100525 + Interview Questions in GENERAL QA IN GENERAL AWARENESS Page 356 InterviewSolution

17751.	Area bounded by Curves
Answer» Correct Answer - 3 `A= underset(0)overset(4)(int) {(6x-x^(2))-(x^(2)-2x)} dx` `A= underset(0)overset(4)(int) (8x-2x^(2))dx` `A=[4x^(2) - 2/3 x^(3)]_(0)^(4)=64-128/3=64/3` sq. units

Discussion

17752.	Complex compound `[Cr(NCS)(NH_(3))_(5)][ZnCl_(4)]` will be -A. diamaganetic and shows linkage isomerismB. colourless and diamagneticC. green coloured and diamagneticD. green coloured and shows co-ordination isomerism.
Answer» Correct Answer - D `[overset(+3)(Cr)(NCS)(NH_(3))_(5)][underset(+2)(Zn)Cl_(4)]` `Cr^(+3) = [Ar] 4s^(0)3d^(3)` It has 3 unpaired `e^(-)` Green coloured and shows co-ordination isomerism

Discussion

17753.	Incorrect order of boiling point is -A. `HF gt HI gt HBr gt HCl`B. `H_(2)O gt H_(2)Te gt H_(2)Se gt H_(2)S`C. `Br_(2) gt Cl_(2) gt F_(2)`D. `CH_(4) gt GeH_(4) gt SiH_(4)`
Answer» Correct Answer - D `CH_(4) gt GeH_(4) gt SiH_(4)`

Discussion

17754.	`{:(MnO_(2)+KOH+O_(2)rarrunderset(("green"))(A)+H_(2)O),(A+Cl_(2)rarrunderset(("purple"))(B)+KCl):}` Select correct statement:-A. compound B is cloured due to change transfer and it is paramagnetic in nature.B. Compound B is `KMnO_(4)`. Tjere is no unparied `e^(-)` in MnC. Compound A is `K_(2)MnO_(4),K_(2)MnO_(4)` has tetrahedral shape.D. `KMnO_(4)` acts as oxidising agent. In acidic medium it form `Mn^(+2)`
Answer» Correct Answer - A `KMnO_(4)` is diamagnetic in nature. Compound B is coloured due to charge transfer and it is paramagnetic in nature.

Discussion

17755.	If `sum_(i=1)^(15)x_(i)=45,A=sum_(i=1)^(15)(x_(i)-2)^(2)` `B=sum_(i=1)^(15)(x_(i)-3)^(2)` and `C=sum_(i=1)^(15)(x_(i)-5)^(2)` then Statement 1: `min(A,B,C)=A` Statement 2: The sum of squares of deviations is least when taken from man.A. Statement 1: is True, Statement 2 is True , Statement 2 is a correct explanation for statement 1B. Statement 1 is True, Statement 2 is True Statement 2 is NOT a correct explanation for Statement 1C. Statement 1 is True, Statement 2 is FalseD. Statement 1 is False, Statement 2 is True
Answer» Correct Answer - D `sum_(i=1)^(n)(x_(i)-barx)^(2)` `implies "min" (A,B,C)=B`

Discussion

17756.	If `4sin^(-1)x+cos^(-1)x=pi`, then `x` is equal toA. `2/3`B. `1/3`C. `1/2`D. `2`
Answer» Correct Answer - C `3sin^(-1)x=pi-(pi)/2` `sin^(-1)x=(pi)/6,x=1/2`

Discussion

17757.	If `sum_(i=1)^(15)x_(i)=45,A=sum_(i=1)^(15)(x_(i)-2)^(2)`, `B=sum_(i=1)^(15)(x_(i)-3)^(2)` and `C=sum_(i=1)^(15)(x_(i)-5)^(2)` then Statement 1: `min(A,B,C)=A` Statement 2: The sum of squares of deviations is least when taken from man.A. Statement 1: is True, Statement 2 is True , Statement 2 is a correct explanation for statement 1B. Statement 1 is True, Statement 2 is True Statement 2 is NOT a correct explanation for Statement 1C. Statement 1 is True, Statement 2 is FalseD. Statement 1 is False, Statement 2 is True
Answer» Correct Answer - D `sum_(i=1)^(n)(x_(i)-barx)^(2)` `implies "min" (A,B,C)=B`

Discussion

17758.	If `x=9` is the chord of contact of the hyperbola `x^2-y^2=9` then the equation of the corresponding pair of tangents is (A) `9x^2-8y^2+18x-9=0` (B) `9x^2-8y^2-18x+9=0` (C) `9x^2-8y^2-18x-9=0` (D) ` `9x^2-8y^2+18x+9=0`
Answer» Correct Answer - 4 Let `x = 9` be the chord of contact of the given hyperbola with respect to the point `(x_(1), y_(1))`. Then its equation is given by `T=0` i.e. `x x_(1)-y y_(1)=9` `x x_(1)-y y_(1)=9` Comparing this equation to `x=9`, we get `x_(1)/1=y_(1)/0=1 implies x_(1)=1, y_(1)=0` Hence tangents are drawn from the point `(1, 0)`. So their combinaed equation is `S S_(1)=T^(2)` `(x^(2)-y^(2)-9) (-8)=(x-9)^(2)` `implies 9 x^(2)-8y^(2)-18x+9=0`

Discussion

17759.	If `f(x)=sin\|x\|-e^(\|x\|)` then at `x=0,f(x)` isA. Continuous but not differentiableB. Neither continuous nor differentiableC. Both continuous and differentiableD. Discontinuous but may be differentiable
Answer» Correct Answer - C `RHD=lim_(hrarr0)(sin\|0+h\|+e^(\|0+h\|)-(-1))/h` `=lim_(hrarr0) (sinh)/h-((e^(h)-1)/h)=1-1=0` Similarly LHD`=0`

Discussion

17760.	The no. of solutions of the equation `a^(f(x)) + g(x)=0` where a>0 , and g(x) has minimum value of 1/2 is :-A. OneB. TwoC. Infinitely manyD. Zero
Answer» Correct Answer - D `a^(f(x))=-g(x)le-1//2`, since `g(x)ge1//2` for all `x`. But this is not possible as `a^(f(x))gt0` for all `x`. Thus the number of solution is zero.

Discussion

17761.	Angle between diagonals of a parallelogram whose side are represented by `veca=2hati+hatj+hatk` and `vecb=hati-hatj-hatk`A. `cos^(-1)(1/3)`B. `cos^(-1)(1/2)`C. `cos^(-1) (4/9)`D. `cos^(-1)(5/9)`
Answer» Correct Answer - A Diagonals are `veca+vecb` and `veca-vecb`

Discussion

17762.	The distance between the origin and the normal to the curve `y=e^(2x)+x^(2)` at `x=0` isA. `2/(sqrt(3))`B. `2/(sqrt(5))`C. `2/(sqrt(7))`D. `1/(sqrt(5))`
Answer» Correct Answer - B `(dy)/(dx)=2e^(2x)+2ximplies((dy)/(dx))_(x=0)=2e^(@)+0=2` Slope of normal `=-1/2` at `x=0,y=1` Equation of normal `y-1=1/2(x-0)` `impliesx+2y-2=0` its distance from `(0,0)=2/(sqrt(5))`

Discussion

17763.	The function `f(x)=1+x(sinx)[cosx], 0ltxlepi//2`, where `[.]` denotes greatest integer functionA. is discontinuous is `(0,pi//2)`B. is strictly decreasing in `(0,pi//2)`C. is strictly increasing in `(0,pi//2)`D. has global maximum value 1
Answer» Correct Answer - D For `0gtxlepi//2,[cosx]=0` Hence `f(x)=1` for all `xepsilon(0,pi//2)`. `f(x)` is continuous on `(0,pi//2)`. This function is neither strictly increasing nor strictly decreasing and its global maximum is 1.

Discussion

17764.	Consider the following statements Statement 1: The range of `log_(1)(1/(1+x^(2)))` is `(-oo,oo)` Statement 2: If `0ltxle1`, then range of `logx epsilon(-oo,0]` Which of the following is correctA. Statement 1: is True, Statement 2 is True , Statement 2 is a correct explanation for statement 1B. Statement 1 is True, Statement 2 is True Statement 2 is NOT a correct explanation for Statement 1C. Statement 1 is True, Statement 2 is FalseD. Statement 1 is False, Statement 2 is True
Answer» Correct Answer - D Range of `1/(1+x^(2))` is `(0,1]` is domain `R`. `:. log(1/(1+x^(2)))epsilon(-oo,0]`

Discussion

17765.	Consider the following statements Statement 1: The range of `log_(1)(1/(1+x^(2)))` is `(-oo,oo)` Statement 2: If `0ltxle1`, then `log_(1)=xepsilon(-oo,0]` Which of the following is correctA. Statement 1: is True, Statement 2 is True , Statement 2 is a correct explanation for statement 1B. Statement 1 is True, Statement 2 is True Statement 2 is NOT a correct explanation for Statement 1C. Statement 1 is True, Statement 2 is FalseD. Statement 1 is False, Statement 2 is True
Answer» Correct Answer - D Range of `1/(1+x^(2))` is `(0,1]` is domain `R`. `:. log(1/(1+x^(2)))epsilon(-oo,0]`

Discussion

17766.	If `y=tan^(-1)x+tan^(-1)(1/x)+cosec^(-1)x,xepsilon(-oo,-1)uu[1,oo)`, then `yepsilon`A. `[-pi,-(pi)/2)uu((pi)/2,pi]`B. `(-(pi)/2,(pi)/2)`C. `(0,pi)`D. `[0,(pi)/2)uu[(pi)/2,pi)`
Answer» Correct Answer - A `y=tan^(-1)x+(tan^(-1))1/x+cosec^(-1)x={((pi)/2+cosec^(-1)x,xgt0),(-(pi)/2+cosec^(-1)x,xlt0):}` if `xgt0`, then `(pi)/2ltylt-pi` if `xlt0`, then `-pileylarr(pi)/2` `:.yepsilon[-pi,-(pi)/2)uu((pi)/2,pi]`

Discussion

17767.	Find the greatest and least value of `(sin^-1x)^3+(cos^-1x)^3.`A. `(pi^(3))/32`B. `(pi^(3))/8`C. `(7pi^(3))/8`D. none of these
Answer» Correct Answer - C We have `(sin^(-1)x)^(3)+(cos^(-1)x)^(3)` `=(sin^(1)x+cos^(-1)x)^(3)-3sin^(-1)xcos^(-1)x(sin^(-1)x+cos^(-1)x)` `=(pi^(3))/8-=3(sin^(-1)xcos^(-1)x)(pi)/2` `=(pi^(3))/8-(3pi)/2x((pi)/2-sin^(-1)x)` `=(pi^(3))/8-(3pi^(2))/4sin^(-1)x+(3pi)/2(sin^(-1)x)^(2)` `=(pi^(3))/8+(3pi)/2[(sin^(-1)x)^(2)-(pi)/2sin^(-1)x]` `=(pi^(3))/8+(3pi)/2[(sin^(-1)x-(pi)/4)^(2)]-(3pi^(3))/32` `=(pi^(3))/32+(3pi)/2(sin^(-1)x-(pi)/4)^(2)` and since `(sin^(-1)x-(pi)/4)^(2)le(-(3pi)/4)^(2)` `:.` The greatest value is `(pi^(3))/32+(9pi^(2))/16xx(3pi)/2=(7pi^(3))/8`

Discussion

17768.	If `sin^(-1)(tan(pi)/4)-sin^(-1)(sqrt(3/y))-(pi)/6=0` and `x^(2)=y` then `x` is equal toA. `2`B. `4`C. `sqrt(2)`D. `sqrt(3)`
Answer» Correct Answer - A `sin^(-1)-sin^(-1)(sqrt(3/y))-(pi)/6=0` `impliessin^(-1)(sqrt(3/y))=(pi)/3implies(sqrt(3))/2=sqrt(3/y)` `impliesy=5impliesx=+-2`

Discussion

17769.	A circle touches the line `y = x` at the point `(2, 2)` and has it centre on y-axis, then square of its radius is
Answer» Correct Answer - 8 A circle touches ………… Equation of a circle touching the line `y = x at (2, 2)` is `(x-2)^(2)+(y-2)^(2)+lambda(x-y) = 0` `i.e. x^(2)y^(2)-(4-lambda)x- (4+lambda)y +8 =0` its centre `((4-lambda)/(2), (4+lambda)/(2))` lies on y-axis `:. (4-lambda)/(2) = 0` i.e. `lambda = 4` `:.` the circle is `x^(2)+y^(2)8y+8=0` `:.` radius `= sqrt(16-8) = sqrt(8)`

Discussion

17770.	Which of the following is not a unit of temperature?(a) Celsius(b) Fahrenheit(c) Therm(d) Rankine
Answer» Right choice is (c) Therm To explain I would say: Them is a unit of energy, 1 therm = 10^5 BTU.

Discussion

17771.	Which of the following is not a unit of pressure?(a) Bar(b) N/m^2(c) Kg/m^2(d) Torr
Answer» Right choice is (c) Kg/m^2 For explanation: Pressure is force per unit area so Kg/m^2 cannot be a unit of pressure.

Discussion

17772.	Which of the following is greatest?(a) 10^oC(b) 10^oR(c) 10^oF(d) 10 K
Answer» Right answer is (a) 10^oC For explanation: 10^oC = 283 K = 50^oF = 510^oR, => 10^oC is greatest.

Discussion

17773.	If change in temperate is 180 degree Rankine, what is the change in temperature in degree Celsius?(a) 100^oC(b) 180^oC(c) 212^oC(d) 273^oC
Answer» The correct choice is (a) 100^oC The explanation is: ∆TR = 1.8∆TC, => Change in temperature = 180/1.8 = 100^oC.

Discussion

17774.	Out of `25` consecutive natural numbers, two numbers can be chosen in `lambda` ways such that their "sum" is divisible by `2`. Then `lambda//36` is.
Answer» Correct Answer - 4 Out of `25` consecutive ……….. `lambda = ^(12)C_(2)+ ^(13)C_(2) = 144`

Discussion

17775.	If change in temperate is 212 degree Fahrenheit, what is the change in temperature in degree Rankine?(a) 100^oR(b) 212^oR(c) 273^oR(d) 460^oR
Answer» The correct answer is (b) 212^oR To explain I would say: Since ∆TR = ∆TF, => 212^oF = 212^oR.

Discussion

17776.	If `x, 2x+ 2, 3x + 3 `are in `G.P. ,` then the fourth term is (A) `27` (B) `-27` (C)`13.5` (D)`-13.5`A. `27`B. `-27`C. `13.5`D. `-13.5`
Answer» Correct Answer - D If `x, 2x+2,3x+3` are …………. Given that `x, 2x+2, 3x+3` are in G.P. Therefore, `(2x+2)^(2)= x(3x+3)` `implies x^(2)+5x+4 = 0` `implies (x+4)(x+1) = 0` `implies x = -1 -4` Now first term `a = x`, second trem `ar = 2(x+1)` `implies r= (2(x+1))/(x)`, then `4^(th)` term `= ar^(3)` `= x[(2(x+1))/(x)]^(-3) = (8)/(x^(2))(x+1)^(3)` Putting `x = -4`, We get `T_(4)= (8)/(16)(-3)^(3) = -(27)/(2)= - 13.5`

Discussion

17777.	What is the 40^oF in degree Rankine?(a) 313^oR(b) 460^oR(c) 500^oR(d) 672^oR
Answer» The correct answer is (c) 500^oR To explain I would say: Temperature = 40 + 460 = 500^oR.

Discussion

17778.	What is the temperature 100^oC in degree Rankine?(a) 100^oR(b) 212^oR(c) 560^oC(d) 672^oC
Answer» Correct answer is (d) 672^oC The explanation is: Temperature = 9(100)/5 + 32 + 460 = 672^oR.

Discussion

17779.	If `x` is real and satisfies `x +2lt sqrt(x +4)`, thenA. `x lt - 2`B. `x gt 0`C. `-3lt x lt 0`D. `-3 lt x lt 4`
Answer» Correct Answer - B If `x` is real and satisfies ……….. Given `x+2 gt sqrt(X +4) implies (x +2)^(2)gt (x+4)` `implies x^(2)+4x+4gt x +4 implies x^(2)+3x gt 0` `implies x(x+3)gt 0 implies x lt - 3 or x gt 0` `implies x gt 0 (x+2` must be positive).

Discussion

17780.	If `alpha` and `beta` are solutions of `sin^2 x + a sin x+b=0` as well as that of `cos^2x + c cosx + d =0` then `sin(alpha + beta) ` is equal toA. `(2bd)/(b^(2)+d^(2))`B. `(a^(2)+c^(2))/(2ac)`C. `(b^(2)+d^(2))/(2bd)`D. `(2ac)/(a^(2)+c^(2))`
Answer» Correct Answer - D If `alpha` and `beta` are ………….. According to the given condition, `sin alpha + sin beta = -a` and `cos alpha+cos beta= -c` . `implies 2 sin. (alpha+beta)/(2)cos.(alpha-beta)/(2)= -a &` `2cos.(alpha+beta)/(2)cos.(alpha-beta)/(2)= -c` `implies tan. (alpha+beta)/(2)= (a)/(c ) implies sin. (alpha + beta)` `(2tan.(alpha+beta)/(2))/(1+tan.^(2)(alpha+beta)/(2)) = (2ac)/(a^(2)+c^(2))`

Discussion

17781.	Let `alpha` and `beta` are roots of `x^(2) - 17x - 6 = 0` with `alpha gt beta, if a_(n) = alpha^(n+2)+beta^(n+2)` for `n ge 5` then the value of `(a_(10)-6a_(8)-a_(9))/(a_(9))`A. `6`B. `16`C. `12`D. `8`
Answer» Correct Answer - B Let `alpha` and `beta` ……….. Let `alpha` and `beta` asre roots of `x^(2)-17x-6=0` `alpha^(2)-17alpha-6=0` `alpha^(n+2)-17alpha^(n+1)-6alpha^(n)=0` `beta^(n+2)-17beta^(n+1)-6beta^(n)=0` By (1) and (2) `a_(n)-17a_(n-1)-6a_(n-2)=0` `a_(10)-17a_(9)-6a_(8) = 0` `a_(10)-6a_(8)-a_(9)=16a_(9)` `implies (a_(10)-6a_(8)-a_(9))/(a_(9)) = 16`

Discussion

17782.	If `x in(1, 30)` and `(1+tan x^(@))(1+tan(x+1)^(@))...(1+tan(x+44)^(@)) = 2^(23)` then value of x isA. `0`B. `1`C. `2`D. `3`
Answer» Correct Answer - B If `x epsilon (1, 30)` and ………… `x = 1` `(1+tan x^(@))(1+tan(x+1)^(@))…. (1+tan(x+44)^(@))ge(1+tan 1^(@))` `(1+tan 2^(@)) ……….. (1+tan 45^(@))` Now `(1+tan1^(@))(1+tan 44^(@))(1+tan2^(@))(tan 43^(@)+1)`……….. using `(1+tan x^(@))(1+tan(45-x^(@)))=2` `(1+tan 1^(@))(1+tan 2^(@))............ (1+tan 45^(@)) = 2^(23)`

Discussion

17783.	Let S=`4/19+44/(19)^2+444/(19)^3+...oo` then find the value of SA. `(38)/(81)`B. `(4)/(19)`C. `(2)/(9)`D. `(36)/(81)`
Answer» Correct Answer - A Let `S =` ………… `S = (4)/(19)+(44)/(19^(2))+(444)/(19^(3))+………..oo` `(S)/(19)=(4)/(19^(2))+(44)/(19^(3))+………oo` Subtracting, we get `S. (18)/(19) = (4)/(19)+(40)/(19^(2))+(400)/(1^(3))+` …………. `=(4)/(19)[1+(10)/(9)+((10)/(9))^(2)+..........]` `= (4)/(19)[(1)/(1-(10)/(19))] = (4)/(9) implies S = (76)/(162) = (38)/(81)`

Discussion

17784.	For the solution of `[x+2]+[x-8]>0`is (`[dot]`is greatest integer function)`[3,oo)`2. `[4,oo)`3. [1,3] 4 . (3,4) 5. RA. `[3, oo)`B. `[4, oo)`C. `[1, 3]`D. `(3,4)`
Answer» Correct Answer - B For x, the solution of ………….. `[x+2]+[x-8]gt 0 implies [x]+2+[x]-8gt0` `implies [x]gt3 implies x epsilon [4, oo)`

Discussion

17785.	Let S=`4/19+44/(19)^2+444/(19)^3+...oo` then find the value of SA. `(38)/(81)`B. `(4)/(19)`C. `(36)/(871)`D. `(4)/(9)`
Answer» Correct Answer - A The sum of the series ……….. `S = (4)/(19)+(44)/(19^(2))+………… oo` `(S)/(19) = (4)/(19^(2))+(44)/(19^(3))+………….oo` `(18S)/(19)= (4)/(19)[1+(10)/(19)+(10^(2))/(19^(2))+………..oo]` `s = (38)/(81)`

Discussion

17786.	The homologue of Ethyl propanoate is :A. Propyl ethanoateB. Methyl butanoateC. Ethyl butanoateD. Isopropyl ethanoate
Answer» Correct Answer - C `underset(("Ethyl propanoate"))(CH_3-CH_2-oversetoverset(O)(\|\|)C-O-CH_2-CH_3) " " & " " underset(("Ethyl butanoate"))(CH_3-CH_2-CH_2-oversetoverset(O)(\|\|)C-O-CH_2-CH_3) `are homologue

Discussion

17787.	Choose the strongest base among the following :A. B. C. D.
Answer» Correct Answer - D Only in (D) the l.p of N atoms is not involved in resonance with benzene ring.

Discussion

17788.	Acidic strength of marked hydrogen of following compound in decreasing order is A. IgtIIgtIIIgtIVB. IIgtIgtIIIgtIVC. IIIgtIIgtIgtIVD. IIgtIIIgtIVgtI
Answer» Correct Answer - B Acidic strength `prop` Stability of conjugate base.

Discussion

17789.	has correct IUPAC name as :A. 3-Carbamoylbenzene-1-carbonitrileB. 3-Cyanobenzene-1-carboxamideC. 3-CyanobenzamideD. 3-Aminocarbonylcyanobenzene
Answer» Correct Answer - B (1)`-oversetoverset(O)(\|\|)C-NH_2`, when attached to a ring, it is named as carboxamide. (2)`-oversetoverser(O)(\|\|)C-NH_2` has higher priority than -C=N (3)-C=N has prefix cyano

Discussion

17790.	Match the order given in column (I) with the property(les) in column (II). `{:("Column I","Column II"),((A)Rb_2CO_3gtK_2CO_3gtNa_2CO_3,(p)"Solubility of salts in water"),((B)SrSO_4gtCaSO_4gtMgSO_4,(q)"Thermal stability of salts"),((C )RbgtKgtNa,(r)"Softness of metals"),((D)BegtMggtCa,(s)"Hydration energy of metals"),(,(t)"Ionisation energy of metals "):}`
Answer» Correct Answer - A-p,q ; B-q ; C-r ; D-s,t (A)Down the group the decrease in the lattice energy is more as compared to that of hydration energy with increase in size of cations.So the solubility order is correct.Similarly the thermal stability of the oxo-salts increases with increase in metallic character.So the thermal stability order is correct. (B)The correct order of solubility is `MgSO_4 gt CaSO_4 gt SrSO_4` as in this case decrease in hydration energy is more as compared to that of lattice energy. The orde of thermal stability is correct, as down the group metallic character increases and thus the thermal stability of oxo-salts increases. (C )Down the group strength of metallic bond decreases Due to this there occurs a decrease in close packing of atoms in crystal lattice from Li to Cs and thus softness increase donw the group. (D)hydration energy `prop 1/ ("size of atom")`So BegtMggtCa is correct order. Ionisation energy `prop 1/("Size of atom")` So BegtMggtCa is correct order.

Discussion

17791.	Based on given information `DeltaG^(@)_(f)(CaO) =- 604.2kJ//mol` and `DeltaG^(@)_(f)(A1_(2)O_(3)) =- 1582kJ//mol`, which of the following is feasible?A. `2Ca +A1_(2)O_(3)rarr2A1+3CaO`B. `3CaO +2A1 rarrA1_(2)O_(3) +3Ca`C. Both `(a)` and `(b)`D. None of the above
Answer» Correct Answer - A `3Ca +A1_(2)O_(3)rarr 2A1 +3CaO` `DeltaG^(@) = 3xxDeltaG^(@) (CaO) - DeltaG^(@) (A1_(2)O_(3))` `= 3xx(-604.2)-(-1582)` `=- 1812 + 1582` `=- 230kJ` `DeltaG^(@)` is negative. Hence, this reaction is feasible.

Discussion

17792.	An isolated system (a) is a specified region where transfer of energy and/or mass take place (b) is a region of constant mass and only energy is allowed to cross the boundaries (c) cannot transfer either energy or mass to or from the surroundings (d) is one in which mass within the system is not necessarily constant (e) none of the above.
Answer» (c) cannot transfer either energy or mass to or from the surroundings

Discussion

17793.	An open system is one in which (a) heat and work cross the boundary of the system, but the mass of the working substance does not (b) mass of working substance crosses the boundary of the system but the heat and work do not (c) both the heat and work as well as mass of the working substances cross the boundary of the system (d) neither the heat and work nor the mass of the working substances cross the boundary of the system.
Answer» (c) both the heat and work as well as mass of the working substances cross the boundary of the system

Discussion

17794.	When two bodies are in thermal equilibrium with a third body they are also in thermal equilibrium with each other. This statement is called (a) Zeroth law of thermodyamics (b) First law of thermodynamics (c) Second law of thermodynamics (d) Kelvin Planck’s law.
Answer» (a) Zeroth law of thermodyamics

Discussion

17795.	In an extensive property of a thermodynamic system (a) extensive heat is transferred (b) extensive work is done (c) extensive energy is utilised (d) all of the above (e) none of the above.
Answer» (e) none of the above.

Discussion

17796.	Which of the following is an intensive property of a thermodynamic system ? (a) Volume (b) Temperature (c) Mass (d) Energy.
Answer» (b) Temperature

Discussion

17797.	A definite area or space where some thermodynamic process takes place is known as (a) thermodynamic system(b) thermodynamic cycle (c) thermodynamic process (d) thermodynamic law.
Answer» (a) thermodynamic system

Discussion

17798.	Which of the following is correct ?A. For a reversible reaction for which `Delta_(f)H = -ve` B. For reversible reaction for which `Delta_(f)H = +ve` C. D. Activation energy of a reaction is a barrier to energy tranfer (KE to PE) between reacting molecules that must be overcome, which is due to need of bonds stretch as well as steric repulsions.
Answer» Correct Answer - D Graph in A is plotted for endothermic reaction and graph in B is plotted for exothermic reactions actually. (C ) `E_(a_(1)) lt E_(a_(2)) lt E_(a_(3))` is correct.

Discussion

17799.	Assertion : Density of `Mg` is more than that of `Ca`. Reason : It is due to the presence of `3d-` orbital.A. If both assertion and reason are true and the reason is the correct explanation of the assertion.B. If both assertion and reason are true but reason is not the correct explanation of the assertion.C. If assertion is true but reason is false.D. If assertion is false but reason is true.
Answer» Correct Answer - C The density of alkaline earth metals decreases from `Be` to `Ca`. Alkaline earth metals have `ns^2` configuration.

Discussion

17800.	One mixing `500 mL` of `10^-6 M Ca^(2+)` ion and `500 mL` of `10^-6 MF^-` ion, no precipitate of `CaF_2` will be obtained. `K_(sp) (CaF_2 = 10^-18)`. If `K_(sp)` is greater than ionic product, a percipitate will develop.A. If both assertion and reason are true and the reason is the correct explanation of the assertion.B. If both assertion and reason are true but reason is not the correct explanation of the assertion.C. If assertion is true but reason is false.D. If assertion is false but reason is true.
Answer» Correct Answer - C `[Ca^(2+)][F^-]^2 = [(500 xx 10^-6)/(100)] xx [(500 xx 10^-6)/(1000)]^2` =`(1)/(8) xx 10^-18 = 0.12 xx 10^-18 lt K_(sp)` Thus, precipitation will not take place.

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Area bounded by Curves

Complex compound `[Cr(NCS)(NH_(3))_(5)][ZnCl_(4)]` will be -A. diamaganetic and shows linkage isomerismB. colourless and diamagneticC. green coloured and diamagneticD. green coloured and shows co-ordination isomerism.

Incorrect order of boiling point is -A. `HF gt HI gt HBr gt HCl`B. `H_(2)O gt H_(2)Te gt H_(2)Se gt H_(2)S`C. `Br_(2) gt Cl_(2) gt F_(2)`D. `CH_(4) gt GeH_(4) gt SiH_(4)`

If `4sin^(-1)x+cos^(-1)x=pi`, then `x` is equal toA. `2/3`B. `1/3`C. `1/2`D. `2`

If `x=9` is the chord of contact of the hyperbola `x^2-y^2=9` then the equation of the corresponding pair of tangents is (A) `9x^2-8y^2+18x-9=0` (B) `9x^2-8y^2-18x+9=0` (C) `9x^2-8y^2-18x-9=0` (D) ` `9x^2-8y^2+18x+9=0`

If `f(x)=sin|x|-e^(|x|)` then at `x=0,f(x)` isA. Continuous but not differentiableB. Neither continuous nor differentiableC. Both continuous and differentiableD. Discontinuous but may be differentiable

The no. of solutions of the equation `a^(f(x)) + g(x)=0` where a>0 , and g(x) has minimum value of 1/2 is :-A. OneB. TwoC. Infinitely manyD. Zero

Angle between diagonals of a parallelogram whose side are represented by `veca=2hati+hatj+hatk` and `vecb=hati-hatj-hatk`A. `cos^(-1)(1/3)`B. `cos^(-1)(1/2)`C. `cos^(-1) (4/9)`D. `cos^(-1)(5/9)`

The distance between the origin and the normal to the curve `y=e^(2x)+x^(2)` at `x=0` isA. `2/(sqrt(3))`B. `2/(sqrt(5))`C. `2/(sqrt(7))`D. `1/(sqrt(5))`

The function `f(x)=1+x(sinx)[cosx], 0ltxlepi//2`, where `[.]` denotes greatest integer functionA. is discontinuous is `(0,pi//2)`B. is strictly decreasing in `(0,pi//2)`C. is strictly increasing in `(0,pi//2)`D. has global maximum value 1

If `y=tan^(-1)x+tan^(-1)(1/x)+cosec^(-1)x,xepsilon(-oo,-1)uu[1,oo)`, then `yepsilon`A. `[-pi,-(pi)/2)uu((pi)/2,pi]`B. `(-(pi)/2,(pi)/2)`C. `(0,pi)`D. `[0,(pi)/2)uu[(pi)/2,pi)`

Find the greatest and least value of `(sin^-1x)^3+(cos^-1x)^3.`A. `(pi^(3))/32`B. `(pi^(3))/8`C. `(7pi^(3))/8`D. none of these

If `sin^(-1)(tan(pi)/4)-sin^(-1)(sqrt(3/y))-(pi)/6=0` and `x^(2)=y` then `x` is equal toA. `2`B. `4`C. `sqrt(2)`D. `sqrt(3)`

A circle touches the line `y = x` at the point `(2, 2)` and has it centre on y-axis, then square of its radius is

Which of the following is not a unit of temperature?(a) Celsius(b) Fahrenheit(c) Therm(d) Rankine

Which of the following is not a unit of pressure?(a) Bar(b) N/m^2(c) Kg/m^2(d) Torr

Which of the following is greatest?(a) 10^oC(b) 10^oR(c) 10^oF(d) 10 K

If change in temperate is 180 degree Rankine, what is the change in temperature in degree Celsius?(a) 100^oC(b) 180^oC(c) 212^oC(d) 273^oC

Out of `25` consecutive natural numbers, two numbers can be chosen in `lambda` ways such that their "sum" is divisible by `2`. Then `lambda//36` is.

If change in temperate is 212 degree Fahrenheit, what is the change in temperature in degree Rankine?(a) 100^oR(b) 212^oR(c) 273^oR(d) 460^oR

If `x, 2x+ 2, 3x + 3 `are in `G.P. ,` then the fourth term is (A) `27` (B) `-27` (C)`13.5` (D)`-13.5`A. `27`B. `-27`C. `13.5`D. `-13.5`

What is the 40^oF in degree Rankine?(a) 313^oR(b) 460^oR(c) 500^oR(d) 672^oR

What is the temperature 100^oC in degree Rankine?(a) 100^oR(b) 212^oR(c) 560^oC(d) 672^oC

If `x` is real and satisfies `x +2lt sqrt(x +4)`, thenA. `x lt - 2`B. `x gt 0`C. `-3lt x lt 0`D. `-3 lt x lt 4`

If `alpha` and `beta` are solutions of `sin^2 x + a sin x+b=0` as well as that of `cos^2x + c cosx + d =0` then `sin(alpha + beta) ` is equal toA. `(2bd)/(b^(2)+d^(2))`B. `(a^(2)+c^(2))/(2ac)`C. `(b^(2)+d^(2))/(2bd)`D. `(2ac)/(a^(2)+c^(2))`

Let `alpha` and `beta` are roots of `x^(2) - 17x - 6 = 0` with `alpha gt beta, if a_(n) = alpha^(n+2)+beta^(n+2)` for `n ge 5` then the value of `(a_(10)-6a_(8)-a_(9))/(a_(9))`A. `6`B. `16`C. `12`D. `8`

If `x in(1, 30)` and `(1+tan x^(@))(1+tan(x+1)^(@))...(1+tan(x+44)^(@)) = 2^(23)` then value of x isA. `0`B. `1`C. `2`D. `3`

Let S=`4/19+44/(19)^2+444/(19)^3+...oo` then find the value of SA. `(38)/(81)`B. `(4)/(19)`C. `(2)/(9)`D. `(36)/(81)`

For the solution of `[x+2]+[x-8]>0`is (`[dot]`is greatest integer function)`[3,oo)`2. `[4,oo)`3. [1,3] 4 . (3,4) 5. RA. `[3, oo)`B. `[4, oo)`C. `[1, 3]`D. `(3,4)`

Let S=`4/19+44/(19)^2+444/(19)^3+...oo` then find the value of SA. `(38)/(81)`B. `(4)/(19)`C. `(36)/(871)`D. `(4)/(9)`

The homologue of Ethyl propanoate is :A. Propyl ethanoateB. Methyl butanoateC. Ethyl butanoateD. Isopropyl ethanoate

Choose the strongest base among the following :A. B. C. D.

Acidic strength of marked hydrogen of following compound in decreasing order is A. IgtIIgtIIIgtIVB. IIgtIgtIIIgtIVC. IIIgtIIgtIgtIVD. IIgtIIIgtIVgtI

has correct IUPAC name as :A. 3-Carbamoylbenzene-1-carbonitrileB. 3-Cyanobenzene-1-carboxamideC. 3-CyanobenzamideD. 3-Aminocarbonylcyanobenzene

Based on given information `DeltaG^(@)_(f)(CaO) =- 604.2kJ//mol` and `DeltaG^(@)_(f)(A1_(2)O_(3)) =- 1582kJ//mol`, which of the following is feasible?A. `2Ca +A1_(2)O_(3)rarr2A1+3CaO`B. `3CaO +2A1 rarrA1_(2)O_(3) +3Ca`C. Both `(a)` and `(b)`D. None of the above

When two bodies are in thermal equilibrium with a third body they are also in thermal equilibrium with each other. This statement is called (a) Zeroth law of thermodyamics (b) First law of thermodynamics (c) Second law of thermodynamics (d) Kelvin Planck’s law.

In an extensive property of a thermodynamic system (a) extensive heat is transferred (b) extensive work is done (c) extensive energy is utilised (d) all of the above (e) none of the above.

Which of the following is an intensive property of a thermodynamic system ? (a) Volume (b) Temperature (c) Mass (d) Energy.

A definite area or space where some thermodynamic process takes place is known as (a) thermodynamic system(b) thermodynamic cycle (c) thermodynamic process (d) thermodynamic law.