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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.
| 751. |
If `a+2b+3c=1` and ` a>0 , b>0 , c>0` and the greatest value of `a^3b^2c` is `1/k` then `(k-5180)` is |
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Answer» Here, `a+2b+3c = 1` We can write it as, `a/3+a/3+a/3+b+b+3c = 1` Now, we know aritmatic mean of `n` numbers is always greater than geometric mean of those `n` numbers. `:. (a/3+a/3+a/3+b+b+3c)/6 ge (a/3*a/3*a/3*b*b*3c)^(1/6)` `=>(a+2b+3c)/6 ge ((a^3b^2c)/9)^(1/6)` `=>1/6 ge ((a^3b^2c)/9)^(1/6)` `=>(1/6)^6(9) ge (a^3b^2c)` `=> a^3b^2c le 9/(216**216)` `=> a^3b^2c le 1/5184` Now, greatest value of ` a^3b^2c` is `1/k`, `:. 1/k = 1/5184` `=> k = 5184` `:. k - 5180 = 5184-5180` `=> k - 5180 = 4.` |
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| 752. |
Perpendiculars are drawn from two points on axis of parabola `y^2=4ax` to a tangent to the parabola. The two point are situated at a distance of d from focus. if the perpendicular distances from the points are `p_1` ND `P_2` THEN FIND THE VALUE OF `P_1^2`-`P_2^2` |
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Answer» `y^2=4ax` `y(2at)=2a(x+at^2)` `ty=x+at^2` `x-ty+at^2=0-(1)` `P_1=(|(a+d)-0+at^3|)/sqrt(1+t^2)` `P_2=(|(a-d)-0+at^3|)/sqrt(1+t^2)` subtracting`P_2^2` from`P_1^2` `=(a+d+at^2)^2/(1+t^2)-(a-d+at^2)^2/(1+t^2)` `=(4ad+4adt^2)/(1+t^2)` `=4ad` `P_1^2-P_2^2=4ad`. |
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| 753. |
If a point P whose position vector is `vec a` lying on the plane ABC where `A(2,3,0), B (3,-2,0), C(2,-1,0)`. Then distance of P from plane ABC is given by- |
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Answer» `vecn=vec(AB)*vec(AC)` `=(hati-5hatj)*(0hati-4hatj)` `=-4hatk` `vec(AP)*vecn=|vec(AP)||vecn|costheta` `(vecAvecP*vecn)/|(vecn)|=|vec(AP)|costheta` `(veca-(2hati+3hatj)*hatk=d` `vec(AP)=veca-vecb` `d=|(veca-4hatk)/4|=|vecahatk|` Option 1 is correct. |
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| 754. |
The projection of the line joining (2,3,4) and (5,6,7) on the plane 2x +y +z =1 is:- |
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Answer» `vec(AB)=3hati+3hatj+3hatk` `costheta=(vec(AB)*vecn)/(|vec(AB)||vecn|)` `=(6+3+3)/(3sqrt3sqrt6)` `=12/(9sqrt2` `=(2sqrt2)/3` `P=3sqrt3sqrt(1-(8/9))` `3sqrt3sqrt(1/9)=sqrt3` Option 3 is correct. |
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| 755. |
AB is the chord on the parabola `y^2=4ax` with its vertex at A. BC is drawn perpendicular to AB meeitng the axis at C. The projection of BC on the axis of the parabola is : |
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Answer» AB:`(2at-0)/(at^2-0)=2/t` BC:slope=`-1/2` `y-2at=-1/2(n-at^2)` `2y-4at=-tx+at^3` `tx+2y-4at-at^3=0` `C(4a-at^2,0)` `DC=at^2+4a-a` `DC=4a` Option 3 is correct. |
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| 756. |
In the adjacent figure `x=` `(1) 5.8 cm (2) 6.8 cm (3) 4.8 cm ` |
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Answer» `PD^2=PA*PB` `7^2=5*(5+x)` `49=25+5x` `x=24/5=4.8cm` option 3 is correct. |
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| 757. |
The length of the projection of the line segment joining the points `(5,-1,4)` and `(4,-1,3)` on the plane `x+y+z=7` is |
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Answer» `A(5,-1,4) and B(4,-1,3)` `AB=(4-5)veci + (-1+1)vecj + (3-4)veck` `=-veci-veck` `abs(AB)=sqrt2` `x+y+z=7` `n=(veci+vecj+veck)` Equation of plane `vecr*vecn=d` `(xveci+yvecj+zveck)(veci+vecj+veck)=7` `absn=sqrt3` `P=ABsintheta` `costheta =(vec(AB)*vecn)/(abs(AB)*absvecn)` `=((-veci-veck)(veci+vecj+veck))/(sqrt2sqrt3)` `=costheta=-sqrt2/sqrt3` `sintheta=sqrt(1-cos^2theta)` `sintheta=1/sqrt3` `P=sqrt2*1/sqrt3=sqrt2/sqrt3` |
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| 758. |
A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density `sigma` at equilibrium position. The extension `x_0` of the spring when it is in equlibrium is:A. `(Mg)/(k)(1-(LAsigma)/(M))`B. `(Mg)/(k)(1-(LAsigma)/(2M))`C. `(Mg)/(k)(1+(LAsigma)/(2M))`D. `(Mg)/(k)` |
| Answer» Correct Answer - B | |
| 759. |
A galvanometer having a coil resistance of `100 omega` gives a full scale deflection , when a current of `1 mA` is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of `10A` , is :A. `2Omega`B. `0.1Omega`C. `3Omega`D. `0.01 Omega` |
| Answer» Correct Answer - D | |
| 760. |
In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of 11 `kOmega` are used. The figure of merit of the galvanometer is 60 `muA//"division"`. In the absence of shunt resistance, the galvanometer produces a deflection of `theta =9` divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of `theta//2`, is closet to :A. `550 Omega`B. `220 Omega`C. `55 Omega`D. `110 Omega` |
| Answer» Correct Answer - D | |
| 761. |
A ray of light is incident at an angle of `60^(@)` on one face of a prism of angle `30^(@)`. The ray emerging out of the prism makes an angle of `30^(@)` with the incident ray. The emergent ray isA. `0^(@)`B. `45^(@)`C. `90^(@)`D. `30^(@)` |
| Answer» Correct Answer - D | |
| 762. |
Which of the following has an optical isomer?A. `[Zn(en)(NH_(3))_(2)]^(2+)`B. `[Co(en)_(3)]^(3+)`C. `[Co(H_(2)O)_(4)(en)]^(3+)`D. `[Zn(en)_(2)]^(2+)` |
| Answer» Correct Answer - B | |
| 763. |
At some instant, a radioactive sample `S_(1)` having an activity 5 `muCi` has twice the number of nuclei as another sample `S_(2)` which has an activity of 10 `muCi`. The half lives of `S_(1) and S_(2)` are :A. 20 years and 5 years, respectivelyB. 20 years and 10 years, respectivelyC. 10 years and 20 years, respectivelyD. 5 years and 20 years, respectively |
| Answer» Correct Answer - A | |
| 764. |
For path `ArarrB` optical path is A. `2(a+b)`B. `2(a-b)`C. `a+b`D. `a-b` |
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Answer» Correct Answer - A |
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| 765. |
Rms speed of `O_(2)` molecule is `200m//s` at `T=300 K` and `P=3`atm. If diameter of molecule is `0.3nm` then collision frequency is :A. `2.9xx10^(7)S^(-1)`B. `2.9xx10^(6)S^(-1)`C. `2.9xx10^(8)`D. `2.9xx10^(5)` |
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Answer» Correct Answer - A |
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| 766. |
r.m.s speed of ideal gas at `127^(@)C` is `200m//s` the rms. Speed of same ideal gas at temperature `227^(@)C` isA. `100sqrt(5)`B. `200sqrt(5)`C. `100sqrt(5)`D. `100sqrt(10)` |
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Answer» Correct Answer - A |
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| 767. |
Considering all type of `D.O.F` for HCl molecule of mass `m` having `V_(rms)` as `overline(v)`. Then the temperature of gas will beA. `(moverline(v)^(2))/(3k)`B. `(moverline(v)^(2))/(5k)`C. `(moverline(v)^(2))/(7k)`D. `(moverline(v)^(2))/(6k)` |
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Answer» Correct Answer - A |
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| 768. |
Rate of `S_(N)1` reactin for the following compounds is: (a). (b). (c). (d). A. `agtbgtcgtd`B. `bgtcgtagtd`C. `bgtcgtdgta`D. `dgtcgtbgta` |
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Answer» Correct Answer - C |
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| 769. |
The product of following reaction A. B. C. D. |
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Answer» Correct Answer - B |
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| 770. |
The product of following reaction is: `underset(CHCl_(3))overset(H_(2)SO_(4)("Cat."))rarr`A. B. C. D. |
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Answer» Correct Answer - A |
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| 771. |
The correct product of the following reaction is: `underset(H_(3)O^(-))overset("Alkaline" KMnO_(4))rarr`A. B. C. D. |
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Answer» Correct Answer - A |
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| 772. |
Noradrenaline is one of the example of :A. Anti-depressantB. Anti-HistamineC. NeurotransmitterD. Antacid |
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Answer» Correct Answer - C |
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| 773. |
Reactivity order of `S_(N)1` reaction for the following compounds is A. `agtbgtcgtd`B. `agtdgtcgtb`C. `cgtdgtbgta`D. `agtbgtdgtc` |
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Answer» Correct Answer - D |
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| 774. |
The temperature of `H_(2)` gas at which `rms` speed of `H_(2)` molecules is equal to escape speed of a particle from earth surface is :A. `10^(3)K`B. `2xx10^(3)K`C. `10^(4)K`D. `10^(5)K` |
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Answer» Correct Answer - C |
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| 775. |
A convex lens `(f=20cm)` is placed at `80 cm` from a concave mirror. An object is placed at `30 cm` in front the lens such that position of its final image is same with or without the mirror. The maximum distance of object and mirror for a virtual image to be formed if only mirror is present is : A. `10 cm`B. `20 cm`C. `30 cm`D. `50 cm` |
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Answer» Correct Answer - A |
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| 776. |
A solid sphere and a solid cylinder are in pure roling on a rough curved surface with the same speed. The ratio of maximum heights reached by the two bodies if they roll without shipping is A. (4)/(5)`B. `(14)/(15)`C. `(7)/(10)`D. `(10)/(13)` |
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Answer» Correct Answer - B |
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| 777. |
The atmosphere between the heights `10` to `50` kilometer above the Sea level is:A. TroposphereB. StratophereC. MesosphereD. Ionosphere |
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Answer» Correct Answer - B |
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| 778. |
What is the effect of release of `CO_(2)` gas on atmosphere?A. Global warmingB. Photochemical smogC. Ozone layer depletionD. Tsunami |
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Answer» Correct Answer - A |
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| 779. |
`underset("heat")overset(H1("excess"))to` major product isA. B. C. D. |
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Answer» Correct Answer - B |
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| 780. |
The gas leaked from a stronge tank of the Union Carbide plant in Bhopal gas tragedy wasA. MethylamineB. AmmoniaC. PhosgeneD. Methylisocyanate |
| Answer» Correct Answer - D | |
| 781. |
Two coaxial solenoids of different radius carry current I in the same direction. `vec(F_1)` be the magnetic force on the inner solenoid due to the outer one and `vec(F_2)` be the magnetic force on the outer solenide due to the inner one. ThenA. `vecF_(1)` is radially inwards and `vecF_(2)` is radially outwardsB. `vecF_(1)` is radially inwards and `vecF_(2) = 0`C. `vecF_(1)` I radially outwards and `vecF_(2) = 0`D. `vecF_(1) = vecF_(2) = 0` |
| Answer» Correct Answer - D | |
| 782. |
In a single slit diffraction set up, second minima is observed at an angle of `60^(@)`. The expected position of first minima isA. `25^(@)`B. `20^(@)`C. `30^(@)`D. `45^(@)` |
| Answer» Correct Answer - A | |
| 783. |
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. `(1)/(R )sqrt((4gh)/(3))`B. `(1)/(R )sqrt((2gh)/(3))`C. `R sqrt((2gh)/(3))`D. `R sqrt((4gh)/(3))` |
| Answer» Correct Answer - A | |
| 784. |
Two particle of masses `m` and `2m` are coliding elastically as given in figure. If `V_(1)` and `V_(2)` speed of particle just after collision then A. `V_(1)=11.16m//s, V_(2)=6.31m//s`B. `V_(1)=10.16m//s,V_(2)=5.31m//s`C. `v_(1)=9.16M//S, v_(2)=6.31M//S`D. `v_(1)=6.31M//S, v_(2)=11.16M//S` |
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Answer» Correct Answer - D |
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| 785. |
Ortho -nitrophenol is less soluble in water than `p`-and `m-`nitrophenols becauseA. o-Nitrophenol is more volatile in stem than those of m- and p-isomersB. o-Nitrophenol shows Intramolecular H-bondingC. o-Nitrophenol shows Intermolecular H-bondingD. Melting point of o-Nitrophenol is lower than those of m- and p-isomers. |
| Answer» Correct Answer - B | |
| 786. |
One mole of and ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, `27^(@)C` . The work done on the gas will be :A. 300 R ln 7B. 300 R ln 2C. 300 RD. 300 R ln 6 |
| Answer» Correct Answer - B | |
| 787. |
The vertices of a triangle are `A(x_1,x_1 tan alpha), B (x_2,x_2 tan Beta) and C(x_3, x_3 tan gamma)`. If the circumcentre of `DeltaABC` coincides with the origin and H (a, b) be its orthocentre, then `a/b` is equal to |
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Answer» `G((x_1+x_2+x_3)/3,(x_1tanalpha+x_2tanbeta+x_3tangamma)/3)` `H(3/2(x_1+x_2+x_3)/3,3/2(xtanalpha+x_2tanbeta+x_3tangamma)/3)` `H(a,b)` `sqrt(x_1^2+x_1^2tan^2alpha)=R` `x_1^2=R^2/(sec^2alpha)` `x_1=R/secalpha` `a/b=(R(cosalpha+cosbeta+cosgamma))/(R(sinalpha+sinbeta+singamma))`. |
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| 788. |
A wave travelling along the x-axis is described by the equation y (x, t) = 0.005 sin (`alphax - betat`). If the wavelength and time period of the wave are 0.08 m and 2 s respectively, then `alpha, beta` in appropriate units areA. `alpha = 25.00 pi, beta = pi`B. `alpha = (0.08)/(pi), (2.0)/(pi)`C. `alpha = (0.04)/(pi), beta = (1.0)/(pi)`D. `alpha = 12.50 pi, beta = (pi)/(2.0)` |
| Answer» Correct Answer - A | |
| 789. |
Two uniform circular rough disc of moment of inertia `I_(1)` and `(I_(1))/(2)` are rotating with angular velocity `omega_(1)` and `(omega_(1))/(2)` respectively in same direction. Now one disc is placed the other disc co-axially. The change in kinetic energy of the system is :A. `-(1)/(24)I_(1)omega_(1^(2))`B. `(1)/(24)I_(1)omega_(1^(2))`C. `(1)/(12)I_(1)omega_(1^(2))`D. `-(1)/(12)I_(1)omega_(1^(2))` |
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Answer» Correct Answer - A |
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| 790. |
In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of `Delta_o` be the highest?A. `[Co(CN)_(6)]^(3-)`B. `[Co(C_(2)O_(4))_(3)]_(3-)`C. `[Co(H_(2)O)_(6)]^(3+)`D. `[Co(NH_(3))_(6)]^(3+)` |
| Answer» Correct Answer - A | |
| 791. |
The marks of a student in 6 tests are `41, 45, 54, 57, 43` and x. If the mean marks of these tests is 48. then standard deviation of these tests isA. `(10)/(sqrt(3))`B. `(10)/(sqrt(2))`C. `(10)/(3)`D. `(20)/(3)` |
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Answer» Correct Answer - A |
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| 792. |
Which of the following is amorphous form of silicaA. QuartzB. KieselguhrC. TridymiteD. Cristobalite |
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Answer» Correct Answer - B |
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