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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.
| 51. |
If `AD, BE and CF`are the medians of a `DeltaA B C ,t h e n(A D^2+B E^2+C F^2):(B C^2+C A^2+A B^2)`is equal toA. `4:3`B. `3:2`C. 3:4D. 2:3 |
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Answer» Correct Answer - 3:4 |
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| 52. |
A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading : `58.5 degree` Vernier scale reading : `09` divisions Given that `1` division on main scale correspods to `0.5` degree. Total divisions on the vernier scale is `30` and match with `29` divisions of the main scale. the angle of the prism from the above data:A. `58.59^(@)`B. `58.77^(@)`C. `58.65^(@)`D. `59^(@)` |
| Answer» Correct Answer - C | |
| 53. |
Diameter of a plano-convex lens is 6cm and thickness at the centre is 3mm. If speed of light in material of lens is `2xx10^(8)(m)/(s)`, The focal length of the lens isA. 20 cmB. 30 cmC. 10 cmD. 15 cm |
| Answer» Correct Answer - B | |
| 54. |
If in a conductor number density of electrons is `8.5xx10^(28)` average relaxation time 25 femtosecond mass of electron being `9.1xx10^(-31)`kg, the resistivity would be of the order.A. `10^(-5)`B. `10^(-6)`C. `10^(-7)`D. `10^(-8)` |
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Answer» Correct Answer - D |
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| 55. |
Find out equivalent focal length of given lens combination A. `((R)/(mu_(1)-mu_(2)))`B. `((2R)/(mu_(1)-mu_(2)))`C. `((4R)/(mu_(1)-mu_(2)))`D. `((R)/(mu_(1)+mu_(2)))` |
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Answer» Correct Answer - A |
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| 56. |
In conducting wire of radius `5mm`, resistivity `p-1.1xx10^(-8)Omega//m` and current of `5A` is flowing. Drift velocity of free electron is `1.1xx10^(-3)m//s` find out mobility of free elctron.A. `1.57m^(2)` volt/sec.B. `1.25m^(2)` volt/sec.C. `1.2m^(2)` volt/sec.D. `2 m^(2)` volt/sec. |
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Answer» Correct Answer - A |
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| 57. |
In `YDSE`, slab of thickness t and refractive index `mu` is placed in front of any slit. Then displacement of central maximu is terms of fringe width when light of wavelength `lamda` is incident on system isA. `(beta(mu-1)t)/(2lamda)`B. `(beta(mu-1)t)/(lamda)`C. `(beta(mu-1)t)/(3lamda)`D. `(beta(mu-1)t)/(4lamda)` |
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Answer» Correct Answer - B |
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| 58. |
A uniform chain of mass m & length L is kept on a smooth horizontal table such that `(L)/(n) `portion of the chaing hangs from the table. The work dione required to slowly bringsthe chain completely on the table isA. `(mgL)/(n)`B. `(mgL)/(2)`C. `(mgL)/(n^(2))`D. `(mgL)/(2n^(2))` |
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Answer» Correct Answer - D |
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| 59. |
In an experiment, electrons are made to pass through a narrow slit of width `d` comparable to their de Broglie wavelength. They are detected on a screen at a distance `D` from the slit (see figure)`. ` Which of the following graphs can be expected to represent the number of electrons `N` detected as a function of the detector position `y` (y=0 corresponds to the middle of the slit ).A. B. C. D. |
| Answer» Correct Answer - D | |
| 60. |
The anode vollage of a photocell is kept fixed . The wavelength `lambda `of the light falling on the cathode varies as followsA. B. C. D. |
| Answer» Correct Answer - C | |
| 61. |
A diode detector is used to detect and amplitude modulated wave of `60%` modulation by using a condenser of capacity 250 pF in parallel with a load resistance `100 kOmega`. Find the maximum modulated frequency which could be detected by itA. 10.62 kHzB. 5.31 MHzC. 5.31 kHzD. 10.62 MHz |
| Answer» Correct Answer - C | |
| 62. |
Experimentally it was found that a metal oxide in formula `M_(0.98)O`. Metal `M` is present as `M^(2+)` and `M^(3+)` in its oxide ,Fraction of the metal which exists as `M^(3+)` would beA. 0.0408B. 0.0605C. 0.0508D. 0.0701 |
| Answer» Correct Answer - A | |
| 63. |
A block of mass `0.50kg` is moving with a speed of `2.00m//s` on a smooth surface. It strikes another mass of `1 kg` at rest and they move as a single body. The energy loss during the collision isA. 0.16 JB. 1.00 JC. 0.67 JD. 0.34 J |
| Answer» Correct Answer - C | |
| 64. |
A capillary tube (A) is dipped in water. Another identical tube (B) is dipped in a soap-water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?A. B. C. D. |
| Answer» Correct Answer - C | |
| 65. |
If a tangent is drawn parallel to the line `6x+18y-11=0` to the curve `y=(x)/(x^(2)-3)` which touches the curve at point `(alpha,beta)` thenA. `|6alpha+2beta|=19`B. `|6alpha+2beta|=11`C. `|2alpha+6beta|=7`D. `|2alpha+6beta|=11` |
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Answer» Correct Answer - A |
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| 66. |
In the circuit given below, find the total current drawn from the battry is A. `(3)/(24)`B. `(14)/(25)`C. `(9)/(32)`D. `(3)/(20)` |
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Answer» Correct Answer - C |
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| 67. |
In a parallel plate capacitor of capacitor `1muF` two plates are given charges `2muC` and `4muC` the potential difference between the plates of the capacitor is A. 2 voltB. 1 voltC. 4 voltD. 3 volt |
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Answer» Correct Answer - B |
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| 68. |
Two balls of mass `m_(1)` and `m_(2)` where `m_(2)=0.5m_(1)`, undergo head on collision as shown in figue. After collision the situation is as shown If `V_(3)=0.5v_(1)`. Value of `V_(4)` isA. `v_(4)=v_(1)+v_(2)`B. `v_(4)=v_(1)+2v_(2)`C. `v_(4)=2v_(1)+v_(2)`D. `v_(4)=2v_(1)+3v_(2)` |
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Answer» Correct Answer - A |
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| 69. |
How many litres of water must be added to `1 L` of an aqueous solution of `HCl` with a `pH` of `1` to create an aqueous solution with `pH` of `2`?A. 0.9 LB. 2.0 LC. 9.0 LD. 0.1 L |
| Answer» Correct Answer - C | |
| 70. |
Let `z=((1+i)^(2))/(a-i),(agt0)` and `|z|=sqrt((2)/(5))` then z is equal toA. `-(1)/(5)-(3i)/(5)`B. `(1)/(5)+(3i)/(5)`C. `(3)/(5)-(1)/(5)i`D. `-(3)/(5)+(i)/(5)` |
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Answer» Correct Answer - A |
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| 71. |
Let `p=lim_(x->0^+)(1+tan^2 sqrt(x))^(1/(2x))` then log p is equal to` |
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Answer» `p=lim_(x->0^+)(1+tan^2sqrtx)^(1/(2x))` `p=e^(lim_(x->0+))1/(2x)(x+tan^2sqrtx-x)` `=e^(lim_(x->0^+)1/2tan^2sqrtx)/sqrtx^2` `=e^(lim_(x->0^+)(1/2(tansqrtx)/sqrtx)^2` `p=e^(1/2)` `logp=log(e^(1/2))=1/2loge` `logp=1/2`. |
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| 72. |
Let `lim_(x to 1) (x^(4)-1)/(x-1)=lim_(k to k ) (x^(3)-k^(3))/(x^(2)-k^(2))` then value of k isA. `(2)/(3)`B. `(3)/(2)`C. `(4)/(3)`D. `(8)/(3)` |
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Answer» Correct Answer - D |
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| 73. |
The value of `lim_(x->0)(sec4x-sec2x)/(sec3x-secx)` is |
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Answer» `limx->0 [(sec4x-sec2x)/(sex3x-secx)]`on puttin `x=0` we get inderminate form ` 0/0 `.therefore we use l-hopital rule and differentiate numerator and denominator seprately. upon differentiating numerator and denominator seprately we get `limx->0[(4sec4xtan4x-2 sec2x tan2x)/(3sec3x tan3x-secxtanx)]` again putting value of x we get indterminate form `0/0` agan using l-hopital rule we get `limx->0[(16 sec4xtan^2 4x+16sec^3 4x-4 sec2xtan^2 2x-4sec^3 2x)/(9sex3x tan^3x+9sec^3x-secxtan^2x-sec^3 x)]` now putting value of x we get`3/2`. |
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| 74. |
`int_(0)^((pi)/(2))(sin^(3)x)/(sinx+cosx)dx` is equal toA. `(pi)/(4)-(1)/(4)`B. `(pi)/(4)+(1)/(4)`C. `(pi)/(4)+(1)/(2)`D. `(pi)/(4)-(1)/(2)` |
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Answer» Correct Answer - A |
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| 75. |
`lim_(x->pi/2` `(cot x - cos x)/(pi-2x)^3` equals |
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Answer» Let `x = pi/2 -h`, then the given expression becomes, `lim_(h->0) (cot(pi/2-h) - cos(pi/2-h))/((pi- 2(pi/2-h))^3)` `=lim_(h->0) (tanh - sinh)/((2h)^3)` `=lim_(h->0) ((sinh/cosh) - sinh)/(8h^3)` `=lim_(h->0) (sinh((1-cosh)/cosh))/(8h^3)` `=lim_(h->0) (tanh(2sin^2(h/2)))/(8h^3)` `=lim_(h->0) tanh/h*(sin^2(h/2))/(4(h/2)^2*4)` `= 1*1^2/(4*4) = 1/16`, which is the required value. |
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| 76. |
If `A=1/pi[[sin^-1(xpi),tan^-1(x/pi)],[sin^-1(x/pi),cot^-1(xpi)]]` and `B=1/pi[[-cos^-1(xpi),tan^-1(x/pi)],[sin^-1(x/pi),-tan^-1(xpi)]]` find the value of A-B in terms of identity matrix |
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Answer» A-B=`1/pi[[sin^(-1)(xpi)+cos^(-1)(xpi),0],[0,cot^(-1)(pix)+tan^(-1)(pix)]]` `=1/pi[[pi/2,0],[0,pi/2]]` `=1/2[[1,0],[0,1]]` A-B=`1/2I`. |
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| 77. |
`int_(0)^(1)x cot^(-1)(1-x^(2)+x^(4))=`A. `(pi)/(2)-"log"2`B. `(pi)/(2)+"log"ssqrt(2)`C. `(pi)/(4)-"log"2`D. `(pi)/(4)-"log"sqrt(2)` |
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Answer» Correct Answer - D |
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| 78. |
The value of `sin10^(@), sin50^(@). Sin70^(@)` isA. `(1)/(36)`B. `(1)/(32)`C. `(1)/(18)`D. `(1)/(16)` |
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Answer» Correct Answer - D |
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| 79. |
The major product obtained on interaction of phenol with sodium hydroxide and carbon dioxide is :A. benzoic acidB. salicylaldehydeC. salicylic acidD. phthalic acid |
| Answer» Correct Answer - C | |
| 80. |
The sum of the infinite series `cot^(-1)(7/4)+cot^(-1)((19)/4) +cot^(-1)((39)/4)....oo` |
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Answer» Here, general term `T_r` can be wriiten as, `T_r = cot^-1((4r^2+3)/(4)) = cot^-1(r^2+3/4)` `=>T_r = tan^-1(1/(r^2+3/4)) = tan^-1(((r+1/2)-(r-1/2))/(1+r^2-1/4))` `= tan^-1(((r+1/2)-(r-1/2))/(1+(r+1/2)(r-1/2)))` We know, `tan^-1((x-y)/(1+xy)) = tan^-1x+tan^-1y` `:. T_r = tan^-1(r+1/2) - tan^-1(r-1/2)``:. T_1 = tan^-1 (3/2)-tan^-1 (1/2)` `T_2 = tan^-1 (5/2)-tan^-1 (3/2)` `T_3 = tan^-1 (7/2)-tan^-1 (5/2)` `T_n = tan^-1 ((2n+1)/2)-tan^-1 ((2n-1)/2)` So, the required sum will be, `sum T_r = tan^-1((2n+1)/2) - tan^-1(1/2)` `=pi/2-tan^-1(1/2)` `:. sumT_r= cot^-1(1/2)` |
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| 81. |
If mean of squares of deviations of a set of n observations about -2 and 2 are 18 and 10 respectively, then standard deviation of this set of observations is |
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Answer» `sum(x_i-22)^2/N` `sum(x_i+2)^2/N=18-(1)` `sum(x_i-2)^2/N=10-(2)` `sum(x_i^2+4+4x_i)=18N` `sumx_i^2+sum4+4sumx_i=18N` `sumx_i^2+4sumx_i=14N-(3)` `sumx_1^2+4N-4sumx_i=10N` `sumx_i^2-4sumx_i=6N-(4)` adding equation 3 and 4 `2sumx_i^2=20N` `sumx_i^2=10N` subtracting equation 2 from 3 `8sumx_i=8N` `sumx_i=N` `sumx_1/N=1` `SD=sqrt(sum(x_i-x)^2/N)` `=sum(x_i-mu)^2/N` `=sum(x_i^2+mu^2-2x_imu)/N` `=(11N-2N)/N=9N/N=9` square of standard deviation=9 standard deviation=3. |
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| 82. |
The algebraic sum of deviations of 10 observations measured from 15 is 7 The mean is |
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Answer» Algebric sum of deviations ` = 7` Total number of observations ` = 10` `:.` Mean `= 7/10 = 0.7` Measured deviation ` = 15` But, here observation starts from `15`. `:.` Actual mean ` = 15+0.7 = 15.7` |
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| 83. |
A special dice with numbers 1,-1,2,-2,0 and 3 is thrown thrice. What is the probability that the sum of the numbers occurring on the upper face is zero? |
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Answer» Below are the cases, when sum of numbers of all dice can be `0`. `(i) (0,0,0) - 1` possibility `(ii)(1,0,-1) - 3! = 6` posiibilities `(iii)(2,0,-2) - 3! = 6` posiibilities `(iv)(1,1,-2) - (3!)/2= 3` possibilities `(v)(-1,-2,3) - 3! = 6` posiibilities `(vi)(2, -1,-1) -(3!)/2= 3` possibilities So, total number of favourable outcomes, `n(E) = 1+6+6+3+6+3 = 25` Total number of outcomes `n(S) = 6^3 = 216` `:.` Required probability, `P(E) = (n(E))/(n(S)) = 25/216` |
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| 84. |
For a particle in uniform circular motion , the acceleration ` vec(a)` at a point ` p ( R, theta )` on the circle of radiu ` R` is ( Here ` theta` is measured from the ` x- axis` )A. `-(v^(2))/(R)cos thetahati+(v^(2))/(R)sin thetahatj`B. `-(v^(2))/(R)sin thetahati+(v^(2))/(R)cos thetahatj`C. `-(v^(2))/(R)cos thetahati-(v^(2))/(R)sinthetahatj`D. `(v^(2))/(R)hati+(v^(2))/(R)hatj` |
| Answer» Correct Answer - C | |
| 85. |
Two fixed frictionless inclined planes making an angle `30^@` and `60^@` with the vertical are shown in figure. Two blocks A and B are planes. What is the relative vertical acceleration of A with respect to B? A. `4.9ms^(-2)` in horizontal directionB. `9.8ms^(-2)` in vertical directionC. zeroD. `4.9 ms^(-2)` in vertical direction |
| Answer» Correct Answer - D | |
| 86. |
The box of a pin hole camera, of length L, has a hole of radius a . It is assumed that when the hole is illuminated by a parallel beam of light of wavelength `lamda` the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say b_(min)) when:A. `a = sqrt(lambda L) and b_(min)=((2lambda^(2))/(L))`B. `a = sqrt(lambda L) and b_(min)=sqrt(4lambdaL)`C. `a=(lambda^(2))/(L)and b_(min)=sqrt(4 lambda L)`D. `a = (lambda^(2))/( L) and b_(min)=((2lambda^(2))/(L))` |
| Answer» Correct Answer - B | |
| 87. |
Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm, the minimum separation between two objects than human eye can resolve at 500nm wavelength is :A. `30 mum`B. `100 mum`C. `300 mum`D. `1 mum` |
| Answer» Correct Answer - A | |
| 88. |
A solid sphere of radius `a` and mass `m` is surrounded by cocentric spherical shell of thickness `2a` and mass `2m` the gravitational field at a distance 3a from their centres isA. `(Gm)/(a^(2))`B. `(Gm)/(3a^(2))`C. `(Gm)/(5a^(2))`D. `(Gm)/(4a^(2))` |
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Answer» Correct Answer - B |
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| 89. |
if the foot of perpendicular drawn from a point on the line `(x-1)/(2)=(y+1)/(-1)=(z)/(1)` on the plane `x+y+z=3` also lies on the plane `x-y+z=3` then the coordinates of the foot of perpendicular isA. `(-2,0,5)`B. `(-1,0,4)`C. `(1,0,2)`D. `(2,0,1)` |
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Answer» Correct Answer - D |
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| 90. |
Let O(0,0), P(3,4), Q(6,0) be the vertices of the triangle OPQ. The point R inside the triangles OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are (1) `(4/3,3)` (2) `(3,2/3)` (3) `(3, 4/3)` (4) `(4/3,2/3)` |
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Answer» Area of `/_ORQ=1/3`Area of `/_OPQ` `=1/3*1/2*4*6` `=4 unit^2` Areaof `/_ORQ=1/2*h*6` `4=3h ` `h=4/3` Co-ordinates of `R(3,4/3)`. |
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| 91. |
Eqation of plane passing through line of intersection of planes `x + y + z = 1` and `2x +3y +z = 5` and perpendicular to the plane `x-y-z = 0` is :A. `vec(r ).(hat(j)-hat(k)) +3 = 0`B. `vec(r ).(hat(j)- hat(k))-3=0`C. `vec(r ). (hat(i)+hat(k)) +2 = 0`D. `vec(r ).(hat(i) +hat(k)) - 2 = 0` |
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Answer» Correct Answer - B |
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| 92. |
If `S={(alpha+i)/(alpha-i),alphainR}` then the S lies onA. a circle with radius `=sqrt(2)`B. a straight line with slope `=-1`C. a straight line with slope `=1`D. a circle with radius `=1` |
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Answer» Correct Answer - D |
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| 93. |
Let the system of linear equations `2x+3y-z=0,2x+ky-3z=0` and `2x-y+z=0` have non trivial solution then `(x)/(y)+(y)/(z)+(z)/(x)+k` will beA. 2B. 3C. 1D. `-4` |
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Answer» Correct Answer - B |
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| 94. |
A long cylindrical shell carries positive surface charge `sigma` in the upper half and negative surface charge `-sigma` in the lower half. The electric field lines around the cylinder will look like figure given in:(figures are schematic and not drawn to scale)A. B. C. D. |
| Answer» Correct Answer - D | |
| 95. |
If 7 points out of 12 are in the same straight line, then the number of triangles formed is |
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Answer» 0 point on triangle=`.^5C_3=10` 1 point on triangle=`.^7C_1*.^5C_2=70` 2 point on triangle=`.^7C_2*.^5C_1=105` Total triangle formed=10+70+105=185. |
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| 96. |
If the lines `x+(a-1)y=1` and `2x+1a^(2)y=1` there `ainR-{0,1}` are perpendicular to each other, Then distance of their point of intersection from the origin isA. `(5)/(2)`B. `(2)/(sqrt(5))`C. `(sqrt(5))/(2)`D. `sqrt((2)/(5))` |
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Answer» Correct Answer - D |
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| 97. |
Consider a plane `x+2y+3z=15` and a line `(x-1)/(2)=(y+1)/(3)=(z-2)/(4)` then find the distance of origin from point of intersection of line and plane.A. `(1)/(2)`B. `(9)/(2)`C. `(5)/(2)`D. `4` |
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Answer» Correct Answer - B |
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| 98. |
Passengers are to travel by a double decked bus which can accommodate 13 in the upper deck and 7 in the lower deck. The number of ways that they can be divided if 5 refuse to sit in the upper deck and 8 refuse to sit in the lower deck, is |
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Answer» `20=13U+7L` Number of ways`=.^7C_5=,^7C_2` `=(7*6)/(2*1)=21`. |
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| 99. |
The greatest possible number of points of intersection of 8 straight lines and 4 circles is: |
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Answer» `.^8C_2*1=28` `.^8C_1*4C_1*2=64` `.^4C_2*2=12` Total=`10^4.` |
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| 100. |
Height of two towers are `20m` and `80`. Join foot of the tower to the top of other and vice versa. Find the height of intersection point from the horizontal plane.A. 15B. 14C. 16D. 12 |
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Answer» Correct Answer - C |
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