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

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 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

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

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

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

Consider the following statements regarding types of supports and beams: 1. When both supports of beams are roller supports, the beam is known as simply supported beam. 2. A beam with one end fixed and the other end free is known as fixed beam. 3. A beam with both ends fixed is known as cantilever beam. 4. A beam with one end fixed and the other simply supported is known as propped cantilever. Which of the above statements is/are correct ?

A

1 only

B

1 and 4 only

C

1, 3 and 4 only

D

2, 3 and 4 only

Below are given two sets in which Set I gives the named theory of Intelligence which set II indicated their main proponents and contentions associated with the theory. Match the two sets. Set I (Theory of Intelligence) Set II (The main proponents and contentions) (a) Multiple Factor Theory (i) Sternberg, intelligence can be taught and the classroom is the logical place to teach it. (b) Theory of Multiple Intelligence (ii) Cattell, intelligence is neither completely monarchic, nor oligarchic nor anarchic. (c) Theory of Fluid and Crystallized Intelligence (iii) Thurstone, intelligence is oligarchic in nature. (d) Coping Theory of Intelligence (iv) Gardner, intelligence is a capacity with component processes and should not be confused with a learning or cognitive style. Choose correct answer from following.

A

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

B

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

C

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

D

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

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

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

A

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

B

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

C

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

D

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

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. In the first column phrases are A, B, and C and in the second column, the phrases are D, E, and F. A phrase from the first column may or may not connect with phrase from the second column to make grammatically and contextually correct sentence. There are five options, four of which display the sequence(s) in which the phrases can be joined to form a grammatically and contextually correct sentence. If none of the options forms a correct sentence after combination, select ‘None of these’ as your answer. Column 1 Column 2 A. There is always a back-to-school atmosphere at Westminster in the autumn, but it will be intensified this D. investment to fund life at university, a survey has suggested. B. Students facing a financial shortfall have increasingly turned to cryptocurrency E. industry and is unlikely to improving before the end of the year, according to Vauxhall Motors. C. The global shortage of computer chips has had a significant impact on the car F. year by the resumption of parliamentary business unmuffled by Covid restrictions.

A

B - E, C - D

B

A - E, B - D, C - F

C

A - F, B - D

D

A - F, B - E, C - D

E

None of these

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

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