Explore topic-wise InterviewSolutions in .

1. 0.063

If $\frac{d^{2}y}{d{t}^2}+y=0$ under the conditions $y=1,\frac{dy}{dt}=0$, when t=0 then y is equal to

The solution of the differential equation

$y\sqrt{1-x^2}dy+x\sqrt{1-y^2}dx=0$ is

A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. 500 and a standard deviation of Rs. 50. The percentage of savings account holders, who maintain an average daily balance more than Rs. 500 is ______.

1. 50

Conisder the complex valued funciton $f\left(z\right)=2z^3+b|z{|}^3$ where $z$ is a complex variable. The value of $b$ for which the function $f\left(z\right)$ is analytic is

1. 0

The probability that a k-digit code does NOT contain the digits 0, 5 or 9 is

Given that x is a random variable in range $[0,\infty ]$ with a probability density function $e^{-x/2}/K,$ the value of the constant K is ______ .

1. 2

Let the probability density function of a random variable, X, be given as:



$f_x\left(x\right)=\frac{3}{2}{e}^{-3x}u\left(x\right)+a{e}^{4x}u(-x)$



where u(x) is the unit step function.



Then the value of 'a' and Prob $X\le 0,$ respectively are

The real part of the complex number $z=x+iy$ is given by

For a small value of $h$, the Taylor series epansion of $f(x+h)$ is

Consider the following differential equation` :

$\frac{dx}{dt}=3x$ initial condition :$x=5$ at $t=0$. The value of $x$ at $t=4$ is

Two dice are thrown together then the probability that the sum of the number on the two faces is divisible by 4 or 6 is_________

The integral $\frac{1}{\sqrt{2\pi }}{\int }_{-\infty }^{\infty }{e}^{-x^2/2}dx$ is equal to

1. 2.09

The box 1 contains chips numbered 3, 6, 9, 12 and 15. The box 2 contains chips numbered 11, 6, 16, 21 and 26. Two chips, one from each box are drawn at random.



The number written on these chips are multiplied. The probability for the product to be an even number is

The integral ${\oint }_{unitcircle}f\left(z\right)dz$ evaluated around the unit circle on the complex plane for $f\left(z\right)=\frac{cosz}{z}$ is

The homogeneous part of the differential equation $\frac{d^{2}y}{d{x}^2}+p\frac{dy}{dx}+qy=r$ ($p,q,r$, are constants) has real distinct roots if

The value of $▽.A$ where $A=3xy{\overrightarrow{a}}_x+x{\overrightarrow{a}}_y+xyz{\overrightarrow{a}}_z$ at a point $(2,-2,2)$ is

1. 2

In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?

For a construction project the mean and standard deviation of the completion time are 200 days and 6.1 days respectively. Assume normal distribution and use the value of standard normal deviate z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be

1. 210

In the Laurent expansion of $f\left(z\right)=\frac{1}{(z-1)(z-2)}$ valid in the region $1<|z|<2$, the coefficient of $\frac{1}{z^2}$ is

The complete solution of the ordinary differential equation $\frac{d^{2}y}{d{x}^2}+p\frac{dy}{dx}+qy=0$ is $y=c_1{e}^{-x}+c_2{e}^{-3x}$



Which of the following is a solution of the differential equation

$\frac{d^{2}y}{d{x}^2}+p\frac{dy}{dx}+(q+1)y=0$?

1. 0.33

Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of type 1 is 0.7, and given that it is of type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is

1. 0.55

1. 1

Two fair dice are rolled and the sum r of the numbers turned up is considered

1. 20

The volume of an object expressed in spherical co-ordinates is given by

$V={\int }_0^{2\pi }{\int }_0^{\pi /3}{\int }_0^1{r}^{2}sin\varphi drd\varphi d\theta$

The value of the integral is

For the equation $x^{\prime \prime }\left(t\right)+3x^{\prime }\left(t\right)+2x\left(t\right)=5$, the solution $x\left(t\right)$ approaches to the following values as $t\to \infty$

The particular solution for the differential equaiton $\frac{d^{2}y}{d{x}^2}+3\frac{dy}{dx}+2y=5cosx$ is

The real part of an analytic funciton $f\left(z\right)$ where $z=x+jy$ is givne by $e^{-y}cos\left(x\right)$. THe imaginary part of $f\left(x\right)$ is

1. 4

The sum of the eigen values of the matrix given below is $\left[\begin{array}{ccc}1& 2& 3\\ 1& 5& 1\\ 3& 1& 1\end{array}\right]$

The value of the integral ${\int }_c\frac{cos2\pi z}{(2z-1)(z-3)}dz$ (Where $C$ is a closed curve given by $|z|=1$ is

1. 0

The solution of the equation $x\frac{dy}{dx}+y=0$ passing through the point $(1,1)$ is

If A and B ae both non-singular $n\times n$ matrices, then which of the following is Not True?

The solution of the differential equation $k^2\frac{d^{2}y}{d{x}^2}=y-y_2$ under the boundary conditions

(i) $y=y_1$ at $x=0$ and

(ii) $y=y_2$ at $x=\infty$, where $k,y_1$ and $y_2$ are constnats, is

The general integral of the partial differential equation $y^{2}p-xyq=x(z-2y)$ is

The value of

$\underset{x\to 4}{lim}\frac{(2x{)}^{1/3}-2}{2x-8}$ is

The probability that a student knows the correct answer to a multiple choice question is 2/3. If the student does not know the answer, then the student guesses the answer. The probability of the gussed answer being correct is 1/4. Given that the student has answreed the question correctly, the conditional probability that the student knows the correct answer is

Consider the following differential equation:



$\frac{dy}{dx}=-5y;$ initial condition : y = 2 at t = 0



The value of y at t = 3 is

Lifetime of an electric bulb is a random variable with density $f\left(x\right)=k{x}^2,$ where x is measured in years. If the minimum and maximum lifetimes of bulb are 1 and 2 years respectively, then the value of k is _____.

1. 0.428

Givne $i=\sqrt{-1}$, what will be the evaluation of the definite intgral ${\int }_0^{\frac{\pi }{2}}\frac{cosx+isinx}{cosx-isinx}dx$

The solution of the initial value problem $\frac{dy}{dx}=-2xy;y\left(0\right)=2$ is

An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is

A solution of the folowing differential equation is given by $\frac{d^{2}y}{d{x}^2}-5\frac{dy}{dx}+6y=0$

The maximum value of the solution $y\left(t\right)$ of the differential equation $y\left(t\right)+\stackrel{..}{y}\left(t\right)=0$ with the initial conditions $\stackrel{.}{y}\left(0\right)=1$ and $y\left(0\right)=1,$ for $t\ge 0$ is