_2+z_3| in (0,12)` option 3 is correct. |
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| 217. |
If `1,alpha_1,alpha_2,alpha_3,alpha_4` be the roots `x^5-1=0`, then value of `[omega-alpha_1]/[omega^2-alpha_1].[omega-alpha_2]/[omega^2-alpha_2].[omega-alpha_3]/[omega^2-alpha_3].[omega-alpha_4]/[omega^2-alpha_4]` is (where `omega` is imaginary cube root of unity) |
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Answer» `x^5-1=(x-1)(x-alpha_1)(x-alpha_2)(x-alpha_3)(x-alpha_4)` `w^5-1=(x-1)(w-alpha_1)(w-alpha_2)(w-alpha_3)(w-alpha_4)` `w^10-1=(w^2-1)(w^2-alpha_1)(w^2-alpha_2)(w^2-alpha_3)(w-alpha_5)` `(w^5-1)/(w^10-1)=((x-1)(w-alpha_1)(w-alpha_2)(w-alpha_3)(w-alpha_4))/((w^2-1)(w^2-alpha_1)(w^2-alpha_2)(w^2-alpha_3)(w-alpha_5))` `(w+1)/(w^5+1)=((w-alpha_1)...(w-alpha_4))/((w^2-alpha_1)....(w^2-alpha_4))` `w^2/w=((w-alpha_1)...(w-alpha_4))/((w^2-alpha_1)....(w^2-alpha_4))` option 1 is correct. |
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| 218. |
Let `z_1 and z_2` be nth roots of unity which subtend a right angle at the origin. Then n must be of the form (1) `4k+1` (2) `4k+2` (3) `4k+3` (4) `4k` |
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Answer» `Z^n-1=0` `Z=1^(1/n)` `Z_1=e^((i2pi)/n)` `Z_2=e^((i2pi)/n)` `theta_1=2pik/n` `theta_2=2pi(k+1)/n` `theta_2-theta_1=pi/2` `2pi(k+1)/n-2pi(k)/n=pi/2` `2pi/n(K+1-k)=pi/2` `n=4` option d is correct. |
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| 219. |
Which of the following statement is falseA. Photon has momentum as well as wavelength.B. Rydberg constant has unit of energy.C. Frequency of emitted radiation from a black body goes from a lower wavelength to higher wavelength as the temperature increases.D. Splitting of spectral lines in electrical field is called Stark effect. |
| Answer» Correct Answer - C | |
| 220. |
The compound that is NOT a common component of photochemical smog is :A. `O_(3)`B. `H_3C-underset(O)underset(|)C-OONO_2`C. `CH_2CHCHO`D. `CH_2CI_2` |
| Answer» Correct Answer - A | |
| 221. |
For a reaction, consider the plot of In K versus `1//T` given in the figure. If the rate constant of this reaction at 400 K is `10^(-5)s^(-1)`, then the rate constant at `500 K` is : A. `10^(-6)S^(-1)`B. `2xx10^(-4)s^(-1)`C. `10^(-4)s^(-1)`D. `4xx10^(-4)s^(-1)` |
| Answer» Correct Answer - A | |
| 222. |
Water is flowing condinuously from a tap of area `10^(-4)m^(2)` the water velocity as it leaves the top is `1m//s` find out area of the water stream at a distance 0.15 m below the topA. `0.5xx10^(-4)m^(2)`B. `1xx10^(-4)m^(2)`C. `2xx10^(-4)m^(2)`D. `0.25xx10^(-4)m^(2)` |
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Answer» Correct Answer - A |
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| 223. |
Which of the following statements are incorrect ? (1) `Co^(+3)` with strong field ligand forms high magnetic moment complex. (2) For `Co^(+3)` if pairing `"energy"(P) gt Delta_o` then the complex formed will have `(t_(2g)^(4),(e_g)^2)` configuration. ltbr. (3) For `[Co(en)^3]^( 3+) lambda_("absorbed")` is less than `lambda_("absorbed")` for `[CoF_6]^( 3–)` (4) If `Delta_o = 18000 cm^(–1)` for `Co^(+3)` then with same ligands for it `Delta_t = 16000 cm^(–1)`A. 1,4B. 2,3C. 1,2D. 1,2,3,4 |
| Answer» Correct Answer - A | |
| 224. |
The major product of the following reaction is : A. `CH_3CH_2underset(CO_2CH_2CH_3)underset(|)(C)=CH_(2)`B. `underset(CH_3C=CHCH_3)underset(|)(CO_2)CH_2CH_3`C. D. |
| Answer» Correct Answer - A | |
| 225. |
Let `{:[(1,2),(0,1):}][{:(1,2),(0,1):}]......[{:(1,n-1),(0,1):}]=[{:(1,78),(0,1):}]` If `A=[{:(1,n),(0,1):}]` then `A^(-1)=`A. `[{:(1,12),(0,1):}]`B. `[{:(1,-13),(0,1):}]`C. `[{:(1,-12),(0,1):}]`D. `[{:(1,0),(-13,1):}]` |
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Answer» Correct Answer - B |
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| 226. |
The major product of the following reaction is : `overset((i)NaNO_2//H^+)undersetunderset((iii)H_2SO_4("conc".),Delta)((ii)CrO_3//H^+)to`A. B. C. D. |
| Answer» Correct Answer - A | |
| 227. |
Chlorine on reaction with hot and concentrated sodium hydroxide gives :A. `CI^(-) and CIO_(3)^(-)`B. `CI^(-) and CIO^(-)`C. `CIO_(3)^(-) and CIO_(2)^(-)`D. `CI^(-) and CIO_(2)^(-)` |
| Answer» Correct Answer - A | |
| 228. |
if `y=mx+7sqrt(3)` is normal to `(x^(2))/(18)-(y^(2))/(24)=1` then the value of m can beA. `(2)/(sqrt(5))`B. `(4)/(sqrt(5))`C. `(1)/(sqrt(5))`D. `(2)/(sqrt(3))` |
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Answer» Correct Answer - A |
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| 229. |
`intsec^((2)/(3))xcosec^((4)/(3))xdx` is equal toA. `3tan^((1)/(3))x+C`B. `-3cot^((1)/(3))x+c`C. `-3tan^((1)/(3))x+c`D. `(3)/(4)cot^((1)/(3))x+c` |
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Answer» Correct Answer - B |
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| 230. |
A committee of 11 person is to be made from 8 male and 5 female where m is number of ways of selecting at least 6 male and n is the number of ways of selecting at least 3 female. ThenA. `m=n=78`B. `m=n=68`C. `m+n=68`D. `m-n=8` |
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Answer» Correct Answer - A |
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| 231. |
There are two newspaper `A & B` published in a city. If `25%` people read `A, 20%` people read `B & 8%` both read. Also `30%` of these who read `A` both `B` look into advertisement `40%` of these who read `B` but not `A` look into advertisement `50%` of these who read both `A & B` look into advetisement then how many `%` of people look into advertisementA. `13.9%`B. `13%`C. `13.1%`D. `13.2%` |
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Answer» Correct Answer - A |
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| 232. |
A Circular ring of radius `3a` is uniformly charged with charge `q` is kept in `x-y` plane with center at origin. A particle of charge `q` and mass `m` is projected frim `x=4` towards origin. Find the minimum speed of projection such that it reaches origin. A. `sqrt((q^(2))/(15piepsilon_(0)ma))`B. `sqrt((q^(2))/(30piepsilon_(0)ma))`C. `sqrt((q^(2))/(10 piepsilon_0(ma))`D. `sqrt((q^(2))/(20 piepsilon_0(ma))` |
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Answer» Correct Answer - A |
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| 233. |
An ideal gas undergoes an isobaric process. If its heat capacity is `C`, at constant volume and number of mole `n,` then the ratio of work done by gas to heat given to gas when temperature of gas changes by `DeltaT` is :A. `((nR)/(C_(v)+R))`B. `((R)/(C_(v)+R))`C. `((nR)/(C_(v)-R))`D. `((R)/(C_(v)-R))` |
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Answer» Correct Answer - A |
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| 234. |
Which of the following are path functions (A) `W` (B) `Q` (C) `Q+W` (D) `H-TS`A. A and DB. A and BC. A,B and DD. A,C and D |
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Answer» Correct Answer - B |
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| 235. |
Let `[in_(0)]` denote the dimensional formula of the permittivity of vacuum. If M= mass, L=length, T=Time and A= electric current, then:A. `[epsilon_(0)]=[M^(-1)L^(-3)T^(4)A^(2)]`B. `[epsilon_(0)]=[M^(-1)L^(2)T^(-1)A^(-2)]`C. `[epsilon_(0)]=[M^(-1)L^(2)T^(-1)A]`D. `[epsilon_(0)]=[M^(-1)L^(-3)T^(2)A]` |
| Answer» Correct Answer - A | |
| 236. |
The graph between angle of deviation `(delta)` and angle of incidence (i) for a triangular prism is represented byA. B. C. D. |
| Answer» Correct Answer - B | |
| 237. |
Arrange in the increasing order of oxidation state of nitrogen for following nitrogen oxides `N_(2)O, NO_(2), NO, N_(2)O_(3)`A. `N_(2)OltNOltNO_(2)ltN_(2)O_(3)`B. `NOltN_(2)OltN_(2)OltN_(2)O_(3)ltNO_(2)`C. `N_(2)OltNOltN_(2)O_(3)ltNO_(2)`D. `NO_(2)ltN_(2)O_(3)ltN_(2)OltNO` |
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Answer» Correct Answer - C |
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| 238. |
The `I-V` characteristic of an `LED` is.A. B. C. D. |
| Answer» Correct Answer - D | |
| 239. |
If a piece of metal is heated to temperature `theta` and the allowed to cool in a room which is at temperature `theta_0`, the graph between the temperature T of the metal and time t will be closet toA. B. C. D. |
| Answer» Correct Answer - B | |
| 240. |
If `(1+x-3x^2)^2145= a0 + a1x + a2x^2 + ......................`then `a0-a1+a2-a3+`...........ends with |
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Answer» Given=>`(1+x-3x^2)^2145=a_0+a_1x+a_2x^2......` substituting x=-1. =>`(-3)^2145=-(3)^2145=a_0-a_1+a_2......` cyclicity of 3=4. `3^2145=3^(4xx536+1)=>`so last digit will be 3. |
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| 241. |
In which of the following pairs, the two species are not isostructural?A. `CO_(3)^(2-) and NO_(3)^(-)`B. `PCI_(4)^(+) and SiCI_(4)`C. `PF_(5) and BrF_(5)`D. `AIF_(6)^(3-) and SF_(6)` |
| Answer» Correct Answer - C | |
| 242. |
The number of normal (s) to the parabola `y^2=8x` through (2, 1) is (B) 2 (A) 1 (D) 3 (C) 0 |
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Answer» Equation of the normal of the parabola ` y^2 = 4ax` is given by, ` y = mx - 2am-am^3->(1)` Now, in the given parabola, `y^2 = 8x` `a = 2` Putting value of `a` in (1), `=>y = mx-4m-2m^3` At point `(2,1)` this equation becomes, `=>1= 2m-4m-2m^3` `=>2m^3+2m-1 = 0->(2)` We know, in a cubic equation, there are `3` roots. One root is always real and remaining two roots can either be real or complex. To find the roots, we will differentiate equation (2). `=>6m^2+2 = 0` `=>m^2 = -1/3` It means two roots are complex as square of `m` is negative. So, only ne root is real, which means we can have only one normal with the given conditions. |
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| 243. |
The number of normal (s) to the parabola `y^2= 8x` through (2, 1) is |
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Answer» Equation of the normal of the parabola ` y^2 = 4ax` is given by, ` y = mx - 2am-am^3->(1)` Now, in the given parabola, `y^2 = 8x` `a = 2` Putting value of `a` in (1), `=>y = mx-4m-2m^3` At point `(2,1)` this equation becomes, `=>1= 2m-4m-2m^3` `=>2m^3+2m-1 = 0->(2)` We know, in a cubic equation, there are `3` roots. One root is always real and remaining two roots can either be real or complex. To find the roots, we will differentiate equation (2). `=>6m^2+2 = 0` `=>m^2 = -1/3` It means two roots are complex as square of `m` is negative. So, only ne root is real, which means we can have only one normal with the given conditions. |
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| 244. |
The line `lx+my+n=0` is a normal to the parabola `y^2 = 4ax` if |
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Answer» Equation of normal to parabola, `y^2 = 4ax` at point `(at^2,2at)` is given by, `y+tx = 2at+at^3` `=tx+y+(-2at-at^3) = 0` Given equation of the normal to this parabola, `lx+my+n = 0` Comparing these two equations, `l/t = m/1 = n/(-2at-at^3)` `=>l/t = m/1 => t = l/m` Now,`m/1 = n/(-2at-at^3)` `=>m = n/(-2a(l/m)-al^3/m^3)` `=>m =(nm^3)/(-2alm^2-al^3)` `=>-2alm^2-al^3 = nm^2` `=>al(2m^2+l^2)+nm^2 = 0`, which is the required condition. |
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| 245. |
If log, 3 9log, 4 10 log, 8x then x (1) 5 (2) 1110 (4) 25 (3) 10 |
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Answer» `4^(log_9 3)+9^(log_2 4) = 10^(log_x 8x)` `=>4^(log_9 9^(1/2))+9^(log_2 2^2) = 10^(log_x 8 + log_x x)` `=>4^(1/2log_9 9)+9^(2log_2 2) = 10^(log_x 8 + 1)` `=>4^(1/2)+9^2 = 10*10^(log_x 8)` `=>2+81 = 10*10^(log_x 8)` `=>83/10 = 10^(log_x 8)` `=>log_10 (83/10) = log_10 (10^(log_x 8))` `=>log_10(8.3) = log_x 8` `=>x ~~ 10` So, approximate value of `x` will be `10` and option `(3)` will be the correct option. |
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| 246. |
Enol content is maximum inA. `CH_(3)-overset(O)overset(||)(C)-CH_(2)-overset(O)overset(||)(C)-CH_(3)`B. `CH_(3)-overset(O)overset(||)(C)-CH_(2)-overset(O)overset(||)(C)-NH_(2)`C. `CH_(3)-overset(O)overset(||)(C)-CH_(2)-overset(O)overset(||)(C)-OCH_(2)`D. `CH_(3)-overset(O)overset(||)(C)-CH_(3)` |
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Answer» Correct Answer - A |
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| 247. |
In the Cannizzaro reaction given below: `2Ph-CHO overset(overset(Θ)OH)rarrPh-CH_(2)OH+PhCO_(2)^(-)` the slowest step is:A. the attack of `overset((-))(OH)` at the carboxyl groupB. the transfer of hydride to the carbonly groupC. the abstraction of proton from the carboxylic groupD. the deportonation of `Ph " " CH_(2)OH` |
| Answer» Correct Answer - B | |
| 248. |
`overset(CH_(3)l)to` product isA. B. C. D. |
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Answer» Correct Answer - A |
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| 249. |
Polysubstitution is drawback of which reactionA. friedel craft alkylationB. friedel craft acylationC. nitration on aromatic ringD. chlorination on aromatic ring |
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Answer» Correct Answer - A |
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| 250. |
In context with the industrial preparation of hydrogen from water gas `(CO+H_(2))` , which of the following is the correct statement ?A. CO and `H_(2)` are fractionally separated using differences in their densitiesB. CO is removed by absorption in aqueous `Cu_(2)Cl_(2)` solutionC. `H_(2)` is removed through occulsion with PdD. CO is oxidised to `CO_(2)` with steam in the presence of a catalyst followed by absorption of `CO_(2)` in alkali |
| Answer» Correct Answer - D | |