CBSE Guess paper class XII Mathematics 2008 1


Guess Paper – 2008

Class – XII

Subject - Mathematics

1. Show that the vector i+j+k is equally inclined with the positive directions of the coordinate axes.

2. Find unit vector perpendicular to each of the vectors 2i-j+k and i+j+k.

3. Examine whether points with position vectors -2i+3j+5k,i+2j+3k,7i-k are collinear.

4. Find distance of point(2,-1,3) from the plane r.(5i+2j-7k)+12=0.

5. Find equation of plane passing through points (1,0,2),(-1,3,2),(2,1,5).

6. Find the vector equation of the plane passing through intersection of the planes r.(i+2j+3k)=4 and r.(2i+j-k)+5=0 and which is perpendicular to the plane r.(5i+3j-6k)+8=0.

7. If a,b,c are position vectors of non-collinear points A,B,C respectively in space , show that bxc+cxa+axb is perpendicular to the plane ABC.

8. Find shortest distance between the lines r=3i+8j+3k+ג (3i-j+k) and r=-3i-7j+6k+µ (-3i+2j+4k).

9. Find foot of perpendicular drawn from the point (1,3,4) on the plane r.(2i-j+k)+3=0.

10. Minimize Z=3x+5y subject to the constraints

x-4y+12≥0, 2x+3y-12≥0, x≤4, y≥2, x≥0.

11. Show that the points with position vectors a-2b+3c,-2a+3b+2c and -8a+13b are collinear.

12. Find area of triangle whose vertices are (3,-1,2),(1,-1,-3),(4,-3,1).

13.A variable plane is at a constant distance p from the origin ,cuts the coordinate axes in A,B,C.Through A,B,C planes are drawn parallel to coordinate planes . Show that the locus of their point of intersection is x-2 + y-2 + z-2 = p-2.

14.Show that the points(0,-1,-1),(-4,4,4),(4,5,1),and (3,9,4) are coplanar also find equation of the plane.

15.Find equation of line joining (3,4,1) and point of intersection of the line r=3i+ ג (i-j) and the plane r.(3i+j)-9=0.

16.Find the distance of the point (2,3,4) from the plane 3x + 2y +2z +5=0 measured parallel to the line

( X+3)/3 = (y-2)/6=z/2

17.Kellogg is a new cereal formed by a mixture of bran and rice that contains at least 88 grams of protein and at least 36 miligram of iron .Knowing that bran contains 80 grams of protein and 40 miligrams of iron per kilogram,and that rice contains 100 grams of protein and 30 miligram of iron per kilogram. Find minimum cost of producing this new cereal if bran costs Rs. 5 per kilogram and rice costs Rs. 4 per kilogram.

 

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