Recent questions tagged 2012

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

1 answer

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 :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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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

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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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

1 answer

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

1 answer

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

1 answer

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

asked Dec 11, 2018 by pady_1

0 answers

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

1 answer

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

1 answer

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

asked Dec 11, 2018 by pady_1

1 answer

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

1 answer

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

1 answer

If the integral $\begin{align} \int \frac{5 \tan x}{\tan x - 2} dx = x + a \;In |\sin x - 2 \cos x | + k \end{align}$, then $a$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

The negation of the statement "If I become a teacher, then I will open a school" is

asked Dec 11, 2018 by pady_1

1 answer

Statement 1 : The sum of the series $ 1 + ( 1 + 2+4) + (4+6+9) + (9+12+16) + .......+ (361 + 380+400)$ is $8000$. Statement 2 : $\displaystyle\sum_{k=1}^{n} (k^3 - ( k-1)^3 ) = n^3$ for any natural number $n$.

asked Dec 11, 2018 by pady_1

2 answers

A spherical balloon is filled with $4500 \pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate if $72 \pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the ballon decreases 49 minutes after the leakage began is

asked Dec 11, 2018 by pady_1

1 answer

Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\overrightarrow{c} = \hat{a} + 2 \hat{b}$ and $\overrightarrow{d} = 5 \hat{a} - 4 \hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is

asked Dec 11, 2018 by pady_1

1 answer

The equation $e^{\sin x }- e^{- \sin x} - 4 = 0 $ has

asked Dec 11, 2018 by pady_1

1 answer

Sulphur trioxide can be obtained by which of the following reaction :

asked Aug 20, 2018 by pady_1

1 answer

Monascus purpureus is a yeast used commercially in the production of :

asked Aug 20, 2018 by pady_1

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People who have migrated from the planes to an area adjoining Rohtang Pass about six months back :

asked Aug 20, 2018 by pady_1

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The most abundant prokaryotes helpful to humans in making curd from milk and in production of antibiotics are the ones categorised as :

asked Aug 20, 2018 by pady_1

1 answer

Measuring biochemical oxygen demand (BOD) is a method used for

asked Aug 20, 2018 by pady_1

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The figure below is the diagrammatic respesentation o the E.Coli vector pBR 322. Which one of the given options correctly identifies its certain component(s) ?

asked Aug 20, 2018 by pady_1

1 answer

In which one of the following options the two examples are correctly matched with their particular type of immunity ?

asked Aug 20, 2018 by pady_1

1 answer

Motile zygote of Plasmodium occurs in

asked Aug 20, 2018 by pady_1

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Which one of the following in not a property of cancerous cells whereas the remaining three are ?

asked Aug 20, 2018 by pady_1

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Cirrhosis of liver is caused by the chronic intake of

asked Aug 20, 2018 by pady_1

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