If `2x=3y\ a n d\ 4y=5z ,` then `x : z=`
(a) `4:3`
(b) `8: 15`
(c) `3:4`
(d) `15 :8`

If x : y=2:3 and y : z=2:3 , then x : z= (a) 2:3 (b) 3:4 (c) 5:7 (d) 4:9

If a : b=4:5 and b : c=2:3, then a : c (a) 4:3 (b) 8: 15 (c) 8:9 (d) 5:3

If theta is the angel between the planes 2x-y+z-1=0 and x-2y+z+2=0 then costheta= (A) 2/3 (B) 3/4 (C) 4/5 (D) 5/6

If P is a point (x ,y) on the line y=-3x such that P and the point (3, 4) are on the opposite sides of the line 3x-4y=8, then x >8/(15) (b) x >8/5 y<-8/5 (d) y<-8/(15)

If the straight lines (x+1)/2=(-y+1)/3=(z+1)/(-2)and (x-3)/1=(y-lamda)/2=z/3 intersect then the value of lamda is (A) -5/8 (B) -17/8 (C) -13/8 (D) -15/8

find the values of x,y and zfrom the following equations : (i) [{:(4,3),(x,5):}]=[{:(y,z),(1,5):}] (ii) [{:(x+y,2),(5+z,xy):}]=[{:(6,2),(5,8):}] (iii) [{:(x+y+z),(x+z),(y+z):}]=[{:(9),(5),(7):}]

The area bounded by parabola y^2=4a x\ a n d\ x^2=4a y is (8a^3)/3 b. (16 a^2)/3 c. (32 a^2)/3 d. (64 a^2)/3

The point from which the tangents to the circle x^2 + y^2 - 4x - 6y - 16 = 0, 3x^2 + 3y^2 - 18x + 9y + 6 = 0 and x^2 + y^2 - 8x - 3y + 24 = 0 are equal in length is : (A) (2/3, 4/17) (B) (51/5, 4/15) (C) (17/16, 4/15) (D) (5/4, 2/3)

If x+y+z=8\ \ a n d\ \ \ x y+y z+z x=20 , find the value of x^3+y^3+z^3-3x y z

Which of the following line is passing through point of intersection of line (x-4)/(2)=(y-3)/(2)=(z-5)/(1) and the plane x+y+z=2 (a) (x)/(2)=(y+1)/(3)=(z-3)/(4) (b) (x-2)/(3)=(y-1)/(3)=(z-3)/(2) (c) (x)/(2)=(y+1)/(3)=(z-2)/(4) (d) (x-2)/(2)=(y+1)/(3)=(z+3)/(4)