Recent questions tagged 2015

A bat moving at $10\; ms^{-1}$ towards a wall sends a sound signal of $8000 \;Hz$ towards it. On reflection it hears a sound of frequency f. The value of f in Hz is close to (speed of sound$=320 ms^{-1}$)

asked Sep 25, 2015 by meena.p

1 answer

A simple harmonic oscillator of angular frequency $2\;rad \;s^{-1}$ is acted upon by an external force $F=\sin t\; N$. If the oscillator is at rest in its equilibrium position at $t=0$,its position at later times is proportional to

asked Sep 25, 2015 by meena.p

1 answer

In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as $T^q$. A good estimate for q is :

asked Sep 25, 2015 by meena.p

1 answer

An ideal gas goes through a reversible cycle $a \to b \to c \to d$ has the V - T diagram shown below. Process $d \to a$ and $b \to c$ are adiabatic.The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) :

asked Sep 25, 2015 by meena.p

1 answer

If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by:

asked Sep 25, 2015 by meena.p

1 answer

If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter $\large\frac{2}{\sqrt {\pi}}$cm then the Reynolds number for the flow is (density of water=$10^{3}\; kg/m^3$ and viscosity of water=$10^{-3}$ Pa.s) close to :

asked Sep 25, 2015 by meena.p

1 answer

A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius $R (R<<L)$. A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T and its distance from the galaxys axis is r, then :

asked Sep 25, 2015 by meena.p

1 answer

Consider a thin uniform square sheet made of a rigid material. If its side is a, mass m and moment of inertia I about one of its diagonals, then :

asked Sep 25, 2015 by meena.p

1 answer

A uniform solid cylindrical roller of mass m is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is a and it is rolling without slipping then the value of F is :

asked Sep 25, 2015 by meena.p

1 answer

A block of mass $m=0.1\;kg$ is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance $\bigg(\large\frac{x}{2} \bigg)$ from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity $3 ms^{-1}$. The total initial energy of the spring is :

asked Sep 25, 2015 by meena.p

1 answer

A block of mass $m=10\;kg$ rests on a horizontal table. The coefficient of friction between the block and the table is $0.05$.When hit by a bullet of mass $50\; g$ moving with speed $v,$ that gets embedded in it, the block moves and comes to stop after moving a distance of $2\; m$ on the table. If a freely falling object were to acquire speed $\large\frac{v}{10}$ after being dropped from height H, then neglecting energy losses and taking $g=10 ms^{-2}$, the value of H is close to :

asked Sep 25, 2015 by meena.p

1 answer

If a body moving in a circular path maintains constant speed of $10\; ms^{-1}$ , then which of the following correctly describes relation between acceleration and radius ?

asked Sep 25, 2015 by meena.p

1 answer

x and y displacements of a particle are given as $x(t)=a \sin \omega t$ and $y(t)=a \sin 2 \omega t$ . Its trajectory will look like

asked Sep 25, 2015 by meena.p

1 answer

A dietician wants to develop a special diet using two foods X and Y. Each packet (contains 30g) of food X contains 12 units of calcium , 4 units of iron, 6 units of cholesterol and $6 \;units$ of vitamin A. Each packet of the same quantity of food Y contains 3 units of calcium, 20 units of iron , 4 units of cholesterol and 3 units of vitamin A. The diet requires at least 240 units of calcium , at least 460 units of iron and at most 300 units of cholesterol. Make an LPP to find how many packets of each food should be used to minimise the amount of vitamin A in the diet, and solve it graphically.

asked Mar 23, 2015 by meena.p

1 answer

A dealer deals in two items only - item A and item B . He has $Rs. 50,000$ to inverst and a space to store at most 60 items. An item A cost $Rs. 2500$ and item B costs $Rs. 500$. A net profit to him on item A is $Rs. 500$ and on item B is $Rs. 150$. If he can sell all the items that he purchases , how should he inverst his amount to have maximum profit ? Formulate an LPP and solve is graphically .

asked Mar 23, 2015 by meena.p

1 answer

Assume that the chances of a patient having a heart attack is $40\%$ . It is also assumed that a meditation and yoga course reduces the risk of heart attack by $30\%$ and the prescription of a certain drug reduces its chance by $25\%$ . At a time a patient can choose any one of the two options with equal probabilities . Its given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of mediation and yoga.

asked Mar 23, 2015 by meena.p

1 answer

Find the vector and cartesian equation of the plane passing through the intersection of the planes $\overrightarrow {r} . (\hat i +\hat j+ \hat k)=6$ and $\overrightarrow {r} . (2\hat i +3\hat j+ 4 \hat k)=-5$ and the point $(1,1,1)$

asked Mar 23, 2015 by meena.p

1 answer

Solve the following differential equation , given that $y=0$ , then $ x= \large\frac{\pi}{4}: $$ \sin 2x \large\frac{dy}{dx}$$-y =\tan x$

asked Mar 23, 2015 by meena.p

1 answer

Find the general Solution of the differential equation $\large\frac{dy}{dx}=\frac{y^2}{xy-x^2}$

asked Mar 23, 2015 by meena.p

1 answer

Find the point on the curve $y= \large\frac{x}{1+x^2} $, Where the tangent to the curve has the greatest slope.

asked Mar 23, 2015 by meena.p

1 answer

Using integration , find the area bounded by the curve $y= |x-1|$ and $y= 3-|x|$

asked Mar 23, 2015 by meena.p

1 answer

Show that the relation R in the set $A= [1,2,3,4,5]$ given by $R= [(a,b):|a-b|] $ is divisible by 2. It is an equivalence relation . Show that all the elements of $[1,3,5]$ are related to each other and all the elements of $[2,4]$ are related to each other , but no element of ${1,3,5}$ is related to any element of $[2,4]$

asked Mar 22, 2015 by meena.p

1 answer

From a set of 100 cards numbered 1 to 100 , one card is drawn at random. Find the probability that the number on the card is divisible by 6 or 8, but not by 24.

asked Mar 22, 2015 by meena.p

1 answer

Find the vector and cartesian equations of the plane which bisects the line joining the points $(3,-2,1) $ and $(1,4,-3)$ at right angles.

asked Mar 22, 2015 by meena.p

1 answer

Let $P(3,2,6)$ be a point in the space and Q be a point on the line $ \overrightarrow{r} =(\hat i - \hat j +2 \hat k) +\mu (-3 \hat i +\hat j +5 \hat k ), $ then find the value of $\mu $ for ehich the vector $\overrightarrow{PQ}$ is parallel to the plane $x -4y+3z=1$

asked Mar 22, 2015 by meena.p

1 answer

Show that the lines $\large\frac{x-1}{3} =\frac{y-1}{-1}$$,z+1=0$ and $\large\frac{x-4}{2} =\frac{z+1}{3}$$,y=0$ intersect each other . Also find their point of intersection .

asked Mar 22, 2015 by meena.p

1 answer

Evaluate : $\lim \int \limits _0^{\pi} \large\frac{x \tan x }{\sec x . \tan x}$$dx$

asked Mar 22, 2015 by meena.p

1 answer

Find $\int \limits_0^2 (x^2+e^{2x+1)}dx$ as the limit of a sum

asked Mar 22, 2015 by meena.p

1 answer

Evaluate : $\int x. \sin ^{-1}x dx$

asked Mar 20, 2015 by meena.p

1 answer

Find : $\int \large\frac{1- \cos x}{\cos x (1+\cos x)}$$dx$

asked Mar 20, 2015 by meena.p

1 answer

If $y= \sqrt {x+1} -\sqrt {x-1} $, prove that $(x^2-1) \large\frac{d^2y}{dx^2} $$+x\large\frac{dy}{dx} -\frac{1}{4}$$y=0$

asked Mar 20, 2015 by meena.p

1 answer

If $\log \sqrt {x^2+y^2}=\tan ^{-1} \bigg( \large\frac{x}{y} \bigg)$, then show that $\large\frac{dy}{dx}=\frac{y-x}{y+x}$

asked Mar 20, 2015 by meena.p

1 answer

If $y=x^{2^{-x^2}}$, find $\large\frac{dy}{dx}$

asked Mar 20, 2015 by meena.p

1 answer

If function $f(x) =|x-3| +|x-4| $, then show that $f(x)$ is not differentiable at $x=3$ and $x=4$

asked Mar 20, 2015 by meena.p

1 answer

Find the inverse of matrix $A=\begin{bmatrix} 3 & -1 & 1 \\ -15 & 6 & -5 \\ 5 & -2 & 2 \end{bmatrix}$ and hence show that $A^{-1} .A =I$

asked Mar 19, 2015 by meena.p

1 answer

If $ X\begin{bmatrix} 1 & 2 & 3 \\4 & 5 & 6 \end{bmatrix}=\begin{bmatrix} -7 & -8 & -9 \\2 & 4 & 6 \end{bmatrix}$, then find the matrix X.

asked Mar 19, 2015 by meena.p

1 answer

If $ a \neq b \neq c$ and $\begin{vmatrix}a & b & c \\b & c & a \\c & a & b \end{vmatrix}$$=0$ , then using properties of determinants, prove that $a+b+c=0$

asked Mar 19, 2015 by meena.p

1 answer

If $\tan ^{-1} x+\tan ^{-1}y+\tan ^{-1} z= \large\frac{\pi}{2}$$,x,y,z>0$, then find the value of $xy+yz+zx$

asked Mar 19, 2015 by meena.p

1 answer

There are 3 families A,B and C. The number of men , women and children in these are as under : Dairy expense of men , women and children are $ Rs 200, Rs .150$ and $Rs 200$ respectively. Only men and women earn and children or not. using matrix multiplication , calculate the dairy expenses of each family. What impact does more children in the family create on the society ?

asked Mar 19, 2015 by meena.p

1 answer

Write the direction cosines of the normal to the plane $3x+4y+12z=52$

asked Mar 19, 2015 by meena.p

1 answer

Write the value of $\hat i. (\hat j \times \hat k) + \hat j .( \hat k \times \hat i) +\hat k.(\hat i \times \hat j)$.

asked Mar 19, 2015 by meena.p

1 answer

Write the projection of vector $2 \hat i +3 \hat j - \hat k$ along the vector $\hat i +\hat j$

asked Mar 19, 2015 by meena.p

1 answer

Write a differential equation $y= A \cos \alpha x + B \sin \alpha x$ , where A and B are arbitrary constants .

asked Mar 19, 2015 by meena.p

1 answer

Find the product of the order and degree of the following different equation : $x \bigg(\large\frac{d^2y}{dx^2} \bigg) +\bigg(\large\frac{dy}{dx}\bigg)^2$$+y^2=0$

asked Mar 19, 2015 by meena.p

1 answer

Write a $ 3\times 3$ skew symmetric matrix

asked Mar 19, 2015 by meena.p

1 answer

Find the value of k for which the points $A(k+1,2k) ,B(3k,2k+3) $ and $ c(5k-1,5k)$ are collinear .

asked Mar 18, 2015 by meena.p

1 answer

A truck covers a distance of $150 km$ at a certain average speed and then covers another 200 km at an average speed which is $20\;km/hr$ more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck?

asked Mar 18, 2015 by meena.p

1 answer

An arithmetic progression $5, 12,19....., $ has I st terms. Find its last term hence find the sum of its last 15 terms.

asked Mar 18, 2015 by meena.p

1 answer

A bag contains white, black and red balls only. A ball is drawn at random from the bag if the probability of getting a white balls is $\large\frac{3}{10} $ and that of black is $\large\frac{2}{5}$, then find the probability of getting a red balls. If the bag contains 20 black balls, then find the total number of balls in the bag.

asked Mar 18, 2015 by meena.p

1 answer

Find the coordinates of a point P on the line segment joining $A(1,2) $ and $B(6,7)$ Such that $AP= \large \frac{2}{5} $$AB$

asked Mar 18, 2015 by meena.p

1 answer

Ask Questions, Get Answers