Q.28. The system of simultaneous equations Kx+2yz 1, (K-1) y-2z=2, (K+2) z=3 have a unique solution if K is (a) (b) 0 (c) (d) 1 2 Q.29. The number of values of a for which (a2-3a+2)x2+(a2-5a+6)x+a²-4=0 is an identity in x is Q.35 If in a triangle PQR, sin P, sin Q, sin R are in A.P. Then: (a) the altitudes are in A.P. (b) the altitudes are in H.P. (c) the medians are in G.P. (d) the medians are in A.P. Q.36. The distance between the parallel lines y=2x+4 and 6x-3y+5 is: (a) 17/√3 (b) 1 (c) 3/√5 (a) 0 (b) 2 (c) 1 (d) 3 DODO (d) 17√5/15 Q.37. The line segment joining the points (-3,-4) and (1,-2) is divided by y-axis in the ratio 0000 3/7 Q.30. Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B is (a) 144 (b) 12 (c) 64 (d) 24 GLA U Q.31. The value of cos 15° is equal to (a) [(√3+1)/2√2] (b) [(√3-1)/2√2] (c) 2-√3 (d) 2+ √3 ES Q.32. The value of tan 10° + tan 35° + tan 10°. tan 35° is equal to: (a) 0 (b) 1/2 (c) -1 (d) 1 Q.33. The value of √3 cosec 20° - sec 20° is equal to: (b) (c) 4 (d) None of these 0000 0000 0000 ज्ञान Q.34. In a right angled ABC, a 2, b=1+ √3, ZC=60° then the side c is equal to : (a) √3-1 (b) √2+1 (c) √6 (D) None of these (a) 1:3 (b) 2:3 (c) 3:1 (d) 3:2 Q.38. The curve represented by x=3(cost+ sint), y=4(cost-sint) is (a) Ellipse (b) Parabola (c) Hyperbola Circle 20d Q.39. Which of the following is the equation of a plane? (a) 1x+my n (b) z=0 (c) 2x+3y=0 (d) y=-x Q.40. The eccentricity of the ellipse 9x+5y-30y 0 is (a) 1/3 (b) 2/3 (c) 3/4 (d) None of these fac Q.41. The function f(x)=1/x on its domain is (a) increasing (b) decreasing (c) constant (d) information insufficient Q.42. The maximum value of x y subject to x+y=8 is (a) 8 (b) 16 (c) 20 (d) 24 Q.43. [cos 2x cos x ] dx is equal to (a) 2 sin x+log (sec x- tan x)+c log (sec x-tan x)+c +log (secx+tan x)+c ☐ (b) 2 sin x (c) 2 sin x (d) 2 sin x log (secx+tan x)+c 0000 Q.50. If a, b and c are three non-coplanar vectors then (a+b+c). {(a+b) x (a+c)} equals (a) 0 (b) [a b c] (c) 2 [a b c] (d) - [a b c] 0.51.A train of length 200 m. travelling at 30 0000 0000 0000 0000