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501.

The INCORRECT statement isA. `Cu^(2+) and Ni^(2+)` ions give black precipitate with `H_(2)S` in presence of HCl solution.B. `Cu^(2+)` ions gives chocolate coloured precipitate with potassium ferrocyanide solution.C. Ferric ions gives blood red colour with potassium thiocyanate.D. `Cu^(2+)` salts give red coloured borax bead test in reducing flame.

Answer» Correct Answer - A
502.

Which of the following is incorrect?A. `wedge_m ^@ NaCl - wedge_m ^@ NaBr = wedge_m ^@ KCl - wedge_m^@ KBr`B. `wedge_m ^@ H_2O = wedge_m ^@ HCl + wedge_m ^@ NaOH - wedge_m^@ NaCl`C. `wedge_m ^@ NaI - wedge_m ^@ NaBr = wedge_m ^@ NaBr - wedge_m^@ KBr`D. `wedge_m ^@ NaCl - wedge_m ^@ KCl = wedge_m ^@ NaBr - wedge_m^@ KBr`

Answer» Correct Answer - C
503.

NaOH (Hot + Conc.) + `Cl_2` rarr A + other products and `Ca(OH)_2`(Cold and dilute) + `Cl_2` rarr B + other products . A and B are respectively:A. `NaClO_3, Ca(OCl)_2`B. `NaClO_3, Ca(ClO_3)_2`C. `NaCl, Ca(ClO_3)_2`D. `NaClO, Ca(ClO_3)_2`

Answer» Correct Answer - A
504.

Which of the following species is not paramagnetic?A. `CO`B. `O_(2)`C. `B_(2)`D. `NO`

Answer» Correct Answer - A
505.

Which of the following compounds will not undergo Friedel`-` Crafts reaction easily ?A. B. C. D.

Answer» Correct Answer - A
506.

Which of the following is paramagnetic ?A. COB. `NO^(+)`C. `O_(2)^(2-)`D. `B_(2)`

Answer» Correct Answer - D
507.

The rate of a reaction doubles when its temperature changes form `300 K` to `310 K`. Activation energy of such a reaction will be: `(R = 8.314 JK^(-1) mol^(-1) and log 2 = 0.301)`A. 4.92 KB. 9.84 KC. 19.67 KD. 2.45 K

Answer» Correct Answer - A
508.

The rate of a reaction doubles when its temperature changes form `300 K` to `310 K`. Activation energy of such a reaction will be: `(R = 8.314 JK^(-1) mol^(-1) and log 2 = 0.301)`A. `48.6 KJ mol^(-1)`B. `58.5 KJ mol^(-1)`C. `60.5 KJ mol^(-1)`D. `53.6 KJ mol^(-1)`

Answer» Correct Answer - D
509.

Two moles of helium are mixed with n moles of hydrogen. If `(Cp)/(Cv)=(3)/(2)` for the mixture, then the value of n is :A. 1B. 2C. 3D. `3//2`

Answer» Correct Answer - B
510.

Two moles of helium gas are taken over the cycle ABCDA, as shown in the P-T diagram The work done on the gas in taking it from D to A is :A. `-414 R`B. `+ 414 R`C. `-690 R`D. `+ 690 R`

Answer» Correct Answer - A
511.

Two moles of helium gas are taken over the cycle ABCDA, as shown in the P-T diagram The net work done on the gas in the cycle ABCDA is :A. zeroB. 276 RC. 1076 RD. 1904 R

Answer» Correct Answer - B
512.

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure `(C_(p))` and at constant volume `(C_(v))` isA. `(7)/(5)`B. 6C. `(7)/(2)`D. `(5)/(2)`

Answer» Correct Answer - A
513.

Two wires `W_(1) "and"W_(2)` have the same radius r and respective densities `p_(1) "and" p_(2)` such that `p_(2) = 4p_(1).` They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept udner tension T. The point O is midway between the two bridges. When a stationary waves is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in `W_(1) "to" W_(2)` is- A. `4:1`B. `1:2`C. `1:1`D. `1:3`

Answer» Correct Answer - B
514.

Two wires `W_(1) "and"W_(2)` have the same radius r and respective densities `p_(1) "and" p_(2)` such that `p_(2) = 4p_(1).` They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept udner tension T. The point O is midway between the two bridges. When a stationary waves is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in `W_(1) "to" W_(2)` is- A. `4:1`B. `1: 2`C. `1:1`D. `1:3`

Answer» Correct Answer - B
515.

Let the refractive index of a denser medium with respect to a rarer medium be `n_(12)` and its critical angle be `theta_(c)`. At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is `90^(@)`, Angle A given by -A. `tan^(-1)(sin theta_(c))`B. `(1)/(tan^(-1)(sintheta_(c)))`C. `cos^(-1)(sin theta_(C))`D. `(1)/(cos^(-1)(sintheta_(c)))`

Answer» Correct Answer - A
516.

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is `10 s^(-1)` At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is `(pi)/(4)`A. `500 m//s^(2)`B. `750 sqrt(2) m//s^(2)`C. `750 m//s^(2)`D. `500 sqrt(2) m//s^(2)`

Answer» Correct Answer - D
517.

Let the refractive index of a denser medium with respect to a rarer medium be `n_(12)` and its critical angle be `theta_(c)`. At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is `90^(@)`, Angle A given by -A. `"tan"^(-1)("sin" theta_(c))`B. `(1)/("tan"^(-1) ("sin"theta_(c)))`C. `"cos"^(-1) ("sin"theta_(c))`D. `(1)/("cos"^(-1)("sin"theta_(c)))`

Answer» Correct Answer - A
518.

The charge on a capacitor plate in a cirucuit, as a function of time,is shown in the figure : What is the value of current at `t=4` s ?A. zeroB. `3muA`C. `2muA`D. `1.5muA`

Answer» Correct Answer - A
519.

The mean intensity of radiation on the surface of the Sun is about `10^(s)W//m^2`. The rms value of the corresponding magnetic field is closed to :A. 1TB. `10^2T`C. `10^(-2)T`D. `10^(-4)T`

Answer» Correct Answer - A
520.

A parallel plate capicitaor with plates of area `1m^2` each, are at a separation of `0.1`m. If the electric field between the plates is 100 `N//C`, the magnitude of charge on each plate is : (Take `epsilon=8.85xx10^-12(C^2)/(N-m^2)`)A. `7.85xx10^(-10)C`B. `6.85xx10^(-10)C`C. `8.85xx10^(-10)C`D. `9.85xx10^(-10)C`

Answer» Correct Answer - A
521.

The charge on a capacitor plate in a cirucuit, as a function of time,is shown in the figure : What is the value of current at `t=4` s ?A. zeroB. `3muA`C. `2muA`D. `1.5muA`

Answer» Correct Answer - A
522.

The maximum velocity of electrons emitted from a metal surface is v. What would be the maximum velocity if the frequency of incident lightis increased by a factor of 4?A. more than `sqrt(3)` vB. equal to `sqrt(3)` vC. vD. less than `sqrt(3)` v

Answer» Correct Answer - B
523.

Identify the semiconductor devices whose characteristics are given below, in the order (a), (b), (c), (d) : A. Zener diode, Simple diode, Light dependent resistance, Solar cellB. Solar cell, Light dependent resistance, Zener diode, Simple diodeC. Zener diode, Solar cell, Simple diode, Light dependent resistanceD. Simple diode, Zener diode, Solar cell, Light dependent resistance

Answer» Correct Answer - D
524.

What is the conductivity of a semiconductor sample having electron concentration of `5 xx 10^(18) m^(-3)` hole concentration of `5 xx 10^(19) m^(-3)`, electron mobility of `2.0 m^(2) V^(-1) s^(-1)` and hole mobility of `0.01 m^(2) V^(-1) s^(-1)?` (Take charge of electron as `1.6 xx 10^(-19)C)`A. `1.83 (Omega -m)^(-1)`B. `1.68 (Omega-m)^(-1)`C. `1.20 (Omega-m)^(-1)`D. `0.59 (W-m)^(-1)`

Answer» Correct Answer - B
525.

What is the conductivity of a semiconductor sample having electron concentration of `5 xx 10^(18) m^(-3)` hole concentration of `5 xx 10^(19) m^(-3)`, electron mobility of `2.0 m^(2) V^(-1) s^(-1)` and hole mobility of `0.01 m^(2) V^(-1) s^(-1)?` (Take charge of electron as `1.6 xx 10^(-19)C)`A. `1.83 (Omega-m)^(-1)`B. `1.68 (Omega-m)^(-1)`C. `1.20 (Omega-m)^(-1)`D. `0.59 (W-m)^(-1)`

Answer» Correct Answer - B
526.

The V-I characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is A. 100B. `10^(6)`C. `10^(-6)`D. 10

Answer» Correct Answer - C
527.

The V-I characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is A. 100B. `10^(6)`C. `10^(-6)`D. `10`

Answer» Correct Answer - C
528.

A very small circular loop of radius a is initially (at t = 0) coplanar and concentric with a much larger fixed circular loop of radius b. A constant current I flows in the larger loop. The smaller loop is rotated with a constant angular speed `omega` about the common diameter. The emf induced in the smaller loop as a function of time t isA. `pi mu_(0)I_(0) (a^(2))/(b)omega "sin"(omegat)`B. `(pi mu_(0) I_(0))/(2) * (a^(2))/(b)omega"cos"(omega t)`C. `(pi mu_(0) I_(0)b^(2))/(a) omega"cos"(omega t)`D. `(pi mu_(0) I_(0))/(2) (a^(2))/(b) omega "sin" (omega t)`

Answer» Correct Answer - D
529.

Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?A. B. C. D.

Answer» Correct Answer - C
530.

A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current `I=I_(0)cos(omegat)`. The emf induced in the smaller inner loop is nearly ?A. `pimu_(0)I_(0)(a^(2))/(b)omegasin(omegat)`B. `(pimu_(0)I_(0))/(2)*(a^(2))/(b)omegacos(omegat)`C. `(pimu_(0)I_(0)b^(2))/(a)omegacos(omegat)`D. `(pimu_(0)I_(0))/(2)*(a^(2))/(b)omegasin(omegat)`

Answer» Correct Answer - D
531.

A 9 V battery with internal resistance of `0.5 Omega` is connected across an infinite network as shown in the figure. All ammeters `A_(1), A_(2), A_(3)` and voltmeter V are ideal.A. Reading of `A_(1)` is 18 AB. Reading of V is 9 VC. Reading of V is 7 VD. Reading of `A_(1)` is 2A

Answer» Correct Answer - D
532.

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is `10 s^(-1)` At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is `(pi)/(4)`A. 500` m//s^(2)`B. `750 sqrt(2) m//s^(2)`C. `750 m//s^(2)`D. `500sqrt(2) m//s^(2)`

Answer» Correct Answer - D
533.

Consider a loop ABCDEFA. With coordinates A (0, 0, 0), B(5, 0, 0), C(5, 5, 0), D(0, 5, 0) E(0, 5, 5) and F(0, 0, 5). Find magnetic flux through loop due to magnetic field ` vecB = 3 hati+4 hatk`

Answer» Correct Answer - 175
534.

Among the following, the essential amino acid is :A. ValineB. AlanineC. SerineD. Aspartic acid

Answer» Correct Answer - A
535.

A particle is moving with velocity ` vecv = k( y hat(i) + x hat(j)) `, where `k` is a constant . The genergal equation for its path isA. `y=x^(2)+"constant"`B. `y^(2)=x+"constant"`C. `xy="constant"`D. `y^(2)=x^(2)+"constant"`

Answer» Correct Answer - D
536.

The chloride that CANNOt get hydrolysed is :A. `PbCl_4`B. `"CC"l_4`C. `SnCl_4`D. `SnCl_4`

Answer» Correct Answer - C::D
537.

The area of triangle formed by tangent and normal at point `(sqrt(3), 1)` of the curve `x^(2) +y^(2) = 4` and x-axis is :A. `(4)/(sqrt(3))`B. `(2)/(sqrt(3))`C. `(8)/(sqrt(3))`D. `(5)/(sqrt(3))`

Answer» Correct Answer - B
538.

Negation of statement `-svv(-r^^s)` isA. `s^^r`B. `svvr`C. `-stor`D. `-s^^r`

Answer» Correct Answer - A
539.

Which of the following is not a tautology.A. `p rarr (p vv q)`B. `(p vv q) rarr p`C. `(p vv q) rarr (p wedge (~ q))`D. `(p vv ~p)`

Answer» Correct Answer - C
540.

Find the negation of `pv(-p^q)`A. `-p^~q`B. `~p^~q`C. p~qD. `p^q`

Answer» Correct Answer - A
541.

If the slope of tangent at point `(x, y)` of curve `y = f(x)` is given by `(2y)/(x^(2))`. If this curve passes through the centre of the circle `x^(2) + y^(2) - 2x - 2y = 0`. Then the curve is :A. `x l n(y) = 2(x-1)`B. `x^(2) l n(y) = 2(x-1)`C. `x^(2) l n(y) = (x-1)`D. `x l n(y) = (x-1)`

Answer» Correct Answer - A
542.

A plane passes through the point `(0,-1,0)` and `(0,0,1)` and makes an angle of `(pi)/(4)` with the plane `y-z=0` then the point which satisfies the desired plane isA. (sqrt(2),-1,4`B. `(sqrt(2),1,2)`C. `(sqrt(2),1,4`D. `(sqrt(2),2,4`

Answer» Correct Answer - D
543.

A curve `f(x)=x^(2)+ax-b` pass through `p(1,-5)` and tangent to `f(x)` at point `p` is perpendicular to `x-y+5=0` then which of the following point will lie on curve ?A. `(2-2)`B. `(2-1)`C. `2,-1)`D. `(-2,2)`

Answer» Correct Answer - D
544.

Solve : `tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x`

Answer» `tan^-1(x-1)+tan^-1x+tan^-1(x+1) = tan^-1(3x)`
`=>tan^-1(x-1)+tan^-1x = tan^-1(3x)-tan^-1(x+1)`
`=>tan^-1((x-1+x)/(1-x(x-1))) =tan^-1((3x-(x+1))/(1+3x(x+1)))`
`=>tan^-1((2x-1)/(1+x-x^2)) =tan^-1((2x-1)/(1+3x+3x^2))`
`=>(2x-1)/(1+x-x^2) =(2x-1)/(1+3x+3x^2)`
`=>(2x-1)/(1+x-x^2) - (2x-1)/(1+3x+3x^2) = 0`
`=>(2x-1)(1/(1+x-x^2) - 1/(1+3x+3x^2) )= 0`
`=>(2x-1)((1+3x+3x^2-1-x+x^2)/((1+x-x^2)(1+3x+3x^2) ))= 0`
`=>(2x-1)((4x^2+2x)/((1+x-x^2)(1+3x+3x^2) ))= 0`
`=>2x(2x-1)(2x+1)= 0`
`:. x = 0 and x = +-1/2`
545.

The equation of tangent to the parabola `y^2 = 9x`, which pass through the point (4, 10) is

Answer» Equation of a tangent to a parabola is given by ,
`y = mx+a/m->(1)`
In the given parabola, `y^2 = 9x`,
`4a = 9=> a = 9/4`
Putting value of `a` in (1),
`y = mx+9/(4m)->(2)`
As the given tangent is passing through point `(4,10)`,
`:. 10 = 4m+9/(4m)`
`=>16m^2-40m + 9 = 0`
`=>16m^2-36m-4m+9 = 0`
`=>4m(4m-9)-1(4m-9) = 0`
`=>(4m-9)(4m-1/4) = 0`
`=> m = 9/4 and m = 1/4`
When `m = 9/4`, required equation will be,
`y = 9/4x+1 => 4y = 9x+4`
When `m = 1/4`, required equation will be,
`y = 1/4x+9 => 4y = x+36`
546.

If `sin^(-1)x+sin^(-1)y+sin^(-1)z=pi`, show that `x^4+y^4+z^4+4x^2y^2z^2=2(x^2y^2+y^2z^2+z^2x^2)`

Answer» `sin^-1x+sin^-1y +sin^-1z = pi`
`=> sin^-1x+sin^-1y = pi - sin^-1z`
`=> sin^-1(xsqrt(1-y^2)+ysqrt(1-x^2)) = pi-sin^-1z`
Taking sin both sides,
`=> sin(sin^-1(xsqrt(1-y^2)+ysqrt(1-x^2))) = sin(pi- sin^-1z)`
`=> xsqrt(1-y^2)+ysqrt(1-x^2) =z`
`=> xsqrt(1-y^2) =z - ysqrt(1-x^2)`
Taking square both sides,
`=>x^2(1-y^2) = z^2+y^2(1-x^2)-2yzsqrt(1-x^2)`
`=>x^2-x^2y^2 = z^2+y^2-x^2y^2 - 2yzsqrt(1-x^2)`
`=>x^2-y^2-z^2 = -2yzsqrt(1-x^2)`
Again squaring both sides,
`=>(x^2-y^2-z^2)^2 = 4y^2z^2(1-x^2)`
`=>x^2+y^4+z^4+2y^2z^2-2x^2y^2-2x^2z^2 = 4y^2z^2-4x^2y^2z^2`
`=>x^2+y^4+z^4+4x^2y^2z^2 = 2(x^2y^2+y^2z^2+z^2x^2)`
547.

`int_0^((pi)/2) cos^5xsin^4x` dx

Answer» `I = int_(pi/2)^0 cos^5x sin^4x dx`
`=>I = int_(pi/2)^0 cos^4x sin^4xcosx dx`
`=>I = int_(pi/2)^0 (1-sin^2x)^2 sin^4xcosx dx`
Let `sinx = t`, then, `cosxdx = dt`
Then, our integral becomes,
`=> I = int_0^1 (1-t^2)^2t^4dt`
`=> I = int_0^1 (1+t^4-2t^2)t^4dt`
`=> I = int_0^1 (t^4+t^8-2t^6)dt`
`=>I = [t^5/5+t^9/9-(2t^7)/7]_0^1`
`=>I = (1/5+1/9-2/7)-(0+0-0) = (63+35-90)/315`
`=> I = 8/315`
548.

Which of the following is not a carbonate ore?A. CalamineB. SideriteC. BauxiteD. Malachite

Answer» Correct Answer - C
549.

Which of the following statements is//are correct? I. `B_(2)O_(3)` is an acidic oxide II. `Ga_(2)O_(3)` and `Al_(2)O_(3)` are amphoteric oxides. III. `In_(2)O_(3)` and `tl_(2)O_(3)` are basic oxides.A. `I,II,III`B. `I,II`C. `II,III`D. `I,III`

Answer» Correct Answer - A
550.

Among the following substituted silanes, the one which will give rise to cross `` linkes silicons polymer on hydrolysis isA. `R_(4)Si`B. `RSiCl_(3)`C. `R_(2)SiCl_(2)`D. `R_(3)SiCl`

Answer» Correct Answer - B