PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

Name the octants in which the following points lie: 

 (7, 4, –3)

Name the octants in which the following points lie: 

(–5, –4, 7) 

Name the octants in which the following points lie: 

(–5, –3, –2) 

Name the octants in which the following points lie:

 (2, –5, –7) 

Name the octants in which the following points lie: 

(–7, 2 – 5)

Find the image  of: 

 (–2, 3, 4) in the yz-plane.

Find the image  of: 

 (–5, 4, –3) in the xz-plane. 

Find the image  of:

 (5, 2, –7) in the xy-plane.

Find the coefficient of: 

(vi) x in the expansion of  \[\left( 1 - 2 x^3 + 3 x^5 \right) \left( 1 + \frac{1}{x} \right)^8\]

Find the coefficient of: 

(vii) \[a^5 b^7\]  in the expansion of  \[\left( a - 2b \right)^{12}\]

Find the coefficient of: 

(viii) x in the expansion of \[\left( 1 - 3x + 7 x^2 \right) \left( 1 - x \right)^{16}\]

Find the image  of: 

 (–5, 0, 3) in the xz-plane. 

Find the image  of: 

 (–4, 0, 0) in the xy-plane. 

Which term in the expansion of \[\left\{ \left( \frac{x}{\sqrt{y}} \right)^{1/3} + \left( \frac{y}{x^{1/3}} \right)^{1/2} \right\}^{21}\]  contains x and y to one and the same power?

Does the expansion of \[\left( 2 x^2 - \frac{1}{x} \right)\] contain any term involving x⁹?

A cube of side 5 has one vertex at the point (1, 0, –1), and the three edges from this vertex are, respectively, parallel to the negative x and y axes and positive z-axis. Find the coordinates of the other vertices of the cube.

Planes are drawn parallel to the coordinate planes through the points (3, 0, –1) and (–2, 5, 4). Find the lengths of the edges of the parallelepiped so formed.

Planes are drawn through the points (5, 0, 2) and (3, –2, 5) parallel to the coordinate planes. Find the lengths of the edges of the rectangular parallelepiped so formed. 

Find the distances of the point P(–4, 3, 5) from the coordinate axes. 

The coordinates of a point are (3, –2, 5). Write down the coordinates of seven points such that the absolute values of their coordinates are the same as those of the coordinates of the given point.