A doubly ionized \[\text{L}{{\text{i}}^{\text{2+}}}\] ion in ground state absorbs 91.8 eV of energy. Find the increase in angular momentum of electron. (Take \[h=6.63\times {{10}^{-34}}J-s\])
A wire whose cross-section is 4mm2 is stretched by 0.1 mm by a certain weight. How far will a wire of the same material and length stretch, if its cross-sectional area is 8 mm2 and the same weight is attached?
A thin ring of mass 2.7 kg and radius 8 cm rotates about an axis through its centre and perpendicular to the plane of the ring at 1.5 rev/s. Calculate the kinetic energy of the ring.
Figure shows the elliptical path of a planet about the sun. The two shaded parts have equal area. If \[{{t}_{1}}\] and \[{{t}_{2}}\] be the time taken by the planet to go from a to b and from c to d respectively, then
A)
\[{{t}_{1}}<{{t}_{2}}\]
doneclear
B)
\[{{t}_{1}}={{t}_{2}}\]
doneclear
C)
\[{{t}_{1}}>{{t}_{2}}\]
doneclear
D)
Insufficient, information to deduce the relation between \[{{t}_{1}}\] and \[{{t}_{2}}\]
A particle has been projected at certain angle \[\text{ }\!\!\theta\!\!\text{ }\]with the horizontal, find the value of \[\text{ }\!\!\theta\!\!\text{ }\] for which the particle hits the ground in such a manner that initial and final velocity vectors are at \[90{}^\circ \].
A)
\[60{}^\circ \]
doneclear
B)
\[30{}^\circ \]
doneclear
C)
\[45{}^\circ \]
doneclear
D)
For any value of \[\text{ }\!\!\theta\!\!\text{ }\]
A particle is moving in a straight line with constant velocity 3 m/s. At t = 0, a force starts acting on the particle in a direction perpendicular to the direction of its initial motion which causes an acceleration of 1 m/s2. Determine the magnitude of particle's velocity at t = 3 s.
Three guns are aimed at the centre of a circle. They are mounted on the circle, \[120{}^\circ \] apart. They fire in a timed sequence, such that the three bullets collide at the centre and mash into a stationary lump. Two of the bullets have identical masses of 4.50 g each and speeds of\[{{v}_{1}}\]and \[{{v}_{2}}\]. The third bullet has a mass of 2.50 g and a speed of 575 m/s. Find the unknown speeds.
Direction: Question are Assertion - Reaction type. Each of these contains two statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes [a], [b], [c] and [d] given below:
Statement I: The fundamental units of velocity of light is \[3\times {{10}^{8}}\] m/s and acceleration. Due to gravity is \[10\text{ }m/{{s}^{2}}\] and the mass of proton is \[1.67\times {{10}^{-27}}\text{kg}\text{.}\]
Statement II: The value of time in such a system is \[3\times {{10}^{7}}\] s.
A)
Statement I is true; Statement II is true: Statement II is not a correct explanation of 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; Statement II is the correct explanation for Statement I.
Direction: Question are Assertion - Reaction type. Each of these contains two statements: Statement I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices, only one of which is correct. You have to select the correct choices from the codes [a], [b], [c] and [d] given below:
Statement I: Angle of repose is equal to the angle of limiting friction.
Statement II: When the body is just at the point of motion, the force of friction in this stage is called limiting friction.
A)
Statement I is true; Statement II is true: Statement II is not a correct explanation of 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; Statement II is the correct explanation for Statement I.
A child pushes a toy box 4.0 m along the floor by means of a force of 6 N directed downward at an angle of \[37{}^\circ \] to the horizontal. How much work does the child do?
Current passes through a solution of sodium chloride. In \[1.00\text{ }s,2.68\times {{10}^{16}}\] ions arrive at the negative electrode and 3.92 x 1016 \[\text{C}{{\text{l}}^{-}}\] ions arrive at positive electrode. Determine the current and the direction in which it is flowing.
The temperature of junction at which thermo emf is maximum, is called the neutral temperature
doneclear
B)
The temperature of the hot junction at which thermo emf changes its sign, is called the inversion temperature
doneclear
C)
If \[{{\theta }_{c}},{{\theta }_{i}}\] and \[{{\theta }_{n}}\] denote the temperature of cold junction, inversion temperature and neutral temperature respectively, then\[{{\theta }_{n}}-{{\theta }_{c}}={{\theta }_{i}}-{{\theta }_{n}}\]
An alternating current having peak value 14 A is used to heat a metal wire; To produce the same heating effect, a constant current i can be used, where i is
An earth satellite of mass M circles the earth with speed u. By how much does its momentum change as it goes halfway around the earth? (Ignore the earth's rotation)
Consider two light sources of wavelength \[{{\lambda }_{1}}\]and \[{{\lambda }_{2}}({{\lambda }_{1}}>{{\lambda }_{2}})\]which are emitting \[{{n}_{1}}\] and \[{{n}_{2}}\] photons respectively, in a given time. Assume equal power for both the sources, then
Ampere's law states that flux of B through any closed surface is \[{{\mu }_{0}}\]times the current passing through the area bounded by closed surface
doneclear
B)
Gauss's law for magnetic field in magneto statics serves the same purpose as Gauss's law for electric field in electrostatics
doneclear
C)
Gauss's law for magnetic field states that the flux of B through any closed surface is always zero, whether or not there are currents within the surface
The period of oscillation of a simple pendulum is given by \[T=2\pi \sqrt{\frac{l}{g}},\]where I is about 100 cm and is known to have 1 mm accuracy. The period is about 2s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is
The gravitational potential energy of a body of mass m at the earth's surface \[-mg{{\operatorname{R}}_{e}}.\]Its gravitational potential energy at a height \[{{\operatorname{R}}_{e}}\]from earth's surface will be (Here, \[{{\operatorname{R}}_{e}}\] is the radius of the earth)
Directions: Two capacitors of capacity 6\[\mu F\]and 3\[\mu F\]are charged to 100 V and 50 V separately and connected as shown. Now all the three switches \[{{S}_{1}},{{S}_{2}}\]and\[{{S}_{3}}\]are closed.
Directions: Two capacitors of capacity 6\[\mu F\]and 3\[\mu F\]are charged to 100 V and 50 V separately and connected as shown. Now all the three switches \[{{S}_{1}},{{S}_{2}}\]and\[{{S}_{3}}\]are closed.
Charges on both the capacitors in steady state will be on \[6\mu F\] first
Directions: Two capacitors of capacity 6\[\mu F\]and 3\[\mu F\]are charged to 100 V and 50 V separately and connected as shown. Now all the three switches \[{{S}_{1}},{{S}_{2}}\]and\[{{S}_{3}}\]are closed.
Suppose \[{{q}_{1}},{{q}_{2}}\]and \[{{q}_{3}}\] be the magnitudes of charges flown from switches \[{{S}_{1}},{{S}_{2}}\]and \[{{S}_{3}}\] after they are closed. Then
In four complete revolution of the cap, the distance travelled on the pitch scale is 2 mm. If there are 50 divisions on the circular scale, then the least count of the screw gauge is
In certain polar solvents, \[\text{PC}{{\text{l}}_{\text{s}}}\]undergoes an ionization reaction in which \[\text{C}{{\text{l}}^{-}}\]ion leaves one \[\text{PC}{{\text{l}}_{\text{5}}}\]molecule and attaches itself to another. \[\text{2PC}{{\text{l}}_{\text{5}}}\text{PCl}_{\text{4}}^{\text{+}}\text{+PCl}_{\text{6}}^{\text{-}}\]
Select incorrect statement (s).
A)
The dissociation is a redox reaction
doneclear
B)
Hybridization changes from \[s{{p}^{3}}d\] to \[s{{p}^{3}}{{d}^{2}}\]\[\text{(PCl}_{\text{6}}^{\text{-}}\text{)}\]and\[\text{s}{{\text{p}}^{\text{3}}}\text{(PCl}_{4}^{+}\text{)}\]
doneclear
C)
Structure changes from trigonal bipyramidal to tetrahedral \[\text{(PCl}_{4}^{+}\text{)}\]and octahedral \[\text{(PCl}_{6}^{-}\text{)}\]
In certain polar solvents, \[\text{PC}{{\text{l}}_{\text{s}}}\]undergoes an ionization reaction in which \[\text{C}{{\text{l}}^{-}}\]ion leaves one \[\text{PC}{{\text{l}}_{\text{5}}}\]molecule and attaches itself to another. \[\text{2PC}{{\text{l}}_{\text{5}}}\text{PCl}_{\text{4}}^{\text{+}}\text{+PCl}_{\text{6}}^{\text{-}}\]
Number of lone pairs around phosphorus in\[\text{PC}{{\text{l}}_{\text{5}}}\text{,PCl}_{\text{4}}^{\text{+}}\]and \[\text{PCl}_{6}^{-}\]are respectively
A compound formed by elements A and B has a cubic structure in which A atoms are at the comers of the cube and B atoms are at the face centres. The formula for the compound is
The vapour pressure of pure liquid solvent A is atm. When a nonvolatile substance B is added to the solvent, its vapour pressure drops to 0.60 atm. What is the mole fraction of component B in the solution?
Direction: Assertion- Reason type each of these contains two statements: Statements I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices. Only one of which is correct. You have to select the correct choices from the codes [a], [b], [c] and [d] given below:
Statement I: pH of 10 M HCI aqueous solution is less than 1.
Statement II: pH is negative logarithm of \[{{\text{H}}^{+}}\]Concentration.
A)
Statements is true; Statement II is true; Statements II is not the correct explanation for Statements 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; Statement II is the correct explanation for Statement I.
Direction: Assertion- Reason type each of these contains two statements: Statements I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices. Only one of which is correct. You have to select the correct choices from the codes [a], [b], [c] and [d] given below:
Statement I: Ethyl xanthate is used as a collector in froth floatation process.
Statement II: Collectors depress the floatation property of one of the components of the ore and thus, help in the separation of different, minerals present in the same ore.
A)
Statements is true; Statement II is true; Statements II is not the correct explanation for Statements 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; Statement II is the correct explanation for Statement I.
Direction: Assertion- Reason type each of these contains two statements: Statements I (Assertion), Statement II (Reason). Each of these questions also has four alternative choices. Only one of which is correct. You have to select the correct choices from the codes [a], [b], [c] and [d] given below:
Statement I: The atomic radii of the elements of the oxygen family are smaller than the atomic radii of the corresponding elements of the nitrogen family.
Statement II: The members of the oxygen family are more electronegative and thus, have lower values of nuclear charge than those of the nitrogen family.
A)
Statements is true; Statement II is true; Statements II is not the correct explanation for Statements 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; Statement II is the correct explanation for Statement I.
A mixture of formic acid and oxalic acid is heated with concentrated\[{{H}_{2}}S{{O}_{4}}\]. The gaseous product is passed into KOH solution where the volume decreases by 1/6th. The molecular proportion of the organic acids, formic acid and oxalic acid in the mixture is
In the preparation of p-nitro acetanilide from aniline, nitration is not done by nitrating mixture (a mixture of cone, \[{{H}_{2}}S{{O}_{4}}\]and cone.\[HN{{O}_{3}}\]) because
At \[20{}^\circ C\] and 1.00 atm partial pressure of hydrogen, 18 mL of hydrogen, measured at STP, dissolves in 1L of water. If water at \[20{}^\circ C\] is exposed to a gaseous mixture having a total pressure of 1400 Torr (excluding the vapour pressure of water) and containing 68.5% \[{{\text{H}}_{\text{2}}}\] by volume, find the volume of H2, measured at STP, which will dissolve in 1L of water.
A mixture of 0.50 mole of H2 and 0.50 mole of \[\text{S}{{\text{O}}_{\text{2}}}\] is introduced into a 10.0 L container at \[25{}^\circ C\]. The container has a 'pinhole' leak. After a period of time the partial pressure of \[{{\text{H}}_{\text{2}}}\] in the remaining mixutre
A)
exceeds that of \[\text{S}{{\text{O}}_{\text{2}}}\]
doneclear
B)
is equal to that of \[\text{S}{{\text{O}}_{\text{2}}}\]
doneclear
C)
is less than that of \[\text{S}{{\text{O}}_{\text{2}}}\]
The tangent at the point \[({{x}_{1}},{{y}_{1}})\]to the parabola y2 = 4ax meets the parabola \[{{y}^{2}}=4a\](x+b) at Q and R, then the midpoint of QR is
If \[{{F}_{1}}\] and \[{{F}_{2}}\] be the feet of the perpendiculars, from the foci \[{{S}_{1}}\] and \[{{S}_{2}}\] of an ellipse \[\frac{{{x}^{2}}}{5}+\frac{{{y}^{2}}}{3}=1\]on the tangent at any point P on the ellipse, then \[({{S}_{1}}{{F}_{1}})({{S}_{2}}{{F}_{2}})\]is equal to
Let \[\overrightarrow{a},\overrightarrow{b}\] and \[\overrightarrow{c}\] be three non-zero vectors, no two of which are collinear. If the vector \[\overrightarrow{a}+2\overrightarrow{b}\]is collinear with \[\overrightarrow{c}\] and \[\overrightarrow{b}+3\overrightarrow{c}\] is collinear with\[\overrightarrow{a}\], then \[\overrightarrow{a}+2\overrightarrow{b}+6\overrightarrow{c}\]is equal to
Direction: Question Based on the following paragraph.
Let \[f:A\to B\]be a function defined by y=f(x) such that f is both one-one (Injective) and onto Surjective), then there exists a unique function \[g:B\to A\]such that \[f(x)=y\leftrightarrow g\] \[(y)=x,\forall x\in A\]and \[y\in B,\]then g is said to be inverse off Thus,\[g={{f}^{-1}}:B\to A=[\{f(x),x\}:\{x,f(x)\}\in {{f}^{-1}}]\] If no branch of an inverse trigonometric function is mentioned, then it means the principal value branch of that function.
If \[\frac{3\pi }{2}\le x\le \frac{5\pi }{2},\]then \[{{\sin }^{-1}}(\sin x)\]is equal to
Direction: Question Based on the following paragraph.
Let \[f:A\to B\]be a function defined by y=f(x) such that f is both one-one (Injective) and onto Surjective), then there exists a unique function \[g:B\to A\]such that \[f(x)=y\leftrightarrow g\] \[(y)=x,\forall x\in A\]and \[y\in B,\]then g is said to be inverse off Thus,\[g={{f}^{-1}}:B\to A=[\{f(x),x\}:\{x,f(x)\}\in {{f}^{-1}}]\] If no branch of an inverse trigonometric function is mentioned, then it means the principal value branch of that function.
If \[x>1,\]then the value of \[2{{\tan }^{-1}}x+{{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right)\]is
The base of a cliff is circular. From the extremities of a diameter of the base of angles of elevation of the top of the cliff are \[30{}^\circ \] and If the height of the cliff be 500 m, then the diameter of the base of the cliff is
If \[f(x)={{\sin }^{2}}x+{{\sin }^{2}}\left( x+\frac{\pi }{3} \right)\] \[+\cos x\cos \left( x+\frac{\pi }{3} \right)\]and \[g\left( \frac{5}{4} \right)=1,\]then g of (x) is equal to
Suppose \[{{A}_{1}},{{A}_{2}},...,{{A}_{30}}\]are thirty sets each with five elements and \[{{B}_{1}},{{B}_{2}},...,{{B}_{n}}\]are n sets each with three elements such that \[\underset{i=1}{\overset{30}{\mathop{\cup }}}\,{{A}_{i}}=\underset{i=1}{\overset{n}{\mathop{\cup }}}\,{{B}_{i}}=S\]. If each element of S belongs to exactly ten of \[{{A}_{i}}'s\] and exactly 9 of the \[{{B}_{j}}'s\], then the value of n is
Directions: Assertion-Reason type questions. Each of these questions contains two statements: Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice in the codes [a], [b], [c] and [d] in the given below:
Statement I : If equations \[a{{x}^{2}}+bx+c=0;\] \[(a,b,c\in R)\]and 2x2 + 3x + 4 = 0 have a common root, then a : b : c = 2 : 3 : 4.
Statement II: Roots of 2x2 + 3x + 4 = 0 are imaginary.
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; Statement II is a correct explanation for Statement I.
Directions: Assertion-Reason type questions. Each of these questions contains two statements: Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice in the codes [a], [b], [c] and [d] in the given below:
Statement I: If a + b + c = 12; (a, b, c > 0), then maximum value of abc is 64.
Statement II: Maximum value occurs when a = b = c.
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; Statement II is a correct explanation for Statement I.
Directions: Assertion-Reason type questions. Each of these questions contains two statements: Statement I (Assertion) and Statement II (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice in the codes [a], [b], [c] and [d] in the given below:
Statement I: The term independent of an the expansion of \[{{\left( x+\frac{1}{x}+2 \right)}^{21}}\]is \[^{42}{{C}_{21}}\].
Statement II: In a binomial expansion middle term is independent of x
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; Statement II is a correct explanation for Statement I.
A box contains 100 tickets numbered only one maximum 1, 2, ...,100. Two tickets are chosen at random. It is given that the maximum number on the t two chosen tickets is not more than 10. Then, the probability that the minimum number on them is 5, is
Let \[p(x)={{a}_{0}}+{{a}_{1}}{{x}^{2}}+{{a}_{2}}{{x}^{4}}+....+{{a}_{n}}{{x}^{2n}}\]be a polynomial in a real variable x with\[0<{{a}_{0}}<{{a}_{1}}<{{a}_{2}}<....<{{a}_{n}}\]. The function p(x) has