Recent questions tagged past papers

A diatomic molecule is made of two masses $m_1$ and $m_2$ which are separated by a distance $r$. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by (n is an integer)

asked Dec 11, 2018 by pady_1

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An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1 cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film ?

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A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now

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Two cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$, respectively. Their speeds are such that they make complete circles in the same times t. The ratio of their centripetal acceleration is

asked Dec 11, 2018 by pady_1

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This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$. If stretched by the same amount, work done on $S_1$, will be more than that on $S_2$. Statement 2 : $k_1 < k_2$.

asked Dec 11, 2018 by pady_1

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A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be

asked Dec 11, 2018 by pady_1

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Assume that a neutron breaks into a proton and an electron. The energy released during this process is (Mass of neutron = $1.6725 \times 10^{-27}\;kg$; mass of proton = $1.6725 \times 10^{-27} \;kg$ mass of electron = $9 \times 10^{-31}\; kg $)

asked Dec 11, 2018 by pady_1

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A radar has a power of 1 Kw and is operating at a frequency of 10 GHz. It is located on a mountain top of height 500 m. The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth = $6.4 \times 10^{6} m$ ) is

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Truth table for system of four NAND gates as shown in figure is

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A charge Q is uniformly distributed over the surface of non conducting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity $\omega$. As a result of this rotation a magnetic field of induction B is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity of be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure

asked Dec 11, 2018 by pady_1

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A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5 \times 10^{-2}N$ (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is

asked Dec 11, 2018 by pady_1

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This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements Statement 1 : Davisson-germer experiment established the wave nature of electrons. Statement 2 : If electrons have wave nature, they can interfere and show diffraction.

asked Dec 11, 2018 by pady_1

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A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be

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Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is

asked Dec 11, 2018 by pady_1

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Two electric bulbs marked 25 W - 220 V and 100 W - 220 V are connected in series to a 440 V supply. Which of the bulbs will fuse ?

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A particle of mass m is at rest at the origin at time t=0. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ direction. Its speed v(t) is depicted by which of the following curves ?

asked Dec 11, 2018 by pady_1

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A liquid in a beaker has temperature $\theta(t)$ at time $t$ and $\theta_0$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between $log_e (\theta - \theta_0)$ and $t$ is

asked Dec 11, 2018 by pady_1

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In Young's double slit experiment, one of the slit is wider than other, so that the amplitude of the light from one slit is double of that from other slit. If $I_m$ be the maximum intensity, the resultant intensity $I$ when they interfere at phase difference $\phi$ is given by

asked Dec 11, 2018 by pady_1

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Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas )

asked Dec 11, 2018 by pady_1

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The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of 'g' and 'R' (radius of earth) are $10\; m/s^2$ and 6400 km respectively. The required energy for this work will be :

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A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to :

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Hydrogen atom is excited from ground state to another state with pricipal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be

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If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between $t = Os$ to $ t = \tau s$, then $\tau$ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is ( assuming damping is small ) in seconds :

asked Dec 11, 2018 by pady_1

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An electromagnetic wave in vacuum has the electric and magnetic fields $\overrightarrow{E}$ and $\overrightarrow{B}$, which are always perpendicular to each other. The direction of polarization is given by $\overrightarrow{X}$ and that of wave propagation by $\overrightarrow{k}$. Then :

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In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as a function of distance from the centre. The graph which would correspond to the above will be

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The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant $\tau$ of this circuit lies between :

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A wooden wheel of radius $R$ is made of two semicircular parts (see figure); The two parts are held together by a ring made of a metal strip of cross sectional area $S$ and length $L$. $L$ is slightly less than $2 \pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$, and its Youngs' modulus is $Y$, the force that one part of the wheel applies on the other part is :

asked Dec 11, 2018 by pady_1

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Let ABCD be a parallelogram such that $\overrightarrow{AB} = \overrightarrow{q}, \overrightarrow{AD} = \overrightarrow{p}$ and $\angle{BAD}$ be an acute angle. If $\overrightarrow{r}$ is the vector that coincides with the altitude directed from the vertex B to the side AD, then $\overrightarrow{r}$ is given by

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A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

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Consider the function $f(x) = |x-2| + |x-5|, x \in R$. Statement 1: $f'(4) = 0$ Statement 2 : $f$ is continuous in [2, 5], differentiable in (2, 5) and $f(2) = f(5)$.

asked Dec 11, 2018 by pady_1

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An ellipse is drawn by taking a diameter of the circle $(x-1)^2 + y^2 = 1$ as its semiminor axis and a diameter of the circle $x^2+(y-2)^2 = 4$ as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipseis

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Let $X = \{1, 2, 3, 4, 5\}$. The number of different ordered pairs $(Y, Z)$ that can be formed such that $Y \subseteq X, Z \subseteq X$ and $ Y \cap Z$ is empty, is

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The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is

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If $\begin{align}g(x) = \int_0^x \cos \; 4t \; dt \end{align}$, then $g(x+ \pi)$ equals

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Let P and Q be $3 \times 3$ matrices with $P \neq Q$. If $P^3 = Q^3$ and $P^2Q= Q^2P$, then determinant of $(P^2+Q^2)$ is equal to

asked Dec 11, 2018 by pady_1

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If $z \neq 1$ and $\frac{z^2}{z-1}$ is real, then the point represented by the complex number $z$ lies

asked Dec 11, 2018 by pady_1

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Three numbers are chosen at random without replacement from $\{1, 2, 3, ....,8 \}$. The probability that their minimum is 3, given that their maximum is 6, is

asked Dec 11, 2018 by pady_1

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If the lines $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $ \frac{x-3}{1} = \frac{y-k}{2} = \frac{z}{1}$ intersect, then $k$ is equal to

asked Dec 11, 2018 by pady_1

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If $f : R \to R$ is a function defined by $f(x) = [x] \cos (\frac{2x-1}{2}) \pi$, where $[x]$ denotes the greatest integer function, then $f$ is

asked Dec 11, 2018 by pady_1

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Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

asked Dec 11, 2018 by pady_1

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The area bounded between the parabolas $x^2 = \frac{y}{4}$ and $x^2= 9y$ and the straight line $y = 2$ is

asked Dec 11, 2018 by pady_1

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Let $a, b \in R$ be such that the function $f$ given by $f(x) = In \; |x| + bx^2 + ax, \; \; x \neq 0$ has extreme values at $x = -1$ and $x = 2$ Statement 1 : $f$ has focal maximum at $x = -1$ and at $x = 2$ Statement 2 : $ a = \frac{1}{2}$ and $b = \frac{-1}{4}$

asked Dec 11, 2018 by pady_1

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Let $x_1, x_2, ....., x_n$ be $n$ observations, and let $\overline{x}$ be their arithematic mean and $\sigma^2$ be their variance. Statement 1 : Variance of $2x_1, 2x_2, ....,2x_n$ is $4 \sigma^2$ Statement 2 : Arithmetic mean of $2x, 2x_2, .... , 2x_n$ is $4 \overline{x}$.

asked Dec 11, 2018 by pady_1

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If the line $2x + y = k$ passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio $ 3 : 2$, then $k$ equals

asked Dec 11, 2018 by pady_1

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An equation of a plane parallel to the plane $ x - 2y + 2z - 5 = 0 $ and at a unit distance from the origin is

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In a $\Delta PQR$, if $ 3 \sin P + 4 \cos Q = 6 $ and $4 \sin Q + 3 \cos P = 1$, then the angle R is equal to

asked Dec 11, 2018 by pady_1

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If 100 times the $100^{th}$ term of an AP with non zero common difference equal the 50 times its $50^{th} $ term, then the $150^{th}$ term of this AP is

asked Dec 11, 2018 by pady_1

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If $n$ is a positive integer, then $(\sqrt{3} + 1)^{2n} - (\sqrt{3} - 1)^{2n}$ is

asked Dec 11, 2018 by pady_1

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Let $A = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{pmatrix}$. If $u_1$ and $u_2$ are column matrices such that $Au_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix} $ and $Au_2 = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} $, then $u_1 + u_2$ is equal to

asked Dec 11, 2018 by pady_1

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Statement 1 : An equation of a common tangent to the parabola $y^2 = 16 \sqrt{3}x$ and the ellipse $2x^2 + y^2 = 4$ is $y = 2x + 2\sqrt{3}$. Statement 2 : If the line $y = mx + \frac{4 \sqrt{3}}{m}, (m \neq 0)$ is a common tangent to the parabola $y^2 = 16 \sqrt{3}x $ and the ellipse $2x^2 + y^2 = 4$, then $m$ satisfies $m^2 + 2m^2 = 24$.

asked Dec 11, 2018 by pady_1

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