In the experiment to determine the speed of sound using a resonance column,
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In the experiment to determine the speed of sound using a resonance column,
A student performs an experiment to determine the Young’s modulus of a wire, exactly 2 m long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of $$\pm 0.05$$ mm at load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of $$\pm 0.01$$ mm. Take g = 9.8 m/s$$^2$$ (exact). The Young’s modulus obtained from the reading is
A particle moves in the X-Y plane underthe influence of a force such that its linear momentum is $$\overrightarrow{p}(t) = A\left[\hat{i} \cos (kt) - \hat{j} \sin (kt)\right]$$, where A and k are constants. The angle between the force and the momentum is
A small object of uniform density rolls up a curved surface with an initial velocity v. It reaches up to a maximum height of $$\frac{3v^2}{4g}$$ with respect to the initial position. The object is
Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is $$\rho$$, the surface tension of water is T and the atmospheric pressure is $$P_0$$. Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude.
A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as showing the figure. The electric field inside the emptied space is
Positive and negative point charges of equal magnitude are kept at $$\left(0, 0, \frac{a}{2}\right)$$ and $$\left(0, 0, \frac{-a}{2}\right)$$, respectively. The work done by the electric field when another positive point charge is moved from (-a, 0, 0) to (0, a, 0) is
A magnetic field $$\overrightarrow{B} = B_0\hat{j}$$ exists in the region a < x < 2a and $$\overrightarrow{B} = -B_0 \hat{j}$$, in the region 2a < x < 3a, where $$B_0$$ is a positive constant. A positive point charge moving with a velocity $$\overrightarrow{v} = v_0 \hat{i}$$, where $$v_0$$ is a positive constant, enters the magnetic field at x = a. The trajectory of the charge in this region can be like,
Electrons with de-Broglie wave length $$\lambda$$ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is
STATEMENT-1
If there is no external torque on a body aboutits center of mass, then the velocity of the center of mass remains constant.
because
STATEMENT-2
The linear momentum of an isolated system remains constant.
STATEMENT-1
A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from thetable.
because
STATEMENT-2
For every action there is an equal and opposite reaction.
STATEMENT-1
A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as showing the figure. The ring can float at a certain height above the coil.
because
STATEMENT-2
In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.
STATEMENT-1
The total translational kinetic energy of all the molecules of a given massof an ideal gas is 1.5 times the product of its pressure and its volume.
because
STATEMENT-2
The molecules of a gas collide with each other and the velocities of the molecules change dueto thecollision.
The speed of sound of the whistle is
The distribution of the sound intensity of the whistle as observed by the passengers in train A is best represented by
The spread of frequency as observed by the passengersin train B is
Light travels as a
The phases of the light wave at c, d, e and f are $$\phi_C, \phi_d, \phi_e$$ and $$\phi_f$$ respectively. It is given that $$\phi_c \neq \phi_f$$.
Speed of light is
Column I describes some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situations in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.
Two wires each carrying a steady current J are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.
Column I gives some devices and Column II gives some processes on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.
Consider a titration of potassium dichromate solution with acidified Mohr’s salt solution using diphenylamine as indicator. The number of moles of Mohr’s salt required per mole of dichromate is
Among the following metal carbonyls, the C-O bond order is lowest in
A solution of a metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give a colourless solution. Moreover, the solution of metal ion on treatment with a solution of cobalt(II) thiocyanate gives rise to a deep blue crystalline precipitate. The metal ion is
Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives compound E. Compound E on further treatment with aqueous KOH yields compound F. Compound F is
The numberof stereoisomers obtained by bromination of trans-2-butene is
Among the following, the least stable resonance structure is
A positron is emitted from $$_{11}^{23}Na$$. The ratio of the atomic mass and atomic number of the resulting nuclide is
For the process $$H_2O(l)$$ (1 bar, 373 K) $$\rightarrow H_2O(g)$$(1 bar, 373 K), the correct set of thermodynamic parameters is
Consider a reaction $$aG + bH \rightarrow$$ Products. When concentration of both the reactants G and is doubled, the rate increases by eight times. However, when concentration of G is doubled keeping the concentration of H fixed, the rate is doubled. The overall order of the reaction is
STATEMENT-1: Alkali metals dissolve in liquid ammoniato give blue solutions.
because
STATEMENT-2: Alkali metals in liquid ammonia give solvated species of the type $$[M(NH_3)_n]^{+}$$ (M = alkali metals).
STATEMENT-1: Glucose gives a reddish-brown precipitate with Fehling’s solution.
because
STATEMENT-2: Reaction of glucose with Fehling’s solution gives CuO and gluconic acid.
STATEMENT-1: Molecules that are not superimposable on their mirror images are chiral.
because
STATEMENT-2: All chiral molecules have chiral centres.
STATEMENT-1: Band gap in germanium is small.
because
STATEMENT-2: The energy spread of each germanium atomic energy level is infinitesimally small.
Among the following, identify the correct statement.
While $$Fe^{3+}$$ is stable, $$Mn^{3+}$$ is not stable in acid solution because
Sodium fusion extract, obtained from aniline, on treatment with iron(II) sulphate and $$H_2SO_4$$ in presence of air gives a Prussian blue precipitate. The blue colour is due to the formation of
Which one of the following reagents is used in the above reaction?
The electrophile in this reaction is
The structure of the intermediate I is
Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.
Match the compounds/ions in Column I with their properties/reactions in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.
Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the $$4 \times 4$$ matrix given in the ORS.
Let O(0, 0), P(3, 4), Q(6, 0) be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are
If $$\mid z \mid = 1$$ and $$z \neq \pm 1$$, then all the values of $$\frac{z}{1 - z^2}$$ lie on
Let $$E^c$$ denote the complement of an event E. Let E, F, G be pairwise independent events with $$P(G) > 0$$ and $$P(E \cap F \cap G) = 0$$. Then $$P(E^c \cap F^c \mid G)$$ equals
$$\frac{d^2x}{dy^2}$$ equals
The differential equation $$\frac{dy}{dx} = \frac{\sqrt{1 - y^2}}{y}$$ determines a family of circles with
Let $$\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$$ be unit vectors such that $$\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} = \overrightarrow{0}$$. Which one of the following is correct?
Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB =2CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touchingall the sides, then its radius is
Lat $$f(x) = \frac{x}{\left(1 + x^n\right)^{\frac{1}{n}}}$$ for $$n \geq 2$$ and $$g(x) = \underbrace{(f\circ f \circ ... \circ f)(x)}_{f occurs n times}$$. Then $$\int x^{n-2}g(x)dx$$ equals
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is
Consider the planes $$3x - 6y - 2z = 15$$ and $$2x + y - 2z = 5$$.
STATEMENT-1: The parametric equations of the line of intersection of the given planes are $$x = 3 + 14t, y = 1 + 2t, z = 15t.
because
STATEMENT-2: The vector $$14\hat{i} + 2 \hat{j} + 15 \hat{k}$$ is parallel to the line ofintersection of given planes.
STATEMENT-1: The curve $$y = \frac{-x^2}{2} + x + 1$$ is symmetric with respect to the line x = 1.
because
STATEMENT-2: A parabola is symmetric aboutits axis.
Let $$f(x) = 2 + \cos x$$ for all real x.
STATEMENT-1: For each real t, there exists a point c in $$[t, t + \pi]$$ such that $$f'(c) = 0.$$
because
STATEMENT-2: $$f(t) = f(t + 2\pi)$$ for each real t.
Lines $$L_1 : y - x = 0$$ and $$L_2 : 2x + y = 0$$ intersect the line $$L_3 : y + 2 = 0$$ at P and Q, respectively. The bisector of the acute angle between $$L_1$$ and $$L_2$$ intersects $$L_3$$ at R.
STATEMENT-1: The ratio PR : RQ equals $$2\sqrt{2} : \sqrt{5}.$$
because
STATEMENT-2: In any triangle, bisector of an angle divides the triangle into two similar triangles.
Which one of the folowing statements is correct?
Which one of the following statements is correct?
Which one of the following statements is correct?
If a continuous function f defined on the real line R, assumespositive and negative values in R then the equation f(x)=0 has a root in R. For example, if it is known that a continuous function f on R is positive at some point and its minimum value is negative then the equation f(x) = 0 has a root in R.
Consider $$f(x) = ke^x - x$$ for all real x where kis a real constant.
The line y = x meets $$y = ke^x$$ for $$k \leq 0$$ at
The positive value of k for which $$ke^x - x = 0$$ has only one root is
For $$k > O$$, the set of all values of k for which $$ke^x - x = 0$$ has two distinct roots is
Let $$f(x) = \frac{x^2 - 6x + 5}{x^2 - 5x + 6}$$.
Match the expressions/statements in Column I with expressions/statements in Column II and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.
Let (x, y) be such that $$\sin^{-1}(ax) + \cos^{-1}(y) + \cos^{-1}(bxy) = \frac{\pi}{2}.$$
Match the statements in Column I with statements in Column II and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.
Match the statements in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.
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