For a spin $$\frac{1}{2}$$ particle, the expectation value of sxsysz, where sx, sy and sz are spin operators, is

Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction ?

A

2 9\/7 km

B

3 7\/5 km

C

1 3\/4 km

D

4 3\/8 km

Let $$\overrightarrow {\bf{L}} $$ = (L_x, L_y, L_z) denotes the orbital angular momentum operators of a particle and let L₊ = L_x + i L_y and L_- = L_x - i L_y. The particle is in aneigen state of L² and L_z eigen values $${\hbar ^2}\left( {l + 1} \right)$$ and $$\hbar l$$ respectively. The expectation value of L₊L_- in this state is

A

$$l{\hbar ^2}$$

B

$$2l{\hbar ^2}$$

C

zero

D

$$l\hbar $$

You are the administrator of eight SQL Server 2000 computers. You configure alerts on each server so that various problem conditions will be reported if they occur.You create 20 operators on one of the servers. You configure these operators by using the e-mail and pager contact information for the employees in your department. You configure the alerts on the server to send e-mail messages and pager messages to the appropriate operators.You need to configure the same 20 operators on the other seven servers. You want to do this with a minimum amount of administrative time.What should you do?

A

Use SQL Server Enterprise Manager to script all of the operators. Use SQL Query Analyzer to run the script on the other seven servers.

B

Detach the msdb database from the first server. Copy the database to the other seven servers. Attach the database on all eight servers.

C

Use snapshot replication to replicate the msdb database from the first server to the other seven servers.

D

Use SQL ServerEnterprise Manager on a single client computer to create the operators on each server.

A particle of mass m is confined in the potential
Quantum Mechanics mcq question image

\[V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{2}m{\omega ^2}{x^2},}&{{\text{for }}x Let the wave function of the particle be given by $$\psi \left( x \right) = - \frac{1}{{\sqrt 5 }}{\psi _0} + \frac{2}{{\sqrt 5 }}{\psi _1}$$
where $${\psi _0}$$ and $${\psi _1}$$ are the eigen functions of the ground state and the first excited slate respectively. The expectation value of the energy is

A

$$\frac{{31}}{{10}}\hbar \omega $$

B

$$\frac{{25}}{{10}}\hbar \omega $$

C

$$\frac{{13}}{{10}}\hbar \omega $$

D

$$\frac{{11}}{{10}}\hbar \omega $$

For a spin s particle, in the eigen basis of $$\overrightarrow {{{\bf{s}}^2}} ,$$ s_z the expectation value $$\left\langle {sm\left| {\overrightarrow {{\bf{s}}_x^2} } \right|sm} \right\rangle $$ is

A

$$\frac{{\hbar \left\{ {s\left( {s + 1} \right) - {m^2}} \right\}}}{2}$$

B

$$\hbar \left\{ {s\left( {s + 1} \right) - 2{m^2}} \right\}$$

C

$${\hbar \left\{ {s\left( {s + 1} \right) - {m^2}} \right\}}$$

D

$${\hbar ^2}{m^2}$$

A spin half particle is in the state $${S_z} = \frac{{{\hbar ^2}}}{2}.$$ The expectation values of $${S_x},\,S_x^2,\,{S_y},\,S_y^2$$ are given by

A

$$0,\,0,\,\frac{{{\hbar ^2}}}{4},\,\frac{{{\hbar ^2}}}{4}$$

B

$$0,\,\frac{{{\hbar ^2}}}{4},\,\frac{{{\hbar ^2}}}{4},\,0$$

C

$$0,\,\frac{{{\hbar ^2}}}{4},\,0,\,\frac{{{\hbar ^2}}}{4}$$

D

$$\frac{{{\hbar ^2}}}{4},\,\frac{{{\hbar ^2}}}{4},\,0,\,0$$

A particle is moving in a spherically symmetric potential V(r) = αr², where α is a positive constant. In a stationary state, the expectation value of the kinetic energy $$\left\langle T \right\rangle $$ of the particle is

A

$$\left\langle T \right\rangle = \left\langle V \right\rangle $$

B

$$\left\langle T \right\rangle = 2\left\langle V \right\rangle $$

C

$$\left\langle T \right\rangle = 3\left\langle V \right\rangle $$

D

$$\left\langle T \right\rangle = 4\left\langle V \right\rangle $$

Consider the postfix expression 4 5 6 a b 7 8 a c, where a, b, c are operators. Operator a has higher precedence over operators b and c. Operators b and c are right associative. Then, equivalent infix expression is

A

4 a 5 6 b 7 8 a c

B

4 a 5 c 6 b 7 a 8

C

4 b 5 a 6 c 7 a 8

D

4 a 5 b 6 c 7 a 8

S₁: Ingratitude stings strongest where relationship is closest.
P: Expectation turns innocent relationship into commerce.
Q: Human relationship is adulterated with sly commerce.
R: In commerce, of course, give and take is understood.
S: Most relationships are founded on mutual expectations.
S₆: From any warm and healthy human relationship expectation of returns has to be weeded out.

The Proper sequence should be:

A

PQRS

B

QSPR

C

RPSQ

D

SRQP

In a C expression using assignment operators, relational operators and arithmetic operators, the hierarchy of operations (in the absence of parenthesis) is

A

Assignment, relational, arithmetic

B

Relational, assignment, arithmetic

C

Arithmetic, assignment, relational

D

Arithmetic, relational, assignment

For a spin $$\frac{1}{2}$$ particle, the expectation value of s_xs_ys_z, where s_x, s_y and s_z are spin operators, is

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