Two bodies of equal mass are projected horizontally with equal velocity V to move along the paths AB and A' B' as shown in the figure. The path AB and A'B' are frictionless and lie in a vertical plane. Let the time taken by body in making displacement \['d'\] be \[{{t}_{1}}\], and \[{{t}_{2}}\] for path AB and A' B' respectively. (Assume that body does not lose contact at any point). Then
Wind is blowing at constant velocity\[\text{\vec{V}}\]towards west. A man initially at rest start moving with constant acceleration \[a\] towards north. Then the moment of time at which direction of wind appears south west to him is
Three gears A, B and C are in contact with each other and rotate about their respective axes passing through their centre of mass. Radius of gear A is R, that of B is 2R and that of C is 3R. When A is given angular velocity co, it rotates B and B in turn rotates C with angular \[\omega ,\]velocity \[{{\omega }_{1}}.\]Now B is replaced with another gear B of radius 4R. Now A is again rotated with angular velocity \[\omega \], it rotates B which in turn rotates C with angular velocity \[{{\omega }_{2}}\] now
A particle is executing SHM with period T and amplitude 13 cm, its equilibrium position being its velocity at a distance of \[x\] cm from O is 96 cm/s. Then T in seconds and \[x\] in cm may be
Two insects P and Q are firmly sitting at the ends of a mass less semicircular wire of radius R and two more insects A and B are firmly sitting at the bottom of the wire. The wire is given an angular velocity\[{{\omega }_{0}}\]about a vertical axis through its centre as shown in the figure. Mass of each insect is M, Now A and B crawl to the opposite ends to meet P and Q. Final angular velocity attained by the rod is equal to
A mass at rest explodes into 4 identical particles which fly in different directions in same plane with equal speeds. Which of the following combination of angles may be the right set showing the possible direction?
If one mole of an ideal monotonic gas \[(\gamma =5\text{/}3)\] is mixed with one mole of ideal diatomic gas \[(\gamma =7\text{/5}),\], the value of \[\gamma \] for the mixture will be
A uniform heavy rod of weight W. cross-sectional area A and length L is hanging from a fixed support. Young's modulus of the material of the rod is Y. Neglect the lateral contraction. Find the elongation of the rod.
Statement I It is convenient to define two specific heats \[{{C}_{p}}\] and \[{{C}_{V}}\] in case of a gas. However it is not generally necessary to define two specific heats in case of a solid or liquid
Statement II For a given temperature rise, the expansion of a solid or liquid is negligible as compared to that of a gas.
A)
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
doneclear
B)
Statement-1 is True, Statement-2 is 'I rue; Statement-2 is NOT a correct explanation for Statement-1
A racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a frequency twice than the actual sound of the horn. If V = the velocity of sound, the velocity of the car is
In a resonance tube water is filled so that height of air column is 0.1 m when it resonates in its fundamental mode. Now water is removed so that the height of air column becomes 0.35 m and it resonates with next higher frequency. Then end correction is
If the Young's modulus of material of rod is \[2\times {{10}^{11}}N/{{m}^{2}}\] and density is 8000 kg/m3, what is the time taken by sound wave to travel 1 m of the rod?
Which of the following graph correctly represents variation of \[emf\] developed in the rectangular conducting loop as it enters a uniform magnetic field with constant acceleration 'a' starting from rest at \[t=0\] as shown in the diagram.
Two long parallel straight conductors carry current \[{{\text{i}}_{\text{1}}}\], and \[{{\text{i}}_{2}}\]\[\text{(}{{\text{i}}_{1}}>{{\text{i}}_{\text{2}}}).\]When the currents are in the same direction, the magnetic field at a point midway between the wires is \[20\mu T\]. If the direction of \[{{\text{i}}_{\text{2}}}\]is reversed, the field becomes \[50\mu T\]. The ratio of the currents \[{{\text{i}}_{1}}\text{/}{{\text{i}}_{\text{2}}}\]is:
A line of charge with linear charge density X extends along the z-axis from \[z=-h\] to \[z=+h\]. The distance of the point on the y-axis where electric field has magnitude \[\frac{\lambda }{\sqrt{8}\pi {{\in }_{0}}h},\]is
Sensitiveness of galvanometer is 10 division per amp. In order to change the sensitiveness to 2 divisions per amp how much shunt should be used? Resistance of galvanometer \[=100\,\Omega \]
A ray of light is incident at angle i on a surface of a prism of small angle A & emerges normally from the opposite surface. If the refractive index of the material of the prism is \[\mu \], the angle of incidence i is nearly equal to:
A vessel is quarter filled with a liquid of refractive index \[\mu \]. The remaining parts of the vessel is filled with an immiscible liquid of refractive index \[3\mu \text{/}2\]. The apparent depth of the vessel is 50% of the actual depth. The value of \[\mu \], is
Consider the nuclear reaction\[{{X}^{200}}\xrightarrow[{}]{{}}{{A}^{110}}+{{B}^{90}}\]. If the binding energy per nucleon for X, A and B is 7.4 MeV, 8.2. MeV and 8.2 MeV respectively, what is the energy released?
The dependence of g on geographical latitude at sea level is given by \[g={{g}_{0}}(1+\beta {{\sin }^{2}}\phi )\]where \[\phi \] is the latitude angle and \[\beta \] is a dimensionless constant. If \[\Delta g\] is the error in the measurement of g then the error in measurement of latitude angle is
You are walking down a long hallway that has many light fixtures in the ceiling and a very shiny newly waxed floor. In the floor, you see reflections of every light fixture. Now you put on sunglasses that are polarized. Some of the reflections of the light fixtures cannot longer be seen. The reflections that disappear are those
A carnot refrigerator A works between \[-10{}^\circ C\] and\[27{}^\circ C\], while refrigerator B works between\[-27{}^\circ C\] and\[17{}^\circ C\], both removing heat equal to 2000 J from the freezer. Which of the two is better refrigerator?
A silverrod is immersed in saturated \[A{{g}_{2}}S{{O}_{4}}\] solution. When connected with SHE, EMF of 0.71 IV was observed. If SRP of \[A{{g}^{+}}/Ag\] is 0.799V then the value of solubility product of \[A{{g}_{2}}S{{O}_{4}}\]will be:
The equilibrium \[{{A}_{4}}(g)+6{{B}_{2}}(g)4A{{B}_{3}}\](g) is established in a closed container by taking equal moles of \[{{A}_{4}}(g)\] and \[{{B}_{2}}(g)\]. Which of the following options must be correct at equilibrium?
Osmotic pressure of urea solution is 380 mm at a temperature of \[10{}^\circ C\]. The solution is diluted and the temperature is raised to \[30{}^\circ C\] and the osmotic pressure is found to be 122 mm. The extent of dilution will be:
In a cubic arrangement of atoms of A, B and C, atoms of A are present at the comers of the unit cell, B atoms are at face centers and C at tetrahedral voids. If one of the atom from one corner is missing in the unit cell , then the simplest formula of compound will be:
[A]\[\xrightarrow[(ii){{H}^{+}}]{(i)KOH\Delta }\] [B]\[\xrightarrow[(1\,equiv)]{B{{r}_{2}}/{{H}_{2}}O}\] \[(E)\xleftarrow[(1\,equiv.)\,]{{{(C{{H}_{3}}CO)}_{2}}O}(D)\] E will be-
Which of the following options is correct regarding spontaneity of a process occurring on a system in which only pressure volume work is involved and S, G, Cl, H, V and P have usual meaning as in thermodynamics.
Give the correct order of initials T or F for following statements. Use T if statement is true and F if it is false. [a]\[SOC{{l}_{2}},PC{{l}_{3}}\] and HCl all converts an alcohol into alkyl halide [b] Mechanism of all the three reagent are identical [c] Mechanism for \[SOC{{l}_{2}}\] and \[PC{{l}_{3}}\] are identical but different mechanism is followed in case of \[HCl\] [d] They all are used commercially to convert acetic acid into acetyl chloride.
For photochemical dimidiation of \[{{C}_{12}}{{H}_{14}}\]to obtain \[{{C}_{24}}{{H}_{24}},\] the proposed rate law is \[\frac{d[{{C}_{24}}{{H}_{28}}]}{dt}=\frac{{{K}_{1}}{{K}_{3}}{{I}_{abs}}[{{C}_{12}}{{H}_{14}}]}{{{K}_{2}}+{{K}_{3}}[{{C}_{12}}{{H}_{14}}]}\] \[{{I}_{abs}}=\] Intensity of absorbed light. What will be the value of rate of formation of \[{{C}_{24}}{{H}_{28}}\] if the reaction follows zero order.
\[\text{M}{{\text{e}}_{\text{3}}}\text{C-}\overset{\begin{smallmatrix} \text{O} \\ \text{ }\!\!|\!\!\text{ }\!\!|\!\!\text{ } \end{smallmatrix}}{\mathop{\text{C}}}\,\text{-}\overset{\text{18}}{\mathop{\text{O}}}\,\text{-CM}{{\text{e}}_{\text{3}}}\xrightarrow[{}]{dil.\,{{H}_{2}}S{{O}_{4}}}\]. Product of this reaction and the mechanism is:
If two tangents drawn from the point P to the parabola \[{{y}^{2}}=12x\] be such that the slope of the tangent is double the other, then' P' lies on the curve
A continuous function \[f:R\to R\] satisfy the differential equation \[f(x)=(1+{{x}^{2}})\] \[\left( l+\int\limits_{0}^{x}{\frac{{{f}^{2}}(t)}{1+{{t}^{2}}}dt} \right)\] then the value of f (-2) is
The probability of India wining a test match against West Indies is 1/2. Assuming independence from match to match the probability that in a 5 match series India's second win occurs at the third test is
If \[\overset{\to }{\mathop{a}}\,,\overset{\to }{\mathop{b}}\,,\overset{\to }{\mathop{c}}\,\] are unit vectors, then the value of \[|\overset{\to }{\mathop{a}}\,-2\overset{\to }{\mathop{b}}\,{{|}^{2}}+|\overset{\to }{\mathop{b}}\,-2\overset{\to }{\mathop{c}}\,{{|}^{2}}+|\overset{\to }{\mathop{c}}\,-2\overset{\to }{\mathop{a}}\,{{|}^{2}}\] does not exceed
Let A be the point (1, 2, 3) and B be a point on the line\[\overset{\to }{\mathop{r}}\,=(\hat{i}-\hat{j}+5\hat{k})+\lambda (-2\hat{i}+3\hat{j}+4\hat{k})\] Then the value of '\[\lambda \]' for which line AB is perpendicular to the plane \[4x+9y-18z=1\] is
The tangent and normal at the point P (18, 12) of the parabola \[{{y}^{2}}=8x\] intersects the x-axis at the points Q and R respectively. The equation of the circle through P, Q and R is given by
The area of the rectangle formed by the perpendicular from centre of \[\frac{{{x}^{2}}}{9}+\frac{{{y}^{2}}}{4}=1,\]to the tangent and normal at the point whose eccentric angle is \[\frac{\pi }{4}\]equals
Let A be a matrix of order \[3\times 3\] such that\[|A|=1.\]Let \[B=2{{A}^{-1}}\]and\[C=\frac{adj.A}{2}.\] Then the value of \[|A{{B}^{2}}{{C}^{3}}|,\]is (where |A| represent det. A)
If z be a complex number such that the equation \[|z-{{k}^{2}}|+|z+2k|=3\] always represents an ellipse then the number of integers in the range of k (where \[k\in R\]) is/are
Let \[x={{4}^{{{\log }_{2}}\sqrt{{{9}^{k-1}}+7}}}\] and \[y=\frac{1}{{{32}^{\log 2\,\sqrt[5]{{{3}^{k-1}}+1}}}}\] and \[xy=4\], then the sum of the cubes of the real value(s) of k is
If the curves \[{{(x-20)}^{2}}+{{(y-20)}^{2}}={{r}^{2}}\] and \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{1}=100\]intersects orthogonally at a point \[(20\cos \theta ,10\sin \theta )\] then
If\[\underset{n\to \infty }{\mathop{\lim }}\,\frac{{{l}^{a}}+{{2}^{n}}+{{3}^{a}}+...+{{n}^{a}}}{{{n}^{a+1}}}=\frac{1}{5},\] (where \[a>-1\]) then the value of 'a' is
The value of \[\int\limits_{0}^{3}{\frac{{{\tan }^{-1}}(x-[x])}{1+{{(x-[x])}^{2}}}}dx\] is equal to [Note: [ y ] denotes greatest integer function of y.]