According to Euler's column theory, the crippling load for a column length $$l$$ hinged at both ends, is

According to Euler's column theory, the crippling load for a column of length (l) fixed at both ends is __________ the crippling load for a similar column hinged at both ends.

A

Equal to

B

Two times

C

Four times

D

Eight times

According to Euler's column theory, the crippling load of a column is given by $${\text{p}} = \frac{{{\pi ^2}{\text{E}}I}}{{{\text{C}}{l^2}}}.$$ In this equation, the value of ‘C’ for a column with both ends hinged, is

A

$$\frac{1}{4}$$

B

$$\frac{1}{2}$$

C

1

D

2

According to Euler's column theory, the crippling load for a column length (l) hinged at both ends, is

A

π²EI/l²

B

π²EI/4l²

C

4π²EI/l²

D

2π²EI/l²

Consider the following statements for Euler’s equation to find the critical load of a column : 1. Critical load of a column is proportional to the flexural rigidity. 2. Critical load of a column depends upon yield stress. 3. Critical load of a column is inversely proportional to the length of the column. 4. Critical load of a column is inversely proportional to the square of the length of the column. Which of the above statements are correct?

A

1 and 2 only

B

1 and 4 only

C

2 and 3 only

D

2 and 4 only

The ratio of crippling loads of a column having both the ends fixed to the column having both the ends hinged, is

A

1

B

2

C

3

D

4

According to Euler's column theory, the crippling load for a column of length ($$l$$) with one end fixed and the other end hinged, is

A

$$\frac{{{\pi ^2}{\text{E}}I}}{{{l^2}}}$$

B

$$\frac{{{\pi ^2}{\text{E}}I}}{{4{l^2}}}$$

C

$$\frac{{2{\pi ^2}{\text{E}}I}}{{{l^2}}}$$

D

$$\frac{{4{\pi ^2}{\text{E}}I}}{{{l^2}}}$$

A column of length ($$l$$) with both ends fixed may be considered as equivalent to a column of length __________ with both ends hinged.

A

$$\frac{l}{8}$$

B

$$\frac{l}{4}$$

C

$$\frac{l}{2}$$

D

$$l$$

According to Euler's column theory, the crippling load of a column is given by $${\text{p}} = \frac{{{\pi ^2}{\text{E}}I}}{{{\text{C}}{l^2}}}.$$ In the Euler's formula, the value of C for a column with one end fixed and the other end free, is

A

$$\frac{1}{2}$$

B

1

C

2

D

4

Consider the following Column A and Column B in which the names of microorganisms are given in Column A and the groups to which they belong are given in Column B: Column A Column B (a) Aspergillus (i) Algae (b) Lactobacillus (ii) Bacteria (c) Paramecium (iii) Fungi (d) Spirogyra (iv) Protozoa (v) Virus The correct match of the items of Column A with that of Column B is

A

a - iii, b - ii, c - iv, d - v

B

a - ii, b - iii, c - iv, d - i

C

a - iii, b - ii, c - iv, d - i

D

a - v, b - iii, c - ii, d - iv

In the following question, two columns are given containing three phrases each. The phrases are labelled A, B, and C in the first column and D, E and F in the second column. A phrase from the first column may or may not connect with a phrase in the second column to make a grammatically and contextually meaningful sentence. Identify the correct option from those given below that gives the correct sequence in which one or more sentences can be formed. If none of the options makes it possible for a meaningful sentence to be formed, indicate 'No of these' as your answer. Column 1 Column 2 A.The Industrial Revolution brought an infusion of untreated chemicals and wastes D. productivity of both indoor and outdoor workers. B. Air pollution comes from both E. into local streams that served as the water supply. C. A number of studies show that pollution has an adverse effect on the F. natural and human-made sources.

A

A-D

B

B-F

C

B-E

D

C-E

E

None of these

According to Euler's column theory, the crippling load for a column length $$l$$ hinged at both ends, is

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