id_ddm stringlengths 32 32 | dialogs listlengths 2 2 | ground_truth stringclasses 10
values | domain stringclasses 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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.