Two bodies A and B of equal mass are suspended from two separate massless springs of spring constant \[{{k}_{1}}\]and \[{{k}_{2}}\] respectively. If the bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of A to that of B is
If some amount of ice is mixed with hot water at \[10{}^\circ C\] in such a way that heat released by ice when melts completely is greater than the heat absorbed by hot water to come at \[0{}^\circ C\], then at steady state
A)
the mixture has ice only and temperature is \[0{}^\circ C\]
doneclear
B)
the mixture is having water and temperature is lower than \[10{}^\circ C\]
doneclear
C)
the mixture has ice and water and temperature is \[0{}^\circ C\]
doneclear
D)
the mixture has ice and water and temperature is greater than \[0{}^\circ C\]
Two bodies of different masses has been released from the top of tower. One is thrown in horizontal direction while other is dropped, then which is reaching the ground first?
A)
The body which has been thrown horizontally
doneclear
B)
The body which has been dropped
doneclear
C)
Both are reaching the ground simultaneously
doneclear
D)
Depends on the velocity with which the 1st body has been projected horizontally
Two identical radioactive nuclide are prepared in identical situation and then kept in identical surroundings. The half-life of nuclide is 6 x 103 days. Both the nuclides get decay in
A)
6 x 103 days
doneclear
B)
greater than or less than 6 x 103 days but takes the same time
An AC source producing emf \[e={{e}_{0}}[\cos (100\pi {{s}^{-1}})t+\cos (500\pi {{s}^{-1}})t]\] is connected in series with a capacitor and resistor. The steady-state current in the circuit is found to be \[i={{i}_{1}}\cos [(100\pi {{s}^{-1}})t+{{\phi }_{1}}]+{{i}_{2}}\cos \]\[[(500\pi {{s}^{-1}})t+{{\phi }_{2}}]\]
A)
\[{{i}_{1}}>{{i}_{2}}\]
doneclear
B)
\[{{i}_{1}}={{i}_{2}}\]
doneclear
C)
\[{{i}_{1}}<{{i}_{2}}\]
doneclear
D)
The information is insufficient to find the relation between \[{{i}_{1}}\] and \[{{i}_{2}}\]
A block of wood has a mass of 25 g. When a 5g metal piece with a volume of 2 cm3 is attached to the bottom of the block, the wood barely floats in water. What is the volume V of the wood?
A man can swim with a speed of 4 km/h in still water. How long does it take to cross a river 1 km wide, if the river flows steadily at 3 km/h and he makes his strokes normal to the river current? How far down the river does he go when he reaches the other bank?
A stone is swinging in a horizontal circle 0.8 m in diameter, at 30 rev/min. A distant light causes a shadow of the stone to be formed on a nearby wall. What is the amplitude of the motion of the shadow? What is the frequency?
A 20 g bullet pierces through plate of mass \[{{m}_{1}}=1\] kg and then comes to rest inside a second plate of mass \[{{m}_{2}}=2.98\]kg. It is found that the two plates, initially at rest, now move with equal velocities. The percentage loss in the initial velocity of bullet when it is between \[{{m}_{1}}\] and \[{{m}_{2}}\] (neglect any loss of material of the bodies, due to action of bullet) will be
A balloon starts ascending in vertical upward direction at a constant rate of 5 m/s2. After 2s of its flight begins, a ball has been dropped from it, find the maximum height attained by ball. Also calculate the position of the balloon relative to ground when ball strikes the ground. (Take g = 10 m/s2)
A hunter is standing on flat ground between two vertical cliffs that are directly opposite to one another. He is closer to one cliff than the other. He fires a gun and after a while, hears three echoes. The second echo arrives 1.6 s after the first, and the third echo arrives 1.1 s after the Second. Assuming that speed of sound is 343 m/s and that there are no reflections of sound from the ground. Find the distance between the cliffs.
A police van moving on a highway with a speed of 30 km/h fires a bullet at a thieve's car moving at a speed of 192 km/h. If muzzle speed of bullet is 150 m/s, with what speed does the bullet hit the thieve's car?
The wavelength of Ka X-ray of certain material is 12.42 pm. It takes 10 keV to knock out the electron from M shell of this A atom. What should be the minimum accelerating potential across an X-ray tube having A target, which allows product of \[{{K}_{\alpha }}X\]-rays?
A non-conducting sheet (infinite plane sheet) has given a charge in such a way that\[{{Q}_{1}}\]appears on one side and \[{{Q}_{2}}\] on other side. The face area of plate is A. Find the electric field at points 1 and 2.
The emf and internal resistance of the battery shown in figure are 4.3 V and 1ft respectively. The external resistance R is\[50\Omega \]. The resistance of the voltmeter and ammeter are \[200\Omega \] and \[2\Omega \] respectively. Find the readings of the two meters.
Three dielectric slabs of thickness d/4, d/7 and d/2 having dielectric constants 2, 8/7 and 4 respectively are inserted between the plates of a parallel plate capacitor having plate separation d and plate area A. The remaining space is filled with a conducting medium. Find the capacitance of the system.
Directions: Question No. 26 are based on the following paragraph. When a composite wire is made by joining two wires as shown in figure In the figure given: \[{{l}_{1}}={{l}_{2}}=l,{{\mu }_{1}}=\frac{{{\mu }_{2}}}{9}=\mu .\] The tension in the strings is T. Here, \[\mu \]is the mass per unit length. What is the lowest frequency such that the junction is a node?
Directions: Question No. 27 are based on the following paragraph. When a composite wire is made by joining two wires as shown in figure In the figure given: \[{{l}_{1}}={{l}_{2}}=l,{{\mu }_{1}}=\frac{{{\mu }_{2}}}{9}=\mu .\] The tension in the strings is T. Here, \[\mu \]is the mass per unit length. What is the lowest frequency such that the junction is an antinode?
Directions: Question No. 30 are Assertion- Reaction type. Each of these contains tow statements Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only on of which is correct. You have to select the correct choices from the codes a, b, c and d given below:
Statement I: The safe velocity limit for taking- a turn on an unbanked road is \[v=\sqrt{\mu rg}.\]
Statement II: Banking of roads will increase the value of limiting velocity.
A)
Statement I is true; Statement B is true; Statement B is not a correct explanation for Statement I,
doneclear
B)
Statement I is true; Statement II is false.
doneclear
C)
Statement I is false; Statement II is true.
doneclear
D)
Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
Directions: Question No. 31 are Assertion- Reaction type. Each of these contains tow statements Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only on of which is correct. You have to select the correct choices from the codes a, b, c and d given below:
Statement I: An electric motor will have maximum efficiency when back emf becomes equal to half of applied emf.
Statement II: Efficiency of electric motor depends only on magnitude of back emf.
A)
Statement I is true; Statement B is true; Statement B is not a correct explanation for Statement I,
doneclear
B)
Statement I is true; Statement II is false.
doneclear
C)
Statement I is false; Statement II is true.
doneclear
D)
Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
Directions: Question No. 32 are Assertion- Reaction type. Each of these contains tow statements Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only on of which is correct. You have to select the correct choices from the codes a, b, c and d given below:
Statement I: Newton's rings are formed in the reflected system when the space between the lens and the glass plate is filled with a liquid of refractive index greater than that of glass, the central spot of the pattern is dark.
Statement II: The reflection in Newton's ring cases will be from a denser to rarer medium and the two interfering rays are reflected under similar conditions.
A)
Statement I is true; Statement B is true; Statement B is not a correct explanation for Statement I,
doneclear
B)
Statement I is true; Statement II is false.
doneclear
C)
Statement I is false; Statement II is true.
doneclear
D)
Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
A container having 1 mole of a gas at temperature \[27{}^\circ C\] has a movable piston which maintains at constant pressure in container of 1 atm. The gas is compressed until temperature becomes \[127{}^\circ C\]. The work done is (\[{{C}_{p}}\] for gas is 7.03 cal/mol-K)
\[\text{C}{{\text{H}}_{\text{3}}}-\text{C}{{\text{H}}_{\text{2}}}-\underset{\begin{smallmatrix} \text{ }\!\!|\!\!\text{ } \\ \text{C}{{\text{H}}_{\text{3}}} \end{smallmatrix}}{\mathop{\text{N}}}\,-\overset{\begin{smallmatrix} \text{O} \\ \text{ }\!\!|\!\!\text{ }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}\,-\text{H}\] The IUPAC name of the compound is
\[{{N}_{0}}/2\]atoms of X(g) are converted into \[{{X}^{+}}(g)\]by energy E. \[{{N}_{0}}/2\] atoms of X(g) are converted into \[{{X}^{-}}\] (g) by energy \[{{E}_{2}}.\]Hence, ionization potential and electron affinity of X(g) are
Directions: Question No. 49 are Assertion- Reaction type. Each of these contains tow statements Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only on of which is correct. You have to select the correct choices from the codes a, b, c and d given below:
Statement I: Colloidal solutions are stable but the colloidal particles do not settle down.
Statement II: Brownian movement counters the force of gravity actively on colloidal particles.
A)
Statement I is true; Statement B is true; Statement B is not a correct explanation for Statement I,
doneclear
B)
Statement I is true; Statement II is false.
doneclear
C)
Statement I is false; Statement II is true.
doneclear
D)
Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
Directions: Question No. 50 are Assertion- Reaction type. Each of these contains tow statements Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only on of which is correct. You have to select the correct choices from the codes a, b, c and d given below:
Statement I : White phosphorus is more reactive than red phosphorus.
Statement II : Red phosphorus consists of \[{{P}_{4}}\]tetrahedral units linked to one another to form linear chains.
A)
Statement I is true; Statement B is true; Statement B is not a correct explanation for Statement I,
doneclear
B)
Statement I is true; Statement II is false.
doneclear
C)
Statement I is false; Statement II is true.
doneclear
D)
Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
Directions: Question No. 51 are Assertion- Reaction type. Each of these contains tow statements Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only on of which is correct. You have to select the correct choices from the codes a, b, c and d given below:
Statement I: The second dissociation constant of maleic acid is greater than fumaric acid.
Statement II: Higher the dissociation constant of acid, more is the acidic character.
A)
Statement I is true; Statement B is true; Statement B is not a correct explanation for Statement I,
doneclear
B)
Statement I is true; Statement II is false.
doneclear
C)
Statement I is false; Statement II is true.
doneclear
D)
Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
For the dissolution of solid solute in liquid solvent the proper dissociation of ionic crystal and then, solvation (sheath formation around ions) are quite required. For the spontaneous dissolution
If n and I are respectively, the principal and azimuthal quantum numbers, then the expression for the calculation of the total number of electrons in any energy level is
Which of the following express correct relation of the cell potential \[({{E}_{3}})\] for the cell reaction, which is actually overall cell reaction on adding two half cell reactions, whose potentials are respectively \[{{E}_{1}}\] and \[{{E}_{2}}\]
Directions: Question No. 63 are based on the following paragraph. Mixture of organic compounds can be separated into individual components based on the solubility in different reagents, for example an acidic compound can be extracted into NaOH solution and a basic compound into HCl solution. Mixtures have been formed from the following compounds. A:naphthalene B: p-dichlorobenzend C: aniline D: phenol E: benzoic acid F: \[C{{H}_{3}}OH\] G: \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}N{{H}_{2}}\] H: \[\text{C}{{\text{H}}_{\text{3}}}\underset{\begin{smallmatrix} \text{ }\!\!|\!\!\text{ } \\ \text{OH} \end{smallmatrix}}{\mathop{\text{C}}}\,\text{HC}{{\text{H}}_{\text{3}}}\] Answer the questions based on the above compounds. HCl can be used to separate mixture of
Directions: Question No. 64 are based on the following paragraph. Mixture of organic compounds can be separated into individual components based on the solubility in different reagents, for example an acidic compound can be extracted into NaOH solution and a basic compound into HCl solution. Mixtures have been formed from the following compounds. A:naphthalene B: p-dichlorobenzend C: aniline D: phenol E: benzoic acid F: \[C{{H}_{3}}OH\] G: \[C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}N{{H}_{2}}\] H: \[\text{C}{{\text{H}}_{\text{3}}}\underset{\begin{smallmatrix} \text{ }\!\!|\!\!\text{ } \\ \text{OH} \end{smallmatrix}}{\mathop{\text{C}}}\,\text{HC}{{\text{H}}_{\text{3}}}\] Answer the questions based on the above compounds. Distinction between F and H can be made by
5.39 g of a mixture of \[FeS{{O}_{4}}.7{{H}_{2}}O\]and anhydrous ferric sulphate requires 80 mL of 0.125 N permanganate solution for complete conversion to the ferric sulphate. The individual weight of ferric sulphate in the original mixture is
The standard enthalpy change for the reaction \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow[{}]{{}}{{H}_{2}}O(g),\]is \[\Delta {{H}^{o}}=-248.8kJ\]It truly suggests, that
A)
248.8 kJ of energy is evolved when reaction is proceeded at 1 atm pressure and 298 K temperature.
doneclear
B)
248.8 kJ of energy is evolved irrespective of reaction conditions (pressure and temperature).
doneclear
C)
the reaction \[2{{H}_{2}}+{{O}_{2}}\xrightarrow[{}]{{}}2{{H}_{2}}O\] evolves same amount of energy 248.8 kJ
doneclear
D)
The reaction is \[{{H}_{2}}(g)+\frac{1}{2}{{O}_{2}}(g)\xrightarrow[{}]{{}}{{H}_{2}}O(l)\]
When 30.0 g of a nonvolatile solute having the empirical formula \[C{{H}_{2}}O\] is dissolved in 800 g of water, the solution freezes at \[-1.16{}^\circ C\]. What is the molecular formula of the solute? \[({{k}_{f}}={{1.86}^{o}}C/m)\]
For the reaction \[3Br{{O}^{-}}\xrightarrow[{}]{{}}BrO_{3}^{-}+2B{{r}^{-}},\] in alkaline solution, the value of the second order (in \[Br{{O}^{-}}\]) rate constant at \[80{}^\circ C\] in the rate law for \[-\Delta [Br{{O}^{-}}]/\Delta t\] was found to be \[0.056L\,mo{{l}^{-1}}{{s}^{-1}}\].Then \[\Delta [BrO_{3}^{-}]/\Delta t\]is
If \[{{z}_{1}}\]and \[{{z}_{2}}\] are two non-zero complex number such that \[|{{z}_{1}}+{{z}_{2}}|=|{{z}_{1}}|+|{{z}_{2}}|,\] \[\arg ({{z}_{1}})-\arg ({{z}_{2}})\]is equal to
The angle of elevation of the top of a tower from point A due south of the tower is \[\alpha \] and from B due east of the tower is (5, If AB = d, then height of the tower is
The chances of defective screws in three boxes A,B,C are \[\frac{1}{5},\frac{1}{6},\frac{1}{7}\] respectively. A box is selected at random and screw drawn from it at random is found to be defective. Then, the probability that it came from box A, is
Directions: Question No. 81 are Assertion-Reason type. Each of these contains tow statements Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only on of which is correct. You have to select the correct choices from the codes a, b, c and d given below:
Statement I : If sum of n terms of a series is \[6{{n}^{2}}+3n+1,\] then the series is in AP.
Statement II: The sum of n terms of an AP is always of the form an2 + bn.
A)
Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I,
doneclear
B)
Statement I is true; Statement II is false.
doneclear
C)
Statement I is false; Statement II is true.
doneclear
D)
Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
Directions: Question No. 82 are Assertion-Reason type. Each of these contains tow statements Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only on of which is correct. You have to select the correct choices from the codes a, b, c and d given below:
Statement I : If u = f(tan x), v = g(sec x) and \[=f'(1)=2,g'(\sqrt{2})=4,\]then \[{{\left( \frac{du}{dv} \right)}_{x=\frac{\pi }{4}}}=\frac{1}{\sqrt{2}}\].
Statement II: If \[u=f(x),v=g(x),\] then the derivative of f with respect to g is \[\frac{du}{dv}=\frac{du/dx}{dv/dx}.\]
A)
Statement I is true; Statement II is true; Statement II is not a correct explanation for Statement I,
doneclear
B)
Statement I is true; Statement II is false.
doneclear
C)
Statement I is false; Statement II is true.
doneclear
D)
Statement I is true; Statement II is true; Statements is the correct explanation for Statement I.
Directions: Question No. 83 are Assertion-Reason type. Each of these contains tow statements Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only on of which is correct. You have to select the correct choices from the codes a, b, c and d given below:
Statement I: If \[\vec{a},\vec{b}\]and \[\vec{c}\] are the unit vectors such that \[\vec{a}+\vec{b}+\vec{c}=\vec{0}\]then \[\vec{a}.\vec{b}+\vec{b}.\vec{c}+\vec{c}.\vec{a}\] \[=-3/2\].
If \[x\cos \theta =y\cos \left( \theta +\frac{2\pi }{3} \right)=z\cos \left( \theta +\frac{4\pi }{3} \right)\], then the value of \[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\] is equal to
The number of ways can 14 identical toys be distributed among three boys, so that each one gets at least one toy and no two boys get equal number of toys, is
If \[^{n}{{C}_{0}}{{,}^{n}}{{C}_{1}}{{,}^{n}}{{C}_{2}},\]????, \[^{n}{{C}_{n}}\]denote the binomial coefficients in the expansion of \[{{(1+x)}^{n}}\] and p + q = 1, then \[\sum\limits_{r=0}^{n}{{{r}^{n}}{{C}_{r}}{{p}^{r}}{{q}^{n-r}}}\]is
If the chords of contact of tangents from two points \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})\] to the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\]are at right angles, then \[\frac{{{x}_{1}}{{x}_{2}}}{{{y}_{1}}{{y}_{2}}}\] is equal to
If the tangent at any point on the curve x4 + y4 = c4 cuts off intercepts a and b on the coordinate axes, then value of \[{{a}^{-4/3}}+{{b}^{-4/3}}\] is
Directions: Question No. 94 are based on the following paragraph. If f(x) and g(x) be two function, such that f [a] = g [a] = 0 and f and g are both differentiable at everywhere in some neighborhood of point a except possibly a. The \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)}{g(x)}=\underset{x\to a}{\mathop{\lim }}\,\frac{f'(x)}{g'(x)'}\] provided \[f'\,(a)\] and \[g'\,(a)\]are not both zero The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\int_{0}^{{{x}^{2}}}{\sin \sqrt{t}dt}}{{{x}^{3}}}\] is
Directions: Question No. 95 are based on the following paragraph. If f(x) and g(x) be two function, such that f [a] = g [a] = 0 and f and g are both differentiable at everywhere in some neighborhood of point a except possibly a. The \[\underset{x\to a}{\mathop{\lim }}\,\frac{f(x)}{g(x)}=\underset{x\to a}{\mathop{\lim }}\,\frac{f'(x)}{g'(x)'}\] provided \[f'\,(a)\] and \[g'\,(a)\]are not both zero The value of \[\underset{x\to a}{\mathop{\lim }}\,\frac{x\int_{a}^{x}{f(t)dt}}{x-a}\] is
Let f: (-1,1) \[\to \] B, be a function defined by \[f(x)={{\tan }^{-1}}\left( \frac{2x}{1-{{x}^{2}}} \right),\] then f is both one-to-one and onto when B is the interval
A variable plane \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\]at a unit distance from origin cuts the coordinate axes at A, B and C. centric (x, y, z) satisfies the equation \[\frac{1}{{{x}^{2}}}+\frac{1}{{{y}^{2}}}+\frac{1}{{{z}^{2}}}=k,\] the value of k is
An unbiased die, with faces numbered 1, 2, 3, 4. 5, 6, is thrown n times and the list of n numbers shown up is noted. Then, the probability that, among the numbers 1,2,3,4, 5. 6, only three numbers appear in this list, is
If \[{{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}}\] are four positive real numbers such that, \[{{x}_{1}}+\frac{1}{{{x}_{2}}}=4,{{x}_{2}}+\frac{1}{{{x}_{3}}}=1,\] \[{{x}_{3}}+\frac{1}{{{x}_{4}}}=4\]and \[{{x}_{4}}+\frac{1}{{{x}_{1}}}=1\]then