Recent questions tagged 2017

In a Young's double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is :

asked Dec 11, 2018 by pady_1

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The temperature of an open room of volume $30 \;m^3$ increased from $17^{\circ}C$ to $27^{\circ}C$ due to the sunshine. The atmospheric pressure in the room remains $1 \times 10^5 \; Pa$. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating, then $n_f – n_i$ will be :

asked Dec 11, 2018 by pady_1

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In amplitude modulation, sinusoidal carrier frequency used is denoted by $\omega_c$ and the signal frequency is denoted by $\omega_m$. The bandwidth $(\Delta \omega_m)$ of the signal is such that $\Delta \omega_m<< \omega_c$. Which of the following frequency is not contained in the modulated wave ?

asked Dec 11, 2018 by pady_1

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A copper ball of mass $100\; gm$ is at a temperature T. It is dropped in a copper calorimeter of mass $100 \;gm$, filled with $170\; gm$ of water at room temperature. Subsequently, the temperature of the system is found to be $75^{\circ} C$. T is given by : (Given : room temperature = $30^{\circ}C$, specific heat of copper = $0.1 \;cal/gm^{\circ}C$)

asked Dec 11, 2018 by pady_1

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$C_p$ and $C_v$ are specific heats at constant pressure and constant volume respectively. It is observed that $C_p - C_v$ = a for hydrogen gas $ C_p - C_v$ = b for nitrogen gas The correct relation between a and b is :

asked Dec 11, 2018 by pady_1

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A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. the angular acceleration of the rod when it makes an angle $\theta$ with the vertical is

asked Dec 11, 2018 by pady_1

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The moment of inertia of a uniform cylinder of length $l$ and radius $R$ about its perpendicular bisector is $I$. What is the ratio $l/R$ such that the moment of inertia is minimum ?

asked Dec 11, 2018 by pady_1

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An electron bean is acceleration by a potential difference $V$ to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If $\lambda_{min}$ is the smallest possible wavelength of X-ray in the spectrum, the variation of log $\lambda_{min}$ with $\log\; V$ is correctly represented in :

asked Dec 11, 2018 by pady_1

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The following observations were taken for determining surface tension T of water by capillary method : diameter of capillary, $D = 1.25 \times 10^{–2}$ m rise of water , $h = 1.45 \times 10^{–2} m$. Using $ g = 9.80\; m/s^2$ and the simplified relation $T = \frac{rhg}{2} \times 10^3\; N/m$, the possible error in surface tension is closest to :

asked Dec 11, 2018 by pady_1

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A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

asked Dec 11, 2018 by pady_1

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The integral $\begin{align} \int^{\frac{3\pi}{4}}_{\frac{\pi}{4}} \frac{dx}{1+ \cos x} \end{align}$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

If, for a positive integer n, the quadratic equation, $x(x + 1) + (x + 1)(x + 2) +.....+ (x + \overline{n – 1})(x + n) = 10n$ has two consecutive integral solutions, then n is equal to

asked Dec 11, 2018 by pady_1

1 answer

The radius of a circle, having minimum area, which touches the curve $y = 4 - x^2$ and the lines, $y = |x|$ is

asked Dec 11, 2018 by pady_1

1 answer

Let $a, \; b, \; c \in R$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f(x+y) = f(x) + f(y) + xy, \forall x, y \in R$, then $ \displaystyle\sum_{n=1}^{10} f(n)$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is

asked Dec 11, 2018 by pady_1

1 answer

The value of $(^{21} C_1 - ^{10}C_1) + (^{21}C_2 - ^{19}C_2) + (^{21}C_3 -^{10}C_3) + (^{21}C_4 - ^{10}C_4) +...+(^{21}C_{10} - ^{10}C_{10})$ is

asked Dec 11, 2018 by pady_1

1 answer

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is

asked Dec 11, 2018 by pady_1

1 answer

It two different numbers are taken from the set $\{0,1,2,3,....., 10\}$; then the probability that their sum as well as absolute difference are both multiple of 4, is

asked Dec 11, 2018 by pady_1

1 answer

The normal to the curve $y(x-2)(x-3) = x+6$ at the point where the curve intersects the y-axis passes through the point :

asked Dec 11, 2018 by pady_1

1 answer

Let $\overrightarrow{a} = 2 \hat{i} +\hat{j} - 2 \hat{k}$ and $\overrightarrow{b} = \hat{i} + \hat{j}$. Let $\overrightarrow{c}$ be a vector such that $| \overrightarrow{c} - \overrightarrow{a} | = 3, \; |(\overrightarrow{a} \times \overrightarrow{b} ) \times \overrightarrow{c} |=3$ and the angle between $\overrightarrow{c}$ and $\overrightarrow{a} \times \overrightarrow{b} $ be $30^{\circ}$. The $\overrightarrow{a}.\overrightarrow{c}$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

$\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{(\pi - 2 x)^3}$ equals

asked Dec 11, 2018 by pady_1

1 answer

The function $f : R \to \begin{bmatrix}-\frac{1}{2}, \frac{1}{2} \end{bmatrix}$ defined as $f(x) = \frac{x}{1+x^2}$, is :

asked Dec 11, 2018 by pady_1

1 answer

A hyperbola passes through the point $P(\sqrt{2}, \sqrt{3})$ and has foci at $(\pm 2, 0)$. Then the tangent to this hyperbola at $P$ also passes through the point :

asked Dec 11, 2018 by pady_1

1 answer

The eccentriciy of an ellipse whose centre is at the origin is $\frac{1}{2}$. If one of its directrices is $x = -4$, then the equation of the normal to it at $(1, \frac{3}{2})$ is

asked Dec 11, 2018 by pady_1

1 answer

Let $I_n = \int \tan^n x\; dx, \; (n > 1)$. If $I_4 + I_6 = a \tan^5 x + bx^5 + C$, where $C$ is a constant of integration, then the ordered pair $(a, b)$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

The distance of the point $(1, 3, -7)$ from the plane passing through the point $(1, -1, -1)$, having normal perpendicular to both the lines $\frac{x-1}{1} = \frac{y+2}{-2} = \frac{z-4}{3}$ and $\frac{x-2}{2} = \frac{y+1}{-1} = \frac{z+7}{-1}$, is

asked Dec 11, 2018 by pady_1

1 answer

For any three positive real numbers $a, \;b$ and $c,\; 9(25a^2 + b^2 ) + 25(c^2 – 3ac) = 15b(3a + c)$, Then

asked Dec 11, 2018 by pady_1

1 answer

If $A = \begin{bmatrix} 2 & -3 \\ -4 & 1 \end{bmatrix}$, then $adj (3A^2 + 12A)$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

A vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that $AP = 2 AB$. If $\angle{BPC} = \beta$, then $\tan \beta$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

If $(2+\sin x) \frac{dy}{dx} +(y+1) \cos x = 0$ and $y(0)=1$, then $y(\frac{\pi}{2})$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

If for $x \in (0, \frac{1}{4})$, the derivative of $\tan^{-1} \begin{pmatrix} \frac{6x \sqrt{x}}{1-9x^3} \end{pmatrix}$ is $\sqrt{x}. g(x)$, then $g(x)$ equals :

asked Dec 11, 2018 by pady_1

1 answer

If the image of the point P(1, -2, 3) in the plane $2x + 3y - 4z + 22 =0$ measured parallel to the line, $\frac{x}{1} = \frac{y}{4} = \frac{z}{5}$ is $Q$, then $PQ$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

The area (in sq. units) of the region $\{ (x, y) : x \geq 0, \; x + y \leq 3, \; x^2 \leq 4y$ and $ y \leq 1 + \sqrt{x} \}$ is :

asked Dec 11, 2018 by pady_1

2 answers

Twenty meters of wires is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is :

asked Dec 11, 2018 by pady_1

1 answer

Let $k$ be an integer such that the triangle with vertices $(k, -3k),\; (5, k)$ and $(-k, 2)$ has area 28 sq. units. Then the orthocentre of this triangle is at the point :

asked Dec 11, 2018 by pady_1

1 answer

Let $\omega$ be a complex number such that $2 \omega + 1 = z$ where $z = \sqrt{-3}$. If $\begin{vmatrix} 1 & 1& 1 \\ 1 & -\omega^2-1& \omega^2 \\ 1 & \omega^2 & \omega^7 \end{vmatrix} = 3k$, then $k$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = $\frac{1}{4}$ and P (All the three events occur simultaneously) = $\frac{1}{6}$. Then the probability that at least one of the events occurs, is :

asked Dec 11, 2018 by pady_1

1 answer

If $5(\tan^2 x – \cos^2 x) = 2 \cos2x + 9$, then the value of $\cos 4 x$ is :

asked Dec 11, 2018 by pady_1

1 answer

The following statement $(p \to q)\; [(\sim p \to q) \to q]$ is :

asked Dec 11, 2018 by pady_1

1 answer

If S is the set of distinct values of 'b' for which of the following system of linear equations $x + y + z = 1$ $x + ay + z = 1$ $ax + by + z = 0$ has no solution, then S is :

asked Dec 11, 2018 by pady_1

1 answer

A spring of force constant k is cut into lengths of ratio 1 : 2 : 3. They are connected in series and the new force constant is k'. Then they are connected in parallel and force constant is k''. Then k' : k'' is :

asked Aug 21, 2018 by pady_1

1 answer

The diagrams below show regions of equipotentials. A positive charge is moved from A to B in each diagram.

asked Aug 21, 2018 by pady_1

1 answer

The x and y coordinates of the particle at any time are $x = 5t – 2t^2$ and $y = 10 t$ respectively, where x and y are in meters and t in seconds. The acceleration of the particle at t = 2s is :

asked Aug 21, 2018 by pady_1

2 answers

The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m, is :

asked Aug 21, 2018 by pady_1

1 answer

Young's double slit experiment is first performed in air and then in a medium other than air. It is found that $8^{th}$ bright fringe in the medium lies where $5^{th}$ dark fringe lies in air. The refractive index of the medium is nearly :

asked Aug 21, 2018 by pady_1

1 answer

A U tube with both ends open to the atmosphere, is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of 10 mm above the water level on the other side. Meanwhile the water rises by 65 mm from its original level (see diagram). The density of the oil is :

asked Aug 21, 2018 by pady_1

1 answer

In an electromagnetic wave in free space the root mean square value of the electric field is $E_{rms} = 6\; V/m$. The peak value of the magnetic field is :

asked Aug 21, 2018 by pady_1

1 answer

A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be :

asked Aug 21, 2018 by pady_1

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Which of the following statements are correct ? (a) Centre of mass of a body always coincides with the centre of gravity of the body. (b) Centre of mass of a body is the point at which the total gravitational torque on the body is zero. (c) A couple on a body produce both translational and rotational motion in a body (d) Mechanical advantage greater than one means that small effort can be used to lift a large load.

asked Aug 21, 2018 by pady_1

1 answer

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $\omega_1$ and $\omega_2$. They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is :

asked Aug 21, 2018 by pady_1

1 answer

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