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3 values
c8909584b1b54f5b83911370b3edd471
[ { "role": "user", "content": "A ball is thrown vertically upwards with a speed of 10 $ m{ s }^{ -1 } $ from the top of a tower 200 m high and another is thrown vertically downwards with the same speed simultaneously . The time difference between them in reaching the ground in seconds (g= 10 $ m{ s }^{ -2 } ...
H
Physics
dd890a4e8d144bbf8f40086359eb621a
[ { "role": "user", "content": "If separate samples of argon, methane, nitrogen and carbon dioxide, all at the same initial temperature and pressure and expanded adiabatically reversibally to double their origin volumes, then which one of these gases will have high temperature as final temperature.\n\n(A) Nit...
B
Physics
a303383177094689a66868bc5b5537f9
[ { "role": "user", "content": "What is the CAS number of alginate?\n\n(A) 9005-32-9\n(B) 9005-32-4\n(C) 9005-32-1\n(D) 9005-32-0\n(E) 9005-32-3\n(F) 9005-32-2\n(G) 9005-32-8\n(H) 9005-32-5\n(I) 9005-32-7\n(J) 9005-32-6\n\nPlease write your final answer in the form of \\boxed{A}, \\boxed{B}, \\boxed{C}, \\box...
I
Chemistry
a42adf124b7b4bf0844317bfa07e8e8c
[ { "role": "user", "content": "Students in a physics class are studying how the angle at which a projectile is launched on level ground affects the projectile's hang time and horizontal range. Hang time can be calculated using the formula $t=\\displaystyle{2v\\cdot \\sin(\\theta)}{g}$, where t is the hang ti...
E
Physics
e513def89f6d4a648b76de1642078b9a
[ { "role": "user", "content": "What is the shear modulus of selenium in gigapascals?\n\n(A) 3.73\n(B) 3.7\n(C) 3.5\n(D) 3.75\n(E) 3.72\n(F) 3.78\n(G) 3.65\n(H) 3.9\n(I) 3.6\n(J) 3.8\n\nPlease write your final answer in the form of \\boxed{A}, \\boxed{B}, \\boxed{C}, \\boxed{D}, \\boxed{E}, \\boxed{F}, \\boxe...
B
Chemistry
d7fb6217a76f4764bfbfb2b7f4be6a31
[ { "role": "user", "content": "Consider the following two statements A and B and identify the correct choice.A) When a body is rotated along a vertical circle with uniform speed then the sum of its kinetic energy and potential energy is constant at all positionsB) To make a body to move along a vertical circ...
D
Physics
44ac16f2d42145ffacd4d58ce75749d7
[ { "role": "user", "content": "The spin Hall effect of photons produces a self-selection split on the order of ( ) under general conditions, which is a subtle physical effect.\n\n(A) millimeter\n(B) angstrom\n(C) micrometer\n(D) femtometer\n(E) nanometer\n(F) picometer\n\nPlease write your final answer in th...
E
Physics
6ebc54a91dd54017b802b83a86be8e0d
[ { "role": "user", "content": "After n generations in a 14N culture medium, how many double-stranded DNA molecules contain only 14N, if a double-stranded DNA fragment was initially labeled with 15N isotope?\n\n(A) 2^(n-1)-1\n(B) 2^n+2\n(C) 2^(n-1)\n(D) 2^n-1\n(E) 2^n-2\n(F) 2^n+1\n(G) 2^(n-1)-2\n(H) 2^(n-2)\...
E
Biology
0908602b64e24ead9813a8e398974ac3
[ { "role": "user", "content": "What is the molar mass of iron pentacarbonyl in g/mol?\n\n(A) 195.90\n(B) 195.80\n(C) 197.90\n(D) 196.90\n(E) 194.90\n(F) 196.80\n(G) 193.90\n(H) 195.89\n(I) 195.85\n(J) 195.88\n\nPlease write your final answer in the form of \\boxed{A}, \\boxed{B}, \\boxed{C}, \\boxed{D}, \\bo...
A
Chemistry
a3c43a8d066445cdaff4a4dfeb051593
[ { "role": "user", "content": "A photon rocket travels at a speed of 0.96c relative to Earth, with a length of 100m. A light pulse travels from the tail to the head of the rocket. The spatial distance that the Earth observer sees the light pulse travel is\n\n(A) 698m\n(B) 54m\n(C) 695m\n(D) 690m\n(E) 700m\n(...
E
Physics
1dca35fb6f844bc5988bbe13861a9a0f
[ { "role": "user", "content": "Who is the chief editor of the 26th volume on invertebrates in the 'Fauna Sinica'?\n\n(A) Nan Xiangchen\n(B) Ou Yangke\n(C) Yue Xinliang\n(D) Xiao Ranzhou\n(E) Zheng Shouyi\n(F) Zi Qiangwu\n(G) Meng Diezhang\n(H) Jing Yisheng\n(I) Shan Yucao\n(J) Qiu Rangu\n\nPlease write your ...
E
Biology
bbcef54004d74b4e864d95297865ce43
[ { "role": "user", "content": "Six forces lying in a plane and forming angles of $60^{0}$ relative to one another are applied to the center of a homogeneous sphere with a mass $m= 6 kg$. These forces are radially outward and consecutively $1N, 2N, 3N, 4N, 5N$ and $6N$. The acceleration of the sphere is:\n\n(...
J
Physics
f23fab62446640bc8f738d659a34cf0d
[ { "role": "user", "content": "10 g of ice cubes at $0^o C$ are released in a tumbler (water equivalent 55 g) at $40^o C$. If negligible heat is taken from surroundings, temperature of water in the tumbler becomes nearly ($L = 80 cal g^{-1}$)\n\n(A) $$31^oC$$\n(B) $$23^oC$$\n(C) $$21.5^oC$$\n(D) $$21^oC$$\n(...
C
Physics
0837f9b9c7c740b0a1d21e3219727f98
[ { "role": "user", "content": "In what pH range will a $1\\times10^{-4}$ M solution of an indicator will $K_{b}$ (indicator)$=1\\times10^{-11}$ change colour?\n\n(A) $$9.0 \\pm 1$$\n(B) $$11.0\\pm 1$$\n(C) $$8.5 \\pm 1$$\n(D) $$6.5\\pm 1$$\n(E) $$5.5\\pm 1$$\n(F) $$7.5 \\pm 1$$\n(G) $$6.0\\pm 1$$\n(H) $$3.0\...
H
Chemistry
3cc95dd1f3554c9a91d7e7a91dcb525e
[ { "role": "user", "content": "A proton is fired from origin with velocity $\\overrightarrow{v}=v_0\\hat {j}+v_0\\hat{k}$ in a uniform magnetic field $\\overrightarrow{B}=B_0\\hat{j}$. In the subsequent motion of the proton\n\n(A) its $x-$ and $z-$coordinate cannot be zero at the same time\n(B) its $x-$coord...
B
Physics
3ccd08b1693b45dfaf656e92b9dd13ac
[ { "role": "user", "content": "The removal of type I self-splicing introns requires ( ).\n\n(A) catalysis by a spliceosome\n(B) initiation of splicing by a free guanosine\n(C) completion by two transesterification reactions\n(D) completion by one transesterification reaction\n(E) common in the processing of ...
C
Biology
3637edda3f7543a99120117183b0a834
[ { "role": "user", "content": "The source producing sound and an observer both are moving along the direction of propagation of sound waves. If the respective velocities of sound, source and an observer are $v, v_s$ and $v_0$, then the apparent frequency heard by the observer will be (n = frequency of sound)...
G
Physics
017f8bd35a2e439d8da15005c135fd9d
[ { "role": "user", "content": "Number of electrons lost during electrolysis of $0.14g$ of $N^{-3}$ is-($N_0$=Avagadro number)\n\n(A) 0.0075\\,N_0\n(B) 0.02\\,N_0\n(C) $$0.015\\,N_0$$\n(D) 0.005\\,N_0\n(E) $$0.03\\,N_0$$\n(F) 0.01\\,N_0\n(G) $$\\dfrac{0.01}{2\\,N_0}$$\n(H) $$0.03$$\n(I) 0.025\\,N_0\n\nPlease ...
E
Chemistry
1cee752ddde645029bc7ea6e2a621acf
[ { "role": "user", "content": "Student-A: at maximum extension $ mv^\\prime(l_0+\\Delta\\ell)=mv_0\\ell_0 $\nStudent-B: at maximum extension $ k\\Delta\\ell=\\dfrac{mv^{\\prime2}}{\\ell_0+\\Delta\\ell}  \n$.\nStudent-C: $ \\dfrac {1}{2} mv_0^2=\\dfrac{1}{2}mv^\\prime{2}+\\dfrac{1}{2}k\\Delta\\ell^2 $\nwhere ...
G
Physics
cff2b50e6e14418fbf03aabc2b5c33fc
[ { "role": "user", "content": "A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure $P_0$, volume $V_0$ and temperature $T_0$. If the gas mixture is adiabatically compressed to a volume $V_0/4$, then the correct statement(s) is/are,\n(Given $2^{...
C
Physics
530a6c1b54cb409c8785941fb637e814
[ { "role": "user", "content": "A reversible adiabatic path on a P- V diagram foran ideal gas passes through state A where P = 0.7$\\times $ ${ 10 }^{ 2  }$ N/${ m }^{ -2 }$ and v=0.0049 $ { m }^{ 3  }$, The ratio of specific heat of the gas is 1.4 , The slop of patch at A is:\n\n(A) $$-2.0\\times{ 10 }^{ 7\\...
A
Physics
19a453d8b3ab471684268017ff86683d
[ { "role": "user", "content": "Consider the reaction of extraction of gold from its ore:\n$$ Au(s)+2CN^{-}(aq)+\\dfrac{1}{4}O_{2}(g)+\\dfrac{1}{2}$$\n$$ H_{2} O(1)\\rightarrow Au(CN)_{2}^{-}(aq)+OH^{-}(aq)$$\nUse the following data to calculate $ \\triangle G^{0}$ for the above reaction.\n$$ K_{f}[Au(CN)_{2}...
H
Chemistry
4ad6b55f60544437882c474ae21b066d
[ { "role": "user", "content": "The compound that produces 2 signals in the range of δ0~70 in the 13CNMR spectrum and 2 signals in the range of δ0~5 in the 1HNMR spectrum (the downfield signal is a triplet) is ( )\n\n(A) 1,2-dichloropropane\n(B) 1,1,2-trichloropropane\n(C) 1,2,3-trichloropropane\n(D) 1,3-dich...
D
Chemistry
48844c3675ed43e6b224141f44516e03
[ { "role": "user", "content": "A body of mass $4.9 kg$ hangs from a spring and oscillates with a period $0.5 s$. On the removal of the body, the spring is shortened by (Take $g =10 ms^{-2}  ,\\pi^2 =10)$\n\n(A) $$6.25cm$$\n(B) 0.64cm\n(C) 6.35cm\n(D) $$0.63cm$$\n(E) $$63cm$$\n(F) $$0.625cm$$\n(G) 0.635cm\n(H...
A
Physics
8e1a40f41f8646cb8e929195d1465fde
[ { "role": "user", "content": "Two litre solution of buffer mixture containing $1.0$ M $NaH_2PO_4$ and $1.0$ M $Na_2HPO_4$ is placed in two compartments (1 L in each) of an electrolytic cell. The platinum electrodes are inserted in each compartment and 1.25 A current is passed for 965 min. Assuming electroly...
F
Chemistry
542d66872a3744ebbe3b7edb81159b87
[ { "role": "user", "content": "A charged particle having some mass is resting in equilibrium at a height H above the centre of a unifomly charged non-conducting horizontal ring of radius R. The force of gravity acts downwards. The equilibrium of the particle will be stable:\n\n(A) only if \\( \\mathrm{H} < \...
G
Physics
3644c3e13efa4c4d90ae3a93e640b5c7
[ { "role": "user", "content": "The equilibrium between gaseous isomers A, B and C can be represented as:$ A(g)  \\leftrightharpoons B(g) ; K_1 = ? $$ B(g) \\leftrightharpoons C(g) ; K_2 = 0.4 $$ C(g) \\leftrightharpoons A(g) ; K_3 = 0.6 $ If one mole of A is taken in closed vessel of volume 1 L, then\n\n(A) ...
G
Chemistry
b993a45ae169466ba0435c7ed77834a5
[ { "role": "user", "content": "Two particles, each of mass $'m'$ are attached to the two ends of a light string of length $L$, which passes through a hole at the centre of a smooth table. One particle describes a circular path on the table with angular velocity $\\omega _{1}$, and the other describes a conic...
D
Physics
b92162c2e99e42e0bb7b8204f88151df
[ { "role": "user", "content": "The equivalent weight of $CuSO_{4}$ (mol. wt. $=M$) in the following reaction is$5CuS + 8KMnO_4 +12 H_2SO_4 \\rightarrow 5CuSO_4 +4 K_2SO_{4} + 8MnSO_4 +12H_2O $\n\n(A) \\(\\dfrac{M}{7} \\)\n(B) $$\\dfrac {M}{6}$$\n(C) $$\\dfrac {M}{2}$$\n(D) \\dfrac{M}{5}\n(E) \\dfrac{M}{12}\n...
F
Chemistry
8050e578b035411a9adf3dc0d955a26c
[ { "role": "user", "content": "Given the following cell at $25^{\\circ}C$. What will be the potential of the cell ? Given $pK_{a}$ of $CH_{3}COOH\\, =\\, 4.74$ :$Pt \\begin{vmatrix} H_2 \\(1 atm) \\end{vmatrix}\\left.\\begin{matrix} CH_3COOH \\(10^{-3} M) \\end{matrix}\\right|\\begin{vmatrix}NaOH \\ (10^{-3}...
C
Chemistry
ce90fcbbceb347d5a4ee8c0c2cbafd9c
[ { "role": "user", "content": "In a thermodynamic process helium gas obeys the law $\\displaystyle \\frac { T }{ { P }^{ { 2 }/{ 5 } } } $ = constant. The heat given to a gas when temperature of m moles of $\\displaystyle He$ is raised from $\\displaystyle T$ to $2T$ is:\n\n(A) 4RT\n(B) 8RT\n(C) 6RT\n(D) 2RT...
J
Physics
6f11304297e6469db8831882293cadec
[ { "role": "user", "content": "Arrange the following resonating structure according to their contribution towards resonance hybrid?\n$$(a)\\ { CH }_{ 2 }=\\overset { \\oplus  }{ N } =\\overset { \\circleddash  }{ N }$$\n$$(b)\\ \\overset { \\circleddash  }{ C } { H }_{ 2 }-N=\\overset { \\oplus  }{ N }$$\n$$...
B
Chemistry
1bcdfc904e89419ba9ec65b68b9c1b41
[ { "role": "user", "content": "The conc. of ${Fe}^{3+}$ ions in a sample of water is found to be $50\\times {10}^{-5}M$. Calculate the $pH$ at which $99$% of ${Fe}^{3+}$ will be precipitated. ${ K }_{ { sp }_{ Fe{ \\left( OH \\right)  }_{ 3 } }\\quad  }={10}^{-36}$.\n\n(A) 4.4\n(B) none of these\n(C) 5.9\n(D...
I
Chemistry
232b4724b75c4e70903fad7e8bf671a0
[ { "role": "user", "content": "A disc of radius R rolls on a horizontal surface with linear velocity $ \\overrightarrow {v} = v \\hat {i} $ and angular velocity $ \\overrightarrow {\\omega} = - \\omega \\hat k $ there is a particle P on the circumference of the disc which has velocity in vertical direction. ...
I
Physics
a51a75dccfd645d5a8dac7691703b1a2
[ { "role": "user", "content": "If a particle is projected from ground at certain angle $\\theta_1$with horizontal with initial velocity $u$ and it strikes perpendicularly (while in air) a rigid wall inclined at angle $\\theta_2$ with respect to ground then : (consider x-axis along horizontal and y-axis perpe...
C
Physics
e29c781a888b4ded9fb90822d0ef24ab
[ { "role": "user", "content": "The rate constant of a reaction increased by $5%$ when temperature is raised from $27^{o}$ to $28^{o}\\ C$. The activation energy of the reaction is $(\\log\\ 7=0.8450)$\n\n(A) $$38.5\\ KJ$$\n(B) $$34.5\\ KJ$$\n(C) $$35.5\\ KJ$$\n(D) $$46.5\\ KJ$$\n(E) $$36.5\\ KJ$$\n(F) $$39.5...
E
Chemistry
79a7b980cf34414abbabb7ed69df504f
[ { "role": "user", "content": "The correct stability order of the following resonating structures is:(I) $H_2C = \\overset{+}{N} = \\overset{-}{N}$                     (II) $H_2\\overset{+}{C}-N=\\overset{-}{N}$(III) $H_2\\overset{-}{C} - \\overset{+}{N} \\equiv N$                  (IV) $H_2\\overset{-}{C} -...
I
Chemistry
60fce05d0409453a951e1c0f2338ea4c
[ { "role": "user", "content": "A particle is projected with speed 100 m/s at angle $\\theta ={ 60 }^{ \\circ  }$ with the horizontal at time t = 0. At time t the velocity vector of the particle becomes perpendicular to the direction of velocity of projection\nIts tangential acceleration at time t is :\n\n(A)...
G
Physics
2f1ca103cd034f65b383f8dc439947d5
[ { "role": "user", "content": "A particle of mass $m$ and charge $q$ is placed in an electric field $E$ which varies with time $t$ as $E=E_o \\sin \\omega t$. It will undergo SHM of amplitude\n\n(A) $$\\dfrac{Q{E_o}^2}{m\\omega}$$\n(B) $$\\dfrac{Q{E_o}}{m\\omega}$$\n(C) $$\\dfrac{Q{E_o}^2}{m\\omega^2}$$\n(D)...
H
Physics
bba65e6a3854425b8ac4229bd6e12799
[ { "role": "user", "content": "A transparent slab of thickness d has a refractive index n(z) that increases with z. Here z is the vertical  distance inside the slab, measured from the top. The slab is placed between two media with uniform refractive indices ${ n }_{ 1 }$ and ${ n }_{ 2 }$ $(>{ n }_{ 1 })$, a...
E
Physics
7ea9917c2e1a4311be5e3fde3e949c6f
[ { "role": "user", "content": "A solid sphere has linear velocity $v_0=4m/s$ and angular velocity ${ \\omega  }_{ 0 }=9rad/s$ as shown. Ground on which it is moving is smooth. It collides elastically with rough wall of coefficient of friction $\\mu .$ Radius of sphere $1 m$ and mass $2 kg.$ Then what is the ...
B
Physics
83e3b2d511de403b860e165ba2cb0f4c
[ { "role": "user", "content": "To beaker containing $ 0.1 M \\ HCl,$ a little pure solid AgCl is added. Both a silver and a hydrogen electrode $ (P_{H_{2}} = 1.0 $ bar) are then placed in the solution. What is the approximate value of EMF measured between the electrodes at $ 25^{\\circ}C?$ (Given: $ E_{Ag^{+...
B
Chemistry
344d985ec0a945e8afb9c44aac3ba000
[ { "role": "user", "content": "The acid catalysed hydrolysis of an organic compound $A$ at $30^{\\circ}C$ has a time for half change of $100$ minutes, when carried out in a buffer solution at $pH\\ 5$ and of $10$ minutes, wen carried out at $pH\\ 4$. Both times of half change are independent of the initial c...
F
Chemistry
9499992218c54e45969736fa0886a165
[ { "role": "user", "content": "A charged particle $(Q = 10^{-4}C)$ is released from rest at $z=0$ in magnetic field given as $\\vec{B}=B_0\\cos(\\omega t - kz)\\hat{i} + B_1 \\cos(\\omega t + kz)\\hat{j}$ where $B_0 = 3\\times 10^{-5}T$ and $B_1 = 2 \\times 10^{-6}T$. Then the rms value of force acting on pa...
C
Physics
5434926dec894d20b1a7d4371be654eb
[ { "role": "user", "content": "Two identical parallel plate capacitors, of capacitance $C$ each, have plates of area $A$, separated by a distance $d$. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants $K_1, K_2$ and $K_3$. The fi...
D
Physics
d7d0b950867b47c8bbfdc4c0e588a72c
[ { "role": "user", "content": "Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of gas $A$ is $m_{A}$ and that in $B$ is $m_{B}$. The change in the pressure in $A$ and $B$ are found to be $\\triangle P$ and $1....
B
Physics
5dd1390559da401ca00fdfec399fd6ca
[ { "role": "user", "content": "Fixed mass of an ideal gas contained in a $24.63L$ sealed rigid vessel at $1$ atm is heated from $-{ 73 }^{ o }C$ to ${ 27 }^{ o }C$. Calculate change in Gibb's energy if entropy of gas is a function of temperature as $S=2+{ 10 }^{ -2 }T(J/K)$: (Use $1$ atm $L=0.1kJ$)\n\n(A) $$...
E
Physics
55ba6f83978142889c49f5d2a86680a7
[ { "role": "user", "content": "A simple pendulum of length L and mass M is oscillating in a plane about a vertical line between angular limits -$\\phi$ and +$\\phi$. For an angular displacement, $\\theta$(|$\\theta$| < $\\phi$) the tension in the string and velocity of the bob are T and v respectively. The f...
E
Physics
e78c81f946704e8ab0fb15182b6f8f68
[ { "role": "user", "content": "A particle of mass $m$ can move in a force field. Potential energy $U$ varies on location of the particle according to the following equation.\n$U=-k(x-a)^2(x-b)^2$ \nHere, $k, a$ and $b$ are positive constants.\nWhat can you conclude about small amplitude oscillations of the p...
D
Physics
7a41db0632d34d4fb75b1d061b443122
[ { "role": "user", "content": "$y(x, t)=\\dfrac{0.8}{(4x+5t)^2+5}$ represents a moving pulse where x and y are in meter and t in seconds. Then.\n\n(A) Pulse is moving in $+$x direction\n(B) It's a symmetric pulse with a maximum displacement of $0.12$ m\n(C) It's a symmetric pulse with a maximum displacement ...
G
Physics
c794f1b6844a42c49bcb2762d5efd0a0
[ { "role": "user", "content": "An ideal gaseous sample at initial state $({P}_{0},{V}_{0},{T}_{0})$ is allowed to expand to volume $2{V}_{0}$ using two different processes. For the first process, the equation of process is $2P{V}^{2}={K}_{1}$ and for the second process, the equation of the process is $PV={K}...
D
Physics
99f7947781a347ebbf9b9d8487aba93f
[ { "role": "user", "content": "Two particles of equal mass go around a circle of radius $R$ under the action of their mutual gravitational attraction.The speed of each particle is\n\n(A) $$v = \\sqrt { \\left( \\dfrac { 4 G m } { R } \\right) }$$\n(B) $$v = \\sqrt { \\left( \\dfrac { 3 G m } { 2 R } \\right)...
H
Physics
332672c1f6d942549a35c2843d92c630
[ { "role": "user", "content": "A composite wire is mad eby joining two uniforms wires. if $ l_1= l_2=l $ and $ \\mu_1= \\dfrac { \\mu_2}{9} = \\mu $ Tension in the string is T, $ \\mu $ is mass per unit length. then lowest frequency such that the junction is antinode.\n\n(A) $$\\dfrac {2}{l} \\sqrt{ \\dfrac ...
I
Physics
6c857ffd9e8541eb8f64b98b459c2a51
[ { "role": "user", "content": "Three point like equal masses $m_1, m_2$ and $m_3$ are connected to the ends of a mass-less rod of length $L$ which lies at rest on a smooth horizontal plane. At $t = 0$, an explosion occurs between $m_2$ and $m_3$, and as a result, mass $m_3$ is detached from the rod, and move...
H
Physics
4513e5f339ea413fb65020d50e8880fe
[ { "role": "user", "content": "The ionization constant of benzoic acid is $6.46 \\times 10^{-5}$ and $K_{sp}$ for silver benzoate is $2.5\\times 10^{-13}$. How many times is silver benzoate more soluble in a buffer of $pH = 3.19$ compared to its solubility in pure water?\n\n(A) $$4$$\n(B) $$3.28$$\n(C) $$3.0...
J
Chemistry
2304647c33d942c286177ebffcb48309
[ { "role": "user", "content": "An open pipe is in resonance in its $2^nd$ harmonic with tuning fork of frequency $f_1$. Now it is closed at one end. If the frequency of the tuning fork is increased slowly from $f_1$ then again a resonance is obtained with a frequency $f_2$. If in this case, the pipe vibrates...
E
Physics
a97ba880abc647b8a4f8ef85406be453
[ { "role": "user", "content": "In the situation shown, the block can execute free oscllation (no damping) with angular frequency $ \\omega _{1} $. In presence of week damping, it executes damped $ SHM $ with angular frequency $ \\omega _{2} $. When it is subjected to a sinusoidal force, it executes forced os...
F
Physics
c1989b20bf8447868a8ad56c1e7be8e4
[ { "role": "user", "content": "Successive acid dissociation consists for a tribasic acid, $H_3XO_3,$ are $k_1=7.5\\times 10^{-10}, k_2=2\\times 10^{-13}, k_3= 1.6\\times 10^{-14}$. Decimolar aqueous solutions of which of the following are expected to be basic?\n\n(A) $$Na_3XO_3$$\n(B) Na_3XO_4\n(C) NaHXO_3\n...
H
Chemistry
a303795f899447c9a86c9bf222885c4d
[ { "role": "user", "content": "An electron gun G emits electrons of energy $2$ keV travelling in the positive x-direction. The electrons are required to hit the spot S where GS$=0.1$m, and the line GS makes an angle $60^o$ with the x-axis, as shown. A uniform magnetic field B parallel to GS exists in the reg...
C
Physics
fa3ead92f6044964aa0549fed5e74304
[ { "role": "user", "content": "Two particles A and B start moving due to their mutual interaction only. If at any time 't', $\\vec{a_{A}}$ and $\\vec{a_{B}}$ are their respective accelerations, $\\vec{v}_{A}$ and $\\vec{v}_{B}$ are their respective velocities, and upto that time $W_{A}$ and $W_{B}$ are the w...
C
Physics
f9d6fbd7fbff434bacb9a52cfc511936
[ { "role": "user", "content": "A sonometer string AB of length 1 m is stretched by a load and the tension T is adjusted sothat the string resonates to a frequency of 1kHz. Any point P of the wire may be held fixed by use of a movable bridge that can slide alomg the base of sonometer.\n\n(A) The fundamental f...
J
Physics
349cfd79611a4e259454813e21460774
[ { "role": "user", "content": "An equal volumes of 1.0 M $KCl$ and 1.0 M $AgNO_3$ are mixed. The elevation of the boiling point of the resulting solution will be:$(K_b = 0.52\\ K/ molal$ and van't Hoff factor for $KNO_3$ is 2)\n\n(A) 2.08\n(B) 1.06\n(C) 2.10\n(D) 0.026\n(E) 2.60\n(F) 0.26\n(G) 1.02\n(H) 1.56...
I
Chemistry
c9bf055bb3c34881898b666d4ca26d39
[ { "role": "user", "content": "A gas park in two processes in which it is hcated from the same initial state 1 to the same final temperature. The processes are shown on the P - V diagram by the straight lines $1-3$ and $1-2$. $2$ and $3$ are the points on the same isothermal curve. $Q_1$ and $Q_2$ are the he...
E
Physics
c1e8da445759498c80ad32262206fe45
[ { "role": "user", "content": "The indicator phenol red is half in the ionic form when $pH$ is $7.2$. If the ration of the undissociated from to the ionic form is $1:5$, find the $pH$ of the solution. With the same $pH$ for solution, if indicator is altered such that the ratio of undissociated form to dissoc...
H
Chemistry
7c336144324a4bf09f0cfb960d853d9b
[ { "role": "user", "content": "Among the following compounds, which one of the following will react with acetone to give a product containing $> C=N $ ?\n\n(A) $$C_6H_5NHNHCH_3$$\n(B) $$C_6H_5NH_2$$\n(C) $$ C_6H_5NHNH_2 $$\n(D) $$C_6H_5NHC_6H_4$$\n(E) $$C_6H_5NHC_2H_5$$\n(F) $$ (CH_3)_3N $$\n(G) $$C_6H_5NHCH...
C
Chemistry
db8ca997b63441ec90078a698088244e
[ { "role": "user", "content": "An ideal gas is expanding such that $\\dfrac{V}{T^{3}}= constant$. The Molar Specific heat of the gas is\n\n(A) $$\\displaystyle \\dfrac{9R}{2}$$\n(B) $$\\dfrac{12R}{2}$$\n(C) $$\\displaystyle \\dfrac{5R}{2}$$\n(D) $$\\displaystyle \\dfrac{11R}{2}$$\n(E) $$\\dfrac{10R}{2}$$\n(F...
A
Physics
925663d204a048a1b5b8034934e9e810
[ { "role": "user", "content": "The correct statement about the magnetic properties of $[Fe(CN)_6]^{3-}$ and $[FeF_6]^{3-}$ is: $(Z=26)$.\n\n(A) Both are paramagnetic\n(B) Both are ferromagnetic\n(C) $[Fe(CN)_6]^{3-}$ is diamagnetic, $[FeF_6]^{3-}$ is paramagnetic\n(D) $[Fe(CN)_6]^{3-}$ is ferromagnetic, $[Fe...
A
Chemistry
943987f4271f4a04a83a2585caa11d51
[ { "role": "user", "content": "How many m moles of sucrose should be dissolved in 500 grams of water so as to get a solution which has a difference of $ 103.57^0 C $ between boiling point and freezing point ? \n$$ (K_f = 1.86 K kg mol^{-2}, K_b = 0.52 K Kg mol^{-1} ) $$\n\n(A) 900 m moles\n(B) 850 m moles\n(...
E
Chemistry
8cecb5c79d1a424ab66b01ff8d051712
[ { "role": "user", "content": "The time taken by block-bullet system to move from $y=\\dfrac{mg}{k}$ (initial equilibrium position) to $y=0$ (natural length of spring) is : [A represents the amplitudes of motion]\n\n(A) $$\\sqrt{\\dfrac{4m}{3k}}\\left[\\cos^{-1}\\left(\\dfrac{2mg}{3kA}\\right)-\\cos^{-1}\\le...
D
Physics
322eeef653964174a164866cce151781
[ { "role": "user", "content": "A uniform circular wire loop is connected to the terminals of a battery. The magnetic field induction at the centre due to ABC portion of the wire will be (length of ABC = ${ l }_{ 1 }$, length of ADC = ${ l }_{ 2 }$)\n\n(A) $$\\dfrac { { \\mu }_{ 0 } { il }_{ 1 } {l}_{2}}{ 8\\...
D
Physics
29dc9791d9af458b9ee137bc9bd7bf83
[ { "role": "user", "content": "Mixture $X=0.02$ mol of $[Co(NH_3)_5SO_4]Br$ and 0.02 mol of $[Co(NH_3)_5Br]SO_4$ was prepared in 2L of solution.1L of mixture X + excess $AgNO_3\\rightarrow Y$1L of mixture X + excess $BaCl_2\\rightarrow Z$Number of moles of Y and Z are :\n\n(A) $$0.02, 0.04$$\n(B) $$0.01, 0.0...
F
Chemistry
9da0d086c10a487eb9f31c4f29f27e1d
[ { "role": "user", "content": "Three large identical conducting parallel plates carrying chrage +Q, -Q, and +2Q, respectively, are placed as shown in figure. If $E_A, E_B$ and $ E_C$ refers to the magnitudes of the electric fields at points A, B, C, respectively, then :\n\n(A) $E_A=0$ and $E_C > E_B$\n(B) $$...
F
Physics
777bc0aef207409680d3f03d6db7c020
[ { "role": "user", "content": "A steel ball is dropped from a height of 1 m on to a horizontal non-conducting surface. Every time it bounces, it reaches 80% of its previous height. Nearly by how much will the temperature of the ball rise after 4 bounces? Specific heat capacity of the $ball \\:(steel) =0.1 \\...
I
Physics
14a829eaab4f4ab29bf31037f56950b3
[ { "role": "user", "content": "Two plates $A$ and $B$ of equal surface area are placed one on top of the other to form a composite plate of the same surface area. The thickness of $A$ and $B$ are $4.0$cm and $6.0$cm respectively. The temperature of the exposed surface of plate $A$ is $-10$$^{o}$C and that of...
J
Physics
951ef64f4138437c81ef1b4d82a5425f
[ { "role": "user", "content": "A $1.025\\space g$ sample containing a weak acid $HX$ (mol. wt. = 82) is dissoved in $60\\space mL$ water and titrated with $0.25\\space M\\space NaOH$. When half of the acid was neutralised the $pH$ was found to be $5.0$ and at the equivalent point the $pH$ is $9.0$. Calculate...
C
Chemistry
af9ae80674604728bb4441954897399a
[ { "role": "user", "content": "Second overtone frequency of a closed pipe and fourth harmonic frequency of an open pipe are same. Which of the following is correct?\n\n(A) Ninth harmonic frequency of closed pipe is equal to eighth harmonic frequency of open pipe\n(B) Ninth harmonic frequency of closed pipe i...
H
Physics
f05c4b2596924d4faea0c3ff6cd8ab13
[ { "role": "user", "content": "A light beam travelling in the x-direction is described by the electric field ${ E }_{ y }=(300V{ m }^{ -1 })sin\\quad \\omega (t-x/c).$ An electron is constrained to move along the y-direction with a speed of $2.0\\times  {10}^7 { m }^{ -1 }$ Find the maximum electric force an...
C
Physics
df307d1210044fc6919f6bbf9a586e99
[ { "role": "user", "content": "One mole of ammonium carbamate dissociate as shown below at $500K$\n${NH}_{3}COO{NH}_{4(s)\\rightleftharpoons  2{NH}_{3}(g}+{CO}_{2}(g)$. If the pressure exerted by the released gases is $3.0$ atm, the value of ${K}_{p}$ is (standard state $=1atm$)\n\n(A) 11\n(B) 3\n(C) 7\n(D) ...
I
Chemistry
100da6dfd1f94997b76946a2db1837bd
[ { "role": "user", "content": "For the change \n$C_{diamond} \\rightarrow C_{graphite} : \\Delta H = -1.89 kJ$.\nIf 6 g of diamond and 6 g graphite are separately burnt to yield $CO_2$ the heat librated in first case is\n\n(A) less than in the second case by $14.34 kJ$\n(B) less than in the second case by $1...
E
Chemistry
40efbcf4af87435892ee546f857d10de
[ { "role": "user", "content": "One mole of a monatomic ideal gas initially at a pressure of 2.00 bar and a temperature of 273 K is taken to a final pressure of 4.00 bar by a reversible path defined by p/V = constant. Taking $C_V$ to be equal to $12.5 J mol^{-1} K^{-1}$, the value of $\\triangle U/ w$ for thi...
G
Physics
2ad84dab86404c8d9d570a983fbed133
[ { "role": "user", "content": "An ideal gas (1 mol, monatomic) is in the initial state $ P $ (see Fig. 2.111 ) on an isothermal $ A $ at temperature $ T_{0} . $ It is brought under a constant volume $ \\left(2 V_{0}\\right) $ process to $ Q $ which lies on an adiabatic $ B $ intersecting the isothermal $ A $...
D
Physics
12540dc81abb43df9dec38e5f9ad24ad
[ { "role": "user", "content": "The waves are represented by the following equations \n$y_{1} =  5 \\sin 2 \\pi  (10t-0.1x)$  \n$y_2 = 10 \\sin 2\\pi  (20t-0.2x)$ \nRatio of intensities $\\dfrac {I_{2} }{I_{1}}$ will be :\n\n(A) $$64$$\n(B) $$8$$\n(C) 32\n(D) $$4$$\n(E) $$36$$\n(F) $$1$$\n(G) $$16$$\n(H) $$2$...
G
Physics
f8d8c836110e4606801bbb9afcd709e8
[ { "role": "user", "content": "One mole of an ideal monoatomic gas expends isothermally against constant external pressure of $1$ atm from initial volume of $1L$ to a state where its final pressure become equal to external pressure. If initial temperature of gas is $300\\ K$ then total entropy change of syst...
C
Physics
d638c218a851446ab3bf2e6a9178d67b
[ { "role": "user", "content": "A body of mass m = ${ m=10 }^{ -2 }$ kg is moving in a medium and experiences a frictional force ${F =kv }^{ -2 }.$ Its initial speed is ${ v }_{ 0 }=10{ ms }^{ -1 }$. If after 10 s,its energy is $\\dfrac { 1 }{ 8 } { mv }_{ 0 }^{ 2 }$, the value of k will be\n\n(A) $${ 10 }^{ ...
E
Physics
f8bd0a3abcd0470c9724c2defa179047
[ { "role": "user", "content": "A particle initially at rest starts moving from point A on the surface of a fixed smooth hemisphere of radius r as shown. The particle looses its contact with hemisphere at point B. C is centre of the hemisphere. The equation relating $\\alpha$ and $\\beta$ is:\n\n(A) $$3sin\\a...
D
Physics
9ff5018e024947818010617717d4e097
[ { "role": "user", "content": "A simplified flute shown in the figure. It is open at end $D$.\nThere is also a large opening at $A$ (near the mouth piece) and there are two holes at $B$ and $C$ [$AB=BD$ and $BC=CD$]. The distance $AD=34\\ cm$. The speed of sound is $340\\ m/s$. What frequency do you expect t...
E
Physics
f195ed580eb447d2bcbc9fa3737e716c
[ { "role": "user", "content": "A certain mirror placed at the origin has $\\hat{j}$ as the normal vector to its reflecting surface. The mirror begins to translate with a velocity $\\hat{i}+\\hat{j}+\\hat{k}$ at $t=0$. At the same time an object which was initially at $\\hat{i}+\\hat{j}$ starts moving with a ...
C
Physics
26e923b357184bf6b94f4c3670fcbc52
[ { "role": "user", "content": "For a binary liquid solution obeying Raoult's law at $300 K$, $X_A = 0.75$, Given: $P_A^o = 400 mm Hg ; P_B^o = 600 mm Hg$ Then select correct statement\n\n(A) Normal boiling point of liquid solution should be more than $300K$\n(B) Vapour pressure of solution will be $475 mm$ $...
A
Chemistry
a303f089f04c43f4b5b1cea0a4f8d280
[ { "role": "user", "content": "One mole of an ideal monoatomic gas is heated in a process $P{V}^{5/2}=$ constant. By what amount heat is absorbed in the process in ${26}^{o}C$ rise in temperature?\n\n(A) 205J\n(B) $$100J$$\n(C) 190J\n(D) 195J\n(E) $$208J$$\n(F) $$200J$$\n(G) 175J\n(H) 170J\n(I) $$180J$$\n(J)...
I
Physics
e62f9dd33fa741ecbb154ff99f4bae03
[ { "role": "user", "content": "$A(aq)\\longrightarrow B(aq)+C(aq)$ is a first order reaction.\nTime\n$$t$$\n$$\\infty$$\nmoles of reagent\n$${ n }_{ 1 }$$\n$${ n }_{ 2 }$$\nReaction progress is measure with help of titration '$R$'. If all $A,B$ and $C$ reacted with reagent and have '$n$' factors [$n$ factor;...
H
Chemistry
d9dae18bc19d4998804a1b49779192a5
[ { "role": "user", "content": "A plane elctromagnetic wave of wavelength $ \\lambda  $ has an intensity I. It is propagating along the positive x-direction. The allowed expressions for the electri and magnetic fields are given by\n\n(A) $$ \\overrightarrow { E } =\\sqrt { \\frac { 2I }{ { { \\epsilon}_{ 0 }C...
F
Physics
99b58474734f4852a34e784cb1bed1d8
[ { "role": "user", "content": "A sample of $U^{238} ((half\\!-\\! life = 4.5\\times 10^9 \\: yr)$ ore is found to contain 23.8 g of $U^{238}$ and 20.6 g of $Pb^{206}$. The age of the ore is :\n\n(A) $$4.00 \\times 10^9 \\:year$$\n(B) $$3.5\\times 10^9 \\:year$$\n(C) $$5.50 \\times 10^9 \\:year$$\n(D) None of...
G
Physics
eb3e00dd0eab4674bf3cd0fa9fcf2d29
[ { "role": "user", "content": "$20$ mL of $0.1M\\ H_2SO_4$ solution is added to $30$ mL of $0.2 M\\, NH_4OH$ solution. The pH of the resultant mixture is: $[ \\ pK_{b (NH_4OH)}=4.7]$.\n\n(A) $$9.4$$\n(B) $$5.0$$\n(C) 8.7\n(D) $$5.2$$\n(E) $$9.0$$\n(F) 8.8\n(G) $$4.9$$\n(H) 8.9\n(I) 9.3\n(J) 5.1\n\nPlease wri...
E
Chemistry
1dbb73d16f0c4f4aab8db57166e5148a
[ { "role": "user", "content": "Enthalpy of formation of $NH_{3}$ is $-X\\ kJ$ and $\\triangle H_{H - H}, \\triangle H_{N-H}$ are respectively $Y\\ kJ\\ mol^{-1}$ and $Z\\ kJ \\ mol^{-1}$. The value of $\\triangle H_{N = N}$ is\n\n(A) $$Y - 6Z - \\dfrac {X}{3}$$\n(B) $$Y - 6Z + \\dfrac{X}{4}$$\n(C) $$Y + 6X +...
G
Physics
585d256377e64bef8b1836fae00d1c49
[ { "role": "user", "content": "Three moles of an ideal gas $\\left (C_{P} = \\dfrac {7R}{2}\\right )$ at pressure $P_{A}$ and temperature $T_{A}$ is isothermally expanded to twice the initial volume. The gas is then compressed at constant pressure to its original volume. Finally the gas is heated at constant...
I
Physics
11bfdd909b3f45159862835e6186a2ac
[ { "role": "user", "content": "A long straight wire (radius $= 3.0 \\mathrm { mm } )$ carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. If the current density is 100$\\mathrm { A } / \\mathrm { m } ^ { 2 }$ . The magnitudes of the magnetic field at (...
J
Physics
c7a1dd07f5a240c094db88ec994e3e92
[ { "role": "user", "content": "A particle which can move along x-axis is released from rest at the position $x = x_0.$ The potential energy (U) of the block is described below :\n$$U=\\begin{Bmatrix} -ax &;x<0 \\    bx^2 &;x\\geq0  \\end{Bmatrix}$$\nWhich of the following statements is/are correct :\n\n(A) T...
F
Physics
44fd9e657e2749d3be7c5576fe95d43e
[ { "role": "user", "content": "A reaction $A+B\\rightarrow C$, follows first order kinetic with respect to each reactant, with an overall rate constant, $k=2.0\\times 10^{-3}M^{-1}s^{-1}$. The initial concentrations of $A$ and $B$ are $0.10M$ and $6.93M$, respectively. Given $ln2=0.693$, choose the correct s...
C
Chemistry
e1e1e89bf10f41999bb714cd67ab0f78
[ { "role": "user", "content": "$9.0\\, g $ water is added into oleum sample labelled as $112\\ % $ $H_2SO_4 $ then the amount free $SO_3 $ remaining in the solution is: (STP = $1$ atm and $273\\,K $)\n\n(A) 10.24\\,L\n(B) $3.73\\,L $ at STP\n(C) $11.2\\,L $ at STP\n(D) 4.73\\,L at STP\n(E) 5.46\\,L at STP\n(...
B
Chemistry
44b2838aa2874f788f9f3b3c566f7cf3
[ { "role": "user", "content": "A quantity of $27.6\\ g$ of $K_2CO_3$ was treated by a series of reagent so as to convert all of its carbon to $K_2Zn_3 [Fe(CN)_6]_2$. The mass of the product formed is $(K=39, Zn=65.4, Fe=56)$\n\n(A) $$69.6\\ g$$\n(B) $$139.2\\ g$$\n(C) $$27.6\\ g$$\n(D) $$12.6\\ g$$\n(E) $$13...
H
Chemistry