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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.
| 451. |
`vec(r)=15t^(2)i+(20-20t^(2))j` find magnitude of acceleration at `t=1` sec.A. `30m//s^(2)`B. `40m//s^(2)`C. `70m//s^(2)`D. `50m//s^(2)` |
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Answer» Correct Answer - D |
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| 452. |
10 different letters of an alphabet are given. Words with 5 letters are formed from these given letters then the numbers of words which have atleast one letter represent is: |
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Answer» Total possible ways=`10^5` Atleast one letter repeat=total number of letter repeat `=10^5-.^10C_5*5!` `=100000-(10*9*8*7*6*5!)/(5!5!)*5!` `=100000-30240` `=169760` Option 1 is correct. |
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| 453. |
y = `log(sqrt((1-cos(3x/2))/(1+ cos(3x/2))))` differentiate w.r.t. x. |
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Answer» `y=logsqrt((1-cos3x/2)/(1+cos3x/2))` `y=logsqrt((2sin^23/4x)/(2cos^23/4x)` `y=logsqrt(tan^23/4x)` `y=log(tan3/4x)` `dy/dx=1/(tan3/4x)sec^2(3/4x)*3/4` `dy/dx=3/4(sec^2 3/4x)/(tan3/4x)` `dy/dx=3/4(1/cos^2 3/4x)/((sin3/4x)/(cos3/4x))` `dy/dx=3/4*sec3/4xcosec3/4x` |
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| 454. |
A two digit number is such that the product of digit is 8 . when 18 is added to the number , the digits are reversed . The number is: |
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Answer» Let the digits of the number are `x` and `y` where `y` is the unit digit. Then, the number will be `10x+y`. It is given that, ` xy = 8=>x = 8/y->(1)` Also, `10x+y +18 = 10y+x` `=>9x-9y = -18` `=>x-y = -2` `=>8/y - y = -2` `=>8-y^2 = -2y` `=>y^2-2y -8 = 0` `=>y^2-4y+2y -8 = 0` `=>y(y-4)+2(y-4) = 0` `=>(y+2)(y-4) = 0` `=> y = -2 or y = 4` We will take positive value for `y`, that is `4`. `:. x = 8/y = 8/4 = 2` So, the number is `2**10+4 = 24.` |
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| 455. |
The set of values of p for which the roots of the equation `3x^2 +2x + p(p-1) =0` are of opposite signs is: |
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Answer» Let one root is `alpha`. So, second root will be `-alpha`. `:.` Sum of roots `= alpha-alpha = 0` `:.` Product of roots `= -alpha^2` It means product of rootsis less than `0`. Product of roots in the given equation is `(p(p-1))/3`. `:. (p(p-1))/3 lt 0` `=> (p(p-1)) lt 0` `:.p in ]0,1[` |
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| 456. |
The perimeter of a rectangle is 82m and its area is `400m^2`. The breadth of the rectangle is: (a)25 m (b) 16 m (c)9 m (d)20 m |
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Answer» Let length of rectangle is `l` and breadth is `b` in metres. Perimeter of a rectangle `(P) = 2(l+b)` `:. 2(l+b) =82` `=>l+b = 41=>l=41-b->(1)` Area of a rectangle `(A) = l**b ` `=>l**b = 400` From (1), `=>(41-b)b = 400` `=>41b-b^2 = 400` `=>b^2-41b+400 = 0` `=>b^2-25b-16b+400 = 0` `=>b(b-25)-16(b-25) = 0` `=>(b-25)(b-16) = 0` `=>b = 16 and b = 25` When `b = 16m, l = 41-16 = 25m` When `b = 25m, l = 41-25 = 16m` |
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| 457. |
Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume `u=U/V propT^4` and pressure `P=1/3(U/V)`. If the shell now undergoes an adiabatic expansion the relation between T and R is :A. `T prop e^(-3R)`B. `T prop 1/R`C. `T prop 1/R^(3)`D. `T prop e^(-R)` |
| Answer» Correct Answer - B | |
| 458. |
Which of the following is the major product of give reation: overset(LiAlH_(4))rarr`A. B. C. D. |
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Answer» Correct Answer - A |
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| 459. |
An intially parallel cyclindrical beam travels in a medium of refractive index `mu (I) = mu_(0) + mu_(2) I`, where `mu_(0)` and `mu_(2)` are positive constants and `I` is intensity of light beam. The intensity of the beam is decreasing with increasing radius. Answer the following questions : The speed of light in the medium isA. minimum on the axis of the beamB. the same everywhere in the beamC. directly proportional to the intensity lD. maximum on the axis of the beam |
| Answer» Correct Answer - A | |
| 460. |
An intially parallel cyclindrical beam travels in a medium of refractive index `mu (I) = mu_(0) + mu_(2) I`, where `mu_(0)` and `mu_(2)` are positive constants and `I` is intensity of light beam. The intensity of the beam is decreasing with increasing radius. Answer the following questions : The initial shape of the wavefront of the beam isA. convexB. concaveC. convex near the axis and concave near the peripheryD. planar |
| Answer» Correct Answer - D | |
| 461. |
Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is `mu`, a ray, incident at an angle `theta`, on the face AB would get transmitted through the face AC of the prism provided: A. `theta lt sin^(-1)[mu sin (A - sin^(-1)(1/mu))]`B. `theta gt cos^(-1)[mu sin (A + sin^(-1)(1/mu))]`C. `theta lt cos^(-1)[mu sin (A + sin^(-1)(1/mu))]`D. `theta gt sin^(-1)[mu sin (A - sin^(-1)(1/mu))]` |
| Answer» Correct Answer - D | |
| 462. |
Very pure hydrogen `(99.9%)` can be made by which of the following processes ?A. Reaction of methane with steamB. Mixing natural hydrocarbos of high molecular weightC. Electrolysis of waterD. Reaction of salt like hydrides with water |
| Answer» Correct Answer - C | |
| 463. |
For which of the following processes is `DeltaS` negative?A. `C("diamond")rarrC("graphite")`B. `N_(2)(g,1" atm")rarrN_(2)(g,5" atm")`C. `H_(2)(g)rarr2H(g)`D. `N_(2)(g, 273 K)rarrN_(2)(g, 300K)` |
| Answer» Correct Answer - B | |
| 464. |
Arrange the following compounds in the correct increasing rate of aromatic electrophilic substitution. A. `AltBltCltD`B. `DltAltBltC`C. `CltBltAltD`D. `CltAltBltD` |
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Answer» Correct Answer - B |
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| 465. |
In which layer of atmosphere there is cloud formation & in which layer we live respectively?A. Troposphere and troposphereB. proposphere and stratosphereC. stratosphere and stratosphereD. stratosphere and troposphere |
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Answer» Correct Answer - A |
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| 466. |
Statement I Nitrogen and oxygen are the main components in the atmosphere but these do not react to from oxides of nitrogen. Statement II the reaction between nitrogen and oxygen requires high temperature.A. Both assertion and reason are correct, but the reason is not the correct explanation for the assertionB. The assertion is incorrect, but the reason is correctC. Both the assertion and reason are incorrectD. Both assertion and reason are correct, and the reason is the correct explanation for the assertion |
| Answer» Correct Answer - D | |
| 467. |
`C_(60)` is aromatic allotrope of carbon containingA. `18` Pentagons, `14` hexagonsB. `16` Pentagons, `16` hexagonsC. `12` Pentagons, `20` hexagonsD. `20` Pentagons, `12` hexagons |
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Answer» Correct Answer - C |
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| 468. |
Which of the following is the correct structure of Adenosine ?A. B. C. D. |
| Answer» Correct Answer - A | |
| 469. |
Which of the following ores contains fluorine ?A. MalachiteB. SphaleriteC. CryoliteD. Bauxite |
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Answer» Correct Answer - C |
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| 470. |
Which of the following will have highest difference between `IE_(1)` and `IE_(2)`?A. `K`B. `Mg`C. `Sr`D. `Sc` |
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Answer» Correct Answer - A |
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| 471. |
Which of the following will show optical activityA. B. C. D. |
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Answer» Correct Answer - A |
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| 472. |
In the given transformation, which of the following is the most appropriate reagent ? A. `NH_(2)NH_(2), overset((-))OH`B. `Zn-Hg//HCI`C. `Na,Liq.NH_(3)`D. `NaBH_(4)` |
| Answer» Correct Answer - A | |
| 473. |
The reagent(s) required for the following conversion are : A. (i) `B_(2)H` , (ii) `SnCl_(2)//HCl` (iii) `H_(3)O^(+)`B. (i) `B_(2)H^(6)`, (ii) `DIBAL-H` (iii) `H_(3)O^(+)`C. (i) `LiAlH_(4)` , (ii) `H_(3)O^(+)`D. (i) `NaBH_(4)` , (ii) Raney `Ni//H_(2)` (iii) `H_(3)O^(+)` |
| Answer» Correct Answer - A | |
| 474. |
Which of the following orbitals are degenerate for `[Cr(H_(2)O)_(6)]^(3-)`A. `d_(x)^(2)-y^(2),d_(xy)`B. `d_(xy),d_(yz)`C. `d_(x^(2))-y_(2),d_(yz)`D. `d_(2),d_(xy)` |
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Answer» Correct Answer - B |
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| 475. |
Which of the following is potential energy diagram for `S_(N)1` reaction?A. B. C. D. |
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Answer» Correct Answer - B |
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| 476. |
Which of the following is Hinsberb reagent ?A. `C_(6)H_(5)SO_(2)CH_(3)`B. `C_(6)H_(5)SO_(2)Cl`C. `SnCl_(2)`D. `CoCl_(2)` |
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Answer» Correct Answer - B |
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| 477. |
If `x_i>0` i=1,2,3,...50 `x_1+x_2...+x_50=50` then the minimum value of `1/(x_1) +1/(x_2) +...+1/(x_50)` equals |
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Answer» AM`>=GM>=HM` `1/x_1*1/x_2*1/x_3...1/x_50` `(1/x_1+1/x_2+1/x_3...1/x_50)/50>=(1/(x_1+x_2+x_3...x+50))/50` `1/x_1+1/x_2+1/x_3+...+1/x_50>=50`. |
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| 478. |
Find the direction cosines of the line segment joining the points `P(2,3 -6)` and `Q(3, -4, 5)` |
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Answer» `PQ=(3-2,-4-3,5-(-6))` DR of PQ=(1,-7,11) distance` PQ=sqrt(1^2+(-7)^2+11^2)` `PQ=sqrt171` `PQ=3sqrt19` Distance of PQ`(1/(3sqrt19),(-7)/(3sqrt19),11/(3sqrt19))`. |
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| 479. |
The sum of the digits in the unit place of all numbers formed with the help of 3,4,5,6 taken all at a time is |
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Answer» Number 3 can be placed 18 times Number 4 can be placed 24 times Number 5 can be placed 30 times Number 6 can be placed 36 times Total patterns=108 Option 3 is correct. |
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| 480. |
Let the orthocentre and centroid of a triangle be `A(-3,5) and B(3,3)` respectively. If C is the circumcentre of the triangle then the radius of the circle having line segment AC as diameter, is |
| Answer» Centroid divides Orthocenter and Circumcentre in the ratio 2:1 respectively.By using Section formula, we get`(2x-3)/3=3`& `(2y+5)/3=3`So, (x,y)=(6,2)`AC=sqrt((6+3)^2+ (2-5)^2)``AC=sqrt90`Required Radius=AC/2=4.74 | |
| 481. |
There are 20 pillars of equal height on a circular ground any two non adjacent pillars joined by a beam. Then the number of such beams are:A. 180B. 210C. `.^(20)C_(2)-20`D. `.^(20)C_(2)` |
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Answer» Correct Answer - C |
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| 482. |
Let ABCD be a square two of whose adjacent vertices, say A, B on the positive X-axis and the positive Y-axis, respectively. If C has co-coordinates (u,v) in the first quadrant, determine the area of ABCD in terms of u and v. |
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Answer» `AB=sqrt(a^2+b^2` `m_(AD)=-b/a` `m_(BC)=a/b= tantheta` `sintheta=a/sqrt(a^2+b^2),costheta=b/sqrt(a^@+b^2` `(x-0)/costheta=(y-b)/sintheta=sqrt(a^2+b^2` `U=b,V-b=a` `V=a+b` `a=(V-U)` Side=`sqrt(V^2-2UV+U^2+U^2` `Area=side^2` `=V^2-2UV+2U^2`. |
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| 483. |
The angle between the tangents drawn from the point (-a, 2a) to `y^2`=4ax is |
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Answer» `y^2=4ax` `y=mx+a/m` `2a=-ma+a/m` `2=(-m+1)/m` `m^2+2m-1=0` `tantheta=|(m_1-m_2)/(1+m_1m_2)|` `tanttheta=1/0=oo` `theta=pi/2`. |
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| 484. |
`x^3-6x^2+11x-6=0` |
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Answer» `x^3-6x^2+11x-6=0` putting x=1 (x-1)(x-2)(x-3)=0 `x=1,2,3. |
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| 485. |
A circle touches the line L and the circle `C_1` externally such that both the circles are on the same side of the line, then the locus of centre of the circle is (a) Ellipse (b) Hyperbola (c) Parabola (d) Parts of straight line |
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Answer» `C_1C_2=r_1+r_2` `C_1C_2=C_2D` option C is correct. |
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| 486. |
The locus of centre of circle which touches the circle `x^(2)+y^(2)=1` and `y-` axis in 1st quadrant isA. `y^(2)=2x-1`B. `x^(2)+1=2y`C. `y^(2)=2x+1`D. `x^(2)-1=2y` |
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Answer» Correct Answer - C |
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| 487. |
`sqrt(x)+y=11`, ` x+sqrt(y) =7` |
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Answer» `sqrtx+y=11` `x=(11-y)^2` `x=121+y^2-22y` `x+sqrty=7` `y=(7-x)^2` `x=121+(x-7)^2-22(x-7)^2` `x^4-28^3+272x^2-1065x+1444=0` `x=4` `sqrtx+y=11` `sqrt4+y=11` `y=11-2` `y=9` `(4,9)` |
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| 488. |
Which of the following statement is false about diabetes ?A. When excess of electrolyteis added to colloidal solution, colloidal particle will be precipitated.B. Colloidal particles can pass through ordinary filter paper.C. When silver nitrate solution is added to potassium iodide solution,a negatively charge colloidal solution is formed.D. Freezing point of colloidal solution is lower than true solution at some concentration of a solute. |
| Answer» Correct Answer - D | |
| 489. |
`C_(p)` nad `C_(v)` are specific heats at constant pressure and constant volume respectively. It is observed that `C_(p)-C_(v)=a` for hydrogen gas `C_(p)-C_(v)=b` for niotrogen gas The correct relation between a and b isA. a=28 bB. `a=(1)/(14)b`C. `a=b`D. `a=14b` |
| Answer» Correct Answer - D | |
| 490. |
A slender uniform rod of mass `M` and length `l` is pivoted at one end so that it can rotate in a vertical plane, Fig. There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle `theta` with the vertical is A. `(2g)/(3l)costheta`B. `(3g)/(2l)sintheta`C. `(2g)/(3l)sintheta`D. `(3g)/(2l)costheta` |
| Answer» Correct Answer - B | |
| 491. |
Identify the pair in which the geometry of the species is T-shape and square- pyramidal, respectively :A. `IO_(3)^(-)` and `IO_(2)F_(2)^(-)`B. `XeOF_(2)` and `XeOF_(4)`C. `ICl_(2^(-))` and `ICl_(5)`D. `ClF_(3)` and `IO_(4)^(-)` |
| Answer» Correct Answer - B | |
| 492. |
The increasing order of nitration of the following compound is : A. `(a) lt (b) lt (d) lt (c )`B. `(b) lt(a) lt (d) lt (c )`C. `(b)lt (a) lt (c ) lt (d)`D. `(a) lt (b) lt (c ) lt (d)` |
| Answer» Correct Answer - A | |
| 493. |
Which of the following compounds does not exist as a zwitter ion ?A. B. C. D. |
| Answer» Correct Answer - B | |
| 494. |
The main oxides formed on combustion of Li,Na and K in excess of air respectively areA. `LiO_(2), Na_(2)O_(2) and K_(2)O`B. `Li_(2)O_(2), Na_(2)O_(2) and KO_(2)`C. `Li_(2)O, Na_(2)O_(2) and KO_(2)`D. `Li_(2)O, Na_(2)O and KO_(2)` |
| Answer» Correct Answer - C | |
| 495. |
Which one of the following amongs each pair will release maximum energy on gaining one electron (A = F, Cl), (B = S, Se), (C = Li, Na)A. (A) = Cl, (B) = S, (C) = LiB. (A) = S, (B) = Cl, (C) = LiC. (A) = Li, (B) = Cl, (C) = SD. (A) = Cl, (B) = Li, (C) = S |
| Answer» Correct Answer - A | |
| 496. |
Let numbers `a_(1),a_(2)…a_(16)` are in AP and `a_(1)+a_(4)+a_(7)+a_(10)+a_(13)+a_(16)=114` then `a_(1)+a_(5)+a_(12)+a_(16)` is equal toA. 36B. 96C. 76D. 38 |
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Answer» Correct Answer - C |
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| 497. |
Let `triangle1=|{:(x,sintheta,costheta),(-sintheta,x,1),(costheta,1,x):}|` and `triangle2=|{:(x,sin2theta,cos2theta),(-sin2theta,x,1),(cos2theta,1,x):}|` then which of following is/are true?A. `triangle1-triangle2=x^(3)`B. `triangle1+triangle2+2x^(3)`C. `triangle1+triangle2=x^(3)`D. `triangle1-triangle2=2x^(3)` |
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Answer» Correct Answer - B |
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| 498. |
Products A and B formed in the following reactions are respectively : A. B. C. D. |
| Answer» Correct Answer - D | |
| 499. |
The incorrect geometry is represented by :A. `NF_(3)` - trigonal planarB. `BF_(3)`-trigonal planarC. `AsF_(5)`-trigonal bipyramidalD. `H_(2)O` - bent |
| Answer» Correct Answer - A | |
| 500. |
Bond order and magnetic nature of `CN^-` are respectivelyA. 3, diamagneticB. 3, paramagneticC. 2.5, paramagneticD. 2.5, diamagnetic |
| Answer» Correct Answer - A | |