महाराष्ट्र अभियंता सेवा (स्थापत्य) पूर्व परीक्षा २०१५

Two non-zero vectors  and are parallel if :

The rank of the following matrix is :

Investigate the values of 1 and u so that the following equations have an infinite number of solutions : 

Laplace transform of e^at Cosh(bt) if S >a is :

The differential equation of xy= Ae^X + Be ^-X is :

Evaluate upto three digits using Trapezoidal rule taking h=1/4

Match the List - I (functions) with List - II (Laplace transforms) and select the correct answer:

A simply supported beam of span 'I' is carrying a uniformly distributed load of  per unit run over the whole span. The magnitude of deflection at mid span is
(EI --flexural rigidity)

Web of ISMB 300 (secondary beam) is transferring reaction to web of another ISMB 300 (main beam). Which of the following connections is most suitable ? Consider the top flange of beams are maintained at the same level.

Two shafts ‘A’ and 'B' are used to transmit power. Shaft A is solid with diameter 'R', whereas shaft ‘B’ is hollow with external diameter 'd' and internal diameter'd/2'. Material, length, maximum shear stresses and speed being the same, what is percentage reduction in power transmission if 'A' is replaced by 'B ?

Which of the following is/are true about a load balancing cable in a prestressed concrete beam?
(a) Bending moment due to working load is counteracted completely.
(b) Shear force due to working load is counteracted completely.

(c) Pressure line will pass from neutral axis throughout the span.
(d) Stresses will be uniform throughout the span and will be equal to direct axial
compressive stresses.

Web crippling in a steel beam, occurs due to : 

A cylindrical vessel whose ends are closed by means of rigid flange plates, is made of steel plate 3 mm thick. The internal length and diameter of vessel are 50 cm and 25 cm respectively. The longitudinal stress of 62.5 MN/m² and circumferential stress of 125 MN/m² is developed in the cylindrical shell due to internal fluid pressure. Taking Poisson's ratio=0.3 and E= 200 GN/m², the change in length of cylinder shall be :

For a plate girder with effective depth of 1500 mm, the connection of vertical stiffner to the web of plate girder, having 10 mm thickness of web and out stand width of stiffner of 50 mm are designed for :

(a) Battens are designed to carry longitudinal shear
(b) Battens are designed to carry moment.

(c) Lacings are designed to carry axial tension.

(d) Lacings are designed to carry axial compression.

(e) Lacings are designed to carry moment.

Which of the above statements are correct ?

If all bolts are equal in diameter, which bolts are critical ?

A perfect pin jointed frame should satisfy the equation (where m=number of members and j=number of joints)

Keeping all other parameters the same, the end condition of four different columns are as shown.

[Same height and cross-section]

Relation for buckling load will be