

InterviewSolution
Saved Bookmarks
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.
551. |
If `(1+m^(2))x^(2)-2(1+3m) x + (1 + 8m) = 0`. Then numbers of values (s) of m for which this equation has no solutionA. 3B. `oo`C. 2D. 1 |
Answer» Correct Answer - B |
|
552. |
A rectangular loop has a sliding connector PQ of length l and resistance `R (Omega)` and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents `I_(1), I_(2)` and I are A. `l_(1)=-l_(2)=(Blv)/(R),l=(2Blv)/(R)`B. `l_(1)=l_(2)=(Blv)/(3R),l=(2Blv)/(3R)`C. `l_(1)=l_(2)=l=(Blv)/(R)`D. `l_(1)=l_(2)=(Blv)/(6R),l=(Blv)/(3R)` |
Answer» Correct Answer - B | |
553. |
The radius of a circle, having minimum area, which touches the curve `y=4−x^2` and the lines, `y=|x|` is: (a) `4(sqrt2+1)` (b) `2(sqrt2+1)` (c) `2(sqrt2-1)` (d) `4(sqrt2-1)` |
Answer» We can create a rough diagram for the curve `y = 4-x^2` and line `y = |x|`. Please refer to video for the figure. From the figure, we can see that x-coordinate of the circle will be `0`. `:.` Curve `y= 4-x^2` will touch the `y`-axis at `y = 4`. Let radius of the circle is `r`. Then, center of the circle will be `(0,4-r)` Also, the distace from the center of the circle to the line `y-x = 0` is `r`. `:. (4-r-0)/(sqrt(1^2+(-1)^2)) = r` `=>4-r = sqrt2r` `=>r = 4/(sqrt2+1)**(sqrt2-1)/(sqrt2-1) = 4(sqrt2-1)` So, option `(d)` is the correct option. |
|
554. |
Prove that :`Det[[1+a,1,1],[1,1+b,1],[1,1,1+c]]=abc(1+1/a+1/b+1/c)` |
Answer» LHS= `|(1+a, 1,1),(1, 1+b, 1),(1,1,1+c)|` `R_1-> R_1-(1+a)R_3` `R_2-> R_2 - R_3` `|(0,-a,1-(1+c)(1+a)),(0,b,-c),(1,1,1+c)|` `= |(0,-a,-c-a+ac),(0,b,-c),(1,1,1+c)|` expand `c_1` `= 0+0+1|(-a,-c-a+ac),(b,-c)| ` `= ac -[(b)(-c-a-ac)]` `= ac +bc +ba + abc` `= abc(1/b +1/a +1/c+1)` Answer |
|
555. |
`lim_(x ->0^+) (cosec x)^(1/logx)` |
Answer» `l = lim_(x->0^+) (cosec x)^(1/logx) , (oo)^(1/oo) x` `log l = lim_(x->0^+) 1/log x log cosecx` `= lim_(x->0^+) (-1/(cosecx) cotxcosecx)/(1/x)` `= lim_(x->0+) x cotx` `log l = 0` `l= 1` Answer |
|
556. |
Number of ways in which all the letters of the words "ALASKA" can be arranged in a circle distinguishing between the clockwise and anticlockwise arrangement, is |
Answer» Total possible combinations=`(6!)/(3!)=120` Total possible ways=`(6!)/(3!)*1/6=120/6=20` Option 3 is correct. |
|
557. |
12 guests at a dinner party are to be seated along a circular table. Supposing that the master and mistress of the house have fixed seats opposite to one another and that there are two specified guests who must always be placed next to one another. The number of ways in which the company can be placed, is |
Answer» combinations that can be made on right side and left side=`5 & 5` total combinations to be made`10` if X,Y are the persons , the combination XY & YX can also be possible no of possibilities will be = `2*(5*2)*10! = 20*10!` option 1 correct. |
|
558. |
Solid `Ba(NO_(3))` is gradually dissolved in a `1.0xx10^(-4) M Na_(2)CO_(3)` solution. At what concentrations of `Ba^(2+)`, will a precipitate begin to form? (`K_(SP)` for `BaCO_(3)=5.1xx10^(-9)`)A. `4.1 xx 10^(-5)M`B. `5.1 xx 10^(-5)M`C. `8.1 xx 10^(-8)M`D. `8.1 xx 10^(-7)M` |
Answer» Correct Answer - B | |
559. |
Decompsition of `H_(2)O_(2)` follows a frist order reactions. In 50 min the concentrations of `H_(2)O_(2)` decreases from 0.5 to 0.125 M in one such decomposition . When the concentration of `H_(2)O_(2)` reaches 0.05 M, the rate of fromation of `O_(2)` will beA. `6.93xx10^(-4) "mol min"^(-1)`B. `2.66L " min"^(-1)"at STP" `C. `1.34xx10^(-2) "mol min"^(-1)`D. `6.93xx10^(-2) "mol min"^(-1)` |
Answer» Correct Answer - A | |
560. |
A person trying to lose weight by burning fat filts a mass of `10 kg` upto a being of `1m 1000` time . Assume that the potential energy lost each time be lower the mass is dissipated . How much far will be use up considering the work done only when the weight is lifted up ? Far supplies `3.8 xx 10^(7) J` of energy per kg wich is canverted to mechanical energy with `x 20 %` efficiency rate Take ` = 9.8 ms^(-2)`A. `6.45xx10^(-3)` kgB. `9.89xx10^(-3)` kgC. `12.89xx10^(-3)` kgD. `2.45xx10^(-3)` kg |
Answer» Correct Answer - C | |
561. |
The equation of a wave on a string of linear mass density `0.04 kgm^(-1)` is given by `y = 0.02(m) sin[2pi((t)/(0.04(s)) -(x)/(0.50(m)))]`. Then tension in the string isA. 4.0 NB. 12.5 NC. 0.5 ND. 6.25 N |
Answer» Correct Answer - D | |
562. |
If `10^(-4) dm^(3)` of water is introduced into a `1.0 dm^(3)` flask to `300K` how many moles of water are in the vapour phase when equilibrium is established ? (Given vapour pressure of `H_(2)O` at `300K` is `3170Pa R =8.314 JK^(-1) mol^(-1))` .A. `5.56xx10^(-3)"mol"`B. `1.53xx10^(-2)"mol"`C. `4.46xx10^(-2)"mol"`D. `1.27xx10^(-3)"mol"` |
Answer» Correct Answer - D | |
563. |
An orgainc compound A upon reacting with `NH_(3)` gives `B` On heating `B` give `C.C` in presence `KOH` reacts with `Br_(2)` to yield `CH_(3)CH_(2)NH_(2) A` is .A. `CH_(3)CH_(2)CH_(2)COOH`B. `H_(3)C-underset(CH_(3))underset(|)"CH"-COOH`C. `CH_(3)CH_(2)COOH`D. `CH_(3)COOH` |
Answer» Correct Answer - C | |
564. |
The absolute configuratin of A. (2S, 3R)B. (2S, 3S)C. (2R, 3R)D. (2R, 3S) |
Answer» Correct Answer - A | |
565. |
An electron beam is acceleration by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If `lambda_(min)` is the smallest possible wavelength of X-rays in the spectrum, the variation of `log lambda_(min)` with `log v` is correctly represented inA. B. C. D. |
Answer» Correct Answer - B | |
566. |
If two different numbers are taken from the set `(0, 1, 2, 3. 10):` then the probability that their sum as well as absolute difference are both multiple of 4 are (a) `14/45` (b) `7/55` (c) `6/55` (d) `12/55` |
Answer» There are `4` sets possible with the numbers having difference multiple of `4`. `A = {1,5,9}` `B = {0,4,8}` `C = {2,6,10}` `D= {3,7}` If we do the sum of any two elements of set `A` and set `D`, it is not a multiple of `4`. If we do the sum of any two elements of set `B` and set `C`, it is a multiple of `4`. Now, we have to select `2` elements from each of the sets `B` and `C`. It can be done in `2**C(3,2)` ways. `:.` Required probability ` = (2C(3,2))/(C(11,2)) = (2**3)/(11**5) = 6/55` |
|
567. |
A signal which can be green or red with probability `4/5 and 1/5` respectively, is received by station A and then and 3 transmitted to station B. The probability of each station receiving the signal correctly is `3/4` If the signal received at station B is green, then the probability that the original signal was green is (a) `3/5` (b) `6/7` (d) `20/23` (d) `9/20` |
Answer» acc to the question `P = (4/5*3/4*3/4 + 4/5*1/4*1/4) + (1/5*3/4*1/4 + 1/5*1/4*3/4)` `P = 46/80 = 23/40` `P [or G] = 40/80 = 20/40` `P= (20/40)/(23/40)= 20/23` |
|
568. |
If `x=a+b+c`, `y=aalpha+betab+c` and `z=abeta+balpha+c` , where `alpha` and `beta` are the complex cube roots of unity, then xyz= |
Answer» `(a+b+c)(a+wb+w^2c)(a+w^2b+wc)=a^3+b^3+c^3-3abc` `w and w^2` are roots of unity. option c is correct. |
|
569. |
A soap bubble,blown by a mechanical pump at the mouth of a tube, increases in volume, with the time, at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by :A. B. C. D. |
Answer» Correct Answer - A | |
570. |
Find the time after which current in the circuit becomes `80%` of its maximum valueA. `(ln2)/(100)`B. `(ln3)/(100)`C. `(ln5)/(100)`D. `(ln6)/(100)` |
Answer» Correct Answer - C |
|
571. |
A sound source is moving with speed `50 m//s` towards a fixed observer. Frequency observed by observer is `1000Hz`. Find out apparent frequency observed by observer when source is moving away from observer (Speed of sound `=350 m//s`)A. `750 Hz`B. `950 Hz`C. `550 Hz`D. `350 Hz` |
Answer» Correct Answer - A |
|
572. |
The relative uncertainty in the period of a satellite orbiting around the earth is `10^(-2)` . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :A. `3xx10^(-2)`B. `6xx10^(-2)`C. `10^(-2)`D. `2xx10^(-2)` |
Answer» Correct Answer - D | |
573. |
The relative error in the determination of the surface area of a sphere is `alpha`. Then the relative error in the determination of its volume is :A. `5/2alpha`B. `alpha`C. `2/3 alpha`D. `3/2 alpha` |
Answer» Correct Answer - D | |
574. |
A monochromatic beam of light has a frequency `v = 3/(2pi) xx 10^(12) Hz` and is propagating along the direction `(hati + hatj)/(sqrt(2))`. It is polarizied along the `hatk` direction. The accpetable fromfor the magnetic field is :A. `(E_(o))/(C ) hatk` `cos[10^(4) ((hati+hatj))/(sqrt(2)).vecr + (3 xx 10^(12)) t]`B. `(E_(o))/(C ) ((hati - hatj))/(sqrt(2))` `cos[10^(4) ((hati+hatj))/(sqrt(2)).vecr - (3 xx 10^(12)) t]`C. `(E_(o))/(C ) ((hati + hatj + hatk))/(sqrt(3))` `cos[10^(4)((hati + hatj))/(sqrt(2)).vecr +(3 xx 10^(12)) t]`D. `(E_(o))/(C ) ((hati - hatj))/(sqrt(2))` `cos[10^(4) ((hati - hatj))/(sqrt(2)).vecr - (3 xx 10^(12)) t]` |
Answer» Correct Answer - B | |
575. |
The energy required to remove the electron from a singly ionized Helium atom is `2.2` times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom ompletelyis:A. `109 eV`B. `34 eV`C. `79 eV`D. `20 eV` |
Answer» Correct Answer - C | |
576. |
An ideal capacitor of capacitance `0.2muF` is charged to a potential difference of `10V`. The charging battery is than disconnected. The capacitor is then connected to an ideal inductor of self inductance `0.5mH`. The current at a time when the potential difference across the capacitor is `5V` is :A. `0.34 A`B. `0.17 A`C. `0.25 A`D. `0.15A` |
Answer» Correct Answer - B | |
577. |
The major product of the following reaction is : A. B. C. D. |
Answer» Correct Answer - A | |
578. |
Among the following, the correct statement (s) is (are)A. Sols of metal sulphides are lyophilicB. Brownian movement is more pronounced for smaller particles than for bigger-particlesC. One would expect charcoal to adsorb chlorine more than hydrogen sulphide.D. Hardy Schulze law states that bigger the size of the ion is, the greater is its coagulating power. |
Answer» Correct Answer - C | |
579. |
The reason for “drug induced poisoning” is :A. Binding irreversibly to the active site of the enzymeB. Binding at the allosteric sites of the enzymeC. Binding reversibly at the active site of the enzymeD. Bringing conformational change in the binding site of enzyme |
Answer» Correct Answer - B | |
580. |
The major product of the following reaction is : `C_(6)H_(5)CH_(2)-underset(Br)underset(|)overset(CH_(3))overset(|)C=CH_(2)-CH_(3)underset(C_(2)H_(5)OH)overset(C_(2)H_(5)O"N"a)to`A. `C_(6)H_(5)CH=underset(CH_(3))underset(|)C-CH_(2)CH_(3)`B. `C_(6)H_(5)CH_(2)-underset(Ch_(3))underset(|)C=CHCH_(3)`C. `C_(6)H_(5)CH_(2)underset(OC_(2)H_(5))underset(|)overset(CH_(3))overset(|)C-CH_(2)CH_(3)`D. `C_(6)H_(5)CH_(2)-underset(CH_(2)CH_(3))underset(|)C=CH_(2)` |
Answer» Correct Answer - A | |
581. |
If `E_(Fe^(3+)//Fe)^(@)` and `E_(Fe^(2+)//Fe)^(@)` are `-0.36 V` and `0.439 V` respectively, then value of `E_(Fe^(3+)//Fe^(2+))^(@)` isA. `-0.057` VB. `+0.30 V`C. `-0.30 `VD. `+0.057` V |
Answer» Correct Answer - A | |
582. |
The standard reduction potential for `Zn^(2+)//Zn, Ni^(2+)//Ni` and `Fe^(2+)//Fe` are `-0.76, -0.23` and `-0.44V` respectively. The reaction `X + Y^(2) rarr X^(2+) + Y` will be spontaneous when:A. X = Ni, Y = FeB. X = Ni, Y = ZnC. X = Fe, Y = ZnD. X = Zn, Y = Ni |
Answer» Correct Answer - D | |
583. |
What is the standard reduction potential `(E^(@))` for `Fe^(3+) to Fe`? Given that : `Fe^(2+) + 2e^(-) to Fe, E_(Fe^(2+)//Fe)^(@)`=-0.47V `Fe^(3+) + e^(-) to Fe^(2+), E_(Fe^(3+)//Fe^(2+))^(@) = +0.77V`A. –0.057 VB. + 0.30 VC. – 0.30 VD. + 0.057 V |
Answer» Correct Answer - A | |
584. |
The major product of the following reaction is : `C_(6)H_(5)CH_(2)-underset(Br)underset(|)overset(CH_(3))overset(|)C-CH_(2)-CH_(3)underset(C_(2)H_(5)OH)overset(C_(2)H_(5)O"N"a)to`A. `C_(6)H_(5)CH=underset(overset(|)(CH_(3)))(C)-CH_(2)-CH_(3)`B. `C_(6)H_(5)CH_(2)-underset(overset(|)(CH_(3)))(C)=CHCH_(3)`C. `C_(6)H_(5)CH_(2)-underset(overset(|)(OC_(2)H_(5)))overset(underset(|)(CH_(3)))(C)-CH_(2)CH_(3)`D. `C_(6)H_(5)CH_(2)-underset(overset(|)(CH_(2)CH_(3)))(C)=CH_(2)` |
Answer» Correct Answer - A | |
585. |
If `a`hyperbola passes through the foci of the ellipse `(x^2)/(25)+(y^2)/(16)=1`. Its transverse and conjugate axes coincide respectively with themajor and minor axes of the ellipse and if the product of eccentricities ofhyperbola and ellipse is 1 thenthe equation ofa. hyperbola is `(x^2)/9-(y^2)/(16)=1`b. the equation of hyperbola is `(x^2)/9-(y^2)/(25)=1`c. focus of hyperbola is (5, 0)d. focusof hyperbola is `(5sqrt(3),0)` |
Answer» Here, equation of ellipse is, `x^2/25+y^2/16 = 1` So, if e is the essentricity of ellipse, then, `e^2 = 1-b^2/a^2 = 1-16/25 = 9/25` `e = 3/5` We know, foci of ellipse is (ae,0). So, focus of given ellipse will be `(3,0)`. Now, let equation of hyperbola is, `x^2/a^2-y^2/b^2 = 1` Now, as hyperbola passes through the foci of the given ellipse`(3,0)`, We can say that.,`9/a^2 - 0 = 1=>a^2=9` Also, we are given product of eccentricity of ellipse and hyperbola is 1. If eccentricity of hyperbola is `e_h`, then, `3/5**e_h = 1=>e_h= 5/3` As we know, `e_h^2 = 1+b^2/a^2` Putting, values of `e_h and a^2`, we get,`b^2 = 16` So, equation of hyperbola is `x^2/9-y^2/16 = 1` Now, focus of hyperbola is `(+-ae_h,0) = (+-5,0)` That means, option B and option C are correct. |
|
586. |
`1.01^365=37.8` , `0.99^365=0.03` |
Answer» (i) Let `t = 1.01^365` `:. log_10t = 365log_10(1.01)` `=> log_10t = 365(log_10(101) - log_10(100))` `=> log_10t = 365(2.00432 - 2)`.... (As `log_10(101) = 2.00432`) `=> log_10t = 365(.00432)` `=> log_10t = 1.5773` `=> t = 10^(1.57773)` `=> t = 37.78` `:. 1.01^365 = 37.78` (ii)Let `z = 0.99^365` `:. log_10z = 365log_10(0.99)` `=> log_10z = 365(log_10(99) - log_10(100))` `=> log_10z = 365(1.9956 - 2)`....(As `log_10(99) = 1.9956`) `=> log_10z = 365(-.0044)` `=> log_10z = -1.606` `=> z = 10^(-1.606)` `=> z = 0.025` `:. 0.99^365 = 0.025 ~= 0.03 ` |
|
587. |
Let `d_1` and `d_2` be the lengths of the perpendiculars drawn from any point of the line `7x-9y+10= 0` upon the lines `3x+ 4y =5` and `12x+ 5y= 7` respectively. Then `(A) d_1> d_2 (B) d_1=d_2 (C) d_1< d_2 (D) d_1= 2d_2` |
Answer» `7h-9y+10=0` `9y=7h+10` `y=(7h+10)/9` `d_1=|(3h+4((7h+10)/9)-5)/sqrt(9+16)|` `d_1=|(27h+28h+40-45)/45|` `d_1=|(55h-5)/45|` `d_1=|(11h-1)/9|` `d_2=|(12h+5((7h+10)/9)-7)/sqrt(140+25)|` `d_2=|(143h-13)/(13*9)|` `d_2=|(11h-1)/9|` so, `d_1-d_2`. |
|
588. |
Let there be a spherically symmetric charge distribution with charge density varying as `rho(r)=rho(5/4-r/R)` upto `r=R`, and `rho(r)=0` for `rgtR`, where r is the distance from the origin. The electric field at a distance r(rltR) from the origin is given byA. `(4pi rho_(0)r)/(3epsilon_(0))((5)/(3)-(r)/(R))`B. `(rho_(0)r)/(4epsilon_(0))((5)/(3)-(r)/(R))`C. `(4rho_(0)r)/(3epsilon_(0))((5)/(4)-(r)/(R))`D. `(rho_(0)r)/(3epsilon_(0))((5)/(4)-(r)/(R))` |
Answer» Correct Answer - B | |
589. |
Area of triangle formed by tangent and normal to ellipse `3x^(2)+5y^(2)=32` at point `(2,2)` and x-axis isA. `(68)/(15)`B. `(36)/(15)`C. `(32)/(3)`D. `(31)/(3)` |
Answer» Correct Answer - A |
|
590. |
The point lying on common tangent to the circles `x^(2)+y^(2)=4` and `x^(2)+y^(2)+6x+8y-24=0` isA. `(6,-2)`B. `(4,-2)`C. `(4,6)`D. `(4)(2,4)` |
Answer» Correct Answer - A |
|
591. |
A square is incribed in a circle `x^2+y^2-6x+8y-103=0` such that its sides are parallel to co-ordinate axis then the distance of the nearest vertex to origin, is equal to (A) `13` (B) `sqrt127` (C) `sqrt41` (D) `1` |
Answer» equation of circle `x^2+y^2-6x+8y-103=0` centre(3,-4) `r^2=8sqrt2` `r=8sqrt2` AP=PC=r=`8sqrt2` AC=`16sqrt2` side=16 OA=`sqrt((-5)^2+(-12)^2)=13` OB=`sqrt(11^2+12^2)=sqrt265` OC=`sqrt(11^2+12^2)=sqrt137` OD=`sqrt(5^2+4^2)=sqrt41` |
|
592. |
A solution containing a group-IV cation gives a precipitate on passing, `H_(2)S.` A solution of this precipitate in dil. HCl produces a white precipitate with NaOH solution and bluish-white prcipitate with basic potassium ferrocyanide. The cation is :A. `Mn^(2+)`B. `Zn^(2+)`C. `Ni^(2+)`D. `Co^(2+)` |
Answer» Correct Answer - B | |
593. |
The equilibrium constants `K_(p1)` and `K_(p2)` for the reactions X `hArr` 2Y and Z `hArr` P + Q, respectively, are in the ratio of `1:9` . If the degree of dissures at these equilibria is:A. `1 : 36`B. `1 : 1`C. `1 : 3`D. `1 : 9` |
Answer» Correct Answer - A | |
594. |
The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line `4x-5y=20` to the circle `x^2+y^2=9` is : (A) `20(x^2+y^2)-36+45y=0` (B) `20(x^2+y^2)+36-45y=0` (C) `20(x^2+y^2)-20x+45y=0` (D) `20(x^2+y^2)+20x-45y=0` |
Answer» `ax+((4a-20)/5)y=9-(1)` Let P(h,k) is midpoint of chord of contract `hx+ky=h^2+k^2-(2)` `5ax+(4a-20)y=45-(3)` Comparing equation 2 and 3 `h/(5a)=k/(4a-20)=(h^2+k^2)/45` `h/(5a)=k/(4a-20)` `h(4a)-20h=52k` `a=(20h)/(4h-5k)` `h/(5a)=(h^2+k^2)/45` `h(4h-5k)/(100h)=(h^2+k^2)/45` `36h-45k=20(h^2+k^2)` `20(x^2+y^2)=36x-45y` `20(x^2+y^2)-36x+45y=0`. |
|
595. |
A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E(r) produced by the shell in the range `0lerltoo`, where r is the distance from the centre of the shell?A. B. C. D. |
Answer» Correct Answer - A | |
596. |
If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of `He^(+)` is:A. `(5A)/(9)`B. `(36A)/(7)`C. `(36A)/(5)`D. `(9A)/(5)` |
Answer» Correct Answer - B | |
597. |
The shortest wavelength of H-atom in Lyman series is x, then longest wavelength in Balmer series of `He^(+)` isA. `(5A)/(9)`B. `(36A)/(7)`C. `(36A)/(5)`D. `(9A)/(5)` |
Answer» Correct Answer - B | |
598. |
In the given circuit all resistances are of value R ohm each. The equivalent resistance between A and Bis : A. 3RB. 2RC. `(5R)/(3)`D. `(5R)/(2)` |
Answer» Correct Answer - B | |
599. |
A hoop of radius `r` mass `m` rotating with an angular velocity `omega_(0)` is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it cases to slip ?A. `(romega_(0))/(3)`B. `(romega_(0))/(2)`C. `romega_(0)`D. `(romega_(0))/(4)` |
Answer» Correct Answer - B | |
600. |
Which complex compound possesses `sp^(3)d^(2)` hybridizationA. `SF_(6)`B. `BrF_(5)`C. `PF_(5)`D. `[CrF_(6)]^(3-)` |
Answer» Correct Answer - C | |