Recent questions tagged 2015

If $12$ identical balls are to be placed in 3 identical boxes ,then the probability that one of the boxes contains exactly 3 balls is :

asked Nov 17, 2015 by meena.p

1 answer

The area (in sq.units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $\large\frac{x^2}{9} + \frac{y^2}{5} $$=1$ is :

asked Nov 17, 2015 by meena.p

1 answer

Let $f(x) $ be a polynomial of degree four having extreme values at $x=1$ and $ x=2$ If $\lim\limits_{x \to 0} \bigg[1+\large\frac{f(x)}{x^2}\bigg]$$=3$ then $(2)$ is equal to :

asked Nov 17, 2015 by meena.p

1 answer

Let $\alpha$ and $\beta$ be the roots of equation $x^2-6x-2 =0$. If $a_n = \alpha ^n -\beta^n$ , for $n \geq 1$, then the value of $\large\frac{a_{10}-2_{a8}}{2_{a9}}$ is equal to :

asked Nov 17, 2015 by meena.p

1 answer

The integral $\int \limits_2^4 \large\frac{\log x^2}{\log x^2+\log(36-12x+x^2)}$$dx$is equal to :

asked Nov 17, 2015 by meena.p

1 answer

The mean of the data set comprising of 16 observations is $16$ . If one of the observation valued 16 is deleted and three new observations, valued 16 is deleted and three new observation valued $3,4$ and $5$ are added to the mean of the resultant data, is :

asked Nov 17, 2015 by meena.p

1 answer

If the function $g(x) = \left\{ \begin{array} {1 1} k \sqrt{x+1} , & \quad 0 \leq x \leq 3 \\ mx+2,& \quad 3 < x \leq 5 \end{array} \right. $ is differentiable , then the value of $k+m$ is :

asked Nov 17, 2015 by meena.p

1 answer

Let $ \tan^{-1}y = \tan ^{-1}x + \tan^{-1} \bigg(\large\frac{2x}{1-x^2}\bigg)$, where $|x| < \frac{1}{\sqrt 3 }$. Then a value of y is :

asked Nov 17, 2015 by meena.p

1 answer

The normal to the curve , $x^2+2xy-3y^2=0$ at (1,1):

asked Nov 17, 2015 by meena.p

1 answer

The integral $\int \frac{dx}{x^2(x^4+1)^{3/4}}$ equals :

asked Nov 17, 2015 by meena.p

1 answer

The negation of $\sim S \vee ( \sim r \wedge s)$ is equivalent to :

asked Nov 13, 2015 by meena.p

1 answer

If m is the A.M of two distinct real number l and n (l,n >1) and $G_1,G_2$ and $G_3$ are three geometric means between l and n, then $G_1^4 +2 G_2^4+G_3^4$ equals

asked Nov 13, 2015 by meena.p

1 answer

If $A=\begin{bmatrix}1 & 2 & 2 \\ 2 & 1 & -2\\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation $AA^T=9I$ , where I is $ 3 \times 3$ identity matrix , then the ordered pair $(a,b)$ is equal to :

asked Nov 13, 2015 by meena.p

1 answer

Let $y(x)$ be the solution of the differential equation $(x log x) \frac{dy}{dz} $$+y=2x \log x , x (\geq 1)$ Then $y(e) $ i equal to :

asked Nov 13, 2015 by meena.p

1 answer

The number of integers greater than $6,000$ that can be formed , using the digits $3,5,6,7$ and $8$, with out repetion, is :

asked Nov 13, 2015 by meena.p

1 answer

The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$, is :

asked Nov 13, 2015 by meena.p

1 answer

A complex number z is said to be uni modular if $|z|=1$. suppose $z_1$ and $z_2$ are complex numbers such that $ \large\frac{z_1-2z_2}{2-z_1z_2}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a :

asked Nov 13, 2015 by meena.p

1 answer

The set of all values of $\lambda$ for which the system of linear of linear equations : $2x_1-2x_2+x_3 =\lambda x_1 \\ 2x_1-3x_2+2x_3 =\lambda x_2 \\ -x_1 + 2x_2 = \lambda x_3$ has a non- trivital solution,

asked Nov 13, 2015 by meena.p

1 answer

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

asked Nov 13, 2015 by meena.p

1 answer

The sum of first 9 terms of the series $\large\frac{1^3}{1} +\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}$+.....is :

asked Nov 13, 2015 by meena.p

1 answer

The sum of coefficient on integral powers of x in the binomial expansion of $(1-2 \sqrt {x})^{50}$ is :

asked Nov 13, 2015 by meena.p

1 answer

The distance of the point $(1,0,2)$ from the point of intersection of the line $\large\frac{x-2}{3} =\frac{y+1}{4} =\frac{z-2}{12}$ and the plane $x-y+z=16,$ is :

asked Nov 13, 2015 by meena.p

1 answer

$lim _ {x \to 0} $$\large\frac{(1-\cos 2x)(3+ \cos x)}{x \tan 4x}$ is equal to :

asked Nov 13, 2015 by meena.p

1 answer

Locus of the image of the point $(2,3)$ in the line $(2x-3y+4)+k(x-2y+3)=0,k \in R$, is a

asked Nov 13, 2015 by meena.p

1 answer

Let A and B be two sets containing four and two elements respectively . Then the number of subset of the set $A \times B$ , each having at least three elements is :

asked Nov 13, 2015 by meena.p

1 answer

The equation of the plane containing the line $2x-5y+z=3; x+y+4z=5$ and parallel to the plane , $x+3y+6z=1$, is :

asked Nov 13, 2015 by meena.p

1 answer

The number of points , having both co-ordinates as integers,that lie in the interior of the triangle of the triangle with vertices $(0,0),(0,41)$ and $(41,0)$ is :

asked Nov 13, 2015 by meena.p

1 answer

If the angles of elevation of the top of a tower from three collinear points A,B and C on a line leading to the foot of the tower, are $30^{\circ}, 45^{\circ}$ and $60^{\circ}$ respectively , the the ratio , $AB:BC$ is

asked Nov 13, 2015 by meena.p

1 answer

Let O be the vertex and Q be any point on the parabola , $x^2=8y$. If the point P divides the line segment OQ internally in the ratio $1:3$ , then the locus of P is :

asked Nov 13, 2015 by meena.p

1 answer

Let $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be three are col linear and $(\overrightarrow{a} \times \overrightarrow{b}) \times \overrightarrow{c}= \large\frac{1}{3} |\overrightarrow{b}||\overrightarrow{c}|\overrightarrow{a}$. If $\theta$ is the angle between vectors $\overrightarrow{b}$ and $\overrightarrow{c}$, then a value of $\sin \theta$ is :

asked Nov 13, 2015 by meena.p

1 answer

Match List I (Fundamental experiement ) with List II (its conclusion ) and select the correct option from the choices given below list :

asked Nov 13, 2015 by meena.p

1 answer

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom /ion:

asked Nov 13, 2015 by meena.p

0 answers

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom /ion:

asked Nov 13, 2015 by meena.p

1 answer

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in : (figure are schematic and not drawn to scale )

asked Nov 13, 2015 by meena.p

1 answer

Given in the figure are two blocks A and NB of weight $20\;N$ and $100\;N$ respectively . These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks uis $0.1$ and between block B and the wall is $0.15$ , the frictional force applied by the wall on block B is :

asked Nov 13, 2015 by meena.p

1 answer

From a solid sphere of mass M and radius R, a spherical portion of radius $\large\frac{R}{2}$ is removed , as shown in fig. Taking gravitational potential $V=0$ at $ r= \infty$ , the potential at the center of the cavity thus formed is:

asked Nov 12, 2015 by meena.p

1 answer

Consider an ideal gas confined in an isolated closed chamber . As the gas undergoes an adiabatic expansion , the average time of collision between molecules increases as $V^{q}$, Where V is the volume of the gas . The value of q is : $\bigg(\gamma = \large\frac{C_p}{C_v}\bigg) $

asked Nov 12, 2015 by meena.p

1 answer

A particle of mass m moving in the x direction with speed $2v$ is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic , the percentage loss in the energy during the collision is close to :

asked Nov 12, 2015 by meena.p

1 answer

Two coaxial solenoids of different radii carry current I in the same direction. Let $\overrightarrow{F_1}$ be the magnetic force on the inner solenoid due to the outer one and $\overrightarrow{F_2}$ be the magnetic force on the outer solenoid due to the inner one . Then :

asked Nov 12, 2015 by meena.p

1 answer

A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figure below : If there is a uniform magnetic field of $0.3\;T$ in the positive z direction , in which orientation the loop would be in (i) stable equilibrium and (ii) unstable equilibrium ?

asked Nov 12, 2015 by meena.p

1 answer

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is $ \mu$, a ray, incident at an angle $\theta$ , on the face $AC$ of the prism provided:

asked Nov 12, 2015 by meena.p

1 answer

A uniformly charged solid sphere of radius R has potential $V_0$ (measured with respect to $\infty$) on its surface. For this sphere the equipotential surfaces with potentials $\large\frac{3V_0}{2},\frac{5V_0}{4},\frac{3V_0}{4}$ and $\large\frac{V_0}{4}$ have radius $R_1, R_2, R_3$ and $R_4$ respectively . Then

asked Nov 12, 2015 by meena.p

1 answer

Two stones are thrown up simultaneously from the edge of a cliff $240\;m$ high with initial speed of $10 m/s$ and $40 m/s$ respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first ? (Assume stones do not rebound after hitting the ground and neglect air resistance , take $g= 10 m/s^2$) (The figures are schematic and not drawn to scale )

asked Nov 12, 2015 by meena.p

1 answer

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u= \large\frac{U}{V}$$ \infty T^4$ and pressure $p= \large\frac{1}{3}\bigg( \frac{U}{V}\bigg)$. If the shell now undergoes an adiabatic expansion the relation between T and R is :

asked Nov 12, 2015 by meena.p

1 answer

A solid body of constant heat capacity $1 J/^{\circ}C$ is being heated by keeping it in contact with reservoirs in two ways : (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat . (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat . In both the cases body is brought from initial temperature $100^{\circ}$ to final temperaure $200 ^{\circ}$ Entropy change of the body in the two cases respectively is :

asked Nov 12, 2015 by meena.p

1 answer

A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal is /are :

asked Nov 12, 2015 by meena.p

1 answer

On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground when a light beam is directed horizontally , the Huygen's principle leads us to conclude that as it travels, the light beam :

asked Nov 12, 2015 by meena.p

1 answer

The period of oscillation of a simple pendulum is $ T= 2 \pi \sqrt {\large\frac{L}{g}}$ Measured value of L is $20.0\;cm$ known to 1mm accuracy and time for 100 oscillation of the pendulum is found to be 90 s using a wrist watch of 1s resolution. The accuracy in the determination of g is :

asked Nov 12, 2015 by meena.p

1 answer

From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is :

asked Nov 12, 2015 by meena.p

1 answer

In the given circuit , charge $Q_2$ on the $2 \mu F$ capacitor changes as C is varied from $1 \mu F$ to $3 \mu F$ . $Q_2$ as function of 'C' is given properly by :

asked Nov 12, 2015 by meena.p

1 answer

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