Tiêu đề NUST past papers (Math).pdf ✅

PAST PAPERS OF MATHS (NET) (1) 1. ∀ a, b, ε R, ab ε R a. Commutative law of multiplication b. Associative law of multiplication c. Closure law of multiplication d. Multiplicative identity 2. If the straight lines x= 1+s, y=-3- λs, z=1 + λs, and x =t/2, y = 1 +t, z =2-t with parameters s and t respectively, are co-planar then λ equal to a. -2 b. -1 c. -1/2 d. 0 3. The intersection of the spheres x2 +y2 +z2 +7x -2y –z=13and x2+ y2+z2-3x+3y+4z =8, x2+ y2+z2- 3x+3y+4z =8 is same as the intersection of one of the sphere and the plane a. X-y-z =1 b. X-2y-z=1 c. X-y-2z=1 d. 2x-y-z=1 4. Let and be three non-zero vectors such that no two of these are collinear. If the vector a + 2b is collinear with c r and b+ 3cr is collinear with a r (being some non-zero scalar ) then a +2b +6cr equal to a. πa  b. πb  c. πc  d. 0 5. A particle is acted upon by constant forces r 4i + j-3k and 3i+j –k which displace it from a point I +2j+3k to the point 5i +4j+k. the work done in standard units by the forces is given by a. 40 b. 30 c. 25 d. 15

11. The probability that A speaks truth is 4/5, while this probability for b is 3⁄4. The probability that they contradict each other when asked to speak on a fact is a. 3/20 b. 1/5 c. 7/20 d. 4/5 12. Division is a binary operation in a. The set of rational numbers b. The set of real numbers c. The set of real numbers d. the set R-(0) 13. If z= (1, 2) then z^ (-1) =? a. (1/5 ,2/5) b. (-1/5, 2/5) c. (1/5,-2/5) d. (-1/5 ,-2/5) 14. With two forces acting at a point, the max effect is obtained when their resultant is 4 N. If they act at right angles then their resultant is 3 N then the forces are a. (2+√2 ) and (2- √2) b. (2+√3 ) and (2- √3) c. (2+ 1⁄2 2 ) and (2- 1⁄2 2) d. (2+ 1⁄2 3 ) and (2- 1⁄2 3 ) 15. In right angle ΔABC ,∠A = 900 and sides a, b ,c are respectively,5 cm, 4 cm and 3 cm. if a force F has moments 0,9 and 16 in N cm. units respectively about vertices A,B and C, then magnitude of F is a. 3 b. 4 c. 5 d. 9 16. Three forces P. Q .R acting along IA, IB and IC where I is the in center of a ΔABC, are in equilibrium. Then P:Q:R us a. Cos A/2: cos B/2 : cos c/2 b. sin A/2: sin B/2 : sin c/2 c. sec A/2: sec B/2 : sec c/2 d. cosec A/2: cosec B/2 : cosec c/2