## GATE 2011 Mining Engineering Paper

**GATE MINING ENGINEERING Paper 2011**

Questions Q.1 – Q.25 carry 1-mark each, and questions Q.26 – Q.55 carry 2-marks each.

**Q.1) The two vectors are orthonormal, if**

(A) vector product is zero and norm of each vector is also zero

(B) vector product is one and norm of each vector is also one

(C) cross product is zero and norm of each vector is one

(D) cross product is one and norm of each vector is zero

Q.2) The largest area of a rectangular shaft for a given constant perimeter is obtained when length is

(A) 2.5 times of breadth (B) 1.5 times of breadth

(C) 2 times of breadth (D) equal to breadth

Q.3) A drive shaft of an engine develops torque of 500 N-m. It rotates at a constant speed of 50 rpm. The

power transmitted by the shaft in kW is

(A) 1.46 (B) 2.05 (C) 2.62 (D) 4.32

Q.4) Stress concentration at a point on the wall of a vertical shaft results in a compressive stress of 59.66 MPa. The wall rock mass has an unconfined compressive strength of 89.49 MPa. The safety factor of the shaft wall at the point is

(A) 0.67 (B) 0.86 (C) 1.23 (D) 1.50

Q.5) A core sample of 54 mm diameter having Young’s modulus of 68.97 GPa fails in uniaxial compression at 0.1% axial strain. The axial load at failure in kN is

(A) 158.00 (B) 68.97 (C) 58.00 (D) 15.80

Q.6) The maximum number of coal faces in an underground bord and pillar development district is 13. The number of headings in the district is

(A) 3 (B) 5 (C) 6 (D) 7

Q.7) It is proposed to connect two straights of a road by a simple circular curve. If the maximum speed of the vehicle is 60 km/h and the centrifugal ratio for the road is 1/4, the minimum radius of the curve in m is

(A) 113.26 (B) 98.18 (C) 25.46 (D) 15.50

Q.8) Water will not be delivered by a centrifugal pump due to

(A) lack of priming (B) too low discharge head

(C) wrong direction of rotation (D) partial obstruction at discharge outlet

Q.9) A longwall face cut by double back shuffle method can be only worked with

(A) fixed drum shearer (B) single ended ranging drum shearer

(C) double ended ranging drum shearer (D) plough

Q.10) 100 ml of waste water is allowed to evaporate in a dish weighing 48.6232 g. The weight of the dish

with dry solids is 48.6432 g. The concentration of dry solids in waste water in mg/l is

(A) 200 (B) 220 (C) 260 (D) 320

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